40238245 Design of Analog CMOS Integrated Circuits Behzad Razavi Marcado

8/13/2019 40238245 Design of Analog CMOS Integrated Circuits Behzad Razavi Marcado

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Chap. 3 Single-Stage Amplifiers

Figure3.1 Input-outputcharacteristicX1 X 2 X of a nonlinear system.

approximation, and higher order terms are insignificant. In other words, y = a Axindicating a linear relationship between the increments at the input and output. As x t )increases in magnitude, higher order terms manifest themselves, leading to nonlinearityand necessitating large-signal analysis. From another point of view, if the slope of thecharacteristic (the incremental gain) v rieswith the signal level, then the system is nonlinear.These concepts are described in detail in Chapter 13.

What aspects of the performance of an amplifier are important? n addition to gain andspeed, such parameters as power dissipation, supply voltage, linearity, noise, or maxim umvoltage swings may be important. Furthermore, the input and output impedances determinehow the circuit interacts with preceding and subsequent stages. In practice, most of theseparameters trade with each other, making the design a multi-dimensional optimizationproblem. Illustrated in the analog design octagon of Fig. 3.2, such trade-offs present manychallenges in the design of high-performance amplifiers, requiring intuition and experienceto arrive at an acceptable compromise.

Noise Linearityf ' .-* .-*+- , \. ..-.: , -,Power +..-, , aDissipation Gain. *+-. . *...+ I

I ,,,.-+*-.... .*,-;,I .. .....,, \InputIOutput ...-- :.. ' ; tSupply,*.Impedance , '. 4. . s\ , .VoltageYtageSpeed ~wings Figure 3.2 Analog design octagon.

3.2 Common Source Stage3.2.1 Common Source Stage with Resistive Load

By virtue of its transconductance, a MOSFET converts variations in its gate-source voltageto a small-signal drain current, which can pass through a resistor to generate an outputvoltage. Shown in Fig. 3.3(a ), the common-source (CS) stage performs such an operation.


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Sec. 3 2 Common-Source Stage 53we note that Vin appears in the square term and VOUt n the linear term. As in increases, VOUtmustdecrease such that the product remains constant. We may nevertheless say ID1 increases as Vinincreases. This statement simply refers to the quadratic part of the equation.

3.2.2 CS Stage with Diode Connected LoadIn many CMOS technologies, it is difficult to fabricate resistors with tightly-controlledvalues or a reasonable physical size (Chapter 17). Consequently, it is desirable to replaceR in Fig. 3.3(a) with a MOS transistor.

A MOSFET can operate as a small-signal resistor if its gate and drain are shorted[Fig. 3.7(a)]. Called a diode-connected device in analogy with its bipolar counterpart,

(a) b)Figure 3 7 (a) Diode-connected NMOS and PMOS devices, (b) small-signal equivalent circuit.

this configuration exhibits a small-signal behavior similar to a two-terminal resistor. Notethat the transistor is always in saturation because the drain and the gate have the samepotential. Using the small-signal equivalent shown in Fig. 3.7(b) to obtain the impedanceof the device, we write Vl Vx and x Vx/ro g Vx. That is, the impedance of thediode is simply equal to I g, ltro = gm If body effect exists, we can use the circuit inFig. 3.8 to write Vl -V x Vbs -VX and

Figure 3.8 (a) Arrangement for measuring the equivalent resistance of a diode-connected MOSFET, b) small-signal equivalent circuit.


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Chap. 3 Single-Stage Amplifiers

Moreover,

yielding

Thus, for a gain of 10, the overdrive of M2 need be only 2.5 times that of M I .Alternatively, for a givenoverdrive voltage, this circuit. achieves a gain four times tha t of the stage in Fig. 3.12. Intuitively, thisis because for a given (VGS2 VTH2(, f the current decreases by a factor of 4, then W / L ) 2mustdecrease proportionally, and g = J 2 p p C o x ~ / ~ ) 2 ~ D 2s lowered by the same factor.

We should also mention that in today s CMOS technology, channel-length modulationis quite significant and, more importantly, the behavior of transistors notably departs fromthe square law (Chapter 16). Thus, the gain of the stage in Fig. 3.9 must be expressed as

where g and g must be obtained as described in Chapter 16.3 2 3 CS Stage with Current Source Load

In applications requiring a large voltage gain in a single stage, the relationship A, -g, R Dsuggests that we increase the load impedance of the CS stage. With a resistor or diode-connected load, however, increasing the load resistance limits the output voltage swing.

A more practical approach is to replace the load with a current source. Described brieflyin Example 3.2, the resulting circuit is shown in Fig. 3.14, where both transistors operate insaturation. Since the total impedance seen at the output node is equal to ro l Ilro2, the gain is

Figure 3 14 CS stage with current-source load.

The key point here is that the output impedance and the minimum required lVnsl ofMz are less strongly coupled than the value and voltage drop of a resistor, The voltage


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Sec 3 2 Common-Source Stage 59vDS2 rninVGS2 VTH21 an be reduced to even a few hundred millivolts by simply

increasing the width of M2. f r -02 is not sufficiently high, the length and width of M2 can beincreased to achieve a smaller while maintaining the same overdrive voltage. The penaltyis the large capacitance introduced by M2 at the output node.We should remark that the output bias voltage of the circuit in Fig. 3.14 is not well-defined. Thus, the stage is reliably biased only if a feedback loop forces V to a knownvalue Chapter 8).The large-signal analysis of the circuit is left as an exercise for the reader.

As explained in Chapter 2, the output impedance of MOSFETs at a given drain currentcan be scaled by changing the channel length, i.e., to the first order, h 1/L and hencero LIZD.Since the gain of the stage shown in Fig. 3.14 is proportional to r01 llrO2 wemay surmise that longer transis tors yield a higher voltage gain.

Let us consider MI and M2 separately. If L is scaled by a factor a > I), then l mayneed to be scaled proportionally as well. This is because , for a given drain current, VGsiV T H l l / J m , i.e., if W1 is not scaled, the overdrive voltage increases, limiting theoutput voltage swing. Also, since g l d m caling up only L 1 lowers g .

In applications where these issues are unimportant, l can remain constant while L 1increases. Thus, the intrinsic gain of the transistor can be written as

indicating that the gain increases with L because h depends more strongly on L than gdoes. Also, note that g ro decreases as ID increases.Increasing L2 while keeping W2constant increases ro2 and hence the voltage gain , butat the cost of higher I VDS21equired to maintain M2 in saturation.

3 2 4 CS Stage with Triode LoadA MOS device operating in deep triode region behaves as a resistor and can therefore serveas the load in a CS stage. Illustrated in Fig. 3.15, such a circuit biases the gate of M2 ata sufficiently low level, ensuring the load is in deep triode region for all output voltageswings.

Figure3 15 CS stagewith triodeload


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Chap. Single StageAmplifiersSince

the voltage gain can be readily calculated.The principal drawback of this circuit stems from the dependence of Ron2 pon p Cox,Vb,

and V T H P .ince pp Co x nd V T H Pary with process and temperature and since generatinga precise value for Vb requires additional complexity, this circuit is difficult to use. Triodeloads, however, consume less voltage headroom then do diode-connected devices becauseinFig. 3.15 Vo = V D D hereas inFi g. 3.12, V,,,,,,, V D D V T H P J .

3 2 5 CS Stage with Source DegenerationIn some applications, the square-law dependence of the drain current upon the overdrivevoltage introduces excessive nonlinearity, making it desirab le to soften the device charac-teristic. In Section 3.2.2, we noted the linear behavior of a CS stage using a diode-connectedload. Alternatively, as depicted in Fig. 3.16, this can be accomplished by placing a degen-eration resistor in series with the source terminal. Here, as Vin ncreases, so do I D and the

Figure 3.16 CS stage with source degeneration.

voltage drop across Rs. That is, a fraction of K n appears across the resistor rather than as thegate-source overdrive, thus leading to a smoother variation of ID .From another perspective,we intend to make the gain equation a weaker function of g . Since V,,, = - I DRD thenonlinearity of the circuit arises from the nonlinear dependence of IDupon Vi We note thataV,,,/a Vin= - a I D / a K n ) R D , nd define the equivalent transconductance of the circuitas G , = I D / aK . Now, assuming ID = VGS), e write


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Sec 3 3 Source Follower

Figure 3 25 Modeling output port of an amplifier by a Norton equivalent.

Defining G, I / Vin e have V,,, Gm R This lemma proves useful if G,and R,,, can be determined by inspection.

Calculate the voltage gain of the circuit shown in Fig. 3.26. Assume 1 s ideal.

Figure3 26SolutionThe transconductance and output resistance of the stage are given by Eqs. 3.55) and (3.60), espec-tively. Thus,

Interestingly, the voltage gain is equal to the intrinsic gain of the transistor and independent of Rs.This is because, if o s ideal, the current through Rs cannot change and hence the small-signal voltagedrop across Rs is zero-as if Rs were zero itself.

3 3 Source FollowerOur analysis of the common-source stage indicates that, to achieve a high voltage gain withlimited supply voltage, the load impedance must be as large as possible. If such a stage isto drive a low-impedance load, then a buffer must be placed after the amplifier so as todrive the load with negligible loss of the signal level. The source follower (also called thecommon-drain stage) can operate as a voltage buffer.

Illustrated in Fig. 3.27(a), the source follower senses the signal at the gate and drives


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Chap. 3 Single-Stage Amplifier:

As explained in Chapter 7, source followers also introduce substantial noise. For thi:reason, the circuit of Fig. 3.39 b) is ill-suited to low-noise applications.

3.4 Common Gate StageIn common-source amplifiers and source followers, the input signal is applied to the gate ofMOSFET. It is also possible to apply the signal to the source terminal. Shown in Fig. 3.40 a).a common-gate CG) stage senses the input at the source and produces the output at thedrain. The gate is connected to a dc voltage to establish proper operating conditions . Notethat theb ias current of M lows through the input signal source. Alternatively, as depictedin Fig. 3.40 b), M can be biased by a constant current source, with the signal capacitivelqcoupled to the circuit.

Figure 3.40 a) Common-gate stage with direct coupling tinput, b) CG stage with capacitive coupling at input.We first study the large-signal behavior of the circuit in Fig. 3.40 a). For simplicity, lel

us assume that K decreases from a large positive value. For in Vb VTH,M I is ofjand V,,, VDD or lower values of Vin,we can write

if M is in saturation. As in decreases, so does V,,,, eventually driving MI into the triodtregion if

The input-output characteristic is shown in Fig. 3.41. If M is saturated, we can express thcoutput voltage as


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Sec 3 5 Cascode Stage

Figure3 49

The output impedance is simply equal to

3 5 Cascode StageAs mentioned in Example 3.10 the input signal of a common-gate stage may be a current.We also know that a transistor in a common-source arrangement converts a voltage signal toa current signal. The cascade of a CS stage and a CG stage is called a cascode ' topology ,providing many useful properties. Fig. 3.50 shows the basic configuration: M I generatesa small-signal drain current proportional to , and M simply routes the current to RD

Figure 3 50 Cascode stage.We call M I the input device and M the cascode device. Note that in this example, M I andM carry equal currents. As we describe the attributes of the circuit in this section, manyadvantages of the cascode topology over a simple common-source stage become evident.

First, let us study the bias conditions of the cascode. For M to operate in saturation,Vx Vi VTH l If M1 and M2 are both in saturation, then Vx is determined primarily by

'The term c scode is believed to be the acronym for cascaded triodes, possibly invented in vacuum tubedays.


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40238245 Design of Analog CMOS Integrated Circuits Behzad Razavi Marcado