ECEG 351
Electronics II
Spring 2016
Homework Assignment #4 – due in class Wednesday, Apr. 6, 2016
[Prob. 5 added 4/3/16; three errors in Prob. 3 statement corrected 4/5/16]
Instructions, notes, and hints:
Provide the details of all solutions, including important intermediate steps. You will not receive
credit if you do not show your work. Some problems might require good engineering
approximations or assumptions to be applied in order to be solved. In those cases, your answer
might differ considerably from the posted answer. Given typical device variations and
component tolerances, some amount of discrepancy is often reasonable. If you justify any
approximations you make, you will be given full credit for such solutions.
Assignment:
1. A standard BJT differential amplifier is needed to provide the largest possible differential
output signal using collector resistors of 10 k each. The input signal is applied to the base
of Q1 and has a sinusoid of 5 mV peak amplitude; the base of Q2 is grounded. A ±10 V
bipolar power supply is used. The bias is provided by a current source I that has such a high
output resistance that it can be ignored. Derive an expression for the total (bias plus small
signal) collector voltages vC1 and vC2 in terms of VCC, I, any needed resistances and other
parameters, and the input signal vin. Under the condition that both transistors should be kept
well out of saturation by maintaining a minimum total collector-base voltage vCB of
approximately 0 V, find the required value of I. Also find the differential gain for the value
of I you obtain. You may assume that  ≈ 1. Recall that  = /( + 1). For the BJTs, VBE|on =
0.7 V, VCE|sat = 0.3 V, and  = 150. The Early effect can be ignored (i.e., ro → ∞.) You may
assume that the emission coefficient n = 1 and the thermal voltage VT = 25 mV.
2. Consider the case of a standard BJT differential amplifier with a current mirror that has bias
current I and output resistance REE. If the output is taken differentially, the resulting CMRR
is 40 dB higher than when a single-ended output is used. Suppose that the collector resistors
are significantly mismatched (i.e., they differ in value by RC) but that the mismatch between
transistors is negligible. Find the collector resistance mismatch RC/RC expressed as a
percentage. For the BJTs, VBE|on = 0.7 V, VCE|sat = 0.3 V, and  = 150. The Early effect can be
ignored (i.e., ro → ∞.) You may assume that the emission coefficient n = 1 and the thermal
voltage VT = 25 mV.
3. In the diff amp circuit shown on the next page, the output is taken differentially between the
collectors (vod = vC2 – vC1) but the load is finite (50 k) rather than infinite. Assume that Q1
and Q2 are perfectly matched and that VBE|on = 0.7 V, VCE|sat = 0.3 V, and  = 200. The
quiescent input voltage is 0 V, and the small-signal input voltage is vin = 10 mV [added
4/5/16]. Ignore the Early effect (i.e., ro → ∞.) Also, the emission coefficient n = 1 and the
thermal voltage VT = 25 mV. Find total collector voltages vC1 and vC2 and the differentialmode voltage gain vod/vid (vid is the signal part of vIN). You will most likely need to express
IC1 and IC2 to several significant digits to solve the problem. [Erroneous statement that Q1
is larger than Q2 removed 4/5/16]
(continued on next page)
VCC = 5 V
RC1
7.5 k
vC1
vIN
RC2
7.5 k
vC2
RL
50 k
Q1
I
1 mA
Q2
REE
50 k
VEE = −5 V
Circuit diagram for Prob. 3 [RC values changed 4/5/16]
4. A standard BJT diff amp has been fabricated in an integrated circuit package. The baseemitter junction area of Q1 is 2% larger than that of Q2, and the values of RC1 and RC2 are
10.02 k and 9.95 k, respectively. The current mirror has a nominal value of I = 2 mA, and
its output resistance is REE = 50 k. The differential signal vid shown below is applied to the
input of the amplifier, but also present at both inputs is the common-mode signal vicm shown
below. Find a time-domain expression for the differential-mode output voltage vod, assuming
that the differential load resistance is infinite. For the BJTs, VBE|on = 0.7 V, VCE|sat = 0.3 V,
and  = 150. The Early effect can be ignored (i.e., ro → ∞.) You may assume that the
emission coefficient n = 1 and the thermal voltage VT = 25 mV.
vid t   1.5 cos240t  82 mV
vicm t   450 cos44,000t  mV
5. [added 4/3/2016] Prove the formula for Acm given in Prob. 9.58 of the textbook for the
indicated errors gm and RD in the values of gm and RD, respectively. You do not have to
solve the problem as written in the textbook.