U niversity of S outhern C alifornia
School Of Engineering
Department Of Electrical Engineering
EE 348:
Homework Assignment #07
(Due 04/10/2001)
Spring, 2001
Choma
Problem #31:
All transistors in the bipolar differential pair of Fig. (P31) are identical.
Each transistor has very large forward beta, negligible internal collector resistance, and infinitely
large forward Early resistance. When biased properly, each transistor conducts identical collector current densities.
 VCC
R1
RCC
RCC
R2
Vo
Q3
Rs
Q1

Q2
Rs
Vs

Q5
R3
Q4
 VEE
Fig. (P31)
(a). In terms of VBE and circuit parameters, find expressions for the quiescent collector currents
flowing in all transistors and the quiescent voltages, with respect to ground, at the collectors of all transistors. The signal source, Vs, has zero static voltage value.
(b). Under small signal operating conditions, find the Thévenin voltage and the Thévenin resistance seen looking back to the collector of transistor Q2. Do balanced conditions prevail
under these Thévenin computational circumstances?
(c). Assuming that balanced conditions prevail in the input differential pair, find the common
mode and differential mode input resistances with respect to the base terminals of transistors Q1 and Q2.
(d). Using the results of Part (b), determine an expression for the overall voltage gain, Av =
Vos/Vs.
Problem #32:
In the differential amplifier of Fig. (P32), all transistors are identical and are
biased to produce identical small signal parameters. Moreover, all transistors have infinitely
large forward Early resistances.
EE 348
University of Southern California
J. Choma, Jr.
(a). Draw the differential mode and common mode half circuit AC schematic diagrams.
(b). Give the expressions for the small signal differential mode voltage gain, Adm, the common
mode voltage gain, Acm, and the overall voltage gain, Av = Vos/Vs.
(c). Give expressions for the small signal common mode input resistance, Rci, the differential
mode input resistance, Rdi, and the net input resistance, Rin.
(d). Give expressions for the small signal common mode output resistance, Rco, the differential
mode output resistance, Rdo, and the net input resistance, Rout.
 VCC
RCC
Rout
Rin
RCC
Vo
R
REE
Q1
Q2
Rs
Q4
Q3
Rs
Q5

Vs
Ra
Rk
Rk

Rk
 VEE
Fig. (P32)
Problem #33:
The three bipolar junction transistors in the folded cascode transconductor
of Fig. (P33) are biased to operate in their linear regimes. For analytical simplicity, assume that
all transistors have identical small signal parameters and that they have infinitely large forward
Early resistances. Note that transistors Q1 and Q3 do not comprise a balanced differential pair.
(a). Assuming that capacitors C1 and C2 behave as AC short circuits over the signal frequency
range of interest, develop an expression for the small signal forward transconductance, Gm
= Ios/Vs, of the amplifier.
(b). If capacitor C2 is sufficiently large to emulate an AC short circuit, give an expression for
the time constant, τ, associated with capacitor C1.
Homework #07
51
Spring Semester, 2001
EE 348
University of Southern California
J. Choma, Jr.
 VCC
Rs
C2
Rk
Q3
R2
Q1
Q3
Rs

Vs
Io
RK
RL
R1
C2

 VEE
Fig. (P33)
Problem #34:
Consider the differential amplifier given in the Fig. (P34).
(a). Transistors Q1a, Q1b, Q2a, and Q2b each have an emitter-base junction area of AE. If the
circuit biasing ensures that all transistors conduct nominally identical current densities,
what must be the emitter-base junction areas, in relationship to AE, of transistors Q3a, Q3b,
Q4a, and Q4b?
(b). For the biasing condition described in Part (a), what are the requisite emitter-base junction
areas of transistors Q7a and Q7b?
(c). For the biasing condition described in Part (a) and deduced in Part (b), is it necessary for
transistor Q6 to have an emitter-base junction area that mirrors that of either transistors
Q7a or Q7b?
(d). Suppose that the emitter-base junction area of a monolithic transistor is scaled upward by a
factor of K to accommodate a collector current that is likewise K-times larger than that
conducted by the collector of the original (smaller) device. If the original transistor is
characterized by the small signal parameters, rb, re, rc, ro, r, and ac, what are the small
signal base resistance, emitter resistance, collector resistance, forward Early resistance,
junction diffusion resistance, and beta of the larger device? Express your answers in terms
of K and the small signal model parameters of the original transistor.
Homework #07
52
Spring Semester, 2001
EE 348
University of Southern California
J. Choma, Jr.
Problem #35:
For the differential amplifier given of Fig. (P34), use half circuit concepts
to evaluate the net input resistance, Rin, the net output resistance, Rout, and the differential voltage gain, Ad = Vo/Vs. For simplicity, assume all transistors have identical small signal model
parameters, inclusive of infinitely large forward Early resistance.
 VCC
Rin
Rcc
Q1a
Rcc
Q5a
Q5b
  Vo 
Q2a
Q3a
Rs
Rout Q2b
Q3b
2Rdd
Q4a
Rs
Q4b
Rk

Vs
Q1b

Rk
2Ree
R3
Q7b
Q7a
Q6
R2
R1
R2
 VEE
Fig. (P34)
Homework #07
53
Spring Semester, 2001
EE 348
University of Southern California
J. Choma, Jr.
U niversity of S outhern C alifornia
School Of Engineering
Department Of Electrical Engineering
EE 348:
Homework Assignment #07
(SOLUTIONS: Due 04/10/2001)
Spring, 2001
Choma
Problem #31:
Homework #07
54
Spring Semester, 2001