Microelectronics: Circuit Analysis and Design
Microelectronics: Circuit Analysis and Design
4th Edition
ISBN: 9780073380643
Author: Donald A. Neamen
Publisher: McGraw-Hill Companies, The
bartleby

Videos

Textbook Question
Book Icon
Chapter 7, Problem 7.23P

Consider the circuit shown in Figure P7.23. (a) Write the transfer function T ( s ) = V o ( s ) / V i ( s ) . Assume λ = 0 for the transistor. (b) Determine the expression for the time constant associated with the input portion of the circuit. (c) Determine the expression for the time constant associated with theoutput portion of the circuit.

Chapter 7, Problem 7.23P, Consider the circuit shown in Figure P7.23. (a) Write the transfer function T(s)=Vo(s)/Vi(s) .
Figure P7.23

a.

Expert Solution
Check Mark
To determine

The transfer function T(s)=Vo(s)/Vi(s) .

Answer to Problem 7.23P

The expression for transfer function of the circuit is,

  T(s)=(gm1+gmRs)1[1+s(1gmRs)Ci][sRDRLCCs(RD+RL)CC+1] .

Explanation of Solution

Given:

The circuit is given as:

  Microelectronics: Circuit Analysis and Design, Chapter 7, Problem 7.23P , additional homework tip  1

Calculation:

Refer to the given circuit:

Drawing the small signal equivalent circuit using the simplified hybrid π model:

  Microelectronics: Circuit Analysis and Design, Chapter 7, Problem 7.23P , additional homework tip  2

Now drawing the frequency domain equivalent circuit of above figure:

  Microelectronics: Circuit Analysis and Design, Chapter 7, Problem 7.23P , additional homework tip  3

Applying the nodal analysis to derive the expression for Vgs(s)Vi(s) associated with the input portion of the circuit:

  Vgs(s)Vi(s)RS+Vgs(s)1sCigmVgs(s)=0Vgs(s)[1RS+sCi+gm]Vi(s)Rs=0Vgs(s)Vi(s)=1RS[1RS+sCi+gm]=11+Rs(gm+sCi)=1gm1gm+Rs1gm(gm+sCi)Vgs(s)Vi(s)=1gm1gm+Rs+s1gmRsCi............(1)

Solving the above equation:

  Vgs(s)Vi(s)=((1gm)1gm+Rs)1(1+s(1gm)Rs1gm+RsCi)=((1gm)1gm+Rs)1[1+s(1gmRs)Ci]

Applying the Kirchhoff s current law at node V1(s) :

  gmVgs(s)+V1(s)V0(s)1sCC+V1(s)RD=0gmVgs(s)+[1RD+sCC]V1(s)sCCV0(s)=0..........(2)

Applying the Kirchhoff s current law at output node:

  V0(s)V1(s)1sCC+V0(s)RL=0V0(s)[sCC+1RL]=sCCV1(s)V1(s)=V0(s)1sCC[sCC+1RL]V1(s)=[1+1sCCRL]V0(s)

Evaluating the expression for V0(s)Vgs(s) associated with the output portion of the circuit:

Substituting [1+1sCCRL]V0(s) for V1(s) in equation (2):

  gmVgs(s)+[1RD+sCC][1+1sCCRL]V0(s)sCCV0(s)=0gmVgs(s)+[1RD+1sCCRDRL+sCC+1RL]V0(s)sCCV0(s)=0gmVgs(s)+[1RD+1sCCRDRL+1RL]V0(s)=01RDRL[RL+1sCC+RD]V0(s)=gmVgs(s)V0(s)=gmVgs(s)RDRL[RL+1sCC+RD]V0(s)Vgs(s)=gmRLRDRD+RL+1sCC

The expression for transfer function of the circuit is given as:

  V0(s)Vi(s)=V0(s)Vgs(s)×Vgs(s)Vi(s)

  =[gmRLRDRD+RL+1sCC](1gm1gm+Rs)1[1+s(1gmRs)Ci]=(11gm+Rs)1[1+s(1gmRs)Ci][sRDRLCCs(RD+RL)CC+1]V0(s)Vi(s)=(gm1+gmRs)1[1+s(1gmRs)Ci][sRDRLCCs(RD+RL)CC+1](RD+RL)(RD+RL)

Solving the above equation:

  V0(s)Vi(s)=(gm1+gmRs)1[1+s(1gmRs)Ci][sRDRLCCs(RD+RL)CC+1](RD+RL)(RD+RL)T(s)=(gm1+gmRs)1[1+s(1gmRs)Ci][sRDRLCCs(RD+RL)CC+1](RDRL)=(gm(RDRL)1+gmRs)1[1+s(1gmRs)Ci][s(RD+RL)CC1+s(RD+RL)CC]=(gm(RDRL)1+gmRs)1[1+sτi][sτc1+sτc]

So,

  τc=(RD+RL)CCandτi=(1gmRs)Ci....................(3)

Therefore, the expression for transfer function of the circuit is,

  T(s)=(gm1+gmRs)1[1+s(1gmRs)Ci][sRDRLCCs(RD+RL)CC+1] .

b.

Expert Solution
Check Mark
To determine

The expression for the time constant associating with the input portion of the circuit.

Answer to Problem 7.23P

The expression of the time constant associated with the input portion of the circuit:

  τi is (1gmRs)Ci

Explanation of Solution

Given:

The circuit is given as:

  Microelectronics: Circuit Analysis and Design, Chapter 7, Problem 7.23P , additional homework tip  4

Calculation:

Evaluating the expression for the time constant associated with the input portion of the circuit.

From the equation (3) , the time constant associated with the input portion of the circuit is,

  τi=(1gmRs)Ci

Hence, the expression of the time constant associated with the input portion of the circuit . τi is (1gmRs)Ci .

c.

Expert Solution
Check Mark
To determine

The expression for the time constant associating with the output portion of the circuit.

Answer to Problem 7.23P

The expression of the time constant associated with the output portion of the circuit:

  τc=(RD+RL)CC

Explanation of Solution

Given:

The circuit is given as:

  Microelectronics: Circuit Analysis and Design, Chapter 7, Problem 7.23P , additional homework tip  5

Calculation:

Evaluating the expression for the time constant associated with the input portion of the circuit.

From equation (3), the time constant associated with the input portion of the circuit is expressed as:

  τc=(RD+RL)CC

Therefore, the expression for the time constant associated with the output portion of the circuit: τc=(RD+RL)CC .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Q2. Consider the circuit shown in Figure P7.15. The transistor has parameters B = 120 and VA collector-emitter voltage is VCEO = 1.25 V. (a) Determine Rc, (b) find Ico, and (c) determine the maximum gain. = ∞. The circuit bandwidth is 800 MHz and the quiescent Vcc= 2.5 V RC CL = 0.08 pF Figure P7.15
(a) Design the circuit shown in Figure P7.18 such that Ipo = 0.8 mA, VDsQ = 3.2 V, Rin K, = 0.5 mA/V², VTN = 1.2 V, and A = 0. (b) What is the midband volt- age gain? (c) Determine the magnitude of the voltage gain at (i) f = 5 Hz, (ii) f = 14 Hz, and (iii) f = 25 Hz. (d) Sketch the Bode plot of the voltage gain magnitude and phase. 160 k2, and fr 16 Hz. The transistor parameters are ass VDD =9 V Rp R1 Rin 1 O vO Cc Rs = 0.5 k2 R2 Figure P7.18 ww ww
Problem 7.133(a): For the circuit shown below, let R1 = 106 kN, Rsig = 69 N, and RL Rsig. Assume that %3D 13 kN. Find the value of the bias current I in mA that results in Rin the source provides a small signal vsie and that B = 100. H RL R1 Rsig Ria 8

Chapter 7 Solutions

Microelectronics: Circuit Analysis and Design

Ch. 7 - The commonemitter circuit shown in Figure 7.34...Ch. 7 - A bipolar transistor has parameters o=120 ,...Ch. 7 - Prob. 7.9EPCh. 7 - For the circuit in Figure 7.41(a), the parameters...Ch. 7 - A bipolar transistor is biased at ICQ=120A and its...Ch. 7 - For the transistor described in Example 7.9 and...Ch. 7 - The parameters of a bipolar transistor are: o=150...Ch. 7 - The parameters of an nchannel MOSFET are...Ch. 7 - For the circuit in Figure 7.55, the transistor...Ch. 7 - An nchannel MOSFET has parameters Kn=0.4mA/V2 ,...Ch. 7 - An nchannel MOSFET has a unitygain bandwidth of...Ch. 7 - For a MOSFET, assume that gm=1.2mA/V . The basic...Ch. 7 - The transistor in the circuit in Figure 7.60 has...Ch. 7 - Consider the commonbase circuit in Figure 7.64....Ch. 7 - The cascode circuit in Figure 7.65 has parameters...Ch. 7 - Prob. 7.12TYUCh. 7 - For the circuit in Figure 7.72, the transistor...Ch. 7 - Describe the general frequency response of an...Ch. 7 - Describe the general characteristics of the...Ch. 7 - Describe what is meant by a system transfer...Ch. 7 - What is the criterion that defines a corner, or...Ch. 7 - Describe what is meant by the phase of the...Ch. 7 - Describe the time constant technique for...Ch. 7 - Describe the general frequency response of a...Ch. 7 - Sketch the expanded hybrid model of the BJT.Ch. 7 - Prob. 9RQCh. 7 - Prob. 10RQCh. 7 - Prob. 11RQCh. 7 - Sketch the expanded smallsignal equivalent circuit...Ch. 7 - Define the cutoff frequency for a MOSFET.Ch. 7 - Prob. 14RQCh. 7 - Why is there not a Miller effect in a commonbase...Ch. 7 - Describe the configuration of a cascode amplifier.Ch. 7 - Why is the bandwidth of a cascode amplifier...Ch. 7 - Why is the bandwidth of the emitterfollower...Ch. 7 - Prob. 7.1PCh. 7 - Prob. 7.2PCh. 7 - Consider the circuit in Figure P7.3. (a) Derive...Ch. 7 - Consider the circuit in Figure P7.4 with a signal...Ch. 7 - Consider the circuit shown in Figure P7.5. (a)...Ch. 7 - A voltage transfer function is given by...Ch. 7 - Sketch the Bode magnitude plots for the following...Ch. 7 - (a) Determine the transfer function corresponding...Ch. 7 - Consider the circuit shown in Figure 7.15 with...Ch. 7 - For the circuit shown in Figure P7.12, the...Ch. 7 - The circuit shown in Figure 7.10 has parameters...Ch. 7 - The transistor shown in Figure P7.14 has...Ch. 7 - Consider the circuit shown in Figure P7.15. The...Ch. 7 - The transistor in the circuit shown in Figure...Ch. 7 - For the common-emitter circuit in Figure P7.17,...Ch. 7 - The transistor in the circuit in Figure P7.20 has...Ch. 7 - For the circuit in Figure P7.21, the transistor...Ch. 7 - (a) For the circuit shown in Figure P7.22, write...Ch. 7 - Consider the circuit shown in Figure P7.23. (a)...Ch. 7 - The parameters of the transistor in the circuit in...Ch. 7 - A capacitor is placed in parallel with RL in the...Ch. 7 - The parameters of the transistor in the circuit in...Ch. 7 - Prob. D7.27PCh. 7 - The circuit in Figure P7.28 is a simple output...Ch. 7 - Reconsider the circuit in Figure P728. The...Ch. 7 - Consider the circuit shown in Figure P7.32. The...Ch. 7 - The commonemitter circuit in Figure P7.35 has an...Ch. 7 - Consider the commonbase circuit in Figure 7.33 in...Ch. 7 - Prob. 7.39PCh. 7 - The parameters of the transistor in the circuit in...Ch. 7 - In the commonsource amplifier in Figure 7.25(a) in...Ch. 7 - A bipolar transistor has fT=4GHz , o=120 , and...Ch. 7 - A highfrequency bipolar transistor is biased at...Ch. 7 - (a) The frequency fT of a bipolar transistor is...Ch. 7 - The circuit in Figure P7.48 is a hybrid ...Ch. 7 - Consider the circuit in Figure P7.49. Calculate...Ch. 7 - A common-emitter equivalent circuit is shown in...Ch. 7 - For the common-emitter circuit in Figure 7.41(a)...Ch. 7 - For the commonemitter circuit in Figure P7.52,...Ch. 7 - Consider the circuit in Figure P7.52. The resistor...Ch. 7 - The parameters of the circuit shown in Figure...Ch. 7 - The parameters of an nchannel MOSFET are kn=80A/V2...Ch. 7 - Find fT for a MOSFET biased at IDQ=120A and...Ch. 7 - Fill in the missing parameter values in the...Ch. 7 - (a) An nchannel MOSFET has an electron mobility of...Ch. 7 - A commonsource equivalent circuit is shown in...Ch. 7 - Prob. 7.60PCh. 7 - The parameters of an ideal nchannel MOSFET are...Ch. 7 - Figure P7.62 shows the highfrequency equivalent...Ch. 7 - For the FET circuit in Figure P7.63, the...Ch. 7 - The midband voltage gain of a commonsource MOSFET...Ch. 7 - Prob. 7.65PCh. 7 - Prob. 7.67PCh. 7 - The bias voltages of the circuit shown in Figure...Ch. 7 - For the PMOS commonsource circuit shown in Figure...Ch. 7 - In the commonbase circuit shown in Figure P7.70,...Ch. 7 - Repeat Problem 7.70 for the commonbase circuit in...Ch. 7 - In the commongate circuit in Figure P7.72, the...
Knowledge Booster
Background pattern image
Electrical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Text book image
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Text book image
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Text book image
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Text book image
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Text book image
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,
Huffman Codes: An Information Theory Perspective; Author: Reducible;https://www.youtube.com/watch?v=B3y0RsVCyrw;License: Standard Youtube License