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VLSI Design 4/M - Analogue
VLSI Design 4/M - 模拟

Edward Wasige
爱德华·瓦西格

EEE, University of Glasgow 74 Oakfield Ave., x8662 edward.wasige@glasgow.ac.uk
EEE,格拉斯哥大学 74 Oakfield Ave.,x8662 edward.wasige@glasgow.ac.uk

Introduction
介绍

CMOS (complimentary metal oxide semiconductor) technology has been the dominant technology for fabricating integrated circuits (ICs or chips). The process of creating an IC by combining thousands of transistors into a single chip is verylargescale−integration (VGSI). CMOS is reliable, manufacturable, low power, low cost, and perhaps most importantly, scalable. For several decades the evolution of integrated circuits has followed Moore’s lam, according to which the number of transistors per square millimetre of silicon doubles every 18 months. At the same time transistors have become faster, making possible ever-increasing clock rates in digital circuits. This trend seems set to continue for at least another decade without slowing down. Thus, in the foreseeable future, the processing power of digital circuits will continue to increase at an accelerating pace. The gate lengths of early CMOS transistors were in the micrometer range (long-channel devices), the feature sizes of the current CMOS devices are in the nanometer range (short-channel devices).
CMOS(互补金属氧化物半导体)技术一直是制造集成电路(IC 或芯片)的主导技术。通过将数千个晶体管组合成单个芯片来创建 IC 的过程isverylargescale−integrationVGSICMOSisreliablemanufacturablelow功率、低成本,也许最重要的是,可 伸缩。几十年来,集成电路的发展一直遵循Moore的 lam,根据该理论,平方毫米晶体管数量18个月翻一番同时,晶体管变得更快,使数字电路中不断提高时钟速率成为可能这一趋势似乎将持续至少十年而不会放缓。因此,在可预见的未来,数字电路的处理能力将继续加速提高早期CMOS晶体管极长度微米范围内(长通道器件),当前CMOS器件特征尺寸纳米范围(短通道器件)。

For analog circuits the evolution of technology is not as beneficial. Thus, there is a trend to move signal prcessing functions from the analog domain to the digital one, which, besides allowing for higher levels of accuracy, provides savings in power consumption and silicon area, increases robustness, speeds up the design process, brings flexibility and programmability, and increases the pos- sibilities for design re-use. In many applications the input and output signals of the system are inherently analog, preventing all-digital realisations; at the very least a conversion between analog and digital is needed at the interfaces. Typi- cally, moving the analog-digital boundary closer to the outside world increases the bit rate across it.
对于模拟电路来说,技术的发展并不那么有益。因此,信号处理功能从模拟域转移到数字域的趋势是,除了允许更高的精度外,还可以节省功耗和硅面积,提高鲁棒性,加快设计过程,带来灵活性和可编程性,并增加设计重用的可能性。在许多应用中系统的输入和输出信号本质上是模拟的,无法实现全数字;至少接口需要在模拟数字之间进行转换通常模拟数字边界移近外部世界会增加其比特率

In telecommunications systems the trend to boost bit rates is based on em- ploying wider bandwidths and a higher signal-to-noise ratio. At the same time radio architectures in many applications are evolving towards software-defined radio, one of the main characteristics of which is the shifting of the analog-digital boundary closer to the antenna. Because of these trends, there is an urgent need for data converters with increasing conversion rates and resolution. A part of
电信系统中提高比特率趋势是基于采用更宽的带宽和更高的信噪比。与此同时许多应用中无线电架构正在软件定义无线电发展主要特征之一是模拟数字的转变边界更靠近天线。由于这些趋势,迫切需要具有更高转化率分辨率的数据转换器的一部分

10

this needed performance upgrade comes with the technology evolution, but of- ten the demand is higher than this alone can provide. Thus, there is still room and need for innovations in circuit design.
这种所需的性能升级伴随着技术的发展而来,OF TEN 的需求高于仅此一项所能提供的需求。因此,电路设计仍有创新空间需求

The increasing integration level leads to systems with a smaller number of chips, the ultimate goal being a single chip solution, the system on a chip (SoC). This means that analog and digital circuits have to live on the same silicon die, which brings additional challenges in analog design, such as mixed signal issues and limitations in the choice of technology. Data converters are inherently mixed-signal circuits and face the same challenges on a smaller scale even without going as far as SoC. Furthermore, the evolution of technology has been driven by the microprocessor industry and hence does not always go in the best direction for analog. However, the recent rapid growth of the wireless telecommunications devices market has given a boost to the development of advanced mixed signal technologies, such as silicon germanium-based BiCMOS. The main challenges in data converter design are decreasing supply volt- age, short channel effects in MOS devices, mixed signal issues, the development of design and simulation tools, and testability.In analog-to-digital convert- ers (ADCs), they need to be met at the same time as the requirements for sampling, linearity, conversion rate, resolution, and power consumption are be- coming tighter. This course will address these issues, including analysis of the
集成度的提高导致系统具有更少的芯片,最终目标是单芯片解决方案,即片上系统 (SoC)。这意味着模拟和数字电路必须位于同一硅芯片上,这给模拟设计带来了额外的挑战,例如混合信号问题和技术选择的限制。数据转换器本质上是混合信号电路,即使没有 SoC 的进一步发展,在较小的规模上也面临着相同的挑战。此外,技术的发展是由微处理器行业推动的,因此并不总是朝着模拟的最佳方向发展。然而,最近无线通信设备市场的快速增长推动了先进的混合信号技术的发展,例如基于硅锗的 BiCMOS。数据转换器设计的主要挑战是降低电源电压、MOS 器件中的短通道效应、混合信号问题、设计和仿真工具的开发以及可测试性。在模数转换器 (ADC) 中,需要同时满足这些要求,同时对采样、线性度、转换速率、分辨率和功耗的要求越来越严格。本课程将解决这些问题,包括分析

circuit toplogies of the various required components.
各种所需元件的电路拓扑。

Basic semiconductor concepts
基本半导体概念

The pn junction
pn

~×

A semiconductor is a crystal lattice structure that can have free electrons and/or free holes (which are an absence of electrons and are equivalent to positive carriers). Silicon is the most common type of semiconductor material. This material has a valence of four, implying that each atom has four free electrons to share with neighbouring atoms when forming the covalent bonds of the crystal lattice. Intrinsic silicon, i.e. undoped silicon, is a very pure crystal structure having an equal number of electrons and holes. These free carriers are due to those electrons that have gained enough energy due to thermal agitation to break from their bonds. At room temperature there are 1.5 1010 carriers of each type per cm3. The number of carriers approx doubles for every 11C increase in temperature.
Asemiconductorisacrystall atticestructurethatcanhavefree lectronsand/or自由空穴(没有电子,相当于正载流子)。硅是最常见的半导体材料类型。这种材料的化合价为 4,这意味着每个原子在形成晶格的共价键时都有四个自由电子与相邻原子共享本征硅,即未掺杂硅,是一种非常纯的晶体结构,具有相同的电子和空穴数量。这些自由载流子是由于那些由于热搅动而获得足够能量以打破其键的电子。在室温下,cm 1有 1 510 10每种类型的载体3。温度每升高 11○C,载流子的数量大约会增加一倍

If one dopes silicon with a pentavalent impurity, i.e. atoms of an element having a valence of five, or equivalently, five electrons in the outer shell available when bonding with neighbouring atoms, there will be an extra free electron for every impurity atom (assuming none recombines with the holes). These free electrons can be used to conduct current. A pentavalent impurity (e.g. P or As) is said to donate free electrons to the silicon crystal, and so the impurity is known as a donor. These impurities are also called n-type dopants since the free carriers resulting from their use have a negative charge. Similarly, if one dopes silicon with atoms having a valence of three, e.g. with boron (B), each of the impurity atoms accepts one one electron from the silicon crystal so that they may form covalent bonds in the lattice structure. Thus each impurity atom results in a vacancy or hole of positive charge, i.e. a trivalent impurity is an acceptor or a p-type dopant. It should emphasized that a piece of n-type or p- type silicon is electrically neutral; the majority free carriers (electrons in n-type silicon and holes in p-type silicon) are netralized by bound charges associated with the impurity atoms.
如果用五价杂质掺杂硅,即与相邻原子键合时外壳具有5 个价态或 5 个电子的元素的原子,则每个杂质原子将有一个额外的自由电子(假设没有与空穴重新结合)。这些自由电子可用于传导电流。据说五价杂质(例如 P 或As)晶体提供自由电子因此杂质称为供体。这些杂质也称为n 型掺杂剂因为它们使用产生的游离载流子带有负电荷。同样,如果用价为 3 的原子掺杂硅,例如用硼 (B),则每个杂质原子都从硅晶体中接受一个 1 电子,以便它们可以晶格结构形成共价因此,每个杂质原子都产生一个带正电荷的空位或空穴,即三价杂质是受体或 p 型掺杂剂。 应该强调一块 n 型或 p 型硅是电中性的;大多数自由载流子(n 型硅中的电子p 型中的空穴杂质原子相关的束缚电荷净化

A pn junction or diode is a semiconductor with one part doped n-type
pn 结或二极管是具有一部分掺杂 n 型的半导体

adjacent to another part doped p-type (Fig.1). The large number of free positive carriers, holes, in the p side will tend to diffuse into the n side, where the free electrons in the n side will tend to diffuse to the p side. As the two types of carriers diffuse together, they recombine. Every electron that diffuses from the n side to the p side leaves behind a bound positive charge close to the transition region. Similarly, every hole that diffuses from the p side leaves behind a bound electron near the pn interface. This results in a region without mobile carriers, a depletion or spacecharge region, at the pn interface (Fig.2a). The charges on both sides of the depletion region cause an electric field to be established across the region; hence a potential difference results across the region, with the n side at a positive voltage relative to the p side (Fig.2b). This field opposes further diffusion of holes into the n region and electrons into the p region, i.e. the voltage drop across the depletion region acts as a barrier. The bound charges are like two plates of a capacitor and so also give rise to a parasitic capacitance
另一个掺杂p 型零件相邻(图 1)。 p 侧的大量自由载流子、空穴将倾向于扩散到 n 侧,而n 侧的自由电子将倾向于扩散到 p 侧。当两种类型的载流子扩散在一起时,它们会重新组合。每个从n扩散p 侧的电子都会过渡附近留下一个束缚电荷同样,p扩散的每个空穴都会在 pn 界面附近留下一个束缚电子。 这导致该地区没有移动运营商,adepletionorspacecharg eregionatt hepninterfaceFig2aThechargeson耗尽区的两侧都会产生电场在整个地区建立;因此在整个区域内产生电位其中n相对于 p 侧处于正电压(图 2b)。该场反对空穴进一步扩散到 n 区,电子进一步扩散到 p 区,即耗尽区的电压降起到屏障的作用。束缚电荷就像电容器块板因此也会产生寄生电容

Figure 1: Simplified physical structure of the junction diode.
图 1:结二极管的简化物理结构。

called the depletion or junction capacitance.
称为耗尽型或结电容。

If the pn junction is reverse biased, i.e. the p side connected to the negative terminal and the n side to the positive terminal of a DC source (a p side to n side voltage of V0 or less), the depletion region increases and no appreciable current flows. On the other hand, a positive voltage applied from the p side to the n side of a diode reduces the electric field opposing the diffusion of free carriers across the depletion region. The width of the depletion region is also reduced. If the forward voltage is large enough (a p side to n side voltage of V0 or higher), the carriers will start to diffuse across the junction, resulting a current flow from the p to the n side. For Silicon, appreciable diode current starts to occur for a forward-bias voltage around 0.5V. An idealised IV characteristic of a pn junction is shown in Figure 3.
如果pn反向偏置的, p连接到n连接到直流电源(apV0更低的 n电压),耗尽增加没有明显的电流流过。另一方面,二极管pn施加的正电压会减小电场,从而阻止自由载流子耗尽的扩散。耗尽宽度减小了。如果正向电压足够pn的电压V0更高),载流子将开始在结处扩散,导致电流从 p 侧流向 n 侧。对于硅,当正向偏置电压约为 0.5V 时,开始产生明显的二极管电流。 pn 结的理想化 IV 特性如图 3 所示

MOS Field-Effect Transistors (MOSFETs)
MOS场效应晶体管 (MOSFET)

CMOS circuits normally use two complementary types of transistors - n-channel and p-channel. n-channel devices conduct with a positive gate voltage, while p-channel devices conduct with a negative gate voltage. Electrons are used to conduct current in n-channel transistors, while holes are used in p-channel transistors. Figure 4 shows the physical structure of the n-channel enhancement- type MOSFET. The transistor is fabricated on a p-type substrate, which is a single-crystal silicon wafer that provides physical support for the device (and for the entire circuit in the case of an integrated circuit). Two heavily doped n-type regions, n+ source and n+ drain regions, are created in the substrate. A thin layer of silicon dioxide (SiO2) of thickness tox (typically 2-50nm), which is an excellent insulator, is grown on the surface of the substrate, covering the area between the source and drain regions. Metal is deposited on top of the oxide layer to form the gate electrode of the device (in fact, modern MOSFETs are fabricated using a process known as silicon-gate technology in which polysil- icon, which is heavily doped noncrystalline (or amorphous) silicon, is used to form the gate electrode). Metal contacts are also made to the source region, the drain region, and the substrate, also known as the body. The gate is electri-
CMOS电路通常使用两种互补类型的晶体管 - n 沟道和 p 沟道。n 沟道器件以正栅极电压导通,而p 沟道器件以负栅极电压导通。电子用于在 n 沟道晶体管中传导电流,而空穴用于 p 沟道晶体管。图 4 显示了 n 沟道增强型 MOSFET 的物理结构。晶体管在 p 型衬底上制造,p 型衬底是一种单晶硅晶片,为器件(在集成电路的情况下,为整个电路)提供物理支持衬底中产生了两个重掺杂n 型区域,即 n+sourcen+drain区域。在衬底表面生长一层厚度为 tox(通常为 2-50nm)的二氧化硅 (SiO2) 薄层,这是一种极好的绝缘体,覆盖了源极和漏极区域之间的区域。金属沉积在氧化的顶部形成器件事实上,现代MOSFET是使用称为硅栅技术的工艺制造的,其中 polysil-icon,即大量掺杂的非结晶(或非晶态)硅,用于形成栅极电极)。金属触点连接到极区域、漏极区域基板,也称为主体。大门带电的

Figure 2: (a) The pn junction with no applied voltage (open-circuited termi- nals). (b) The potential distribution along an axis perpendicular to the junction.
图 2:(a) 未施加电压的 pn 结(开路端)。(b) 沿垂直于结的轴的电位分布。

Figure 3: The IV characteristic of a silicon junction diode.
图 3:硅结二极管的 IV 特性。

Figure 4: Physical structure of the enhancement-type NMOS transistor: (a) perspective view; (b) cross-section. Typically L = 0.1 to 3 µm, W = 0.2 to 100 µm, and the thickness of the oxide layer (tox) is in the range of 2 to 50 nm.
图 4:增强型 NMOS 晶体管的物理结构:(a) 透视图;(b) 横截面。通常 L = 0.1 至 3 μm,W = 0.2 至 100 μm,氧化层 (tox) 的厚度在 2 至 50 nm 范围内。

cally isolated from the channel by the SiO2 and affects the channel (and hence, the transistor current) only through electrostatic coupling, similar to capaci- tive coupling. Therefore, the gate never conducts dc current. Normally, the p substrate is connected to the most negative voltage in the circuit which in analog circuits might be the negative power supply, but in digital circuits it is normally ground or 0 V . This connection results in all transistors placed in the substrate being surrounded by reverse-biased junctions, which electrically isolates the transistors and thereby prevent conduction through the substrate between transistors.
通过SiO2通道隔离,并且仅通过静电耦合影响通道(因此晶体管电流),类似于电容耦合。因此,栅极永远不会传导直流电流。通常,p 衬底连接到电路中最负的电压,模拟电路可能是电源但在数字电路,它通常是接地0V连接导致放置在衬底中的所有晶体管都被反向偏置结包围,从而在电气上隔离晶体管,从而防止晶体管之间通过衬底传导

Basic operation
基本操作

With no bias voltage applied to the gate, two back-to-back diodes exist in series between drain and source. One diode is formed by the pn junction between the n+ drain region and the p-type substrate, and the other diode is formed by the pn junction between the p-type substrate and the n+ source. These diodes prevent current conduction from drain to source when a voltage VDS is applied. Now consider the case where the source, drain and substrate are all connected to ground, Fig.5. In this case, the MOS transistor operates similarly to a capacitor. The gate acts as one plate of the capacitor, and the surface of the silicon, just under the thin insultaing SiO2, acts as the other plate. For small positive gate voltages, the positive carriers in the channel under the gate are initially repulsed and the channel changes from a p-doping level to a depletion region. As a more positive gate voltage is applied, the gate attracts negative charge from the source and drain regions, and the channel becomes an n region with mobile electrons connecting the drain and source regions. In short, a sufficiently large positive gate-source voltage changes the channel beneath the gate to an n region, and the channel is said to be inverted. The gate-to-source voltage, VCS, for which
由于没有极施加偏置电压极和源极之间有两个背靠背二极管串联。一个二极管由 n+漏极区和 p 型衬底之间的 pn 结形成,另一个二极管由 p 型衬底n+源极之间的pn形成。施加电压VDS,这些二极管可防止电流漏极传导到源极现在考虑源极、漏极和衬底都接地的情况图 5。在这种情况下MOS晶体管的工作原理类似于电容器。栅极充当电容器的一块板,而硅表面(就在薄绝缘 SiO2 下方)充当另一块板。对于小的正栅极电压,极下方通道中的载流子最初排斥,通道p 掺杂能级变为耗尽区。施加正的栅极电压时,栅极会从源漏极区域吸引负电荷,并且通道变成一个n区域,移动电子连接漏极和源极区域。简而言之,足够大的正栅极-源极电压栅极下方沟道变为n区,沟道称为倒置。栅源电压 VCS其中

Figure 5: The enhancement-type NMOS transistor with a positive voltage ap- plied to the gate. An n channel is induced at the top of the substrate beneath the gate.
图 5:增强型 NMOS 晶体管,正电压接合到栅极。栅极下方衬底顶部感应出一个n通道

the concentration of electrons under the gate is equal to the concentration of holes in the p substrate far from the gate is known as the threshold voltage, Vtn, and typically lies in the range 0.5 V to 1.0 V.
栅极下的电子浓度等于远离栅极的 P 衬底中空穴的浓度,称为阈值电压,Vtnand 通常位于 0.5 V 至 1.0 V 的范围内。

When VCS > Vtn the channel is present. As VCS is increased, the density of electrons in the channel increases. The carrier density, and therefore the charge density, is proportional to VCS Vtn, which is often called the effective or overdrive gate-source voltage, Veff
当 VCS> Vtn 通道存在时。随着 VCSis 的增加,通道中的电子密度增加。载流子密度,因此电荷密度,与 VCSVtn 成正比,这通常称为有效或过驱动栅极-源极电压 Veff
.

Veff = VCS Vtn(1)
Veff= VCS— Vtn(1)

The charge density of the electrons is then given by
电子的电荷密度由下式给出

n = Cox (VCS Vtn)(2)
n= 考克斯(VCS— Vtn) (2)

Here, Cox, is the gate capacitance per unit area and is given by
其中,Cox是每单位面积的栅极电容,由下式给出

Cox

= Koxo0
= 科索0

tox

(3)

where Kox (the symbol r is used in other branches of electronics) is the relative permittivity of SiO2 ( 3.9) and tox is the thickness of SiO2. The total gate capacitance, Cgs, is thus given by
其中 Kox(电子学其他分支中使用的符号 ris)是 SiO2 的相对介电常数( 39),tox是 SiO2 的厚度。总栅极电容 Cgsis 由下式给出

Cgs = CoxW G(4)
Cgs= CoxW G (4)

where WL is the effective gate area, i.e. W is the gate width and L is the effective gate length. The gate capacitance is one of the major load capacitances that
其中 WL 是有效栅极面积,即 W 是栅极宽度,L 是有效极长度。极电容主要的负载电容之一,它

circuits must be capable of driving. It is also important because when a MOS transistor is being turned off, the channel charge must flow from under the gate out through the terminals to other places in the circuit.
电路必须能够驱动。这也很重要,因为当 MOS 晶体管关闭时,通道电荷必须从栅极下方流出,通过端子流到电路中的其他位置。

Next, with VCS > Vtn, if the drain voltage VDS in increased above 0 V, a drain-source potential difference exists which results in a current flowing from drain to source, ID. The relationship between ID and VDS is the same as for a resistor, assuming VDS is small, and is given by
接下来,对于 VCS> Vtn,如果漏极电压 VDS增加到 0 V 以上,则存在漏源电位差,导致电流从漏极流向源极 ID。ID和 VDS 之间的关系与电阻器的关系相同假设VDS很小下式给出

W

ID = µn n G VDS
DS 系列
(5)

where µn 0.06 m2/V s is the mobili
伊犁
ty of electrons near the sili
伊犁
con surface, and so
所以

W

ID = µnCox
G Veff
伊芙
VDS
DS 系列
(6)

Note that this relationship is only valid for V
请注意,此关系仅对 V 有效
DS
DS 系列
near zero, i.e. V
接近零,即 V
DS
DS 系列
Veff
伊芙
. In
.在
this
case
ID is
linearly related
线性相关
to
VDS
DS 系列
. Note
注意
also
that
the
relationship
关系

vd = µnE(7)
vd= μnE (7)

has been used, where vd is the drift velocity of electrons, µn is the electron mobility and E is the applied electric field.
,其中 VD是电子的漂移速度,μn 是电子迁移率E施加的电场。

As the drain-source voltage increases, the channel charge concetration de-
随着漏源电压的增加,沟道电荷阻抗降低
creases at the drain end due to the smaller gate-to-channel voltage difference as
由于栅极到通道电压差较小,因此漏极端的折痕为
one moves closer to the drain, i.e. since the drain sits at a higher voltage (po-
一个更靠近漏极,即因为漏极处于更高的电压 (PO-
tential)
暂定)
than
the
source,
there
那里
is
an
increasing
增加
voltage
电压
gradient
梯度
from
the
source
to the drain, resulting in smaller gate-to-channel voltage near the drain.
到漏极,导致漏极附近的栅极-通道电压较小。
The
charge density therefore decreases across the channel as shown in Figure 6, i.e.
因此,如图 6 所示,整个通道的电荷密度降低,即
the channel becomes more tapered and its resistance increases correspondingly.
通道变得更加锥形,其电阻也相应增加。
Thus the I
因此,I
D-VDS
DS 系列
curve does not continue in a straight line but bends as shown
曲线不是沿直线继续,而是如图所示弯曲
in
Figure
数字
7. As
the
drain
排水
voltage
电压
is
increased,
增加
at
some
一些
point
the
gate-to-channel
门到通道
voltage
电压
at
the
drain
排水
end
结束
will
decrease
减少
to
the
threshold
门槛
value
价值
Vtn - the
minimum
最低
gate-to-channel voltage needed for n carriers in the channel to exist. Thus at
通道中存在 n 载流子所需的 gate-to-channel voltage因此,在
the
drain
排水
end
结束
the
channel
渠道
depth
深度
decreases
减少
to
almost
几乎
zero,
and
the
channel
渠道
be-
是-
comes
pinched
off,
关闭,
with pinch-off occuring at V
在 V 处发生夹断
CD
光盘
= Vtn or
VCS
CS 系列
VDS
DS 系列
= Vtn or V
或 V
DS
DS 系列
= VCS
CS 系列
Vtn. If the gate-drain voltage falls below this critical pinch-off
.如果栅极-漏极电压低于此临界夹断
voltage of V
电压 V
tn, the charge concentration in the channel remains constant (to a
,则通道中的电荷浓度保持恒定(到
1st
第一
order
次序
approximation)
approximation)
and
the
drain
排水
current
当前
no
longer
increases
增加
with
increas-
增加-
ing VDS
DS 系列
. The drain current thus saturates at this value and the MOSFET is
因此,漏极电流在该值处饱和,MOSFET 为
said to be in the saturation (now commonly referred to as the active) region of
据说位于 的饱和(现在通常称为活动)区域
operation. The result is the current-voltage relationship shown in Fig. 7 for a
操作。结果是图 7 所示的电流-电压关系。
given gate-source voltage. The region where
给定栅极-源极电压。其中
ID changes with V
随 V 的变化
DS
DS 系列
is called
称为
the
triode
三极管
region.
地区。
When
什么时候
MOS
MOS 系列
transistors
晶体管
are
used
使用
in
analog
模拟
amplifiers,
放大 器
they
他们
almost
几乎
always
总是
are
biased
偏见
in
the
active
积极
region.
地区。

It is important to point out that the channel does not become inverted sud- denly, but rather gradually. In most circuit applications, non-cutoff MOSFETs are operated in strong inversion, with Veff > 100 mV (many designers use
需要指出的是,通道不会突然倒置,而是逐渐倒置。在大多数电路应用中,非截止 MOSFET逆变下工作Veff>为 100mV(许多设计人员使用

Figure 6: Operation of the enhancement NMOS transistor as VDS is increased. The induced channel acquires a tapered shape, and its resistance increases as VDS is increased. Here, VCS is kept constant at a value > Vtn
图 6:随着 VDSis 的增加,增强型 NMOS 晶体管的运行情况。感应通道呈锥形,其电阻随着 VDSis 的增加而增加。这里,VCSis 保持恒定在 Vtn >值
.

Figure 7: The drain current ID versus the drain-to-source voltage VDS for an enhancement-type NMOS transistor operated with VCS > Vtn
图 7:使用 VCS>Vtn 工作的增强型NMOS晶体管漏极电流 I D与漏源电压 VDS 的关系
.

Figure 8: An n-channel enhancement-type MOSFET with VCS and VDS applied and with the normal directions of current flow indicated. (b) The ID–VDS characteristics for a device with k'n (W/L) = 1.0 mA/V2
图 8:应用 VCS 和 VDS 并指示电流法向的 n 沟道增强型 MOSFET。(b) k'n(W/L) = 1.0 mA/V2 的器件的 ID-VDS 特性
.

Veff > 200 mV ). Weak inversion occurs when VCS is approx. 100 mV or less above Vtn
V有效> 200 mV )。当 VCS约为Vtn 以上 100 mV或更低
.

The circuit of Figure 8a is used to determine the current-voltage character- istics of a MOSFET (Fig.8b). In the triode region, it can be shown that the drain current is given by
图 8a 的电路用于确定 MOSFET 的电流-电压特性(图 8b)。在三极管区域中,可以显示漏极电流下式给出

Dn

I= k' W G
I = 千瓦 G

2

V

DS

(VCS Vtn) VDS 2
(VCS— VTN)VDS— 2

(8)

where kn' = µnCoxis the process transconductance parameter; its value is
其中 kn= μnCox是过程跨导参数;其值为

determined by the fabrication technology. In the active region, the drain current
由制造技术决定。在有源区域中,漏极电流

is given by
下式给出

D

2

G

CS

tn

I= kn' W (V
I = knW (V

V)2(9)
— V )2(9)

Exercise 1 Dram the crosssection of a pchannel MOSFEf fabricated on a p−type substrate and explain clearly the operation of this device.
练习 1 简要介绍在 p-type 衬底上制造的 p-通道 MOSFEf 的横截面,并清楚地解释该器件的工作原理。

CMOS processing and layout
CMOS处理布局

IC fabrication basics
IC制造基础知识

To develop a fundamental understanding of CMOS integrated circuit design and layout, a good understanding of the fabrication processes is necessary. CMOS integrated circuits are formed by patterning different layers on and in the silicon wafer. This wafer is doped with acceptor atoms such as boron for a p-type wafer (this is the most common substrate used in CMOS processing), or donor atoms such as phosphorous for an n-type wafer. When designing CMOS ICs with a p-type wafer, n-channel MOSFETs (NMOS for short) are fabricated directly on the p-type wafer, while p-channel transistors, PMOS, are fabricated in an n−mell (Depending on the choice of starting material (substrate), CMOS processes can be identified as nmell, pmell or tminmell processes)
要对 CMOS 集成电路设计和布局有基本的了解,必须对制造过程有很好的了解。CMOS 集成电路是通过在硅晶片上和硅晶片中对不同层进行图案化而形成的。该晶圆掺杂了受体原子,例如用于 p 型晶圆的硼(这是 CMOS 加工中最常用的衬底),或用于 n 型晶圆的供体原子,例如磷。在设计具有 p 型晶圆的 CMOS IC 时,n 沟道 MOSFET(简称 NMOS)直接在 p 型晶圆上制造,而 p 沟道晶体管 PMOS 则在 n-mell 中制造(根据起始材料(衬底)的选择,CMOS 工艺可以确定为 n-mellp-mell 或 tmin-mell 工艺)
.

The following sequence of events apply, in a fundamental way, to any layer that we need to pattern. We start out with a clean, bare wafer, as shown in Fig. 9a. The distance given by the line A to B will be used as a reference is Figs. 9b-j, which are cross-sectional views of the dashed line shown in (a) . The small box in Fig. 9a is drawn with a layout program (and used for mask generation) to indicate where to put the patterned layer.
以下事件序列根本适用于我们需要 pattern 的任何我们从一块干净的晶圆开始如图1 所示9a.线 A 到 B 给出的距离将用作参考,如图所示。9b-j,它们是线横截面如图 9a 中的框是用布局程序绘制的(用于掩模生成),指示图案层放置的位置

First an oxide, SiO2 or glass, a very good insulator is grown on the wafer.
首先在晶圆上生长氧化物 SiO2 或玻璃,这是一种非常好的绝缘体。

This is done using a reaction with steam, H2O, or with O2 alone. The oxide resulting from the reaction with steam is called a wet oxide, while the reaction with O2 is a dry oxide. Both are called thermal oxides due to the increased temperature used during oxide growth. Next, a photosensitive resist layer is spun across the wafer (Fig. 9)1 . After the resist is baked, the mask derived from the layout program, Figs. 9e and f, is used to selectively illuminate areas of the wafer, Fig. 9g. The photoresist is developed (Fig. 9h), removing the areas that were illuminated. This process illustrated here is a positive resist process because the area that was illuminated is removed. A negative resist process removes the areas of resist that were not exposed to the light.
这是通过与蒸汽、H2O 或单独与 O2 反应来完成的。与蒸汽反应产生的氧化物称为湿氧化物,而与 O2 的反应是干氧化物。由于氧化物生长过程中使用的温度升高,因此两者都被称为热氧化物接下来,在晶圆上旋转光敏光刻胶层(图 D)。9)1 .光刻胶烘烤后,使用从布局程序(图 9e 和 f)得出的掩模选择性地照亮晶圆的区域,图 9e 和 f。9g.显影光刻胶(图 D)。9h),删除被照亮的区域。此处说明的这个过程是一个正性光刻胶过程,因为被照亮的区域被去除了。负性光刻胶工艺去除暴露在光线下的光刻胶区域

The next step in the patterning process is to remove the exposed oxide areas (Fig. 9i). Notice that the etchant etches under the resist, causing the opening in the oxide to be larger than what was specified by the mask. Fig. 9j shows the cross-sectional view of the opening after the resist has been removed. Because creating the masks is expensive, lowering the number of masks is equated with lowering the cost of a process. Standard CMOS processes require only 10 to 12 masking levels (compared with e.g. 15 to 20 for BiCMOS).
图案化过程的下一步是去除暴露的氧化物区域(图 9i)。请注意,蚀刻剂在光刻胶下方蚀刻,导致氧化物中的开口大于掩模指定的开口。图 9j 显示了去除光刻胶后开口的横截面图。由于创建掩码的成本很高,因此减少掩码的数量等同于降低过程的成本。标准 CMOS 工艺只需要 10 到 12 个掩蔽级别(而 BiCMOS 则需要 15 到 20 个掩蔽级别)。

n-Well CMOS process
n-WellCMOS工艺

The starting material for the n-well CMOS is a p-type substrate. The process begins with an n-well diffusion (Fig.10a). The n-well is required wherever p- type MOSFETs are to be placed. A thick SiO2 is etched to expose the regions
n-well CMOS 的起始材料是 p 型衬底。该过程从 n 孔扩散开始(图 10a)。无论在哪里放置 p MOSFET,都需要 n 孔厚的SiO2暴露区域

1 Note that the dimensions of the layers, i.e. oxide, resit and wafer are not drawn to scale. Typical wafer thickness is ~ 500µm while thickness of grown oxide or spun resist is ~ 1µm
1 请注意,层的尺寸,即氧化物、reit 和 wafer 不是按比例绘制的。典型的晶圆厚度为 ~ 500μm,而生长的氧化物或纺丝光刻胶的厚度为 ~ 1μm
.

Figure 9: Generic sequence of events used in photo patterning.
图 9:照片图案化中使用的通用事件序列。

Define n-well diffusion (mask #1)
定义 n 孔扩散(掩码 #1)

Define active regions (mask #2)
定义活动区域(蒙版 #2)

LOCOS oxidation
LOCOS氧化

n+ diffusion (mask #4)
n+ 扩散(掩码 #4)

p+ diffusion (mask #5)
P+ 扩散(掩码 #5)

(d) Contact holes (mask #6)
(d) 接触孔(面罩 #6)

(d) Polysilicon gate (mask #3)(h) Metallization (mask #7)
(d) 多晶硅栅极(掩模 #3)(h) 金属化(掩模 #7)

Figure 10: A typical n-well CMOS process flow.
10:典型的 n 阱 CMOS 工艺流程。

for n-well diffusion. The unexposed regions will be protected from the n-type phosphorous impurity.
用于 N 孔扩散。未曝光的区域将受到保护,免受 n 型磷杂质的影响。

The second step is to define the active region (where transistors are to be placed) using a technique called local oxidation (LOCOS). A silicon nitride (Si3N4) layer is deposited and patterned relative to the previous n-well re- gions (Fig.10b). The nitride-covered regions will not be oxidized. After a long wet oxidation step, thick field-oxide will appear in regions between transistors (Fig.10c). This thick field-oxide is necessary for isolating the transistors. It also allows interconnection layers to be routed on top.
第二步是使用称为局部氧化 (LOCOS) 的技术定义有源区域(晶体管放置的位置)。氮化硅 (Si3N4) 层沉积并相对于之前的 n 阱重新形成图案化(图 10b)。氮化物覆盖的区域不会被氧化。经过漫长的湿式氧化步骤后,晶体管之间的区域会出现厚场氧化物(图 10c)。这种的场氧化物对于隔离晶体管是必需的它还允许在顶部布线互连层。

The next step is the formation of the polysilicon gate (Fig.10d). This is one of the most critical steps in the CMOS process. The thin oxide layer in the active region is first removed using wet etching followed by the growth of a high quality thin gate oxide (0.13 µm and 0.18 µm processes use oxide thicknesses
下一步是形成多晶硅栅极(图 10d)。这是CMOS 工艺中最关键的步骤之一。首先使用湿法蚀刻去除活性区域中的薄氧化层,然后生长高质量的极氧化物(0.13μm0.18μm工艺使用氧化层厚度

as thin as 2nm to 50nm). A polysilicon layer, usually arsenic doped (n type), is then deposited and patterned. The photolithography is most demanding in this step, since the finest resolution is required to produce the shortest possible MOS channel length.
薄至 2nm 至 50nm)。然后沉积多晶硅层,通常是掺砷(n 型),并形成图案化。在此步骤中,光刻技术要求最高,因为需要最精细的分辨率来产生尽可能短的 MOS 通道长度。

The polysilicon gate is a self−aligned structure. A heavy arsenic implant can be used to form the n+ source and drain regions of the n-MOSFETs. The polysilicon acts as a barrier for this implant to protect the channel region. A layer of photoresit can be used to block the regions where the p-MOSFETs are to be formed (Fig.10e). The thick field-oxide stops the implant and prevents n+ regions forming outside the active regions. A reversed photolithography step can be used to protect the n-MOSFETs during the p+ boron source and drain implant for the p-MOSFETs (Fig.10f). In both cases the separation between the source and drain diffusions - the channel length - is defined by the polysilicon gate mask alone, hench the self-alignment.
多晶硅栅极是一种自对准结构。砷植入物可用于形成 n-MOSFET 的 n+ 源极和漏极区域。多晶硅充当该植入物的屏障,以保护通道区域。可以使用photoresit阻挡要形成 p-MOSFET的区域(图 10e)。厚场氧化物会阻止植入物并防止活动区域之外形成n+区域在 p-MOSFET 的 p+ 硼源极和漏极注入过程中,可以使用反向光刻步骤来保护 n-MOSFET(图 10f)。在这两种情况下,源极和漏极扩散之间的分离 - 沟道长度 - 仅由多晶硅极掩膜定义自对准有关。

A thick layer of CVD2 oxide is next deposited over the entire wafer before contact holes are opened. A photomask is used to define the contact window opening (Fig.10g) followed by a wet or dry oxide etch. A thin aluminium layer is then evaporated or sputtered onto the wafer. A final masking and etching step is used to pattern the interconnection (Fig.10h). A final passivation step the follows prior to packaging and wire bonding in which a thick CVD oxide or pyrex glass is deposited on the wafer to serve as a protective layer. A minimum of 7 masking levels are necessary, but in practice additional levels such as n and p guards for better latch-up immunity, a second polysilicon layer for capacitors, and multilayer metals for high-density interconnections are used.
打开接触孔之前接下来在整个晶圆沉积层厚厚CVD2氧化物。光掩模用于定义接触窗口开口(图 10g),然后湿式或式氧化物蚀刻。然后,蒸发或溅射到晶圆上。最后的掩蔽和蚀刻步骤用于对互连进行图案化(图 10h)。在封装和引线键合之前,最后的钝化步骤如下,其中厚的 CVD 氧化物或耐热玻璃沉积晶圆用作保护层。至少需要 7 个掩蔽级别,但在实践中使用额外的级别,例如用于更好闩锁扰度的 n 和 p 保护用于电容器第二个多晶硅以及用于高密度互连多层金属

Available components: integrated devices
可用组件:集成设备

Resistors
电阻

Besides the n- and p-channel devices, other devices including pn junction diodes, MOS capacitors and resistors can be fabricated on the same wafer alongside the transistors. Resistors can be made from various diffusion regions as shown in Fig.11 (different diffusion regions have different resistivity). The n+ and p+ diffusion regions are useful for low-value resistors, while the n-well is for higher value resistors with the actual resistance defined by the length and width of diffused regions. The tolerance of the resistor value is very poor (20-50%), but matching of two similar resistor values is quite good (5%). Thus circuits should be designed to exploit resistor matching and not specific resistor values.
除了 n 沟道和 p 沟道器件外,其他器件(包括 pn 结二极管、MOS 电容器和电阻器)可以与晶体管一起制造在同一晶圆上。电阻器可以由各种扩散区制成,如图 11 所示(不同的扩散区具有不同的电阻率)。n+ 和 p+扩散适用于低值电阻器,n-well适用于较高值的电阻器,实际电阻由扩散区的长度和宽度定义电阻值的容差 (20-50%),两个相似电阻值的匹配相当 (5%)。因此,电路设计为利用resistor matching 而不是特定的 resistor 值。

All diffused resistors are self-isolated by the reverse-biased pn junctions, and so exhibit a variation of resistance with bias and also include a parasitic jucntion capacitance making them unsuitable for high-frequency applications. They also exhibit a significant temperature coefficient (since carrier mobility varies with temperature).
所有扩散电阻器都通过反向偏置 pn 结进行自隔离,因此电阻偏置而变化并且还包括寄生共聚电容使其不适合高频应用。它们表现出显著的温度系数(因为载流子迁移率随温度变化)。

2 Chemical-vapour deposition (CVD) is a process by which gases or vapours are chemically reacted, leading to formation of solids on a substrate (can be used for SiO2, Si3N4 and polysilicon).
2 化学气相沉积 (CVD) 是气体或蒸气发生化学反应,从而在衬底上形成固体的过程(可用于 SiO2Si3N4 和多晶硅)。

Figure 11: Cross sections of resistors of various types available from a typical n-well CMOS process.
图 11:典型 n 阱 CMOS 工艺提供的各种类型的电阻器的横截面。

Figure 12: Interpoly and MOS capacitors in an n-well CMOS process.
图 12:n-well CMOS 工艺中的 Interpoly 和 MOS 电容器。

Better resistors can be fabricated using the polysilicon layer that is placed on top of the thick field-oxide. The thin polysilicon provides better surface area matching and hence more accurate resistor ratios. Since this resistor (called polyresistor) is physically separated from the substrate, it much lower parasitic capacitance.
可以使用放置在场氧化物顶部的多晶硅层来制造更好的电阻器型多晶硅提供更好的面积匹配,因此电阻比更准确。由于该电阻器(称为polyresistor)基板物理分离因此电容要低得多。

Capacitors
电容器

~

Two types of capacitors are available in CMOS processes, MOS and interpoly ca- pacitors (see Fig. 12). The MOS gate capacitance is basically the gate-to-source capacitance. It exhibits a large voltage dependence which can be eliminated by an additional n+ implant as shown in the figure. MOS capacitors exhibit a large a large parasitic pn junction capacitance. The interpoly capacitor requires de- position of a second polysilicon layer but exhibits near ideal characteristics. Capacitance values can be controlled to within 1%, with values ranging from 0.5pF to a few tens of pF. Matching between similar-size capacitors can be
CMOS 工艺中有两种类型的电容器,MOS 和 interpoly 电容器(见图 12)。MOS 栅极电容基本上是栅极到源极的电容。它表现出很大的电压依赖性,如图所示,可以通过额外的 n+ 植入物来消除。MOS 电容器具有较大的寄生 pn 结电容。间聚电容器需要沉积第二个多晶硅层,但表现出接近理想的特性。电容值可以控制在 1% 以内,值范围为 0.5pF 至几十 pF。相似尺寸的电容器之间的匹配可以是

within 0.1%.
0.1% 以内

Figure 13: A pn junction diode in an n-well CMOS process.
图 13:n 孔 CMOS 工艺中的 pn 结二极管。

Field-oxide regionPolysilicon mask
场氧化物区域多晶硅掩模



Active-region mask



W



Contact mask
隐形眼镜



Effective gate region L
有效浇口区域L

Figure 14: The layout of the active, polysilicon,and contact masks.
图 14:有源掩模、多晶硅和接触掩模的布局。

pn Junction diodes
pn二极管

An n-well diode is shown in Fig.13. It has high breakdown voltage, and finds use in input clamping circuits for protection against electrostatic discharge. It is also very useful as an on-chip temperature sensor (by the variation of its forward voltage drop).
n 井二极管如图 13 所示。它具有很高的击穿电压,可用于输入箝位电路以防止静电放电。它也非常有用作为片上温度传感器(通过其正向电压的变化)。

CMOS Layout and design rules
CMOS 布局和设计规则

Layout is the design portion of integrated-circuit manufacturing in which the geometry of circuit elements and wiring connections is defined. This process leads to the development of photographic masks used in manufacturing a mi- crocircuit. The two most important masks are those for the active region and for the gate polysilicon. The intersection of these two masks becomes the channel region of MOS transistors (Fig.14).
布局是集成电路制造的设计部分,其中定义了电路元件和布线连接的几何图形。这个过程导致了用于制造 mi-crocircuit 的摄影掩模的开发两个最重要的掩模有源区域栅极多晶硅的掩模。这两个掩模交点成为MOS晶体管的通道区域(图 14)。

The design rules for laying out transistors are often expressed in terms of a quantity, Z, where Z is half the gate length. Fig.14 shows the smallest possible
布局晶体管的设计规则通常用量 Z 表示,其中 Z 是栅极长度的一半。图 14 显示了可能的最小值

Gate poly
Gate poly (浇口多边形

Source junctionDrain junction
Drainjunction

Source-to-gate short circuit
源极到栅极短路

Source-to-drain short circuit
源极-漏极短路

Noncatastrophic misalignment
非灾难性错

Figure 15: Mask misalignment that results in catastrophic short circuits and an example of a noncatastrophic misalignment.
图 15:导致灾难性短路的掩模错位和非灾难性错位的示例

transistor that can be realised when a contact is made to each junction. Also shown are many of the minimum dimensions in terms of Z. Assuming a worst- case (mis)alignment of under 0.75Z for each mask, we can guarantee that the relative misalignment between any two masks is under 1.5Z. If an overlap be- tween any two regions of a circuit would cause a destructive short circuit, then a separation between the corresponding regions in a layout of 2Z guarantees this will never happen. For example, consider the poly mask and the contact mask. If these two regions overlap in the fabricated circuit, then the metal used to contact the source junction is also short-circuited to the gate poly, causing the transistor to be always turned off (Fig.15). To prevent this type of short, the contact openings must be kept at least 2Z away from the polysilicon gates.
当与每个结点接触时可以实现的晶体管。还显示了许多以 Z 表示的最小尺寸。假设每个掩模的最坏情况(错误)对齐低于 0.75Z,我们可以保证任意两个掩模之间的相对错位低于 1.5Z。如果电路任意两个区域之间的重叠会导致破坏性短路那么2Z的布局,相应区域之间的间隔可以保证这将从来没有发生过。例如考虑多边形蒙版接触蒙版。如果这两个区域在制造电路中重叠,则用于接触源极结的金属也会与栅极多晶片短路,导致晶体管始终关闭(图 15)。防止此类短路,触点开口必须与多晶硅栅极保持至少 2Z 的距离

Misalignment may also result in a gate that does not fully cross the active region (Fig.15). Since the active region is implanted everywhere in the active region except under the gate, this misalignment causes a short circuit between the source and drain - hence the design rule that polysilicon must always extend at least 2Z past the active region.
错位也可能导致门不完全穿过有源区域(图 15)。由于有源区在有栅极下以外的任何地方都植入,这种错位会导致漏极之间短路因此晶硅必须始终至少超出活动区域 2Z

Another design rule is that active regions should surround contacts by at least 1Z. This guarantees an overlap between the metal contact and the n+ active region of at least 1.5Z (since the minimum contact wifth is 2Z). No disastrous shorts occur if overlap exists between the contacts and edge of the active region (Fig.15).
另一个设计规则是活动区域应至少将触点包围1Z。这保证了金属触点和 n+有源区域之间的重叠至少为 1.5Z(因为最小触点为 2Z)。如果触点和活动区域的边缘之间存在重叠,则不会发生灾难性的短路(图 15)。

Figure 16: (a) Basic structure of the common-source amplifier. (b) Graphical construction to determine the transfer characteristic of the amplifier in (a).
图 16:(a) 共源放大器的基本结构。(b)确定 (a中放大器传输特性的图形结构

Building blocks for analog IC design
模拟 IC 设计的构建模块

The MOSFET as an amplifier
MOSFET 作为放大器

When operated in the active (saturation) region, MOSFETs can be used in the design of amplifier circuits. In the active region, the MOSFET acts as a voltage-controlled current source, i.e. changes in the gate-to-source voltage vCS gives rise to changes in the drain current iD. Amplification can be achieved because a small or low power signal controls a larger or higher power signal. The MOSFET can be biased to operate at a certain VCS and corresponding ID and the superimposing the voltage to be amplified, vgs, on the dc bias voltage VCS. By keeping "small", the resulting change in drain current, id, can be made proportional to vgs, and so obtaining linear amplification.
在有源(饱和)区域工作时,MOSFET 可用于放大器电路的设计。在有源区,MOSFET 充当电压控制电流源,栅源电压v CS的变化会引起漏极电流 iD 的变化之所以能够实现放大,是因为小功率或低功率信号控制着更大或高功率的信号。MOSFET 可以偏置以在一定的 VCS和相应的 ID 下工作,并将要放大的电压 vgs 叠加在直流偏置电压VCS上通过保持“小”,产生的漏极电流 id 的变化可以与v gs 成正比从而获得线性扩增。

Figure 16a shows the basic structure of the most commonly used MOSFET amplifier, the common-source configuration. Although the basic control action of the MOSFET is that changes vCS in (here, vCS = vI) give rise to changes in iD, a resistor RD is used here to obtain an output voltage vO
16a显示了最常用的MOSFET 放大器的基本结构,即共源配置。尽管MOSFET 的基本控制作用是 vCS的变化(这里为 vCS= vI)引起iD 的变化但这里使用电阻器RD获得输出电压vO
,

vO = vDS = VDD iDRD(10)
vO= vDS= VDD— iDRD(10)

or equivalently
同等

i= VDD 1 v

(11)

DRDRD DS

iD-vDS are the transistor current and voltage, i.e.and lie on the transis- tor output IV characteristics.From equation (11) iD-vDS must also lie on
iD-vDS是晶体管电流和电压,即 和 取决于转换器输出 IV 特性。从公式 (11) 中,iD-vDS也必须位于

the straight line (of slope -1/RD, 'y'-intercept (0, VDD/RD) and 'x'-intercept (VDD, 0)) known as the load line. The transistor IV curves and the load line are shown in Figure 16b.
称为负载线的直线(斜率 -1/RD'y' 截距 (0VDD/RD) 和 'x' 截距 (VDD, 0))。晶体管 IV 曲线和负载线如图 16b 所示。

Qualitatively, the circuit works as follows: for vI < Vtn, the transistor will be cut off, i.e.
从定性上讲,该电路的工作原理如下:对于 vI< Vtn,晶体管将被切断

iD = 0;vO = vDS = VDD(12)
iD= 0;vO= vDS= VDD(12)

which is point A on Fig.16b. As vI exceeds Vtn, the transistor turns on, iD increases, and vO decreases. Since vO will initially be high, the transistor will be operating in the active region, corresponding to points along the segment of the load line from A to B. Active region operation continues until vI vO = Vtn or vDS = vCS Vtn, the point at which the MOSFET enters its triode region of operation (point B on Fig.16b). At point B
即图 16b 中的 A 点。当 vI超过 Vtn,晶体管导通,iD增加,vO减小。由于 vO最初为高电平,晶体管将在有源区域工作对应于A 到 B 的负载线段上的点。有源区域操作一直持续到 vIVO = VTN或 vDS= vCSVtn,MOSFET 进入其三极管工作区域的点图 16b 中的B )。B

VOB = VIB Vtn(13)
VOB= VIB— Vtn(13)

For vI > VIB, the transistor is driven deeper into the triode region. Because the characteristic curves in the triode region are bunched together, the output voltage decreases slowly towards zero. For vI = VDD, the operating point will be C as shown on Fig.16b, and the output voltage VOC will be very small. A plot of vI versus vO results in a transfer characteristic shown in Fig.17. To operate the MOSFET as an amplifier the active/saturation-mode segment of the transfer curve is used. The device is located somewhere close to the middle of the curve, e.g. point Q, which is also known as the quiescent point. The voltage to be amplified vi is then superimposed on the dc voltage VIQ. By keeping vi sufficiently small to restrict operation to an almost linear segment of the transfer curve, the resulting output voltage vo will be proportional to v
对于 vI> VIB,晶体管被驱动到更深的三极管区域。由于三极管区域的特性曲线聚集在一起,因此输出电压缓慢下降到零。当 VI= VDD,工作点为C,如图 16b 所示输出电压VOC非常小。vI与 vO的关系图导致传输特性如图 17 所示。TooperatetheMOSFETasanamplifiertheactive/saturatio n-m odesegmentof使用传输曲线该设备位于曲线中间附近的某个位置,例如 Q 点,也称为静态点。然后,将要放大的电压 v叠加在直流电压 VIQ上,通过保持v足够操作限制在传输曲线几乎线性上,产生的输出电压VO将与V 成正比
i.

i.e. the amplifier will be very nearly linear, and vo will have the same waveform as vi except that it will be larger by a factor equal to the voltage gain of the amplifier at Q.
放大器非常接近线性,并且Vo具有与 V相同的波形,只是它会大一个系数,等于放大器Q 处的电压增益。

CMOS small-signal modeling in the active region
有源区域中的 CMOS 小信号建模

The most commonly used small-signal model for a MOS transistor operating in the active region is shown in Fig.18. The voltage-controlled current source, gmvgs, is the most important component of the model, with the transistor transconductance gm defined as
在有源区域工作的MOS晶体管最常用的小信号模型如图 18 所示。压控电流源 gmvgs 是该模型最重要的组件,晶体管跨导gm定义为

g= 6ID

m6VCS

(14)

where ID is the drain-source current and VCS the gate-source voltage. The resistor rds accounts for the finite output resistance, i.e
其中 ID为漏源电流,VCS为栅极-源极电压。电阻器 rdsaccounts 为有限输出电阻,即

1

rds

= gds

= 6ID 6VDS

(15)

An alternative low-frequency model, known as the T model, is shown in Fig.19.
另一种低频模型,称为 T 模型,如图 19 所示。

Figure 17: Transfer characteristic showing operation as an amplifier biased at point Q.
图 17:传输特性显示了放大器在 Q 点偏置时的工作。

g

vgs

ig=0id d

ss
s s

Figure 18: The low-frequency, small-signal model for a MOS transistor in the active region.
图 18:有源区域中 MOS 晶体管的低频、小信号模型。

g

vgs

s

ig=0 gmvgs

gmvgs
mgs

id d

rds
云数据库 RDS

s

d

g

vgs

s

ig=0

gmvgs
mgs

1/gm
1/克

id d

rds

s

g ig=0

gmvgs
mgs

1/gm
1/克

s

rds

Figure 19: The small-signal, low-frequency T model for an active MOS transis- tor.
图 19:有源 MOS 收发器的小信号、低频 T 模型。

Its derivation from the model of Fig.18 is illustrated. Note that the drain current must always equal the source current, and, therefore, the gate current must always be zero.
它从图 18 的模型中推导出来。请注意,漏极电流必须始终等于源电流,因此,栅极电流必须始终为零

Simple CMOS current mirror
简单的CMOS电流

A simple CMOS current mirror is shown in Fig.20, in which it is assumed that both transistors are in the active region. If both transistors are the same size, then Q1 and Q2 will have the same current since they both have the same gate voltage, i.e.
图 20 显示了一个简单的 CMOS 电流镜,其中假设两个晶体管都位于有源区域。如果两个晶体管的尺寸相同,则 Q1 和 Q2 将具有相同的电流,因为它们具有相同的栅极电压,即

Iout = Iin(16)
Iout= Iin(16)

Note that transistor Q1 is diode connected, i.e. its drain and gate are connected.
请注意,晶体管 Q1 是二极管连接的,即它的漏极和栅极是连接的。

The output resistance of the current mirror, rout, is given by
电流镜的输出电阻 routis 由下式给出

rout = rds2(17)
路由= rds2(17)

The current mirror active load is a way to accomplish high gain for a single stage (differential) amplifier. By using an active load, a high-impedance output load can be realised without using excessively large resistors or a large power- supply voltage. As a result, for a given power-supply voltage, a larger voltage gain can be achieved using an active load than would be possible if a resistor were used for the load.
电流镜像有源负载是一种为单(差分)放大器实现高增益的方法。通过使用有源负载,无需使用的电阻器较大的电源电压即可实现高阻抗输出负载。因此,对于给定的电源电压,使用有源负载可以实现负载使用电阻器更大的电压增益

Common-source amplifier
共源放大器

A common-source amplifier with an active load is shown in Fig.22. This common- source topology is the most popular gain stage, especially when high-input im-
具有有源负载的共源放大器如图 22 所示。这种共源拓扑是最常用的增益级,尤其是当高输入阻抗

out

Figure 20: A simple CMOS current mirror.
图 20:一个简单的 CMOS 电流镜。

Active load
有源负载

ut

Figure 21:
21:

pedance is desired. Here, an n-channel common-source amplifier has a p-channel current mirror used as an active load and to supply the bias current for the drive transistor. A small-signal equivalent circuit for low-frequency analysis of the common-source amplifier of Fig.22 is shown in Fig.23. Vin and Rin are the Thévenin equivalent of the input source. It is assumed that the bias voltages are such that both transistors are in the active region. Using small-signal analysis, the voltage gain as
pedance可取的。这里,n 沟道共源放大器有一个p 沟道电流镜,用作有源负载,并为驱动晶体管提供偏置电流22 中用于共放大器低频分析的小信号等效电路如图23 所示VinRin输入戴维南等效假设偏置电压这样的,两个晶体管都位于有源区域。采用小信号分析,电压增益

A = Vout vVin

= gm1R2

= gm1
=m1

(rds1
RDS1

ǁ rds2
RDS2

)(18)
)(18)

Depending on the device sizes, currents, and the technology used, a typical gain for this circuit is in the range of -10 to -100.
根据器件尺寸、电流和所用技术,电路的典型增益在 -10 100 之间

Cascode gain stage
共源共栅增益

The cascode configuration consists of a common-source-connected transistor feeding into a common-gate-connected transistor (see Fig.24). Cascode stages can have quite large gain for a single stage due to the large impedances at the output. To enable this high gain, the current sources connected to the output nodes are realised using high-quality cascode current mirrors. Normally this high gain is obtained without any degradation in speed (explain? hint: miller effect).
共源共栅配置包括一个共源连接的晶体管该晶体管馈入一个共栅连接的晶体管(见图 24)。由于输出阻抗很大共源共栅级对于可能具有相当大的增益。为了实现这种高增益,连接到输出节点的电流源使用高质量的共源共栅电流镜来实现。通常,这种高增益是在没有降低速度的情况下获得的(解释一下? 提示:Miller效应)。

Ibia
ba
s

Vin

Active load
有源负载

Q2
问 2

Vout

rou
t

Figure 22: A common-source amplifier with a) resistive load and b) current- mirror active load.
图 22:具有 a) 电阻负载b) 电流有源负载共源放大器

Vin

Rin

gm1vgs1

Vout

R2=rds1||rds2

Figure 23: A small-signal equivalent circuit for the common-source amplifier (with active load)
图 23:共源放大器的小信号等效电路(带有源负载)

Figure 24: The cascode configuration.
图 24:共源共栅配置。

vG1vG2

-VSS

Figure 25: The basic MOS differential-pair configuration.
图 25:基本的 MOS 差分对配置。

MOS differential pair and gain stage
MOS 差分对和增益级

The differential pair or differential amplfier configuration is the most widely used building block in analog integrated-circuit design. For example, the input stage of every op amp is a differential amplfifier. Compared to single-ended amplifiers, differential circuits are much less sensitive to noise and interference. Consider for instance two wires carrying a small differential signal as the voltage difference between the two wires. If an interference signal is coupled to the two wires (either capacitvely or inductively), the interference voltages on the two wires (i.e. between each wire and ground) will be equal. This will be so because the two wires are physically close together. Since in a differential system only the difference signal between the two wires is sensed, it will contain no interference component!
差分对或差分放大器配置是模拟集成电路设计中使用最广泛的构建模块。例如,每个运算放大器的输入级都是一个差分放大器。与单端放大器相比差分电路噪声干扰敏感度要低得多例如,考虑两根承载小差分信号的导线作为根导线之间的电压如果干扰信号耦合到根电线上(电容或感应),则两根电线上的干扰电压(即根电线接地之间相等。之所以如此是因为两条电线在物理上是靠得很近的。由于在差分系统中仅感应到两根线之间的差分信号因此不包含干扰分量!

The differential configuration also enables us to bias the amplifier and to couple amplifier stages together without the need for bypass or coupling capaci- tors. Since large capacitors are impossible to fabricate economically, differential amplifiers are very well suited for IC fabrication. Also, the performance of the differential pair depends critically on the matching between two sides of the circuit, and IC fabriaction is capable of providing such matched devices whose parameters track over wide ranges of changes in environmental conditions. To realize this differential input, almost all amplifiers use what is commonly called a differential pair (see Fig.25). It consists of two matched transistors, Q1 and Q2, whose sources are joined together and biased by a constant-current source I. Resistive loads RD will be used here to explain the essence of the differential pair operation, but usually active (current-source) loads are employed.
差分配置还使我们能够偏置放大器并将放大器耦合在一起而无需旁路耦合电容由于无法经济地制造大型电容器因此差分放大器非常适合 IC 制造。此外,差分对的性能在很大程度上取决于电路两侧之间的匹配而 ICfabriaction能够提供这种匹配的器件,其参数可跟踪环境条件。为了实现这种差分输入,几乎所有的放大器都使用通常所说的差分对(见图 25)。它由两个匹配的晶体管 Q1 和Q2 组成,连接在一起,并由 I 偏置这里将使用电阻负载RD解释差分操作本质通常采用有源(电流-源)负载

vD1

+

RD
研发

I/2

v

I/2 Q2
I/2第 2 季度

RD
研发

vD2

+

vCM +

VGS

SVGS
SVG S

VGS=Vtn+Veff

I

-VSS

Figure 26: The MOS differential pair with a common-mode input voltage v CM
图 26:共模输入电压 v CM 的 MOS 差分对
.

Operation with a common-mode input voltage
采用共模输入电压工作

Consider first the case of the two gate terminals joined together and connected to a voltage v CM, called the common−mode voltage ( Fig.26), i.e.
首先考虑两个栅极端子连接在一起并连接到电压 v CM 的情况,称为共模电压(图 26),即

vC1 = vC2 = vCM(19)
vC1= vC2= vCM(19)

Since Q1 and Q2 are matched, it follows from symmetry that the current I will divide equally between the two transistors. Thus
由于 Q1 和 Q2 匹配,因此从对称性可以看出,电流 I 将在两个晶体管之间平均分配。因此

I

iD1 = iD2 = 2(20)
iD1= iD2= 2 (20)

and the voltage at the sources, v S, will be
和源极的电压 v S将为

vCM = VCS + vSorvS = vCM VCS(21)
vCM= VCS+ vSor vS= vCM— VCS(21)

where VCS is the gate-to-source voltage corresponding to a drain current I/2. The voltage at each drain will be
其中 VCS是对应于漏极电流 I/2 的栅源电压,每个漏极处的电压为

I

vD1 = vD2 = VDD 2 RD(22)
vD1= vD2= VDD— 2 RD(22)

If v CM is varied, the current I will divide equally between Q1 and Q2 so long as the transistors remain in the active region, and the voltages at the drains will not change. Thus the differential pair does not respond to (i.e. it re(ects) common-mode input signals.
如果 v CM发生变化,只要晶体管保持在有源区域,电流 I 将在 Q1 和 Q2之间平均分配,并且漏极处的电压不会改变。因此差分响应(即它重新响应)共模输入信号。

vid

-VSS

Figure 27: The MOS differential pair with a differential input signal vid applied.
图 27:带有差分输入信号的 MOS 差分对 vidapplied。

Operation with a differential input voltage
采用差分输入电压工作

Now consider the case when a difference or differential input voltage is applied as shown in Fig.27. Since
现在考虑施加差分或差分输入电压的情况,如图 27 所示。因为

vid = vCS1 vCS2(23)
vid= vCS1— vCS2(23)

if vid is positive, vCS1 > vCS2, and vD1 < vD2; thus the difference output voltage (vD2 vD1) will be positive. On the other hand, when vid is negative, vCS1 < vCS2, and vD1 > vD2; and the differential output voltage (vD2 vD1) will be negative. Thus the differential pair responds to differencemode or differential input signals by providing a corresponding differential output signal between the two drains.
如果 vid 为正,则 vCS1> vCS2 和 vD1< vD2;因此差输出电压 (vD2vD1) 将为正。另一方面,当 vid 为负时,vCS1< vCS2 和 vD1> vD2;差分输出电压 (vD2vD1) 将为负,因此差分对通过在两个漏极之间提供相应的差分输出信号来响应差模或差分输入信号。

Operation of the MOS differential pair as a linear amplifier
MOS 差分对作为线性放大器运行

Figure 28 shows the MOS differential amplifier with input voltages
图 28 显示了具有输入电压的 MOS 差分放大器

and

vC1

1

= VCM + 2 vid
= 市调 + 2 视频

1

(24)

vC2 = VCM 2 vid(25)
vC2= VCM— 2 视频 (25)

where VCM is a common-mode dc voltage needed to set the dc voltage of the MOSFET gates (typically 0 V where two complementary supplies are utilised). Note that each of the transistors Q1 and Q2 is biased at a dc current of I/2 and is operating at an effective or overdrive voltage Veff
其中 VCM 是设置 MOSFET 栅极直流电压所需的共模直流电压使用两个互补电源时通常为 0 V)。请注意,每个晶体管 Q1 和 Q2 都偏置在 I/2 的直流电流下,并在有效过驱动电压Veff 工作
.

The differential input signal vid is applied in a complimentary (or balanced) manner, i.e. v C1 is increased by vid/2 and v C2 is decreased by vid/2 (e.g. if
以互补(或平衡)方式施加的差分输入信号 vidis v1 增加 vd/2,v C2 减少 vd/2 (egif

vO1

RDRD
研发D研发

vO

+

vO2

vG1=VCM+vid/2

Q2
问 2

vG2=VCM-vid/2

I

-VSS

Figure 28: The MOS differential amplifier with a common-mode voltage applied to set the dc bias voltage at the gates and with vid applied in a complementary (or balanced) manner.
图 28:MOS 差分放大器,施加共模电压以设置栅极的直流偏置电压,并以互补(或平衡)方式进行 vid 应用。

VR, but the differential output vtaken between the two drains willDDD0

the differential amplifier were fed from the output of another differential ampli- fier). Single-ended outputs v 01 and v 02 ride on top of dc voltages at the drains
差分放大器由另一个差分放大器的输出馈送单端输出v01v02位于漏极的直流电压之上

I

2

be an entirely signal (or ac) component (having a 0 V dc component).
完全是信号(或交流)分量(具有 0 V 直流分量)。

The small-signal equivalent circuit of the differential amplifier in Fig.28 is shown in Fig.29a. From the symmetry of the circuit as well as because of the balanced manner in which vid is applied, the signal voltage at the joint source connection must be zero (it acts as a virtual ground). Thus
图 28差分放大器的小信号等效电路如图29a 所示。从电路的对称性以及vid的平衡方式来看,联合源极连接的信号电压必须为零(它充当虚拟接地)。因此

vgs1 = vid/2andvgs2 = vid/2(26)
VGS1= VD/2 和 VGS2= —VD/2 (26)

and so Q1 will have a drain current increment gm (vid/2) and Q2 will have a drain current decrement gm (vid/2). Thus complimentary current signals are available at the drains. These may be converted into voltages by passing them through RD, in which case
因此 Q1 的漏极电流增量 gmvid/2),Q2 的漏极电流递减 gmvid/2) 因此,漏极处有互补电流信号这些可以通过通过RD转换为电压,在这种情况下

01

m

v= g

vid R

andv
v

= +g
=+

vid R

(27)

2

D

02

m

2

D

and the resulting gain becomes
,由此产生的增益变为

v01
01

= 1 g R
= — 1 克 R

andv021
v021

(28)

vid

2 m D
2D

vid

= 2 gmRD
= 2 克 RD

if the output is taken in a single-ended fashion. Alternatively, if the output is taken differentially, the gain becomes
如果输出以单端方式获取。或者,如果输出是差分取的,则增益变为

A = v02 v01

dvid

= gmRD

(29)

vO1

RDRD
研发D研发

vO

+

O2
O2 (二)

v

vO2

+vid/2

Q2+
问题 2 +

+

v

-vid/2

gs1

0 Vv
0VV 电压
gs2

b)c)
b) c)

Figure 29: Small-signal equivalent circuit of the MOS differential amplifier. (a) Circuit as seen by an ac/RFor small-signal. (b) An alternative way of looking at the small-signal operation of the circuit. (c) Same circuit but with transistors replaced by their small-signal equivalent circuit T-models.
图 29:MOS 差分放大器的小信号等效电路。(a) 用 ac/RFor 小信号看到的电路(b) 另一种看待电路小信号工作的方法。(c) 相同的电路,但晶体管被它们的小信号等效电路 T 模型取代。

An alternative way of analysing the differential pair is shown in Fig.29b and c, in which the transistor T-model is used.
分析差分对的另一种方法如图 29b 和 c 所示,其中使用了晶体管 T 模型。

r

id1 =
d1=

s1
S1 系列

vid

+ rs2

=1

gm1

vid

1

+ gm2
+m2

(30)

Since both Q1 and Q2 have the same bias currents, gm1 = gm2 = gm, and
由于 Q1 和 Q2 具有相同的偏置电流,因此 gm1= gm2= gm和

therefore
因此

Also, since id2 = id1, then
此外,由于 id2= —id1then

id1 =
d1=

gm v(31)
GMV(31)

2id
2个 ID

g

2

id2 = m vid(32)
id2= — mvid(32)

Differential pair with an active load (differential amplifier)
带有源负载的差分对(差分放大器)

If a differential pair has a current mirror as an active load, a complete differential- input, single-ended-output gain stage can be realised as shown in Fig.30a. The differential pair is formed by transistors Q1 and Q2, loaded in a current mirror formed by transistors Q3 and Q4. If the two input terminals are connected to a dc voltage (0 V ), the bias current I divides equally between Q1 and Q2 (as- suming perfect matching), Fig.30b. The drain current of Q1 is fed to the input transistor of the current mirror, Q3. Thus, a replica of this current is provided by Q4. Observe that at the output node, the two currents I/2 balance each other out, leaving a zero current to flow out to the next stage.
如果差分电流作为有源负载,则可以实现完整的差分输入、单端输出增益如图30a 所示差分对由晶体管 Q1 和 Q2 形成,负载在晶体管Q3Q4 形成的电流镜中。如果两个输入端子连接到直流电压 (0 V),偏置电流 I 在 Q1 和 Q2 之间平均分配(假设完美匹配),图 30b。Q1 的漏极电流馈送到电流 Q3 输入晶体管因此,Q4提供了电流的副本。观察,在输出节点,两个电流 I/2 相互平衡留下零电流流下一级。

With a differential input vżd applied to the input (Fig.30c), a virtual ground
将差分输入 vżd应用于输入(图 30c)时,虚拟接地

develops at the common-source terminal of Q1 and Q2. Q1 will conduct a drain
在 Q1 和 Q2 的共源末端发展。Q1 将进行引流

signal current
信号电流

i = gm1vid/2(33)
i = gm1vd/2 (33)

and Q2 will conduct an equal and opposite current i. The drain signal current i of Q1 is fed to the input of the Q3-Q4 current mirror, which responds by providing a replica in the drain of Q4. Therefore, at the output node we have two currents, each equal to i, which sum together to provide an output current 2i. Thus
Q2传导相等相反电流i.Q1漏极信号电流i 被馈送到 Q3-Q4 电流镜的输入端,该电流镜通过在Q4 漏极中提供复制品来响应。因此,输出节点,我们有两个电流,每个电流都等于 i,它们相加得到输出电流2i。

io = gm1vid(34)
io= gm1vid(34)

Since output resistance is given by
由于输出电阻由下式给出

rout = rds2||rds4(35)
路由= RDS2||RDS4(35)

the differential gain becomes
差分增益变为

Ad = gm1rout(36)
广告= gm1rout(36)

A figure of merit for this amplifier is the so called common mode re(ection ratio
该放大器的品质因数是所谓的共模谐振比

(CMRR)
(CMRR)

CMRR
CMRR (共模抑制比)

differential gain
差分增益

(37)

common mode gain
增益

(38)
(38)

Basic Opamp Circuit Topology
基本运算放大器电路拓扑

The two-stage circuit architecture has historically been the most popular ap- proach for CMOS opamps. A block diagram of a typical two-stage CMOS opamp is shown in Fig.31. "Two-stage" refers to the number of gain stages in the opamp. Fig.31 actually shows three stages - two gain stages and a unity- gain stage. The output buffer is normally present only when resistive loads need to be driven. In a CMOS IC, opamp loads are often, but not always, purely capacitive, so the output buffer is seldom included. The first gain stage is a differential-input single ended output, often very similar to that shown in Fig.30a. The second gain stage is normally a common-source gain stage that has an active load, often very similar to that shown previously in Fig.22. Capacitor Ccmp is included to ensure stability when the opamp is used with feedback.
两级电路架构历来是 CMOS 运算放大器最流行的应用。典型的两级 CMOS 运算放大器的框图如图 31 所示。“Two-stage” 是指运算放大器中 gain 级的数量。图 31 实际上显示了三个阶段 - 两个增益阶段和一个单位增益阶段。输出缓冲器通常仅在需要驱动电阻负载时才存在在 CMOS IC 中,运算放大器负载通常是(但并非总是)纯电容性的,因此很少包含输出缓冲器。第一个增益级是差分输入单端输出,通常与图 30a 所示非常相似。第二个增益级通常是具有有源负载的共源增益级,通常与前面的图 22 所示非常相似。包括电容器 Ccmp,以确保运算放大器反馈一起使用时的稳定性

The CMOS realisation of a basic opamp is shown in Fig.32. Note that the first stage has a p-channel differential input pair with an n-channel current mirror active load. The gain of the differential stage is given by
基本运算放大器的 CMOS 实现如图 32 所示。请注意,第一级具有一个 p 沟道差分输入对和一个 n 沟道电流镜像有源负载。差分增益由下式给出

Av1 = gm1 (rds2||rds4)(39) for the second inverter stage by
Av1= gm1(rds2||rds4) (39) 用于第二逆变器级

Av2 = gm7 (rds6||rds7)(40)
Av2= —gm7(rds6||RDS 7) (40)

VDD

VDD

VSG3
VSG3 系列

I/2

Q4
问 4

V0=VDD-VSG3

I/2

I/2

I/20

I/2Q2
I/2 第 2 季度

-VSS

I

-VSS

vid

gm1vid

vo

rou
你好
t

0 Vc)
0 c)

Figure 30: a) The active-loaded MOS differential pair. b) The circuit at equilib- rium assuming perfect matching. c) The circuit with a differential input signal applied and its small-signal model.
图 30: a)有源负载 MOS 差分对。b) 假设完美匹配的电路处于平衡状态。c)施加了差分输入信号电路及其小信号模型。

vin
v

Differential input stage
差分输入

Second gain stage (inverter)
第二增益(逆变器)

Output buffer
输出缓冲器

Ibias
I偏倚

Figure 31: A block diagram of a two-stage opamp
图 31:两级运算放大器的框图

Vbias
V偏压

Q10
问 10

v

Differential input stage
差分输入

Second gain stage (inverter)
第二增益(逆变器)

Output buffer
输出缓冲器

Figure 32: A CMOS realisation of a two-stage amplifier. The bias circuitry is usually more complex than shown.
图 32:两级放大器的 CMOS 实现。偏置电路通常所示复杂

The third stage is a source follower.
第三个阶段是源跟随者。

The two-stage opamp in Fig.32 has p-channel input transistors. It is also possible to realise a complimentary opamp where the first stage has an n-channel differential pair and the second stage is a common source amplifier having a p- channel input drive transistor. However, having a p-channel input first stage implies that the second stage has an n-channel drive transistor. This arrange- ment maximises the transconductance of the drive transistor of the second stage, which is critical when high-frequency operation is important. Also a n-channel source follower is preferable because this will have less voltage drop. Also, for a given power dissipation, and therefore bias current, having a p-channel input- pair maximises the slew rate. It also minimises the 1/f noise
图 32 中的两级运算放大器具有 p 沟道输入晶体管。也可以实现互补运算放大器,其中第一级具有 n 沟道差分对,第二级是具有 p 沟道输入驱动晶体管的共源放大器。然而,具有 p 通道输入第一级意味着第二级具有 n 通道驱动晶体管。这种布置最大限度地提高了第二级驱动晶体管的跨导性,这在高频操作很重要时至关重要。此外,n 通道源极跟随器是可取的,因为这将具有较小的电压降。此外,对于给定的功率耗散,因此偏置电流,具有 p 通道输入对可最大限度地提高转换速率它还使 1/f 噪声最小
.

Analog
模拟

continuous time
连续时间

continuous amplitude
连续振幅

Clk
时钟

Analog
模拟

discrete time
离散时间

continuous amplitude
连续振幅

Digital
数字

discrete time
离散时间

discrete amplitude
离散振幅

digital codeword rep.
数字码字代表

Clk
时钟

010 001 001

010 111 111

INOUT

SamplerQuantizer
采样器量化器

Figure 33: Principle of A/D conversion
图 33:A/D 转换的原理

Analog-to-Digital Conversion
模数转换

Analog-to-digital (A/D) conversion can be separated into two distinct opera- tions: sampling and quantization. Sampling transforms a continuous time signal into a corresponding discrete time signal, while quantisation converts continu- ous amplitude distribution into a set of discrete levels, which can be expressed with digital codewords. Figure 33 shows the principle of A/D conversion.
模数 (A/D) 转换可以分为两个不同的操作采样量化。采样连续时间信号转换为相应的离散时间信号,而量化将连续幅度分布转换为一组离散电平,可以用数字码字表示33显示了A/D转换的原理

Sampling
采样

A sample-and-hold (S/H) circuit is used to take samples of its input signal and hold these samples in its output for some period of time. Typically, the samples are taken at uniform time intervals; thus, the sampling rate (or clock rate) of the circuit can be determined. This is illustrated in Figure 34 for ideal sampling (Fig.34a) and the sample-and-hold case (Fig.34b).
采样保持 (S/H) 电路用于对其输入信号进行采样,并将这些样本保存在其输出中一段时间。通常,样本以统一的时间间隔采集;因此,可以确定 circuit 的采样率 (或 clock rate)。这在图 34 中说明了理想采样 (图 34a) 和采样保持情况 (图 34b)。

Figure 35 shows an analog signal of bandwidth B (i.e. highest freqeuncy component is B Hz). An ideal S/H circuit takes samples of this signal at uniform intervals T. In the time domain this corresponds to multiplying the signal by an impluse train
图 35 显示了带宽 B 的模拟信号(即最高频率分量为 B Hz)理想的 S/H 电路以均匀的间隔 T 获取该信号的样本。在时域中,这对应于将信号乘以 impluse 序列

y (t) = x (t) ·
y (t) = x (t) ·

n=Σ
n=Σ - ∞

6 (t nT )(41)
6 (t — nT ) (41)

where 6 (t) represents Dirac's delta function. The result is a train of impulses whose values correspond to the instantaneous values of the input signal. The spectrum of the sampled signal is a convolution of the input spectrum and the
其中 6 t表示 Dirac 的 delta 函数。结果是一连串脉冲其值对应于输入信号的瞬时值。采样信号频谱输入频谱卷积

(b)
(二)

Figure 34: Sampling in time domain. Figure (a) shows the sampling instants. Figure (b) is a sample-and-held signal.
图 34:时域中的采样。图 (a) 显示了采样时刻。图 (b) 是采样保持信号。

T

x(t)
x(吨)

Figure 35: Sampling in time domain of signal of bandwidth B.
图 35:带宽 B 信号的时域采样。

spectrum of the impulse train, which is also an impulse train (see Sec 5.1.1).
脉冲序列的频谱,它也是一个脉冲序列(参见 Sec 5.1.1)。

n=—∞

T

T

Y (f) = X (f) ω Σ1 6 f n(42)
Y (f) = X (f) ω Σ 1 6 f — n (42)

This is illustrated in Figure 36, where fs is the sampling freqency and B the signal bandwidth. The resulting spectrum is the original spectrum plus an infinite number of images of the original spectrum centered at multiples of the sampling frequency. The figure also clearly shows that as long as the bandwidth of the input signal is less than half the sampling frequency the images do not overlap and thus the original signal can be restored by filtering - this is the Nyquist criterion. If this condition is not satisfied, a part of the image is aliased (mixed with) into the desired signal, causing irreversible distortion. Because of this, the input signal usually has to be bandlimited before sampling in order to avoid the aliasing of noise and other unwanted signals present outside the desired signal band.
如图36 所示,其中 fs是采样频率B信号带宽。 生成的频谱是原始频谱加上采样频率的倍数为中心的原始频谱的无限数量图像该图清楚地表明只要输入信号的带宽小于采样频率的一半,图像就不会重叠,因此可以通过滤波恢复原始信号 - 这就是奈奎斯特准则。如果不满足此条件,则图像的一部分将被别名 混合) 所需的信号中,从而导致不可逆的失真。因此采样之前,通常必须输入信号进行频带限制以避免噪声和其他不需要的信号所需信号频带之外出现混叠。

In practice, the output waveform of a sampling circuit cannot be a train of infinitely narrow impulses. In most practical implementations the sample is held in the output of the circuit until the next sample is taken (Fig.34). The spectrum of a sample-and-held signal is also shown in Fig.36; which in time domain is a convolution of the sampled signal with a square pulse.
在实践中,采样电路的输出波形不能是一连串无限窄的脉冲。在大多数实际实现中,样本被保存在电路的输出中,直到下一个样本被采集(图 34)。采样保持信号的频谱也显示在图 36 中;在时域中采样信号方波脉冲卷积

0Bf
0 B f

Spectrum of the sampling waveform
采样波形的频谱

-2fs

-fs 0

fs2fsf

Spectrum of the sampled signal
采样信号的频谱

-2fs

-fs 0

fs2fsf

Spectrum of sampled-and-held signal
采样保持信号的频谱

-2fs

-fs 0

fs2fsf

Figure 36: Spectrum of a sampled signal
图 36:采样信号的频谱

5.1.1More on impulse train
5.1.1 有关脉冲序列的更多信息

We have two expressions for a periodic impulse train,
我们有两个周期性脉冲序列的表达式,

s (t) =
s (t) =

n=Σ
n=Σ - ∞

6 (tnT ) = 1
6 (吨 nT ) = 1

T

n=Σ
n=Σ - ∞

e(2vnt/T(43)
e(2vnt/T(43)

The Fourier transform of each expression is
每个表达式的傅里叶变换为

S (f) =
S (f) =

n=Σ
n=Σ - ∞

e(2vnT f = 1
e—(2vnT = 1

T

n=Σ
n=Σ - ∞

6 f n(44)
6 F — N (44)

T

Therefore, the Fourier transform3 of a periodic impulse train in time is a periodic impulse train in frequency.
因此,时间周期性脉冲序列的傅里叶变换3 是频率周期性脉冲序列。

Quantization: an ideal A/D converter
量化:理想的 A/D 转换器

The block diagram representation for an A/D converter (ADC) is shown in Figure 37a, where Bout is the digital output word while Vin and Vref are the analog input and reference signals, respectively. A transfer curve for an A/D converter can be sketched as shown in Figure 37b for a 2-bit and 3-bit converter. We use the 2-bit ADC as an example. Since there are 4 digital output levels, we can only also divide the input amplitude into 4 levels. We therefore need a reference voltage Vref such that if:
模数转换器 (ADC) 的框图如图37a 所示,其中 Bout是数字输出字,而 Vin和 Vref 分别模拟输入和参考信号。A/D 转换器的传输曲线可以如图 37b 所示,用于 2 位和 3 位转换器。我们以 2 位 ADC 为例。由于有 4 个数字输出电平,我们也只能将输入幅度分为 4 个电平。因此,我们需要一个参考电压Vref如果

Vin = 0thenBout Ξ 00
Vin= 0 则 BoutΞ 00

V= 1 V

thenB
然后是B

Ξ 01

in4 ref
4ref

2

out

Vin = 4 VrefthenBout Ξ 10

3

in

4

ref

V=V

thenB
然后是B

Ξ 11

out

Since Vin is continuous in amplitude, we split it up as shown on the transfer curve in Fig.37b. Now defining
由于 Vinis 的振幅是连续的,我们将其拆分,如图 37b 中的传输曲线所示。现在定义

VKSB

Vref
V参考

Ξ 2N

(45)

which is the change in input voltage required for the output to change the least significant bit (for an N-bit ADC). It becomes clear that there is a range of valid input values that produce the same digital output word. This signal ambiquity
这是输出更改最低有效位所需的输入电压变化(对于 N 位 ADC)。很明显,有一系列有效的 input 值产生相同的 digital output 字。这个信号是模棱两可的

3 The Fourier transform of a function x(t) is E (ƒ) =
3函数 x(t) 的傅里叶变换为 E (ƒ) =

transform is given by x (t) =

E (ƒ) e(2πftdƒ

—∞

x (t) e(2πftdt and the inverse
∞x (t) e—(2πdt 和逆

—∞

Analog
模拟

Digital output
数字输出

Bout

a)

Bout

Bout

111

Digital output

110

101

100

Digital output

11

10

01

00

01/4
0 1/4

2/4

3/4 1

V /V

011

010

001

000

0

2/84/86/81

in ref
参考

Analog inputb)
模拟输入 b)

Vin/Vref Analog input
VV 模拟输入

Figure 37: a) A block diagram representing an A/D converter, b) Input-output transfer curve for a 2-bit and 3-bit A/D converter.
图 37:a) 表示 A/D 转换器的框图,b) 2 位和 3 位 A/D 转换器的输入-输出传输曲线。

1

1

1

Vx is known as quantixation error. Note also that this signal ambiguity has a value of
Vx称为定量误差。另请注意,此信号模糊度的值为

V

ref

. 2 · 22 .orVx . 2 VKSB.(46)

.

.

..

Vx

for the 2-bit converter and
对于 2 位转换器和

V

ref

1

. 2 · 23 .orVx . 2 VKSB.(47)

.

.

1

..

Vx1

for the 3-bit converter.Therefore, for an A/D converter, the following equation relates the input and output signals
对于 3 位转换器。因此,对于 A/D 转换器,以下公式将输入和输出信号相关联

Vin Vx = kVref(48)
VinVx= kVref(48)

where k is a scaling factor determined from the digital output word (k < 1), and
其中 k 是由数字输出字 (k < 1) 确定的比例因子,并且

11

with

2 VKSB Vx 2 VKSB(49)
— 2 VKSB≤ Vx≤ 2 VKSB(49)

and

VKSB

Vref
V参考

Ξ 2N

(50)

Vin,max
V英寸,最大值

=11 2N

Vref
V参考

(51)

Digital input Bin
数字输入B输入

Vref
V参考

Analog output
模拟输出

D/AVout
D/A V输出

Vout/Vref
V输出/V参考

Analog output1
模拟输出 1

¾

½

¼

0

b)

0001 10 11

Digital input
数字输入

Bout
B出局

Figure 38: a) A block diagram representing a D/A converter, b) Input-output transfer curve for an ideal 2-bit DAC.
图 38:a) 代表 D/A 转换器的框图,b) 理想 2 位 DAC 的输入-输出传输曲线。

Since k < 1, conversion of an N-bit digital output word to decimal is via
由于 k < 1,因此 N 位数字输出字到十进制字的转换是通过

21

22

2N

k = b1 + b2 + · · · + bN
k = b1 + b2 + ····+ bN

(52)

Exercise 2 An 8−bit A/D converter has Vref = 5V . What is the input voltage mhen Bout = 10110100?
练习 2 一个 8 位 A/D 转换器的 Vref= 5V 。输入电压 mhen Bout= 10110100是多少?
.

5.2.1Ideal D/A converter
5.2.1理想的D/A转换器

Consider the block diagram of an n-bit D/A converter (DAC) shown in Fig.38a. It convertes/decodes a digital (coded) signal Bin into an analogue signal Vout according to the expression
考虑图 38a 所示的 n 位 D/A 转换器 (DAC) 的框图。它将数字(编码)信号 Bn(编码)信号转换/解码为模拟信号 Vout(根据表达式)

Vout = BinVref(53)
输出电压 = BinVref (53)

where Vref is an analogue reference voltage. For an n-bit binary DAC
其中 Vref 为模拟参考电压。对于 n 位二进制 DAC

B= b1 + b2

+ b3 + · · · + bn
+ b3 + ····+ 十亿

(54)

and so
等等

in2
2

22232n

out

2

22

23

V= b1 + b2 + b3

+ · · · + bn V
+ · · ·+ 十亿 V

(55)

2n

ref

(Bin is a fractional binary value since Vout < Vref ). Bin can assume 2n equally
(Bin是自 Vout< Vref 以来的小数二进制值)。Bincan 假设 2nequal

2n

spaced values from 0 (when all bits are '0') to 1 1 (when all bits are '1').
从 0 (当所有位都是 '0' 时) 到 1 — 1 (当所有位都是 '1' 时)的间隔值。

2n

Spacing between adjacent values is 1 . The DAC output is the result of mul- tiplying the analogue input signal Vref by the digital variable Bin. A transfer curve for a 2-bit DAC is shown in Fig.38b.
相邻值之间的间距为1。DAC 输出是数字变量 Bin模拟输入信号 Vref 叠加的结果2 位DAC传输曲线如图38b 所示

Basic Digital-to-Analog Converters
基本型数模转换器

ADCs and DACs are available in a variety of architectures and technologies. In the section, we will examine the most common examples starting with DACs (since many ADCs utilize DACs in their configurations).
ADCDAC有多种架构和技术可供选择。在本节中,我们将研究以 DAC 开头的最常见示例(因为许多ADC在其配置中使用DAC)。

i

R1RF

1

v

vO

v

Figure 39: Summing amplifier
39:求和放大器

Weighted-Resistor DACs
加权电阻DAC

This configuration is based on the use of operational amplifier (OPAMP) as a summing circuit. Consider an example of such a circuit as shown in Fig.39. To obtain a relationship between the output and inputs, we impose that the total current entering the virtual ground node equals that exiting it (standard assumptions on OPAMP characteristics apply, i.e. infinite input impedance and gain), or
此配置基于使用运算放大器 (OPAMP) 作为求和电路。考虑一个如图 39 所示的电路示例。为了获得输出和输入之间的关系,我们假设进入虚拟接地节点的总电流等于离开虚拟接地节点的总电流OPAMP特性的标准假设适用,无限输入阻抗gain)

i1 + i2 + i3 = iT(56)
i1+ i2+ i3= iT(56)

Using Ohm's law, we obtain
使用欧姆定律,我们得到

and therefore
因此

v1 + v2 R1R2

+ v3 R3

=vO RT

(57)

vO = RT

v1 + v2

R1R2

+ v3(58)
+v3(58)

R3
R3 系列

Though in this example three inputs have been used, this analysis can readily be generalized to an arbitrary number of them.
尽管在此示例中使用了三个输入,但此分析可以很容易地推广任意数量的输入。

The weighted-resistor DAC is the simplest and most straight forward of all DACs and is based on the summing amplifier concept described above. The DAC of Fig.40 uses an OPAMP to sum n binary-weighted currents derived from Vref via the scaling resistors 2R, 4R, 8R, ..., 2nR. Whether the current
加权电阻 DAC 是所有 DAC 中最简单、最直接的,它基于上述求和放大器概念。图 40 的 DAC 使用运算放大器通过缩放电阻 2R,4R,8R...,2nR.电流对Vref 得出的 n 个二进制加权电流求和。

ih =

Vref
V参考

2 R

appears in the sum depends on whether the corresponding switch is
出现在 SUM 中取决于对应的开关是否为

22

23

2n

closed (bh = 1) or open (bh = 0) . The output voltage is given by (show?)
闭合 (bh= 1) 或开路 (bh= 0) 输出电压由下式给出 (show?)

O

R

2

v= Vref RT

b1 + b2

+ b3

+ · · · + bn(59)
+ · · ·+ BN (59)

vref
v参考

vO

Figure 40: Weighted-resistor DAC
40:加权电阻DAC

2R2R2R2R2R
2R2R2R2R 2R 2R

vref
v参考

Figure 41: Resistor-ladder (R-2R) network.
图 41:梯形电阻 (R-2R) 网络。

R-2R Ladder DACs
R-2R梯形DAC

Most DACs architectures are based on the popular R-2R ladder depicted in Fig.41. Starting from the right and working toward the left, the equivalent resistance to the right of each labelled node (n1, n2, ... nn) equals 2R. Thus, the current at each node divides equally into two components, i.e. the current i sourced by Vref divides along the branches as follows
大多数 DAC 架构都基于图 41 中描述的流行的 R-2R 梯形图从右侧开始,向左工作,每个标记节点右侧的等效电阻 (n1n2...因此每个节点的电流平均分为两个分量,即Vref产生的电流i 沿分支分得如下

i

i =;i
i =;

= i1 ;i
= i1 ;我

= i2 ;· · ·i
= i2 ; · · ·我

= in1
= 英寸 - 1

(60)

122232n2

or

iiii
i ii

where
哪里

i1 = 2 ;i2 = 22 ;i3 = 23 ;· · ·in = 2n(61)
i1= 2 ;i2= 22 ;i3= 23 ; · · ·in= 2n (61)

i = Vref
i=V参考

2R

(62)

Therefore, at each node the current decreases in a binary weighted sequence. Note that the rightmost 2R resistance serves a purely terminating function. By summing up the appropriate branch currents, this R-2R network is utilized to realise DACs. With a resistance spread of only 2-to-1 (compare this mith the meighted−resistor DAGs and comment), R-2R ladders can be fabricated mono- lithically to a high degree of accuracy and stability. DACs with n 12 can be realised.
因此,在每个节点,电流以二进制加权序列的形式降低请注意,最右边的 2R 电阻仅具有终止功能。通过汇总适当的支路电流,该 R-2R 网络用于实现 DAC。R-2R 梯形图的电阻扩展仅为 2 比 1(比较此 mithmeighted-resistorDAG 并评论),可以高精度和稳定性单片制造 R-2R梯形图。可以实现具有 n 12 的 DAC。

The architecture of Fig.42 utilizes the R-2R ladder network to realise a DAC. Here, the branch currents are
图 42 的架构利用 R-2R 梯形网络来实现 DAC。在这里,分支电流是

i = Vref
i=V参考

12R

= Vref /R;(63)
= Vre/R;(63)

2

i = i1

22

= Vref /R; · · ·(64)
= Vre/R; · · ·(64)

22

i = in1
i = 英寸 - 1

n2
2

= Vref /R
=V参考/R

2n
2

(65)

and they are diverted either to the ground bus or to the virtual ground bus.
它们被转移到 Ground Bus 或 Virtual Ground Bus。

Using bit bi to identify the status of switch Si and since
使用位 b来标识开关 Sand 的状态,因为

vO = RT iO(66)
vO= —RTiO(66)

ref

R

2

22

23

2n

gives

O

v= V

RT b1 + b2

+ b3

+ · · · + bn(67)
+ · · ·+ BN (67)

Weighted-Capacitor DACs
加权电容DAC

Complex MOS ICs such as microcomputers require on-chip data conversion capabilities using only MOSFETs and capacitors, which are the natural compo- nents of this technology. The DAC of Figure 43 can be viewed as the switched- capacitor counterpart of the weighted-resistor DAC discussed in Sec. 3.1. Its heart is an array of binary-weighted capacitances plus a terminating capacitance equal in value to the LSB capacitance.
复杂的 MOS IC(如微型计算机)需要仅使用MOSFET电容器的片上数据转换功能这是该技术的自然组成部分43中的DAC可以3.1 节中讨论的加权电阻 DAC 的开关电容对应物。它的核心是一组二进制加权电容和一个等于LSB电容终端电容。

Circuit operation alternates between two cycles called the reset and sample cycles. During the reset cycle, shown in the figure, all switches are connected to ground to completely discharge all capacitors. During the sample cycle, switch S0 is opened while each of the remaining switches is either left at ground or con- nected to Vref . The capacitors thus form a potential divider with some of them connected to Vref and the others to ground. The voltage across the capacitors to ground corresponds to the binary input and is connected the positive input of the OPAMP (which is connected in a voltage follower configuration). As a reminder, consider the simple capacitor circuits shown in Fig. 44. Here,
电路操作两个周期之间交替称为reset周期和sample周期。复位周期,如图所示所有开关接地,以完全放电所有电容器。采样循环期间开关S0打开,而其余每个开关要么保持接地或连接到 Vref。因此,电容器形成一个分压器,其中一些连接到 Vref其他连接到地。电容器对地的电压对应于二进制输入,并连接到OPAMP 正输入电压跟随器配置连接)。提醒一下,请考虑图 1 中所示的简单电容器电路44.这里,

V= V

C1

(68)

and

out

ref C1 + C2
参考 C1 + C2

Ceq = C1 + C2(69)
Ceq= C1+ C2(69)

Thus the output voltage of the DAC in Fig 43 is given by
因此,图 43 中 DAC 的输出电压由下式给出

Cr

v= V

(70)

Oref Ct
O参考Ct

where Cr represents the sum of all capacitances connected to Vref , and Ct the total capacitance of the array. Therefore, we can write
其中 Cr 表示连接到 Vref 的所有电容之和,Ct表示阵列的总电容。因此,我们可以编写

CC

Cr = b1C + b2 2 + · · · + bn 2n1(71)
铬= b1C + b22 + · · · ·+ BN2N—1 (71)

vref

vO

Figure 42: R-2R ladder DAC.
图 42:R-2R 梯形 DAC。

vref
v参考

vO

S0

S1

S2

S3

Figure 43: Weighted-capacitor DAC.
43:加权电容DAC。

Vref

Ceq

(a)
(一)

Vout

C2

(b)
(二)

Figure 44: a) Potential division with capacitors, b) capacitors connected in parallel - equivalent capacitance equals sum of the individual capacitors.
图 44:a) 电容的分电,b) 并联的电容 - 等效电容等于各个电容的总和。

and

CCC
CC C

and so
等等

Ct = C +

2 + · · · + 2n1 + 2n1 = 2C(72)
2 + · · ·+ 2n—1 + 2n—1 = 2C (72)

O

v= V

b1 + b2 + b3 + · · · + bn(73)
B1 + B2 + B3 + · ·+ BN (73)

ref

2

22

23

2n

indicating that the sample cycle provides an n-bit D-A conversion. (Comment on the drawbacks of the DAC architecture).
表示 sample cycle 提供 n 位 D-A 转换。(评论关于DAC架构缺点)。

Potentiometric DACs
电位DAC

One of the first integrated MOS 8-bit DACs was based on selecting one tap of a segmented resistor string by a switch network. The switch network was connected in a tree-like decoder, as in the 3-bit DAC shown in Fig.45. Notice that there will be one, and only one, low-impedance path between the resistor string and the input of the amplifier, and the path is determined by the digital input word, Bin
最早集成的 MOS 8 位 DAC 之一基于通过开关网络从分段电阻器串中选择一个抽头开关网络连接在一个树状解码器中,如图 45 所示的 3 位 DAC。请注意,在电阻放大器输入之间将有一条且只有一条低阻抗路径该路径数字输入 B决定
:

B= b1 + b2

+ b3

(74)

in2
2

2223
222 3

A string of 2n resistors partition Vref into 2n identical intervals. With this approach, the DAC has guaranteed monotonicity since any tap on the resistor string must have a lower voltage than its upper, neighbour tap. No matter how mismatched the resistors, v0 will always increase as the amplifier is switched from one tap to the next, up the ladder, hence the inherent monotonicity. This is to be contrasted with the impact of component mismatches in the most sig- nificant bit positions of the previously discussed DACs may have on differential nonlinearity and monotoncity. Another advantage of the potentiometric DAC is that if the top and bottom nodes of the resistive string are biased at some arbitrary voltages VH and VK, the DAC will interpolate between VK and VH with a resolution of 2n steps. However, the large number of resistors (2n) and switches (2n+1 2) required limits practical potentiometric DACs to n 8, even though the switches can be fabricated very efficiently in MOS technology.
一串 2n个电阻将 Vref划分为 2n 个相同的区间。通过这种方法,DAC 保证了单调性,因为电阻串上的任何抽头都必须具有低于其上相邻抽头的电压。无论resistor 多么不匹配, v0总是会随着放大器从一个抽头切换到下一个抽头而增加,因此具有固有的单调性。这与前面讨论DAC最大信号位位置的元件失配微分非线性和单调性的影响形成对比。电位 DAC 的另一个优点是如果电阻的顶部底部节点任意电压 VH和 VK偏置,则 DAC 将在 VK和VH,分辨率为 2n步长。 然而,所需的大量电阻器 (2n) 和开关 (2n+12) 将实际电位 DAC 限制为 n8即使这些开关可以用MOS 技术非常高效地制造

Segmentation
分割

The matching and tracking capabilities of IC components limit the resolution of the DAC structures considered so far to n12. However, the areas of pre- cision instrumentation and test equipment, process control, industrial weighing systems, and digital audio playback often require resolutions and linearity per- formance well in excess of 12 bits. One of the most important performance requirements is monotonicity.For instance, to ensure a high signal-to-noise ratio, digital audio playback systems use 16 bits or more of differential linearity. In conventional binary-weighted DACs, monotonicity is hardest to realize at the point of major carry due to the difficulty in realizing the required degree of match between the MSB and the combined sum of all remaining bits. To ensure monotonicity, this match must be better than one part in 2n1, indicating
IC 元件的匹配和跟踪能力将迄今为止考虑的 DAC 结构的分辨率限制在 n 12 然而,精密仪器和测试设备、过程控制、工业称重系统和数字音频播放领域通常需要远超过 12 位的分辨率和线性度性能。最重要的性能要求之一是单调性。例如,为了确保高信噪比,数字音频播放系统使用 16 位或更高的差分线性度。在传统的二进制加权 DAC 中,由于难以实现 MSB 与所有剩余位的总和之间所需的匹配程度,因此在主要进位点最难实现单调性。为确保单调性,此匹配必须优于 2n—1 中的一个部分表示

Vref

b3b2b
BBB的
1

Figure 45: Potentiometric (resistor-string) DAC. An n-bit DAC uses 2n resistors.
图 45:电位(电阻串)DAC。一个 n-bit DAC 使用 2nresistor。

vref

b1 b
哈必斯
2

bn

vin

Figure 46: Functional diagram of a DAC-based ADC.
图 46:基于 DAC 的 ADC 的功能图。

that the difficulty increases expontially with n. High-resolution DACs achieve monotonicity by a technique know as segmentation. Here the reference range is partitioned into a sufficiently large number of contigous segments, and a DAC of lesser resolution is then used to interpolate between the extremes of the selected segment (the interested student can refer to the course texts for more information).
难度随 n 的增加呈指数级增加。高分辨率 DAC通过一种称为分割的技术实现单调性。在这里,参考范围被划分为足够多的连续段,然后使用分辨率较低的 DAC 在所选段的极值之间进行插值感兴趣的学生可以参考课程文本了解更多信息)。

DAC-Based A-D Conversion
基于 DAC 的A-D转换

2

1

A-D conversion can be accomplished by using a DAC and a suitable register to adjust the DAC's input code until the DAC's output comes within1 VKSB of the analog input. The code that achieves this is the desired ADC output b1, b2, ...bn.As shown in Fig.46, this technique requires suitable logic circuitry to direct the register to perform the code search on the arrival of the START command, and a voltage comparator to announce when vO has come within 2 VKSB of vin and thus issue an end-of-conversion (EOC) command. Moreover,
A-D 转换可以通过使用 DAC 和合适的寄存器来调整 DAC 的输入代码,直到 DAC 的输出达到模拟输入的 1VKSB范围内来完成。实现此目的的代码是所需的 ADC 输出 b1b2...bn如图 46 所示,该技术需要合适的逻辑电路来指导寄存器在 START 命令到达时执行代码搜索,并且需要一个电压比较器来宣布当 vOhas 在 2 VKSBof vinI 范围内时,从而发出转换结束 (EOC) 命令。此外

2

to centre the analog range properly, the DAC output must be offset by + 1 VKSB
为了正确地将模拟范围居中,DAC 输出必须偏移 + 1VKSB
,

per Fig.37.
如图37 所示。

The simplest code search is the sequential search, obtained by operating the register as a binary counter. As the counter steps through consecutive codes starting from 00 ...0, the DAC produces an increasing staircase, which the comparator then compares against vin. As soon as this staircase reaches vin, CMP fires and stops the counter. This also serves as an EOC command to notify that the desired code is sitting in the counter. The counter must be stepped at a low enough frequency to allow the DAC to settle within each clock
最简单的代码搜索是 sequential search,通过将register 作为二进制计数器进行操作来获得。当计数器逐步显示从 00 ...0,则 DAC 产生一个递增的阶梯,然后比较器将其与 v in 进行比较。一旦此楼梯到达v in,CMP 就会触发并停止计数器。这也可以用作 EOC 命令以通知所需的代码位于计数器计数器必须足够的频率步进以允许DAC 在每个 clock 建立

cycle. Considering that a conversion can take as many as
周期。考虑到一次转换可能需要多达
2n 1 clock periods,
时钟周期 /
this
techniques
技术
is
limited
有限
to
low-speed
低速
applications.
应用。

A better approach is to allow the counter to start counting from the most recent code rather than restarting from zero. If vin has not changed drastically since the last conversion, fewer counts will be needed for vO to catch up with vin. Also referred to as a tracking or a servo converter, this scheme uses the register as an up/down counter with the count direction controlled by the comparator: counting will be up when vO < vin, and down when vO > vin. Whenever vO crosses vin, the comparator changes state and this is taken as an EOC command. Clearly, conversions will be relatively fast only as long as vin does not change too rapidly between consecutive conversions. For a full-scale change, the conversion will still take 2n-1 clock periods.
更好的方法是允许计数器最近的代码开始计数而不是从零重新开始。如果 vin 自上次转换以来没有发生重大变化,则 v O 需要更少的计数才能赶上vin。也称为跟踪或伺服转换器,该方案使用registerasanup/do wncounterwi th t hecountdirectioncontrolledbythe比较器:当 vO< v,当 vO>v 在比较器中越过v时,当状态发生变化被关闭被视为EOC 命令。 显然,只要 vin连续转换之间变化不会太快,转换才会相对较快。对于全量程更改,转换将需要2n-1 clockperiod。

The fastest code-search strategy uses binary search algorithm to complete an n-bit conversion in just n clock periods, regardless of vin. Following is a de- scription of two implementations: the successiveapproximation and the charge redistribution ADCs.
最快的代码搜索策略使用二叉搜索算法在短短 n 个时钟周期内完成 n 位转换,而不管 VIN 如何。以下是两种实施方式的描述:逐次逼近型和电荷再分配 ADC。

Successive-Approximation Converters
逐次逼近型转换器

This technique uses the register as a successive−approximation register (SAR) to find each bit by trial and error. Starting from the MSB, the SAR inserts a trial 1 and the interrogates the comparator to find whether this causes vO to rise above vin. If it does, the trial bit is changed back to 0; otherwise it is left at 1. The procedure is repeated for all subsequent bits, one bit at a time.
该技术将寄存器用作逐次逼近寄存器 (SAR),通过反复试验找到每个位。从 MSB 开始,SAR 插入一个试验1询问比较器以查找是否会导致vO高于v如果是这样,试验更改回到0;否则,它保持1。对所有后续重复此过程一次一个

causes the DAC output v= 16+ 0.5 = 8.5V . At the end of clock periodO

2

To
illustrate
说明
this
consider
考虑
the
conversion
转换
of
a 10.8V input
输入
to
a 4-bit
4 位
code
法典
with
a Vref
裁判
= 16V . To
ensure
确保
correct
正确
results,
结果
the
DAC
DAC 系列
output
输出
must
必须
be
offset
抵消
by
+ 1 VKSB or 0.5V. Following
或 0.5V。以后
the arrival of the START command, the SAR
START 命令 SAR 的到来
sets
b1 to
1 with
all
remaining
剩余
bits
at
0 so
所以
that
the
trial
试验
code
法典
is
1000. This

1

2

T1, vO is compared against vin and since 8.5 < 10.8, b1 is left at 1.
T1vOis 与 vinand 相比,因为 85 < 108b1 保持在 1。

At
the
beginning
开始
of
T2, b2 is
set
设置
to
1, so
所以
the
trial
试验
code
法典
is
now
现在
1100 and

2

22

vO = 16 1 + 1+ 0.5 = 12.5V. Since
因为
12.5 > 10.8, b2 is
changed
改变
back
返回
to
zero

at the end of T2.
在 T2 结束时。

At the beginning of T3, b3 is set to 1, so the trial code is now 1010 and
在 T3b3 的开头设置为 1,因此 Trial 代码现在是 1010,并且

vO = 10.5V. Since 10.5 < 10.8, b3 is left at 1.
vO = 105V。从 105 开始< 108b3 保留为 1。

At the beginning of T4, b4 is set to 1, so the trial code is now 1011 and vO = 11.5V. Since 11.5 > 10.8, b4 is changed back to zero. Thus when leaving T4, the SAR has generated the code 1010, which corresponds to 10.5V. Since the entire conversion takes a total of n clock cycles, a SA ADC offers a major speed improvement over a sequential search ADC.
在 T4 开始时,b4设置为 1,因此试验代码现在是 1011,vO= 115V。由于 115 > 10 8,b4改回零。 因此,当离开T4 时,SAR生成了代码1010,对应于10.5V。由于整个转换总共需要 n 个 clock cycles,因此 SA ADC 的速度sequentialsearchADC 有很大的提高

Charge-Redistribution ADCs
电荷再分配ADC

The circuit of Fig.47 performs a successive-approximation conversion using a weighted-capacitor DAC of the type of Fig.43. Its operation involves three cycles called the sample, hold, and redistribution cycles. During the sample
图 47 中的电路使用图 43 类型的加权电容器 DAC 执行逐次逼近转换。其操作涉及三个周期称为采样、保持重新分配周期。期间

vin

START
开始

Clk
时钟

EOC
平等机会

Figure 47: Charge-redistribution ADC.
47:电荷再分配ADC。

cycle, S0 grounds the top-plate bus while Si and S1 through Sn+1 connect the bottom plates to vin, thus precharging the entire capacitor array to vin. During the hold cycle, S0 is opened and the bottom plates are switched to ground, thus causing the top-plate voltage to swing to -vin. The voltage presented to the comparator at the end of this cycle is thus vp = vin. During the redistribution cycle, S0 is still open, Si is connected to Vref , and the remaining switches are sequentially flipped from ground to Vref , and possibly back to ground, to perform a successive-approximation for the desired code.
循环时,S0将顶板总线接地,而 S和 S1通过 Sn+1底板连接到 vin,从而将整个电容器阵列预充电至 vin。在保持周期S0打开切换到地,从而导致顶板电压摆动至 -vin因此,在此周期结束时呈现给比较器的电压为 v p=vin。在重分配周期中S0仍然打开,S连接到Vref其余开关依次从地翻转到 Vref,并可能回到地,执行successive-approximation 的 Successive-Approximation请求。

Flipping switch S1 from ground to Vref causes vp to increase by the amount
将开关 S1 从地拨动到 Vref导致 vpto 增加量

v=v+ V

C (75)
丙(75)

pin
p

ref
裁判

C + C + C + · · · + C
C + C+ C+ · · ·+ C

+ C

=vin
=v输入

24

+ Vref
+V参考

2

2n—1

2n—1

(76)

Similarly, flipping switch S2 from ground to Vref gives (with all other switches grounded)
同样,将开关 S2 从地拨到 Vrefgives (所有其他开关都接地)

vp = vin

+ Vref
+V参考

22

(77)

and so, in general, flipping switch Sh from ground to Vref gives
因此,一般来说,将开关 Shfrom ground 拨到 Vrefgives

vp = vin

+ Vref
+V参考

2h
2小时

(78)

If it is found that this increase causes the comparator to change state, then Sh is returned to ground; otherwise it is left at Vref and the next switch is tried. This procedure is repeated at each bit position, starting from the MSB and progressing down to the LSB (excluding the terminating capacitor switch,
如果发现 这种增加导致比较器改变状态,则Sh返回接地;否则,它留在 Vref并尝试下一个开关在每个位置重复此过程MSB 开始向下发展LSB(不包括端接电容器开关,

Vref
V参考

vin
v

Clk
时钟

1.5R

R

b1 b
哈必
2

Rbn

R

R

0.5R
0.5 叶

Figure 48: n-bit flash converter
48:n 位闪存转换器

which is left permanently grounded). Therefore at the end of the search the voltage presented to the comparator is
永久接地)。因此,在搜索结束时,呈现给比较器的电压为

p

in

v = v+ V

b1 + b2

+ · · · + bn(79)
+ · · ·+ 十亿 (79)

2

ref

2

22

2n

and that vp is within 1 VKSB of 0V. Thus the final switch pattern provides the
并且 vpis 在 1 VKSBof 0V 以内。因此,最终的 switch 模式提供了

desired output code.
所需的输出代码。

Exercise 3 Gonsider a chargeredistribution ADG of the type of Fig.07 mith n = 4, Vref = 3.0V , and C = 8pF. Assuming node vp has a parasitic ca− pacitance of 0pF tomard ground, 3nd the intermediate values of vp during the conversion of vin = 1.00V
练习 3 Gonsider a 图 07 mith n = 4Vref= 30V 类型的电荷再分配 ADG,C = 8pF。假设节点 vp 具有 0pF tomard 接地的寄生 ca− pacance,在 vin= 100V 转换期间 vp 的中间值第 3 位
.

Exercise 4 Find the intermediate node voltages at the inverting input of the comparator during the operation of a 6−bit charge redistribution ADG. Vin=1.2hV and Vref=5V. What is the 3nal output digital mord? If a parastic capacitance of G/9 exists at the comparator input, mhat mould be the 3nal output digital mord?
练习 4 求 6 位电荷再分配 ADG 操作期间比较器反相输入端的中间节点电压。Vin=1.2hV 和 Vref=5V。什么是 3 小时输出数字 mord?如果比较器输入端存在 G/9的参数电容、则 3 nal 输出数字 mord是否为3nal 输出 moded?

Flash Converters
Flash转换器

The circuit of Fig.48 uses a resistor string to create 2n 1 reference levels separated from each other by 1 VKSB, and a bank of 2n 1 high speed latched
图 48 的电路使用电阻串创建 2n— 1 个参考电平,彼此之间由 1 个 VKSB 和一个 2n— 1 个高速锁存的组

comparators to simultaneously compare vin against each level. Note that to position the analog signal properly, the top and bottom resistors must be 1.5R and 0.5R, as shown. As the comparators are strobed by the clock, the ones whose reference levels are below vin will output a logic 1, and the remaining ones a logic 0. The result, referred to as a bar graph, or also as a thermometer code, is then converted to the desired output code b1, b2, ... bn by a suitable decoder, such as a priority encoder4
comparators 同时比较 Vin与每个级别。请注意,要正确定位模拟信号,顶部和底部电阻器必须为 1.5R和 0.5R,如图所示。当 comparator 被 clockstrodamp;时,reference 电平低于 vin 的那些将输出 logic 1,其余的 logic0结果称为条形图,也称为温度计代码)然后转换为所需的输出代码 b1、b2、...bn通过合适的解码器,优先编码器4
.

Since the input sampling and latching take place during the first phase of the clock period, and decoding during the second phase, the entire conversion takes only one clock cycle, so this ADC is the fastest possible. The <ash con− verter is therefore used in high-speed applications, such as video and radar signal processing, where conversion rates on the order of millions of samples per second are required, and successive approximation ADCs are generally not fast enough. Most high-speed oscilloscopes and some RF test instruments use flash ADCs because of their fast digitizing rate, which now reaches 5 Gsamples/s for off-the-shelf devices and 20 Gsamples/s for proprietary designs. The typical flash converter resolves analog voltages to 8 bits, although some flash convert- ers can resolve 10 bits.The main disadvantage of this converter is the number of comparators required. Hom many does an 8bit converter require? The large number of comparators required, associated high power dissipation, and stray input capacitance makes flash converters impractical for n > 10
由于 input sampling 和 latching 发生在 clock period 的第一阶段,而解码发生在第二阶段,因此整个转换只需要一个 clock cycle,因此该 ADC 是最快的。因此,<灰视频转换器用于高速应用,例如视频和雷达信号处理,这些应用需要每秒数百万个样本的转换速率,而逐次逼近型 ADC 通常不够快。大多数高速示波器和一些射频测试仪器都使用闪存 ADC,因为它们的数字化速率很快,现在现成设备达到 5 Gsamples/s,专有设计达到 20 Gsamples/s典型的闪存转换器将模拟电压解析为 8 位,尽管一些闪存转换器可以解析 10 位。这个转换器的主要缺点是需要的比较器数量 8 位转换器需要多少?所需的大量比较器、相关的高功率耗散和杂散输入电容使得闪存转换器不适用于 n > 10
.

Exercise 5 Gonsider a hbit <ash ADG mith Vref = 3 V . i) hom many com parators does this ADG use and mhat are their voltage reference levels? ii) 3nd the digital output for Vin = 1 V
练习 5 Gonsider a h−bit
.

Two-step (Subranging) Converters
两步(子范围)转换器

Two-step (or subranging) converters trade speed for circuit complexity by split- ting conversion into two subtasks, each requiring less complex circuitry. Com- pared to flash converters, two-step converters require less silcon area, dissipate less power, have less capacitive loading, and the voltages the comparators need to resolve are less stringent than for flash equivalents. However, two-step con- verters do have a larger latency delay, although their throughput approaches that of flash converters.
两步或子范围)转换器通过将转换分成两个子任务来牺牲速度电路复杂性,每个子任务都需要不太复杂的电路。闪存转换器相比两步转换器需要更小硅面积耗散更少的功率,具有更少的电容负载,并且比较器需要解析的电压比闪存等效更宽松然而,two-stepcon-converter 确实具有更大的延迟,尽管它们的吞吐量接近flashconverters。

The block diagram for a two-step ADC is shown in Fig.49. The 4-bit MSB ADC determines the first four MSBs. To determine the remaining LSBs, the quantisation error (also called the residue) is found by reconverting the 4-bit digital signal to an analog value using the DAC and subtracting that value from the input signal. To ease requirements in the circuitry for finding the remaining LSBs, the quantisation error is first multiplied by 24 using the gain amplifier, and the LSBs are determined using the 4-bit LSB ADC. Besides the sample- and-hold (SH), the DAC and the gain amplifier, the circuit uses 2 24 1 = 30 comparators, indicating a substantial saving compared to the 255 comparators
两步ADC如图49 所示4 位MSBADC 确定前四个 MSB。为了确定剩余的 LSB,通过使用 DAC 将 4 位数字信号重新转换为模拟并从输入信号中减去该值找到量化误差(也称为余数)。为了降低电路中查找剩余LSB 的要求,首先使用增益放大器量化误差24然后使用 4 位 LSB ADC 确定 LSB。除了采样保持 (SH)、DAC 和增益放大器外,该电路还使用了 2 241= 30比较器,255比较器相比节省了大量成本

4 A priority encoder circuit basically converts an n-bit input into a binary representation.
4 优先编码器电路基本上将 n 位输入转换为二进制表示。

If the input m is active, all lower inputs (m-1 .. 0) are ignored.
如果输入 m 处于活动状态,则忽略所有较低的输入 (m-1 .. 0)。

v

First 4 bits
前 4

(b1, b2, b3, b
哈哈哈 b
4)

Lower 4 bits
4

(b5, b6, b7, b
哈哈哈 b
8)

Figure 49: 8-bit subranging ADC.
图 49:8 位子范围 ADC。

required by full-flash. (This saving is even more dramatic for n 10). The main price for this saving is a longer conversion time. Also, this approach requires that the DAC be n-bit accurate which may be a heavy requirement.
full-flash 需要(这种节省对于n10 来说更加引人注目)。这种节省的主要代价是更长的转换时间。此外,这种方法要求DACn 位精度,这可能是一个很高的要求。

Although not as fast as a parallel ADC, subranging (also called pipelined) ADCs can digitize at speeds greater than 100 Msamples/s at 8-bit resolution. They can resolve signals to 16 bits at slower speeds. Subranging ADCs often find use in RF test equipment, lower-speed digitizing oscilloscopes, and high-end PC plug-in digitizer cards and PC-external data-acquisition systems.
虽然不如并行 ADC 快,但子范围(也称为流水线)ADCscandigitizeatspeedsgreaterthan100Msamples/sat 8-b itresolution 他们可以以较慢的速度将信号解析为 16 位。子范围 ADC 通常用于RF 测试设备、低速数字化示波器以及高端PC插入式数字化仪PC 外部数据采集系统。

Pipelined Converters
流水线转换器

The two-stage architecture described in the preceeding section can be general- ized to multiple stages, where each stage finds a single bit. Specifically, the first stage finds the most significant bit, b1, the second stage finds the next bit, b2, and so on. To avoid having to wait until residual errors ripple through the en- tire converter for a given sample, the approach incorporates pipelining such that once the first stage completes its work, it does not sit idle while the remaining lower bits are found, but immediately starts to work on the next input sample. A block diagram of a pipelined ADC is shown in Fig.50. Each subtask stage consists of an SH, and ADC, a DAC, a subtractor, and a gain amplifier. The SH in each stage stores the input signal. This SH allows the preceeding stage to be immediately used to process its next input before the succeeding stage has finished, as long as the preceeding stage's digital output is also stored. Pipeline architectures are used in a variety of formats (k > 1), but with k = 1 this architecture results in the simplest per-stage circuitry, though n such stages are
上一节中描述的两阶段架构可以推广到多个阶段,其中每个阶段找到一个 bit。具体来说,第一阶段找到最高有效位,b1第二阶段找到下一个位,b2 依此类推。为了避免必须等到残余误差波纹通过给定样本的整个转换器,该方法采用了流水线,这样一旦第一阶段完成其工作,它不会在找到剩余的较低位时闲置,而是立即开始处理下一个输入样本。流水线 ADC 的框图如图 50 所示。每个 subtask 阶段由一个 SH 和 ADC、一个 DAC、一个减法器和一个增益放大器组成。每个 stage 中的 SH 存储输入信号。此 SH 允许在下一阶段完成之前立即使用前一阶段处理其下一个输入,只要前一阶段的数字输出也被存储。流水线架构以多种格式使用(k > 1),但是当 k = 1 时,这种架构会产生最简单的每级电路,尽管 n 个这样的级是

needed.
需要。

Exercise 6 Assume the 8bit subranging ADG of Fig.09 has Vref = 2.560V
练习 6 假设图 09 的 8 位子范围 ADG 的 Vref= 2560V
.

2

(a) Find the total number of comparators, their voltage reference levels, and the maximum level tolerances allomed for a 1 VKSB accuracy. (b) Find b1 ... b8, vRES,and the quantixation error for vin = 0.5V , 1.054V , and 2.543V
(a) 求比较器的总数、它们的电压基准电平以及1VKSB精度的最大电平容差。(b) 查找 b1...b8vRES,以及 vin= 05V、1054V 和 2543V 的定量误差
.

Clk1ClkjClkN

vin
v

vRES

2k
2

Gain amp
增益放大器

Figure 50: Pipeline ADC architecture
图 50:流水线 ADC 架构

Switched-Capacitor Circuits
Switched-CapacitorCircuits 开关电容器电路

Switched capacitor (SC) filters simulate resistors by periodically operating MOS capacitors with MOSFET switches, and produce time constants that depend on capacitance ratios rather than RC products. Note that conventional filters produce time constants that depend on RC time constants. IC processes do not lend themselves to the fabrication of resistances and capacitances with the magnitudes (103 to 106 and 109 to 106 F) and accuracies (1% or better) typically required in audio and instrumentation applications. The switched capacitor technique is useful in simulating a large value resistor, generally > 1 M
开关电容 (SC) 滤波器通过周期性地操作带有 MOSFET 开关的 MOS 电容器来模拟电阻器,并产生取决于电容比而不是 RC 产品的时间常数。请注意,传统滤波器产生的时间常数取决于 RC 时间常数。IC 工艺不适合制造音频和仪器仪表应用中通常所需的幅度(103 至 106Ω 和 10—9 至 10—6F)和精度(1% 或更高)的电阻和电容。开关电容器技术可用于模拟大值电阻器,通常> 1 MΩ
.

Consider the basic MOSFET-capacitor arrangement of Fig.51. The transis- tors are characterised by a low channel resistance (typically <103 ) when the gate voltage is high, and a high resistance (typically >1012 ) when the gate voltage is low. With an off/on ratio this high, a MOSFET can be regarded for all practical purposes as a switch. If the gates are driven with nonoverlapping out-of-phase clock signals, the transistors will conduct on alternate half-cycles, thus providing a single-pole double throw (SPDT) switch function with make- before-break characteristics.
考虑图 51 的基本MOSFET 电容布置当栅极电压高时,变压器的特点是低通道电阻(通常为 <103 Ω),当栅极voltageislowWi t 时,高电阻(通常为 >1012Ωhanoff/onratiothishighaMOSFETcanberegardedfor所有实际用途都作为开关。如果栅极由非重叠的异相时钟信号驱动,晶体管将在交替半周期上导通从而提供具有先合后断特性的单刀双掷 (SPDT) 开关功能

Assuming V1 > V2, flipping the switch to the left charges C to V1, and flipping it to the right discharges C to V2. The net charge transfer from V1 to V2 is
假设 V1> V2,将开关向左拨动,将 C 充电到 V1向右C放电到V2电荷V1转移到V阿拉伯数字

A = C (V1 V2)(80)
A = C (V1— V2) (80)

If the switch is flipped back and forth at rate of fCK cycles per second, the charge transferred in 1 second from V1 to V2 defines an average current
如果开关以每秒 fCKcycles 的速率来回翻转,则在 1 秒内从 V1 转移到 V2 的电荷定义了平均电流

Iavg
平均

=fCKA

(81)

=CfCK (V1 V2)
= CfCK(V1— V2)

(82)

t

V1V2

Figure 51: Switched capacitor using a MOSFET SPDT switch, and clock drive for the MOSFETs.
图 51:使用 MOSFET SPDT 开关的开关电容器和 MOSFET 的时钟驱动。

V1V2

Iavg
平均

V1V2

Figure 52: Resistance simulation using a switched capacitor.
图 52:使用开关电容器的电阻仿真。

Note that the charge is flowing in packets rather than continously. However, if fCK is made sufficiently higher than the highest frequency components of V1 and V2, the process can be regarded as continuous and the switch capacitor combination can be modeled with an equivalent resistance (see Fig.52):
请注意,电荷是以数据包形式流动的,而不是连续流动的。但是,如果fCK足够高于V1和 V2 的最高频率分量,则可以认为该过程是连续的,并且开关电容器组合可以用等效电阻(见图 52):

Req

= V1 V2

Iavg
平均

=1

CfCK
参见混沌骑士

(83)

SC integrators
SC集成商

We will now investigate how a 'simulated' switched capacitor resistance can be used to implement the integrator (the workhorse of active filters). The RC integrator of Fig.53a yields
现在,我们将研究如何使用“模拟”开关电容器电阻来实现积分器(有源滤波器的主力)。图 53a RC 积分器得出

Vin R1
R1 中的 V

or

= V0

1/(cC2
1/(cC2

(84)

H ((c) = V0
H ((c) = V0

Vin
V输入

1

0

= (c/c
= —(c/c

(85)

Vin
V输入

Vin
V输入

b)

a)

Figure 53: Converting an RC integrator to an SC integrator.
图 53:将 RC 积分器转换为 SC 积分器。

where the unity gain frequency is given by
其中单位增益频率由下式给出

c =1

R1C2

(86)

Replacing R1 by an SC resistance gives the SC integrator of Fig.53b. If the input frequency is such that c cCK then the current flow from Vin to the summing node can be regarded as continuous, and R1 would be given by
用 SC 电阻代替 R1 得到图 53b 的 SC 积分器。如果输入频率为 ccCK则从 V流向求和节点的电流可以视为连续的,R1下式给出

R =1

C1fCK

or

(87)

c = C1 f

(88)

0C2 CK

This expression reveals three important features that hold for SC filters in general:
此表达式揭示了通常适用于 SC 滤波器的三个重要特征

There are no resistors. This is highly desirable from the viewpoint of IC fabrication, since monolithic resistors are plagued by large tolerances and thermal drift, and also take up precious chip area. Swiches, on the other hand, are implemented with MOSFETs, which are the basic ingredients of VLSI technology and occupy very little chip area.
没有电阻器。从 IC 制造的角度来看,这是非常可取因为单片电阻器受到容差热漂移的困扰,并且还占用了宝贵的芯片面积。另一方面,开关是通过 MOSFET 实现的,MOSFET 是VLSI技术的基本组成部分占用芯片面积非常小

The characteristic frequency c0 depends on capacitance ratios, which are much easier to control and maintain with temperature and time than RC products.
特征频率c0 取决于电容比,RC产品相比,电容比更容易随温度和时间进行控制和维持

c0 is proportional to fCK indicating that SC filters are inherently of pro- grammable type.
c0与 fCK 成正比,表示 SC 滤波器本身是可编程类型的。

It is desirable to keep C1 larger than the associated parasitics present in the circuit (e.g. depletion capacitances of the source/drain implants and the stray capacitances to substrate). Therefore, practical SC integrators are implemented with SPDT switch pairs to minimise the effect of parasitic capacitances and also increase circuit versatility (Fig.54). The switched-capacitor integrator of Fig.54 is not sensitive to parasitic or stray capacitances. The parasitic capacitances are
最好保持 C1 大于电路中存在的相关寄生效应 (源极/漏极植入物的耗尽电容和衬底的杂散电容)。因此,实用的 SC 积分器使用 SPDT 开关对实现,以最大限度地减少寄生电容的影响,并增加电路的多功能性 (图 54)。图 54 中的开关电容积分器对寄生电容或杂散电容不敏感。寄生电容为

Vin

a)

Vin

Figure 54: a) Inverting and b) noninverting SC integrators.
图 54:a) 反相和 b) 同相 SC 积分器。

Vin
V输入

Figure 55: Parasitic capacitances associated with a switched-capacitor resistor.
图 55:与开关电容电阻器相关的寄生电容。

shown explicitly in Fig.55: consider first the parasitic capacitance Cp2, this is always grounded either through S4 or through the virtual ground of the inverting input of the op-amp. Thus Cp2 does not have a change in the charge stored on it. Next, the parasitic capacitance Cp1 is charged to V żı when S1 is closed and then discharged when S2 closes. Since none of the charge stored on Cp1 when S1 is closed is transferred to C1, it does not affect the integrating function.
如图 55 中明确显示:首先考虑寄生电容 Cp2,它总是通过 S4 或通过运算放大器反相输入的虚拟接地接地。因此 Cp2 上存储的电荷没有变化接下来寄生电容 Cp1在 S1 闭合时充电至 V,然后在 S2 闭合时放电。由于当 S1 闭合时,存储在 Cp1 上的任何电荷都不会转移到 C1,因此不会影响积分函数。

6.1.1Basic filters
6.1.1基本过滤器

Some special cases of the very basic filter types with passive (RC) and active (op amp-RC) realizations are shown in Fig.56 and Fig.57. For the passive low pass filter (Fig.56a), the DC gain and RC time constant are given by
具有无源 (RC) 和有源 (op amp-RC) 实现的非常基本的滤波器类型的一些特殊情况如图 56 和图 57 所示。对于无源低滤波器(图 56a),DC增益RC时间常数下式给出

DC gain = 1(89)
直流增益 = 1 (89)

RC = 1

c0

while for the op amp realization (Fig.56b)
而用于运算放大器实现 (图 56b)

DC gain =R2
直流增益 = R2

R1
R1

(90)

(91)

R C = 1

2c0

(92)

R2

C

RVinR1

1

Vout

Vin

C

Vout+

b)

Figure 56: Low pass first-order filter a) passive realization, b) Op amp realiza- tion.
图 56:低通一阶滤波器 a) 无源实现,b) 运算放大器实现。

R2

CVinR1

a)b)
a) b)

Figure 57: High pass first-order filter a) passive realization, b) Op amp realiza- tion.
图 57:高通一阶滤波器 a) 无源实现,b) 运算放大器实现。

And for the passive high pass filter (Fig.57a), the high frequency gain and RC time constant are given by
对于无源高通滤波器 (图 57a),高频增益和 RC 时间常数由下式给出

High F requency gain = 1(93)
高 F 频率增益 = 1 (93)

RC = 1

c0

while for the op amp realization (Fig.57b)
而用于运算放大器实现 (图 57b)

High Frequency gain =R2
高频增益 = R2

R1
R1

(94)

(95)

1

c

R1C =

0

(96)

Exercise 7 Obtain the smitchedcapacitor counterparts of the op amp realixa tions of the 3lters in Fig.56b and Fig.57b.
练习 7 获得图 56b 和 图 57b 中 3 升的运算放大器实现的涂抹电容对应物。

fs

vin

Anti-aliasing filter
抗锯齿滤镜

Sampling ADC
采样ADC

Bou
t

Figure 58: Nyquist sampling with analog filtering.
图 58:使用模拟滤波的奈奎斯特采样。

Oversampling ADCs
过采样ADC

Oversampling A/D and D/A converters have become popular for very high- resolution ( 16 bits) medium-to-low speed applications such as high-quality digital audio. The major reasons for this include: i) oversampling convert- ers relax the requirements placed on the analog circuitry at the expense of more complicated digital circuitry. This trade-off becomes more desirable for modern submicron technologies with 3.3V power supplies where complicated high-speed digital circuitry is more easily realized in less area, but realisation of high-resolution analog circuitry is complicated by low power-supply volt- age. With oversampling data converters, the analog components have reduced requirements on matching tolerances and amplifier gains. Oversampling con- verters simplify the requirements placed on the analog anti-aliasing filters for ADCs and smoothing filters for DACs. Also, a sample-and-hold is usually not required at the input of an oversampling ADC; and ii) Oversampling followed by digital filtering also results in reduced quantization-noise.
过采样 A/D 和 D/A 转换器在高分辨率 16 位) 中低速应用(如高质量数字音频)中已变得很受欢迎。 造成这种情况的主要原因包括: i) 过采样转换器放宽了对模拟电路的要求,但牺牲了更复杂的数字电路。对于具有 3.3V 电源的现代亚微米技术来说,这种权衡变得更加可取,在这些技术中,复杂的高速数字电路更容易在更小的面积内实现,但高分辨率模拟电路的实现因低电源电压而变得复杂使用过采样数据转换器,模拟元件降低了对匹配容差和放大器增益的要求。过采样转换器简化了对 ADC 的模拟抗混叠滤波器和 DAC 的平滑滤波器的要求。此外,在过采样 ADC 的输入端通常不需要采样保持;ii) 过采样进行数字滤波会导致量化噪声降低。

Nyquist-Rate Sampling
奈奎斯特速率采样

The digitisation process, depicted in Fig.58, has a profound impact on the fre- quency spectrum of the input signal. As earlier discussed in Sec. 2.1, digitisa- tion, viewed as discretisation in time, creates additional spectral components, called images, at locations symmetric about the midpoint fS/2. Nyquists cri terion states that if we want to recover or reconstruct a signal of a given band- width B (i.e. highest frequency component B Hz) from its digitised version, the sampling rate fS must be such that
图 58 中描述的数字化过程输入信号的频率频谱有深远的影响。正如前面在第 2.1 节中所讨论的,数字化被视为时间离散化,会产生额外的频谱分量,calledimagesatlocationssymmet ricaboutt hemidpointfS/2Nyquistscr iterion 指出,如果我们想从其数字化版本中恢复或重建给定带宽 B (即最高频率分量 B Hz) 的信号,采样fS必须使

fS > 2B(97)
fS> 2B (97)

where 2B is called the Nyquist rate. This requirement can be met either by bandlimiting vin below fS/2, or by raising fS above the Nyquist rate. In order to prevent any noise or spurious input spectral components above fS/2 from folding into the baseband (DC to fS/2), an anti-aliasing filter is required
其中 2B 称为奈奎斯特速率。可以通过将 vn低于 fS/2 的带宽限制或将 fSs 提高到奈奎斯特速率以上来满足这一要求为了防止任何高于 fS/2 的噪声或杂散输入频谱分量折叠到基带中(DC 到 fS/2),需要一个抗混叠滤波器
.

Digitisation, viewed as discretisation in amplitude, introduces quantisation noise. Consider the ideal characteristic of a 3-bit ADC shown in Fig.59. The con-
数字化,被视为振幅的离散化,引入了量化噪声考虑图 59 所示3 位ADC的理想特性

version process partitions the analog input into 2n intervals called code ranges, and all values if vin within a given code range are represented by the same code, namely, that corresponding to the midrange value. For example, code
version过程模拟输入划分为2n个间隔称为代码范围,如果 v in给定代码范围内,则所有值都由相同的代码表示,对应于中间值的代码。例如code

011, corresponding to the midrange value Vin = 3 , actually represents all inputs
011,对应中间值 Vin = 3 实际上代表所有输入

Vref8
V参考文献 8

8

16

within the range 3 1 . Due to the inability by the ADC to distinquish among
在 31 范围内由于 ADC 无法区分

1

different values within this range, the output code can be in error by as much as 2 VKSB. This uncertainity, called quantisation error, or also called quantisation noise v Q, is an inherent limitation of any digitisation process. An obvious way
在此范围内的不同值,则输出代码的误差可能高达 2 VKSB。这种不确定性称为量化误差,或也称为量化噪声 v Q,是任何数字化过程的固有限制。显而易见的方法

to improve it is by increasing n. This error is modelled as being equivalent to an additive noise source, see Fig.60. From Fig.60 , where both n-bit converters are considered ideal, we have
要改善,就是增加 n。这个误差被建模为等同于一个加性噪声源,图 60。图 60中,两个n 位转换器被认为是理想的,我们有

v1 = vin + vQ(98)
v1= vin+ vQ(98)

2

where the quantised signal v 1 has been modelled as the input signal vżı plus some additive quantisation noise signal v Q . As shown in Fig.59 (and Fig. 61 for a ramp input), v Q is a sawtooth-like variable with a peak value of 1 VKSB
其中量化信号 v 1 被建模为输入信号 vż 加上一些加性量化噪声信号 v QAs,如图 59 所示(和图 61 为斜坡输入),v Qi 是一个锯齿状变量,峰值为 1VKSB

(this is for a ramp input but is typical). Its rms value is given by
(这是针对 Ramp 输入的,但通常是典型的)。它的 rms 值由下式给出

1 T/2

. 1 T/2
‚.1 ∫ —T/2

Q

t 2

V

VQ(rms)=
VQ(有效值)=

T

VKSB

T/2

V 2dt=

,

T

T/2

2

KSBT
KSBT 系列

dt(99)
DT(99)

=12(100)
=12(100元)

Note from equation (100) that the noise power is independent of the sampling rate. If vin is a sinusoidal signal, the signal-to-noise ratio ism aximised when
从等式 (100) 中注意,噪声功率与采样率无关如果 vn是正弦信号,则信噪比为 √m 轴化,当

vin has a peak value of Vref /2, or an rms value of (Vref /2) / 2. Thus
vn的峰值为 Vref/2 或 rms 值为 (Vref/2) / 2因此
,

SNRmax=20 log 10

/12

(101)

(Vref /2) /2
(Vref/2) /√2

VKSB

=6.02n + 1.76dB(102)
= 602n + 176 分贝 (102)

Quantisation noise spectrum & oversampling
量化噪声频谱和过采样

For Nyquist rate sampling, the spectrum of the quantisation noise signal will be limited by the highest frequency component, which in this case is the rate of sampling, see Fig. 61, or
对于奈奎斯特速率采样,量化噪声信号的频谱将受到最高频率分量的限制,在本例中为采样率,参见图 61,或

fmax
F最大值

(vQ
vQ

) = fS
=fS

2

(103)

If the input signal is a relatively active or busy signal, its quantisation noise can be treated as white noise, i.e of constant amplitude across the bandwidth. Since the noise power is given by
如果输入信号是一个相对活跃繁忙信号,则其量化噪声可以被视为白噪声,即在整个带宽上具有恒定幅度。由于噪声功率式给出

Q

12

PQ = V 2 =

VKSB 2
型号 VKSB2

(104)

Digital output Bout
数字输出B输出

111

110

101

100

011

010

001

000

vQ

0.5VLSB
0.5VLSB的

-0.5VLSB
-0.5VLSB电压

1234

8888

567

888

Vin/Vref
V输入/V参考

67

01
0 1
2

88

345

888

8 Vin/Vref Analog input
Vin/Vref 模拟输入

Figure 59: ADC ideal transfer characteristic and quantisation noise for n = 3
图 59:n = 3 时的 ADC 理想传输特性和量化噪声
.

vin

Figure 60: A circuit to investigate quantisation noise behaviour.
图 60:研究量化噪声行为的电路。

vQ

0.5VLSB
0.5VLSB的

-0.5VLSB
-0.5VLSB电压

T

t (time)
t(时间)

Figure 61: Quantisation noise signal for a ramp input as a function of time.
图 61:斜坡输入的量化噪声信号与时间的关系。

kfs

vin

Anti-aliasing filter
抗锯齿滤镜

Oversampling ADC
过采样ADC

1?

(kfs)
kf

Digital filter & decimator
数字滤波器抽取器

n (fs)
nf

Figure 62: Oversampling with analog and digital filtering.
图 62:使用模拟和数字滤波进行过采样。

the noise (power) spectral density5 kx in V/Hz can be derived from
噪声(功率)谱密度5kxin V/√Hz 可由以下公式推导

fs/22

VKSB 2
型号 VKSB2

2

fs/2

or

kxdf = kxfs =

VKSB

s

kx = 12f

12

(105)

(106)

Now consider the effect of speeding up the sampling rate by a factor of k,
现在考虑将采样率加快 k 倍的效果,

k 1 (see Fig.62). The ensuing benefits are twofold:
k 1 (见图 62)。随之而来的好处是双重的:

The frequency band between the signal and the first image about kfs is now much wider. This is the transition band of the analog filter preceding the digitizer, and thus the circuit complexity of this filter can be reduced. In fact, in oversampling converters of the C-A type, this filter can be as simple as a mere RC stage.
信号和第一张图像之间大约 kf s 的频带现在要宽得多这是数字转换器之前的模拟滤波器过渡,因此可以降低该滤波器的电路复杂性。事实上,C-A 类型的过采样转换器中,该滤波器可以像单纯RC一样简单

The quantisation noise is now spread over a wider band, or
量化噪声现在分布在更宽的频段上,或者

VKSB

s

kx = 12kf

indicating a spectral density reduction by k.
表示光谱密度降低了 √k。

(107)

The price for the preceeding benefits is the need for a digital 3lter at the output of the digitizer to (a) suppress any spectral components and noise above fs/2, and (b) reduce the data rate from kfs back to fs, a process known as
上述优势的代价是,数字化仪的输出端需要一个数字 3 升,以 (a) 抑制任何高于 fs/2 的频谱分量和噪声,以及 (b) 降低从 kfsback 到 fsa 过程的数据速率,称为

decimation.
抽取。

We observe that the rms noise at the output of the digitizer is still Vref /2n
我们观察到数字化仪输出端的 rms 噪声仍然是 Vref/2n

12;

however, only the spectra up to fs/2 will make it past the filter/decimator, so
但是,只有 FS/2 以下的谱图才能通过滤波器/抽取器

5 Power spectral density (PSD) describes how the power of a signal is distributed with frequency. It can be defined as the squared value of the signal, that is, as the actual power if the signal was a voltage applied to a 1-ohm load. For voltage signals, it is customary to use
5 功率密度 (PSD) 描述了信号功率如何随频率分布它可以定义为信号的平方值,即,如果信号施加1 欧姆负载电压,则定义为实际功率。对于电压信号,习惯上使用

units of V2Hz1 for PSD.
单位 V2Hz - 1 表示 PSD。

x1x2x3

xixO

Figure 63: Investigating the effect of negative feedback on disturbances and noise.
图 63:研究负反馈对干扰和噪声的影响。

the rms noise at the output is (calculated from the noise power)
输出端的 RMS 噪声为(根据噪声功率计算得出)

VQ1(rms) =
VQ1(有效值)=

fs/2

k2 df = VKSB

(108)

x

fs/2

12 k
12千米

Expressing k in the form k = 2m, we now have
以 k = 2m 的形式表示 k,我们现在有

SNRmax = 6.02 (n + 0.5m) + 1.76dB(109)
SNRmax= 602 (n + 05m) + 176 dB (109)

2

indicating a 1 -bit improvement for every octave of oversampling. Its actual resolution (often known as its Effective Number of Bits or ENOB) is defined as
表示过采样的每个八度音程都有 1 位的改进。其实际分辨率(通常称为其有效位数或 ENOB)定义为

ENOB = (SNR 1.76) dB
ENOB = (信噪比 — 176) 分贝

6.02 dB
602分贝

(110)

Example 8 An audio signal is oversampled mith a 12bit ADG. Find the over sampling frequency needed to achieve a 16bit resolution. fs = 44.1kHz. What is the corresponding SNRmax? Ans:11.29MHx, 98.09 dB
示例 8:音频信号在 12 位 ADG 中过采样实现 16 位分辨率所需的过采样频率fs= 441kHz 相应的 SNRmax 是多少?答案:11.29MHx, 98.09 分贝

Effect of feedback on noise
反馈对噪声的影响

Negative feedback provides a means also for reducing circuit sensitivity to cer- tain types of disturbances. Figure 63 illustrates three types of disturbances x1, x2, and x3 entering the circuit at different stages as shown. The output is found as
负反馈也提供了一种降低电路对特定类型干扰的敏感性的方法。图 63 说明了三种类型的干扰 x1x2 和 x3 在不同阶段进入电路,如图所示。输出为

x0 = x3 + a2 [x2 + a1 (xi βx0 + x1)](111)
x0= x3+ a2[x2+ a1(x— βx0+ x1)] (111)

or

0

1 + a1a2β

i

1

a1

a1a2

x =a1a2x + x

+ x2 + x3

(112)

kf
卡尔费休
s

vin
v

Anti-aliasing filter
抗锯齿滤镜

Sample & hold
采样并保持



ADC
模数转换器

1

(kfs)
(千方英尺

Digital filter & decimator
数字滤波器抽取器

n (fs)
n(f

Figure 64: Block diagram of an oversampling ADC.
图 64:过采样 ADC 的框图。

Note that x1 undergoes no attenuation relative to xi. However, x2 and x3 are attenuated by the forward gains from the input to the points of entry of the disturbances themselves. This feature is exploited in oversampling converters to reduce quantisation noise (aka noise shaping).
请注意x1相对于x没有衰减但是,x2x3从输入到干扰本身入口点的正向增益衰减。此功能在过采样转换器中被利用来减少量化噪声(又名噪声整形)。

Oversampling, noise shaping and Z converters
过采样、噪声整形和 Z — ∆ 转换器

In this section, the advantage of noise shaping the quantisation noise through the use of feedback is discussed. Note that equation (109) indicates that we need four samples to increase the resolution by 1 bit, sixteen samples to increase by 2 bits, sixty-four samples to increase by 3 bits, and so forth. The system architecture of a C-A oversampling ADC is shown in Fig.64 (see also Fig.62).C- A ADCs use feedback for the double purpose of a) generating dither to keep the input busy - ensures quantisation noise of uniform spectral density, and b) reshaping the noise spectrum to reduce the amount of oversampling required. In its simplest form depicted in Fig.65, a C-A ADC consists of a 1-bit digitizer or modulator to convert v żı to a high-frequency serial data stream v O, followed by a digital filter/decimator to convert this stream to a sequence of n-bit words of fractional binary value Bout at a lower rate of fS words per second. The modulator is made up of a latched comparator acting as a 1-bit ADC, a 1-bit DAC, and an integrator to integrate (C) the difference (A) between vżı and the DAC output; hence the name C-A ADC. The comparator is strobed at a rate of kfS samples per second, where k, usually a power of 2, is called the oversampling ratio (OSR).
在本节中,讨论了通过使用反馈来塑造量化噪声的优势请注意方程 (109) 表示我们需要4 个样本才能将分辨率提高 1 位,需要 16 个样本才能增加2 位,需要 64 个样本才能增加 3 位,依此类推。 C-A 过采样 ADC 的系统架构如图 64 所示(另见图 62)。C-A ADC 使用反馈有两个目的:a) 产生抖动以保持输入繁忙 - 确保量子化噪声具有均匀的频谱密度,以及 b) 重塑噪声频谱以减少所需的过采样量。其最简单的形式如图 1 所示。65,一个 C-A ADC 由一个 1 位数字化仪 ormodulatortoconvertvżt oahigh- 组成FrequencyserialdatastreamvOfollowedbyadigitalfilter/decimatortoconvertthisstreamtoasequenceof n-b itwords的小数二进制值 B以每秒 fS的较低速率输出调制器由一个充当 1 位 ADC 的锁存比较器、一个 1 位DACandanintegratort ointegr 组成ateCthediff erenceAbetweenvżandtheDAC 输出;因此得名 C-A ADC。比较器以每秒 kfS 样本的速率选通,其中 k(通常是 2 的幂)称为过采样 (OSR)。

To understand how noise shaping comes about, refer to Fig.66, where the quantisation error is modeled additively. By inspection, the various Fourier transforms are related as
要了解噪声整形是如何产生的,请参考图 66,其中量化误差是加法建模的。通过检查,各种傅里叶变换

V0 = VQ + H (Vin V0)(113)
V0= VQ+ H (Vin— V0) (113)

or

H (f)
Hf

V0 =

1 + H (f)
1 + H (f)

Vin
V输入

+1V
+1

1 + H (f) Q
1 + H (f) Q

(114)

Choosing H(f) such that its magnitude is sufficiently large over the frequency band of interest will provide simultaneous benefits of a) making V0 closely track
选择 H(f) 使其幅度在目标频带上足够大,将同时提供 a) 使 V0 密切跟踪

vinB
v
out

Figure 65: First-order CA ADC.
图 65:一阶CAADC。

VQ(f)
VQ(f)

Vin(f)
Vn(f) 

H(f)
H(f)

Vo(f)
 Vo(f) 声

Figure 66: Linear system model of a C-A ADC.
图 66: C-A ADC 的线性系统模型。

Vin over the given band, and b) drastically reducing quantisation noise over the same band.
Vinover 给定频段,以及 b) 大幅降低同一频段上的量化噪声。

For frequency bands extending down to dc, H(f) is usually implemented with integrators. In mixed-mode IC processes, H(f) is implemented using switched capacitor techniques.
对于向下延伸到直流频段H(f) 通常由积分器实现。在混合模式 IC 工艺中,H(f) 使用开关电容器技术实现。

Example 9 Given that a 1−bit ADG has a 6−dB SNR, mhat sample rate is required to obtain a 96−dB SNR (or 16 bits) if fS = 25kHx for straight oversam pling as mell as 3rstorder noise shaping? Ans: 27000 GHx, 819 MHx. Note: SNRmax = 6.02(n + 1.5m) 3.41dB for a 3rst order CA ADG
例 9 假设 1 位 ADG 具有 6 dB SNR,如果 fS= 25kHx 则需要 mhat 采样率才能获得 96 dB SNR(或 16 位),用于 3rst 阶噪声整形?答案:27000 GHx819 MHxNoteSNRmax= 602(n + 15m) — 341dB 用于 3rsst 阶 C-A ADG
.

Oversampling with noise shaping using an SC integra- tor
使用 SC 积分器进行噪声整形的过采样

Referring to the noninverting SC_ integrator circuit of Fig.54, we observe that $ pulses charge C1 to Vin, while $ pulses pull the charge accumulated in C1 out of C2, causing a step increase in V0. Letting n denote an arbitrary clock period,
参考图 54 的同相 SC_ 积分器电路,我们观察到 $ 脉冲将 C1 充电到 Vin,而 $ 脉冲将 C1 中积累的电荷从 C2 中拉出,导致 V0 的阶跃增加,让 n 表示任意时钟周期,

we have
我们有

or

v0 [nTCK

] = v0

[(n 1) TCK
[(n — 1) TCK

] + A [(n 1) TCK]
] + A [(n — 1) TCK]

C2

(115)

v0 [nTCK] = v0

C1

2

[(n 1) TCK] + C vin [(n 1) TCK
[(n — 1) TCK] + C vn[(n — 1) TCK

](116)
](116)

where A [(n 1) TCK] = C1vin [(n 1) TCK] denotes the charge accumulated by C1 during the previous $ pulse. Equation (116) represents a discrete time sequence relating input and output values. In the frequency domain6 , equation
其中 A [(n 1) TCK] = C1vn[(n 1) TCK] 表示 C1 在前一个 $ 脉冲期间累积的电荷。等式 (116) 表示与输入和输出值相关的离散时间序列。在频域6方程中

(116) becomes
(116)变为

V0 ((c) = V0
V0((c) = V0

((c) e(uTCK + C1 V
((c) e—(uTCK + C1 V

C2 in
C2英寸

((c) e(uTCK(117)
((c) e—(uTCK (117)

hfS

Letting C1 = C2 and TCK = 1
设 C1= C2和 TCK= 1

, we can express the SC integrator transfer
我们可以表示 SC 集成商转移

function as
函数设置为

H (f)=V0
H (f) = V0

Vin
V输入

=1

e(uTCK 1
e(uTCK1

(118)

=1

e(2vf/hfS1
e(2vf/hfS1

(119)

Here, k is the oversampling ratio while fS is the Nyquist rate. Now referring to Fig.65, Fig.66 and equation (114), the noise transfer function N (f) becomes
其中,k 是过采样率,而 fS是奈奎斯特率。现在参考图 65、图 66 和方程 (114),噪声传递函数 N (f) 变为

N (f) =1= 1e(2vf/hfS(120)
N (f) = 1 = 1 e—(2vf/hfS (120)

1 + H (f)
1 + H (f)

||

or

N (f) = 2 sinπf
N (f) = 2 正弦 πf

kfS
KFS 系列

(121)

|

where the identity sin 8 = eθ eθ /2( has been used. Thus
其中,恒等式 sin 8 = eθ— e—θ/2( 已被使用。因此

|VQout

= 2 sinπf kfS
= 2 正弦 πf kfS

|V
|

Qin

|(122)
|(122)

Since the spectral density of VQin was found to be (see equation (107))
由于发现 VQin 的光谱密度为(参见方程 (107))

VKSB

s

kx = 12kf

the spectral density of VQout, i.e. after feedback, is given by
VQout频谱密度,即反馈后,由下式给出

(123)

kx'

=2 sinπf kfS
= 2 正弦 πf kfS

VKSB
VKSB

12kfs
12kf

(124)

πf

S

2 kf
2千克力

VKSB

12kfs

fork πand/orf <
对于 k π 和/或 f<

fS(125)
fS(125)

2

2πVKSB
2πVKSB型

S

=12k3f3 f(126)
= √12√k3√f3 华氏度 (126)

6 x (tT ) e(ctdt = E((c)e(cT i.e delaying a signal by one period T is equivalent
6 ∞ x (t T ) e—(cdt = E((c)e—(cTe deayng a sgnaby one perod T s equvaent

to multiplying its Fourier transform by e

.

—∞(cT
—∞(cT

Spectral density
光谱密度

Figure 67: First-order noise shaping (k = 16).
图 67:一阶噪声整形 (k = 16)。

The approx.sin 8 8 for 8 1 has been used. Fig.67 shows a sketch of
大约的罪 8 8 换 8 1 已被使用。图 67 显示了

kx and kx' which reveals that the modulator shifts most of the noise energy
kx和 kx,这表明调制器转移了大部分噪声能量

toward higher frequencies. Only the shaded portion will make it past the fil-
朝向更高的频率。只有阴影部分才能通过过滤器

ter/decimator. Thus the output noise power is
ter/decimator因此,输出噪声功率为

fS/2
S/2 系列

x

fS/2

(k' )2
k2

df(127)
df(127)

from which the output rms noise signal is found to be
从中可以找到输出 RMS 噪声信号

VQout (rms)=
VQout(均方根) =

fS/2

x

(k' )2
k2

df(128)
df(128)

2πVKSB fS/2

fS/2

f

12

k3

3

S

= f2df(129)
= √ √ √ f2df (129)

fS/2

πVKSB
πVKSB

=6k3(130)
= 6√k3 (130)

Expressing k in the form k = 2m gives, for a first-order C-A ADC,
以 k = 2mgives 的形式表示 k,对于一阶 C-A ADC,

SNRmax = 6.02(n + 1.5m) 3.41 dB(131)
SNRmax= 602(n + 15m) — 341 分贝 (131)

indicating a 1.5 bit improvement for every octave of oversampling; this is better than the 0.5-bit improvement without noise shaping. Here,
表示过采样的每个八度音程都有 1.5 位的改进;这比没有噪声整形的 0.5 位改进要好。这里

ENOB = (SNR + 3.41) dB
ENOB = (信噪比 + 341) 分贝

6.02 dB
602分贝

Ξ n + 1.5m(132)
ξ n + 15m (132)

The benefits of noise shaping can be enhanced further by using higher-order modulators.
通过使用高阶调制器,可以进一步增强 noise shaping 的优势

Besides offering the aforementioned advantages of undemanding and mixed- mode-compatible analog circuitry, 1-bit quantizers are inherently linear; since only two output levels are provided, a straight characteristic results. Practical upper limits on sampling rates currently restrict C-A ADCs to moderate speed but high-resolution applications, such as digital audio, digital telephony, and
除了提供上述要求不高且兼容混合模式的模拟电路的优势外,1 位量化器本质上是线性的;由于仅提供两个输出电平,因此会产生直接特性。目前,采样速率的实际上限将 C-A ADC 限制在中等速度高分辨率的应用,例如数字音频、数字电话

low-frequency measurement instrumentation, with resolutions ranging from 16 to 24 bits. Note that since the digital filter/decimator computes each high- resolution sample using many previous low-resolution samples, there is latency as information progress from input to output through the various stages of the filter. This delay may be intolerable in certain real-time applications, such as control.
低频测量仪器,分辨率范围为 16 至 24 位请注意,由于数字滤波器/抽取器使用许多先前的低分辨率样本来计算每个高分辨率样本,因此当信息通过滤波器的各个阶段从输入到输出时,存在延迟。在某些实时应用程序 (如 control) 中,这种延迟可能是无法容忍的。

References
引用

R Jacob Baker, GMOS: Gircuit Design,Gayout D Simulation, Wiley-IEEE, 2010.
R Jacob Baker,GMOS:Gircuit Design,Gayout D 仿真,Wiley-IEEE,2010 年。

A S Sedra & K C Smith, Microelectronic Gircuits, 5th Ed., Oxford Univ. Press, 2004.
A S Sedra & K C Smith,微电子学,第5版,牛津大学出版社,2004年。