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 11.62P

Consider the diff-amp shown in Figure P 11.62 . The circuit parameters are V + = 3 V , V = 3 V , and I Q = 0.4 mA . The npn transistor parameters are β npn = 180 , V B E ( on ) = 0.7 V , and V A N = 120 V , and the pnp transistor parameters are β pnp = 120 , V E B ( on ) = 0.7 V , and V A P = 80 V Sketch the small-signal equivalent circuit for the diff-amp assuming an ideal differential-mode input signal. (b) Determine the one-sided differential-mode gain A d 1 = Δ v O 1 / v d . (c) Determine the one-sided differential mode gain A d 2 = Δ v O 2 / v d . (d) Find the two-sided differential-mode gain A d 3 = Δ ( v O 2 v O 1 ) / v d .

(a)

Expert Solution
Check Mark
To determine

To sketch: The small signal equivalent circuit for the differential amplifier.

Answer to Problem 11.62P

The small signal circuit is shown in Figure 2.

Explanation of Solution

Given:

The given circuit is shown below.

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.62P , additional homework tip  1

Calculation:

The small signal equivalent circuit for the above circuit is shown in Figure 1.

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.62P , additional homework tip  2

Figure 1

Because of symmetry the value of the currents IEQ1 , IEQ2 are given by,

  IE=IQ2=0.4mA2=0.2mA

The value of the currents ICQ1=ICQ2 which are equal to IC1 and is given by,

  IC1=βm1+βmIE1=1801+180(0.2mA)0.2mA

The value of the currents IEQ4=IEQ4 which are equal to IC1 and is given by,

  IEQ4,IEQ4=0.2mA

The value of the currents ICQ3=ICQ4 which are equal to IC1 and is given by,

  ICQ3=ICQ4=IE2βmpβmp+1=120121(0.2mA)0.2mA

For differential up circuit emitter current Q1 or Q2 is grounded in incremental circuit because of the symmetry of the circuit.

Modify the circuit, the required diagram is shown in Figure 2

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.62P , additional homework tip  3

Figure 2

Conclusion:

Therefore, the small signal circuit is shown in Figure 3

(b)

Expert Solution
Check Mark
To determine

The value of one sided differential voltage gain.

Answer to Problem 11.62P

The value of the differential mode voltage gain is 0.4996 .

Explanation of Solution

Given:

The given circuit is shown below.

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.62P , additional homework tip  4Calculation:

Consider the left portion of the circuit as,

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.62P , additional homework tip  5

Figure 3

Modify the circuit as shown in Figure 4

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.62P , additional homework tip  6

Figure 4

The expression for the output voltage of the above circuit is given by,

  vO=(gm1Vπ1+gm3Vπ2)(rO1||rO3||rπ3)=[gm1(vd2)+gm3vO1][11rO1+1rO3+1rπ3]

The emitter current of the transistor is calculated as,

  IE1=IQ2=0.4mA2=0.2mA

The expression for the collector current of the transistor IC1 is evaluated as,

  IE1=IC1+IB1IE1=IC1+IC1βnpnIC1=(βnpn1+βnpn)IE1

Substitute 180 for βnpn and 0.2mA for IE1 in the above equation.

  IC1=(1801+180)0.2mA=0.1989mA

Apply KCL at the output node vO1 .

  IC1=IC3+IB3IC1=IC3+IC1βpnpIC3=(βpnpβpnp+1)IC1

Substitute 120 for βpnp and 0.1989mA for IC1 in the above equation. βpnp

  IC3=(120120+1)0.1989mAIC3=0.1973mA

The transconductance of transistor Q1 is calculated as,

  gm1=IC10.026V=0.1989mA0.026V=7.956mA/V

The transconductance of transistor Q3 is calculated as,

  gm3=IC30.026V=0.1973mA0.026V=7.892mA/V

The small signal output resistance of Q1 is calculated as,

  rO1=VABIC1=120V0.1989mA=603.3182kΩ

The small signal output resistance of Q3 is calculated as,

  rO3=VAPIC3=80V0.1973mA=405.4739kΩ

The small signal resistance rπ3 is calculated as,

  rπ3=VTβpnpIC3=(120)(0.026V)0.1973mA=15.2052kΩ

The value of the voltage vO1 is calculated as,

  vO1=[(7.965mA/V)(vd2)+(7.892mA/V)vO1][11603.3182kΩ+14.5.4739+115.2052kΩ]113.9219vO1=56.9188vO1vd=0.4996

Conclusion:

Therefore, the value of the differential mode voltage gain is 0.4996 .

(c)

Expert Solution
Check Mark
To determine

The differential voltage gain of both the sides.

Answer to Problem 11.62P

The value of differential voltage gain is 0.4996 .

Explanation of Solution

Given:

The given circuit is shown below.

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.62P , additional homework tip  7

Calculation:

The expression for the output voltage of the above circuit is given by,

  vO2=(gm1Vπ1+gm3Vπ2)(rO1||rO3||rπ3)=[gm2(vd2)+gm34vO1][11rO2+1rO4+1rπ4]

The value of the voltage vO1 is calculated as,

  vO1=[(7.965mA/V)(vd2)+(7.892mA/V)vO1][11603.3182kΩ+14.5.4739+115.2052kΩ]113.9219vO1=56.9188vO1vd=0.4996

Conclusion:

Therefore, the value of differential voltage gain is 0.4996 .

(d)

Expert Solution
Check Mark
To determine

The value of the differential voltage gain of both the sides.

Answer to Problem 11.62P

The value of differential voltage gain is 0.9992 .

Explanation of Solution

Given:

The given circuit is shown below.

  Microelectronics: Circuit Analysis and Design, Chapter 11, Problem 11.62P , additional homework tip  8

Calculation:

The expression to determine the value of the two sided differential voltage gain is given by,

  Ad3=Δ(vO2vO1)vd=ΔvO2vd0ΔvO1vd=0.4996(0.4996)=0.9992

Conclusion:

Therefore, the value of differential voltage gain is 0.9992 .

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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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Differential Amplifiers Made Easy; Author: The AudioPhool;https://www.youtube.com/watch?v=Mcxpn2HMgtU;License: Standard Youtube License