noise, gain and bandwidth in analog...

Chapter 8

NOISE, GAIN AND BANDWIDTH INANALOG DESIGN

Robert G. MeyerDepartment of Electrical Engineering and Computer Sciences, University of California

Trade-offs between noise, gain and bandwidth are important issues in analogcircuit design. Noise performance is a primary concern when low-level sig-nals must be amplified. Optimization of noise performance is a complex taskinvolving many parameters. The circuit designer must decide the basic form ofamplification required – whether current input, voltage input or an impedance-matched input. Various parameters which can then be manipulated to optimizethe noise performance include device sizes and bias currents, device types (FETor bipolar), circuit topologies (Darlington, cascode, etc.) and circuit impedancelevels. The complexity of this situation is then further compounded when theissue of gain–bandwidth is included. A fundamental distinction to be madehere is between noise issues in wideband amplifier design versus narrowbandamplifier design. Wideband amplifiers generally have bandwidths of severaloctaves or more and may have to operate down to dc. This generally meansthat inductive elements cannot be used to enhance performance. By contrast,narrowband amplifiers may have bandwidths of as little as 10% or less of theircenter frequency, and inductors can be used to great advantage in trading gainfor bandwidth and also in improving the circuit noise performance. In order toexplore these issues and trade-offs, we begin first with a description of gain–bandwidth concepts as applied to both wideband and narrowband amplifiers,followed by a treatment of electronic circuit noise modeling. These conceptsare then used in combination to define the trade-offs in circuit design betweennoise, gain and bandwidth.

8.1. Gain–Bandwidth ConceptsAll commonly used active devices in modern electronics are shown in

Figure 8.1(a) and may be represented by the simple equivalent circuit shownin Figure 8.1(b). Thus the bipolar junction transistor (BJT), metal-oxide-semiconductor field-effect transistor (MOSFET), junction field-effect transistor(JFET) and the gallium arsenide field-effect transistor (GaAsFET) can all begeneralized to a voltage-controlled device whose small-signal output currentis related to the input control voltage by the transconductance In this

227C. Toumazou et al. (eds), Trade-Offs in Analog Circuit Design: The Designer’s Companion, 227–256.© 2002 Kluwer Academic Publishers. Printed in the Netherlands.

228 Chapter 8

simplified representation, the output signal is assumed to be a perfect currentsource and any series input resistance or shunt feedback capacitance is initiallyneglected. This enables us to focus first on the dominant gain- bandwidth lim-itations as they relate to noise performance. (Note that for the FETs.)The effective transit time of charge carriers traversing the active region of thedevice is [1]

and the effective low-frequency current gain is

Again note that for the FETs. In this simple model neglecting parasiticcapacitance, we find that the frequency of unity small-signal current gain is [1]

In order to obtain broadband amplification of signals we commonly connectamplifying devices in a cascade with load resistance on each stage. Considera typical multistage amplifier as shown in Figure 8.2.

The portion of Figure 8.2 enclosed in dotted lines can be considered arepetitive element that comprises the cascade. The gain of this element orstage is

Noise, Gain and Bandwidth in Analog Design 229

from which we see that the mid-band gain magnitude is

and the – 3 dB bandwidth (rad/sec) is

Thus the gain–bandwidth product of this stage is

The importance of the device (or process for integrated circuits) is thusapparent. From (8.7) we can conclude that in a cascade we cannot achieve gainover a wider bandwidth than the device (excluding inductors) and that wecan trade-off gain against bandwidth by choosing This process is calledresistive broadbanding. Wider bandwidth is achieved at the expense of lowergain by using low values of These conclusions also apply if the signalinput to the amplifier approximates a current source and the stage consideredis not part of a multi-stage amplifier but is an isolated single gain stage. Thisis the case, for example, in fiber-optic preamplifiers. However, if the signalsource to the amplifier approximates a voltage source, then the single-stagebandwidth (and thus the gain–bandwidth) is ideally infinite. This case is rarelyencountered in practice at high frequencies (gigahertz range), but may be foundin sub-gigahertz applications. More commonly at frequencies in the gigahertzrange, we find the first stage of an amplifier driven by a voltage source (e.g.coming from an antenna) in series with a resistive source impedance (often50 or In that case the signal input can be represented by a Nortonequivalent current source in parallel with and the previous analysis is valid,as can be lumped in with

230 Chapter 8

8.1.1. Gain–Bandwidth Shrinkage

If we construct a multi-stage amplifier consisting of N identical stages withresistive interstage loads as shown in Figure 8.2, we can describe the gain–bandwidth behavior of the amplifier as follows. If the gain per stage is G andthe bandwidth per stage is B then the overall amplifier transfer function for Nstage is

The overall – 3 dB frequency of the amplifier is the frequency whereFrom (8.8) this is

Thus, we see that the bandwidth shrinks as we add stages. For example,for N = 2 and for N = 3. In an N-stage

amplifier, the overall mid-band gain is and we can define a per-stagegain–bandwidth figure-of-merit as

We conclude that the cascading of stages each with a negative-real-pole transferfunction results in significant loss of gain–bandwidth product.

Gain–bandwidth shrinkage is also caused by parasitic elements. The inclu-sion of parasitic capacitance in shunt with causes a reduction of the device

and consequent loss of gain–bandwidth. Thus, in wideband integrated cir-cuit (IC) design, the layout must be carefully chosen to minimize parasiticcapacitance. Any resistance in series with the input lead (such as the baseresistance of a BJT) also causes loss of gain–bandwidth. Consider the cas-cade of Figure 8.2 with parasitic resistance added to each device as shownin Figure 8.3 where is now neglected. Taking one section as shown in thedotted line, we find

from which the mid-band gain is

and the –3 dB bandwidth is


Thus the gain–bandwidth product of the stage is

We see that the gain–bandwidth is reduced by the ratio Thisleads to trade-offs in wideband design since we can reduce the magnitude of

by increasing the device size in the IC layout. This also reduces the noisecontribution from (to be considered later) which is highly desirable, but hasthe unwanted effect of increasing the parasitic device capacitance which leadsto a reduction of and consequent loss of gain–bandwidth.

Loss of gain–bandwidth also occurs in simple amplifier cascades due toMiller effect, although the loss becomes less severe as is reduced, whichis often the case for high-frequency wideband amplifiers. Consider the singleamplifier stage shown in Figure 8.4 where feedback capacitance is included.(This represents the collector–base parasitic capacitance in BJTs and the drain–gate parasitic in FETs.)

232 Chapter 8

The Miller capacitance seen across the input terminals is [2]

Thus, the total input capacitance is

The time constant can be compared with to determine theloss of stage gain–bandwidth. The smaller the less the effect. For example,if and GHz, we find and

In this case, Miller effect reduces the stage gain–bandwidthby 10%. A trade-off occurs again if noise must be minimized by increasing thedevice size (to reduce in that this will increase and increase the Millereffect.

8.1.2. Gain–Bandwidth Trade-Offs Using Inductors

Inductive elements have long been used to advantage in electronic amplifiers.Inductors can be used to obtain a frequency response which peaks in a narrowrange and thus tends to reject unwanted out-of-band signals. However, theadvantages of using inductors extend beyond this as they allow the inherentdevice gain–bandwidth to be arbitrarily moved across the spectrum, as willnow be shown. Consider the single-stage amplifier shown in Figure 8.5 andinitially neglect feedback capacitance. The input resistance represents thebasic device input resistance in shunt with any external resistors such as biasresistors. The stage transfer function is

The stage gain is

and the – 3 dB bandwidth is

giving the stage gain–bandwidth product as


as before. The frequency response given by (8.19) is plotted in Figure 8.6.Now consider adding a shunt inductor as shown in Figure 8.7. The transfer

function of the circuit of Figure 8.7 is

At resonance

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where

The – 3 dB bandwidth of the transfer function is

where

From (8.25) and (8.26), we find the gain–bandwidth product of the circuitis now

as before. However, the gain is now realized in a narrow band centered on thefrequency as shown in Figure 8.8.

We can thus shift the high-gain region of the device transfer function to highfrequencies using the inductor. In practice, the existence of lossy parasiticssuch as reduces the gain at very high frequencies, but nonetheless we arestill able to trade-off gain for bandwidth quite effectively in this way. Typicalperformance is shown in Figure 8.9 where ideal lossless behavior is comparedwith typical practical results. High-frequency gain larger than the lowpassasymptote is readily achieved.

8.2. Device Noise Representation

In order to examine trade-offs between noise performance and gain–bandwidth, we need a convenient means to compare the noise performanceof different devices and different configurations. This is best done by repre-senting the active-device noise behavior by equivalent input noise voltage and


current generators [3]. Although these generators are correlated in general, wefind in many applications that one or other generator is dominant and thus theother generator and the correlation can be neglected. Once again we begin withthe simple general representation of Figure 8.1 and add noise generators asshown in Figure 8.10(a) (white noise only is considered).

We then calculate equivalent input generators which model the device noisebehavior as shown in Figure 8.10(b). In Figure 8.10(a), the output noise source

is caused by thermal noise in FETs and shot noise in BJTs. Thus,

236 Chapter 8

for BJTs and

for FETs.The input noise generator can be assumed zero for FETs and for BJTs it is

caused by shot noise in the base current given by

Note that if a physical shunt resistor R is connected in shunt with the deviceinput (e.g. due to bias circuits), then this can be folded into the noise repre-sentation by including it in (which becomes and adding a thermal noisegenerator to of value

The equivalent input generators of Figure 8.10(b) now become

and

where the ac current gain of the device is given by

The expression for in (8.33) can be related to the device transconductancein general for any active device by using for BJTs and deriving:

for FETs and

for BJTs. Finally, the representation of Figure 8.10(b) can be enhanced byadding to a thermal noise generator due to any physical series input resistancesuch as base resistance for BJTs, given by


The equivalent input noise representation of Figure 8.10(b) can now be usedto generate some general conclusions regarding low-noise design before weexamine the specifics of the gain–bandwidth noise trade-off. For amplifiers inwhich the input noise current is important (such as fiber-optic amplifiers drivenby a high-impedance source), the noise is dominated by Thus FETs have anadvantage in that there is no input shot noise contribution as in BJTs. However,both FETs and BJTs tend to be dominated in high-frequency wideband appli-cations by the frequency-dependent second term in (8.34). At high frequencies,this asymptotes to

for all devices. Thus a high device becomes important as does minimization

dissipation. The use of low collector current in BJTs can help the noiseperformance but may degrade the device In the case of FETs the designerhas more degrees of freedom in that the FET transconductance depends on bothdrain bias current and device geometry via W/L.

For applications where the input noise voltage generator is dominant(where the driving source impedance is low) all active devices are operatedwith the maximum possible transconductance This in general calls forhigh bias currents and large area devices with high W/L when using FETs.If BJTs are used, then high bias currents are also required to give a largevalue of gm, and in addition, the base resistance must be minimized which alsorequires large device area. The trade-offs here involve dc power dissipation andthe deleterious effects of increasing device parasitic capacitance as the activedevice area is increased.

The issue of the impact of negative feedback on the noise-gain–bandwidthtrade-off will be discussed in a later section. However, at this point it is worthconsidering the impact of noise performance of the most common form offeedback-series resistive degeneration (local series feedback) in the common

of This then involves trade-offs involving device bias point and dc power

238 Chapter 8

lead as shown in Figure 8.11, This connection can be used with all activedevices.

It leads to improved linearity, facilitates the trade-off of gain for bandwidthand allows the manipulation of the device input and output impedances. How-ever, there is a noise penalty in that the equivalent input noise voltage generator

of the circuit is increased by the amount of thermal noise in which isThe equivalent input noise current is unchanged. The gain of the

circuit as expressed by the transconductance is reduced by the negative feedbackdue to and is given by

Note that the feedback loop gain in this circuit is

8.2.1. Effect of Inductors on Noise PerformanceThe use of inductors to trade-off bandwidth versus gain was described above.

Inductors also offer the opportunity to realize significantly improved noiseperformance in high-frequency amplifiers. This can be appreciated by addinga shunt inductor L as shown in Figure 8.7 across the input of the equivalentcircuits of Figure 8.10. Then at the parallel resonant frequency,the inductive and capacitive impedances cancel at the input of the device andthe frequency dependent term in in (8.34) disappears. This gives significantlyimproved noise performance in many high-frequency applications, although thetechnique is obviously restricted to narrowband circuits. Inductive optimizationof noise performance based on these principles is commonly implementedin gigahertz range narrowband low-noise amplifiers (LNAs) used in wirelesscommunication systems.

Another common and important use of the inductors in high-frequencylow-noise circuits is in inductive common-lead degeneration as shown inFigure 8.12(a). The small-signal equivalent of this connection is shown inFigure 8.12(b), where a simplified active device equivalent has been used.In order to examine the effect of on noise performance, the output noisegenerator is also included.

First, we omit and examine the effect of on the gain and inputimpedance of the stage. The major benefit of is in boosting the resistive partof the input impedance of the stage without degrading the noise performance,as happens with resistive degeneration. The use of common-lead inductance iswidespread in LNA design using both FETs and BJTs, although once again thetechnique is limited to narrowband applications. The physical inductor is oftenrealized using the package bond wires [4], or on-chip spiral inductors can alsobe used [5–7]. By calculating the current flowing into the equivalent circuit


of Figure 8.12(b), we find the input impedance is

This expression can be represented by the equivalent circuit of Figure 8.13.We see that a resistive portion appears which can be chosento have an appropriate value to allow matching to typical RF source resis-tances of 50 or 75 This same result could be achieved by simply adding aphysical series input resistor, but this would add a large amount of noise tothe circuit and is generally an unacceptable option. Additional input induc-tive and capacitive elements are usually added to produce a purely resistiveexternal input impedance. Typical values in (8.42) might be

240 Chapter 8

and giving the resistive portion of a valueThis would correspond to

andThe introduction of typically causes a reduction in gain and this can be

estimated from

idea can be obtained by referring the noise generator in Figure 8.12(b) backto the input, giving an equivalent input noise voltage generator

We see that the effect of is to reduce the magnitude of compared to thecase where is absent. In practice, we find small but useful improvementsin the noise performance of high-frequency LNAs when this technique is usedto help match the input. For and we find the factor

to have values 0.96 (–0.2 dB) at 1 GHz and 0.67 (–1.7 dB) at3 GHz.

8.3. Trade-Offs in Noise and Gain–Bandwidth

The considerations described above focused on noise and gain–bandwidthrepresentation of electronic circuits. We now use these tools to examine issuesand methods of trade-off between these quantities.

8.3.1. Methods of Trading Gain for Bandwidth and theAssociated Noise Performance Implications [8]

The trade-off of gain for bandwidth can be achieved in a number of ways,with noise performance, terminal impedances and the form of the circuit trans-fer function being important constraints. The use of inductors to transfer thedevice gain to a higher frequency in narrowband applications has been treatedin Subsection 8.1.2 and will not be considered further. For broadband ampli-fiers, the simplest method of trading gain for bandwidth is the use of resistivebroadbanding as described in Section 8.1. This method has the advantage ofsimplicity, but has the drawbacks of gain–bandwidth shrinkage over multi-ple stages and limitations on control of the circuit terminal impedances. Forexample, if a resistive input impedance of is required to match a source

tor to ground as shown in Figure 8.14. Assume the device input resistanceis large and let

The effect of on noise performance is somewhat complicated, but a rough

resistance of the only option available is connection of a shunt resis-


We can calculate the circuit noise figure by comparing the total noise atwith that due to the source resistance. The input impedance of the active devicedoes not affect the following noise figure calculation and is neglected. Using

we find for the total noise at

where correlation has been neglected. The noise at due to the sourceresistance is

From the definition of noise figure, we have

and using (8.45) and (8.46) in (8.47), we find

If is omitted from the calculation, the circuit noise figure is

From (8.48) and (8.49), we see that for low-noise circuits, the degradation incircuit noise figure caused by the addition of is about 3 dB and canbe higher. This is unacceptable in many applications.

These limitations on simple resistive broadbanding lead us to examine otheroptions. One of the most widely used is negative feedback [9]. The basic

242 Chapter 8

trade-off of gain and bandwidth allowed by the use of negative feedback canbe illustrated by the following simple example. Consider an idealized neg-ative feedback amplifier with a one-pole forward gain function as shown inFigure 8.15.

The forward gain path has a transfer function

where

The gain versus frequency of the open and closed loop amplifier is shown inFigure 8.16 where f is assumed frequency independent.

The gain of the feedback amplifier is


where the loop gain is

the mid-band gain is

and the – 3 dB frequency is

From (8.52) and Figure 8.16, we see that the use of negative feedback allows adirect trade-off of gain for bandwidth while maintaining a fixed gain–bandwidthproduct.

In addition to the gain–bandwidth trade-off, the use of feedback allowsmodification of the terminal impedance of the amplifier. If the forward gainblock has an input resistance then shunt feedback at the input gives amodified (lowered) input resistance

Series feedback at the input raises the input resistance to

The use of combined shunt and series feedback can give intermediate valuesof terminal impedances and this technique will be described below. The use ofcombined feedback allows realization of matched terminal impedances withmuch less noise-figure degradation than is caused by simple shunt or seriesresistive matching.

8.3.2. The Use of Single-Stage Feedback for theNoise-Gain–Bandwidth Trade-Off

Consider a cascade of local series feedback stages as shown in Figure 8.17.The active device with feedback resistor can be represented by the simplifiedhigh-frequency equivalent circuit of Figure 8.18. If the loop gainis large, this equivalent circuit reduces to that shown in Figure 8.19, where theeffective transconductance is given by

The transconductance has a pole with magnitude that can usually beneglected. We see that the input capacitance and transconductance are both

244 Chapter 8

reduced by the factor (1 + T). Thus using the analysis of Section 8.1, weconclude that gain and bandwidth can be traded off via the feedback resistorA significant advantage of this technique over simple resistive broadbanding isthe linearization produced by The noise introduced by is described inSection 8.2. The device dc power dissipation is also part of this trade-off since

and increases as the bias current increases. This trade-off allowssmaller to be used for a given value of T with improved noise performance.Note that the input resistance of this stage is now quite large and will generallynot meet matching requirements.

Single-stage feedback can also be implemented in the form of shunt feedbackas shown in Figure 8.20. The shunt feedback stage has low input and outputimpedances and is not suitable for cascading. It can be used as a stand-alone sin-gle stage and if parasitic capacitances are neglected, we find the transimpedancegain is


From (8.59), we see that the gain–bandwidth product is

Thus, gain and bandwidth can be traded using the value of The inputimpedance is given by

The input impedance is usually dominated by the last term in (8.61) and islow. Thus, this stage is well suited to current amplification and is often used inthat role.

The noise performance of the shunt feedback stage of Figure 8.20 is easilyestimated by recognizing that a shunt feedback resistor such as contributesto the equivalent input current noise generator

Thus, as the stage is broadbanded by reducing the equivalent input noisecurrent increases. This trade-off is well known to designers of high-speedwideband current amplifiers such as are used in fiber-optic receivers [10,11].

246 Chapter 8

The single-stage feedback circuits described above can be used in mis-matched cascades to form wideband voltage or current amplifiers using twostages as shown in Figure 8.21 [12]. Transimpedance and transresistanceamplifiers can be implemented by adding additional stages. The advantageof the configurations of Figure 8.21 is the minimal interaction between stagesand the dependence of the gain solely on resistor ratios for large values of loopgain T.

The single-stage feedback amplifiers considered so far do not allow realiza-tion of low-noise wideband matched-impedance amplifiers. This function can,however, be achieved by appropriate use of multiple feedback loops. Considera single-stage dual-feedback amplifier as shown in Figure 8.22. We assume


and we find if In a matched amplifier we setThe gain is then given by

The – 3 dB bandwidth is set by the time constant of and (the impedancelevel at the input node) giving

Thus the gain–bandwidth of the stage is

using (8.63), (8.66) and (8.67). We can thus realize a matched impedanceamplifier and trade gain for bandwidth using resistor values.

The advantages of the circuit of Figure 8.22 are further evident when weexamine the noise performance. If the basic active device has equivalent inputnoise generators and then the addition of resistors and modifythese to

The noise figure of the amplifier can now be calculated as

If and the input impedance can be approximated bya parallel RC combination with values

The output resistance is approximately

248 Chapter 8

We see that the noise figure is degraded by an additive factor ofand this can be made a reasonably small contribution. For example, if

and then the amplifier gain is G = 5,bandwidth and If the basic device noisefigure is 2 dB (8.58), then the overall amplifier noise figure is 1.58+0.2 = 1.78which is 2.5 dB. The addition of the matching resistors has only degraded thedevice noise figure by 0.5 dB.

8.3.3. Use of Multi-Stage Feedback to Trade-Off Gain,Bandwidth and Noise Performance

The single-stage feedback circuits described above are widely used in prac-tice because of their ease of design and good overall performance. However,higher levels of performance can be achieved (higher gain and bandwidth andlower noise) if we allow use of feedback over multiple stages. The price paidfor this improved performance is increased complexity of design and, in partic-ular, the possibility of oscillation [13] which must be addressed by appropriatecircuit compensation.

Consider the two-stage shunt–series feedback amplifier in Figure 8.23[9–11,14,15]. This circuit has low input impedance, high output impedanceand a well-stabilized current gain given by

for high loop gain. This is called a current-feedback pair.The gain–bandwidth trade-off in this circuit can be calculated from the small-

signal equivalent circuit of Figure 8.24. The feedback current is given by

The feedback loading on the input is and this is lumped in withto form The input resistance and capacitance of the second stage are


and respectively and are given by

and

for Resistors and are lumped to form Feedbackcapacitor includes the inherent feedback capacitance of the input deviceplus any added capacitance used for frequency compensation.

The forward path gain function of the amplifier is [2]

If and then

and Note that as is made larger, the dominant pole decreasesin magnitude and increases while the product is constant.

250 Chapter 8

The frequency response of the circuit can be estimated using the rootlocus [13] of Figure 8.25. As the loop gain is increased from zero, the polesof the circuit transfer function come together and then split out in the s -plane.We assume the loop gain is adjusted to give pole positions as shown at AA atangles of 45° to the real axis. This gives a maximally flat frequency response(no peaking) and a circuit – 3 dB bandwidth equal to the distance from A tothe origin. If this is Thus the bandwidth of the circuit is

These pole positions give the maximum possible gain–bandwidth without peak-ing and are set by manipulating the loop gain and the compensation capacitor

Note that a similar compensation function can be achieved by a capacitorconnected across The loop gain required to set the poles in the positionAA is [13]

The mid-band forward gain (current gain) is given by

From (8.80), we have


where has been used. In practice, parasiticcapacitance shunting at the internal node will cause a degradation of devicefrequency capability and (8.84) becomes where is theeffective value of which is realized in practice with parasitic capacitanceincluded.

The mid-band forward gain of the circuit (current gain) with feedbackapplied is

Using the multistage gain–bandwidth figure-of-merit defined in (8.10), we find

using (8.88) and (8.81). Thus, for this two-stage feedback connection, the fulldevice gain–bandwidth per stage is preserved. This is a significant advantagewhen compared to the gain–bandwidth shrinkage experienced in a cascade oftwo single stages.

The noise performance of the two-stage amplifier is simply that of the ampli-fier input device with the addition of thermal noise due tothe feedback resistor. However, due to the extra gain–bandwidth available inthe two-stage configuration compared with a single-stage cascade, we find thatlarger values of can be used in the two-stage amplifier, giving improvednoise performance. It should also be noted that the compensation capacitordoes not appreciably degrade the circuit noise performance as long as

A two-stage feedback voltage amplifier can be realized using the series–shunt configuration of Figure 8.26. The series feedback at the input gives thestage a high input impedance while the shunt feedback at the output producesa low output impedance. For large loop gain, the overall voltage gain is set by

Substituting (8.84) and (8.82) in (8.86), we find

252 Chapter 8

resistor ratios and is

If the gain–bandwidth product is again given by (8.89), where G isnow the amplifier voltage gain. In this case, the noise performance is that ofthe input device with an addition of to the equivalent inputnoise voltage.

Finally, in the realm of two-stage feedback amplifiers, we examine the two-stage dual-feedback amplifier shown in Figure 8.27 [16–19]. This is derived byanalogy and extension from the single-stage version in Figure 8.22 and incorpo-rates both series–shunt and shunt–series feedback loops. Like the single-stageversion of Figure 8.22, the circuit of Figure 8.27 gives excellent gain–bandwidthperformance while simultaneously allowing realization of matched terminalimpedances with good noise performance. A simplified small-signal equivalentcircuit of the amplifier in Figure 8.27 is shown in Figure 8.28 where


and

The circuit of Figure 8.28 can be manipulated into the equivalent form ofFigure 8.29 where

and it is assumed that andThe circuit of Figure 8.29 is in the form of the ideal feedback configuration

of Figure 8.15. The total feedback voltage is

where has been used and assumed. The voltagegain from to is set by the series–shunt feedback loop and is given by

254 Chapter 8

If the input resistance seen at is set to match then the voltage gain

The input resistance seen at can be estimated by a resistive Millerapproximation

where

from is

If then substitution of (8.103) in (8.102) gives


For we require

Note that in (8.99) this implies that the influence of both feedback loops isequal.

The output resistance can be estimated by driving the output node with a testvoltage and calculating the current response. This gives

Again, if (8.105) holds, then and we have both input andoutput ports matched. This circuit has the advantage that since and

the input and output ports retain their impedance matches for a rangeof system impedances [19] (unlike the single-stage dual-feedback circuit where

andFurther advantages of the two-stage dual feedback configuration are

improved noise performance and gain–bandwidth. A calculation similar tothat for the current feedback pair shows that the gain–bandwidth of this cir-cuit is also so that can be traded for bandwidth. The noiseperformance is functionally the same as the single-stage dual feedback config-uration except that with two-stage feedback, the values of and (whichcontribute to the equivalent input noise) can be made smaller and larger respec-tively, due to the larger loop gain of the two-stage configuration. Thus, theirnoise contributions can be made lower.

References

[1]

[2]

[3]

[4]

[5]

[6]

P. R. Gray and R. G. Meyer. Analysis and Design of Analog IntegratedCircuits, 3rd edn, Wiley, New York, 1993, Ch. 1.

P. R. Gray and R. G. Meyer, op. cit., Ch. 7.


R. G. Meyer and W. D. Mack, “A 1-GHz BiCMOS RF front–end IC”,IEEE Journal of Solid–State Circuits, vol. 29, no. 3, pp. 350–355, March1994.

N. Nguyen and R. G. Meyer, “Si IC-compatible inductors and LC passivefilters”, IEEE Journal of Solid-State Circuits, vol. 25, no. 4, pp. 1028-1031, August 1990.

R. G. Meyer, W. D. Mack and H. Hageraats, “A 2.5 GHz BiCMOS trans-ceiver for wireless LAN”, IEEE Journal of Solid-State Circuits, vol. 32,no. 12, pp. 2097–2104, December 1997.

256 Chapter 8

[7]

[8]

[9][10]

[11]

[12]

[13][14]

[15]

[16]

[17]

[18]

[19]

A. M. Niknejad and R. G. Meyer, “Analysis, design and optimization ofspiral inductors and transformers for RF ICs”, IEEE Journal of Solid-StateCircuits, vol. 33, no. 10, pp. 1470–1481, October 1998.

C. D. Hull and R. G. Meyer, “Principles of wideband monolithic feedbackamplifier design”, International Journal of High Speed Electronics, vol. 3,no. 1, pp. 53–93, March 1992.


Philips Semiconductors SA 5212 Data Sheet.

R. G. Meyer and R. A. Blauschild, “A wideband low-noise mono-lithic transimpedance amplifier”, IEEE Journal of Solid-State Circuits,vol. SC-21, no. 4, pp. 530–533, August 1986.

E. M. Cherry and D. E. Hooper, Amplifying Devices and Low-PassAmplifier Design. New York: Wiley, 1968.


R. G. Meyer and W. D. Mack, “A wideband low-noise variable-gain BiCMOS transimpedance amplifier”, IEEE Journal of Solid-StateCircuits, vol. 29, no. 6, pp. 701–706, June 1994.

Philips Semiconductors SA5223 Data Sheet.

R. G. Meyer, R. Eschenbach and R. Chin, “A wide-band ultralinear ampli-fier from 3 to 300 MHz”, IEEE Journal of Solid-State Circuits, vol. SC-9,no. 4, pp. 167–175, August 1974.

K. H. Chan and R. G. Meyer, “A low-distortion monolithic widebandamplifier”, IEEE Journal of Solid-State Circuits, vol. SC-12, no. 6,pp. 685–690, December 1977.

R. G. Meyer and R. A. Blauschild, “A four-terminal wideband mono-lithic amplifier”, IEEE Journal of Solid-State Circuits, vol. SC-16, no. 6,pp. 634–638, December 1981.

Philips Semiconductors SA 5205 Data Sheet.

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