Microelectronics: Circuit Analysis and Design
Microelectronics: Circuit Analysis and Design
4th Edition
ISBN: 9780073380643
Author: Donald A. Neamen
Publisher: McGraw-Hill Companies, The
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Chapter 11, Problem 11.84P

a.

To determine

The small-signal voltage gain Av=vo/vi and the output resistance Ro for the given circuit.

a.

Expert Solution
Check Mark

Answer to Problem 11.84P

  Av=30053Ro=192.2MΩ

Explanation of Solution

Given:

The given circuit is,

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.84P , additional homework tip  1

  IQ=25μA,β=100VA=50V,VTN=0.8V,Kn=0.25mA/V2,λ=0.02V1

The two amplifying transistors M1andQ1 are biased in the saturation region and forward-active region.

Calculation:

Consider the given figure,

  Ic=IQ=25μA,

Now find trans-conductance,

  gm2=IcVT=25×10626×103gm2=0.9615mA/VNowfindrπ,rπ=βVTIc=(100)26×10325×106rπ=104kΩnowgm1gm1=2kpIQgm1=20.25×103(25×106)gm1=0.158mA/V

Now calculate r01,r02 ,

  r01=1λIQ=1(0.02)25μAr01=2MΩr02=VAIQ=5025μAr02=2MΩ

Now consider small-signal equivalent circuit,

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.84P , additional homework tip  2

Apply nodal method at node Vπ ,

  VπrπVπr01+gm1Vi=0Vπ=(rπr01gm1rπ+r01)ViPutthevalues,Vπ=((104×103)(2×106)(0.158×103)(104×103)+(2×106))ViVπ=15.62Vi

Now apply nodal method at node Vo ,

  Vo(Vπ)r02gm2Vπ=0Vo(1r02)+Vπ(1r02+gm2)=0Putthevalues,Vo(12×106)+15.62Vi(12×106+0.9615×103)=0Vo=30053ViAv=30053

Now consider,

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.84P , additional homework tip  3

Find Vπ ,

  Vπ=Ix(r01||rπ)Vπ=Ix(r01rπr01+rπ)Vπ=Ix((2×106)(104×103)(2×106)+(104×103))Vπ=9868×103Ix

Apply nodal analysis at node Vx ,

  Ix=gm2Vπ+Vx(Vπ)r02Ix=gm2Vπ+Vx+Vπr02Ix=(0.9615×103)(98.86×103)Ix+Vx(98.86×103)Ix(2×106)VxIx=Ro=96.1(2×106)Ro=192.2MΩ

Hence,

  Av=30053Ro=192.2MΩ

b.

To determine

The small-signal voltage gain Av=vo/vi and the output resistance Ro for the given circuit.

b.

Expert Solution
Check Mark

Answer to Problem 11.84P

  Av=5.80×107Ro=192.2MΩ

Explanation of Solution

Given:

The given circuit is,

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.84P , additional homework tip  4

  IQ=25μA,β=100VA=50V,VTN=0.8V,Kn=0.25mA/V2,λ=0.02V1

The two amplifying transistors M1andQ1 are biased in the saturation region and forward-active region.

Calculation:

Consider the given figure,

  Ic=IQ=25μA,

Now find trans-conductance,

  gm1=IcVT=25×10626×103gm1=0.9615mA/Vgm1=gm2=0.9615mA/VNowfindrπ,forQ1rπ1=βVTIc=(100)26×10325×106rπ1=104kΩrπ1=rπ2=104kΩ

Now,

  gm3=2kpIQgm3=20.25×103(25×106)gm3=0.158mA/V

  r03=1λIQr03=10.02(25×106)r03=2MΩr01=VAIQr01=50(25×106)r01=2MΩr01=r02=2MΩ

Now consider circuit,

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.84P , additional homework tip  5

Apply nodal at top part of the circuit,

  Vo(Vgs)r03gm3Vgs=0Vo(1r03)=+Vgs(1r03+gm3)Vgs=(11+gm3r03)Voputthevalues,Vgs=(11+(0.158×103)2×106)VoVgs=Vo/317

Apply nodal at middle part of the circuit,

  Vgs(Vπ2)r02gm2Vπ2=0Vgs(1r02)+Vπ2(1r02+gm2)=0Vπ2=(11+gm2r02)Vgsputthevalues,Vπ2=(11+0.9615×103(2×106))(Vo317)Vπ2=Vo/725348

  Vo=117.28×107ViVπ=1923ViVgs=3699852Vi

  Av=Vo/ViAv=5.80×107

Find Vπ ,

  Vπ=Ix(r01||rπ)Vπ=Ix(r01rπr01+rπ)Vπ=Ix((2×106)(104×103)(2×106)+(104×103))Vπ=9868×103Ix

Apply nodal analysis at node Vx ,

  Ix=gm2Vπ+Vx(Vπ)r02Ix=gm2Vπ+Vx+Vπr02Ix=(0.9615×103)(98.86×103)Ix+Vx(98.86×103)Ix(2×106)VxIx=Ro=96.1(2×106)Ro=192.2MΩ

Hence,

  Av=5.80×107Ro=192.2MΩ

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Chapter 11 Solutions

Microelectronics: Circuit Analysis and Design

Ch. 11 - Prob. 11.7EPCh. 11 - Prob. 11.4TYUCh. 11 - Prob. 11.5TYUCh. 11 - The parameters of the diff-amp shown in Figure...Ch. 11 - For the differential amplifier in Figure 11.20,...Ch. 11 - The parameters of the circuit shown in Figure...Ch. 11 - The circuit parameters of the diff-amp shown in...Ch. 11 - Consider the differential amplifier in Figure...Ch. 11 - The diff-amp in Figure 11.19 is biased at IQ=100A....Ch. 11 - Prob. 11.10TYUCh. 11 - The diff-amp circuit in Figure 11.30 is biased at...Ch. 11 - Prob. 11.11EPCh. 11 - Prob. 11.12EPCh. 11 - Prob. 11.11TYUCh. 11 - Prob. 11.12TYUCh. 11 - Redesign the circuit in Figure 11.30 using a...Ch. 11 - Prob. 11.14TYUCh. 11 - Prob. 11.15TYUCh. 11 - Prob. 11.16TYUCh. 11 - Prob. 11.17TYUCh. 11 - Consider the Darlington pair Q6 and Q7 in Figure...Ch. 11 - Prob. 11.14EPCh. 11 - Consider the Darlington pair and emitter-follower...Ch. 11 - Prob. 11.19TYUCh. 11 - Prob. 11.15EPCh. 11 - Consider the simple bipolar op-amp circuit in...Ch. 11 - Prob. 11.17EPCh. 11 - Define differential-mode and common-mode input...Ch. 11 - Prob. 2RQCh. 11 - From the dc transfer characteristics,...Ch. 11 - What is meant by matched transistors and why are...Ch. 11 - Prob. 5RQCh. 11 - Explain how a common-mode output signal is...Ch. 11 - Define the common-mode rejection ratio, CMRR. What...Ch. 11 - What design criteria will yield a large value of...Ch. 11 - Prob. 9RQCh. 11 - Define differential-mode and common-mode input...Ch. 11 - Sketch the de transfer characteristics of a MOSFET...Ch. 11 - Sketch and describe the advantages of a MOSFET...Ch. 11 - Prob. 13RQCh. 11 - Prob. 14RQCh. 11 - Describe the loading effects of connecting a...Ch. 11 - Prob. 16RQCh. 11 - Prob. 17RQCh. 11 - Prob. 18RQCh. 11 - (a) A differential-amplifier has a...Ch. 11 - Prob. 11.2PCh. 11 - Consider the differential amplifier shown in...Ch. 11 - Prob. 11.4PCh. 11 - Prob. D11.5PCh. 11 - The diff-amp in Figure 11.3 of the text has...Ch. 11 - The diff-amp configuration shown in Figure P11.7...Ch. 11 - Consider the circuit in Figure P11.8, with...Ch. 11 - The transistor parameters for the circuit in...Ch. 11 - Prob. 11.10PCh. 11 - Prob. 11.11PCh. 11 - The circuit and transistor parameters for the...Ch. 11 - Prob. 11.13PCh. 11 - Consider the differential amplifier shown in...Ch. 11 - Consider the circuit in Figure P11.15. The...Ch. 11 - Prob. 11.16PCh. 11 - Prob. 11.17PCh. 11 - For the diff-amp in Figure 11.2, determine the...Ch. 11 - Prob. 11.19PCh. 11 - Prob. D11.20PCh. 11 - Prob. 11.21PCh. 11 - The circuit parameters of the diff-amp shown in...Ch. 11 - Consider the circuit in Figure P11.23. Assume the...Ch. 11 - Prob. 11.24PCh. 11 - Consider the small-signal equivalent circuit of...Ch. 11 - Prob. D11.26PCh. 11 - Prob. 11.27PCh. 11 - A diff-amp is biased with a constant-current...Ch. 11 - The transistor parameters for the circuit shown in...Ch. 11 - Prob. D11.30PCh. 11 - For the differential amplifier in Figure P 11.31...Ch. 11 - Prob. 11.32PCh. 11 - Prob. 11.33PCh. 11 - Prob. 11.34PCh. 11 - Prob. 11.35PCh. 11 - Prob. 11.36PCh. 11 - Consider the normalized de transfer...Ch. 11 - Prob. 11.38PCh. 11 - Consider the circuit shown in Figure P 11.39 . The...Ch. 11 - Prob. 11.40PCh. 11 - Prob. 11.41PCh. 11 - Prob. 11.42PCh. 11 - Prob. 11.43PCh. 11 - Prob. D11.44PCh. 11 - Prob. D11.45PCh. 11 - Prob. 11.46PCh. 11 - Consider the circuit shown in Figure P 11.47 ....Ch. 11 - Prob. 11.48PCh. 11 - Prob. 11.49PCh. 11 - Prob. 11.50PCh. 11 - Consider the MOSFET diff-amp with the...Ch. 11 - Consider the bridge circuit and diff-amp described...Ch. 11 - Prob. D11.53PCh. 11 - Prob. 11.54PCh. 11 - Prob. 11.55PCh. 11 - Consider the JFET diff-amp shown in Figure P11.56....Ch. 11 - Prob. 11.57PCh. 11 - Prob. 11.58PCh. 11 - Prob. D11.59PCh. 11 - The differential amplifier shown in Figure P 11.60...Ch. 11 - Prob. 11.61PCh. 11 - Consider the diff-amp shown in Figure P 11.62 ....Ch. 11 - Prob. 11.63PCh. 11 - The differential amplifier in Figure P11.64 has a...Ch. 11 - Prob. 11.65PCh. 11 - Consider the diff-amp with active load in Figure...Ch. 11 - The diff-amp in Figure P 11.67 has a...Ch. 11 - Consider the diff-amp in Figure P11.68. The PMOS...Ch. 11 - Prob. 11.69PCh. 11 - Prob. 11.70PCh. 11 - Prob. D11.71PCh. 11 - Prob. D11.72PCh. 11 - An all-CMOS diff-amp, including the current source...Ch. 11 - Prob. D11.74PCh. 11 - Consider the fully cascoded diff-amp in Figure...Ch. 11 - Consider the diff-amp that was shown in Figure...Ch. 11 - Prob. 11.77PCh. 11 - Prob. 11.78PCh. 11 - Prob. 11.79PCh. 11 - Prob. 11.80PCh. 11 - Consider the BiCMOS diff-amp in Figure 11.44 ,...Ch. 11 - The BiCMOS circuit shown in Figure P11.82 is...Ch. 11 - Prob. 11.83PCh. 11 - Prob. 11.84PCh. 11 - For the circuit shown in Figure P11.85, determine...Ch. 11 - The output stage in the circuit shown in Figure P...Ch. 11 - Prob. 11.87PCh. 11 - Consider the circuit in Figure P11.88. The bias...Ch. 11 - Prob. 11.89PCh. 11 - Consider the multistage bipolar circuit in Figure...Ch. 11 - Prob. D11.91PCh. 11 - Prob. 11.92PCh. 11 - For the transistors in the circuit in Figure...Ch. 11 - Prob. 11.94PCh. 11 - Prob. 11.95PCh. 11 - Prob. 11.96PCh. 11 - Consider the diff-amp in Figure 11.55 . The...Ch. 11 - The transistor parameters for the circuit in...
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