NAME _____________________________________
ES 330 Electronics Homework #5
(Fall 2015 – Due October 12, 2015)
This problem set deals with MOSFET field-effect transistors used in circuit analysis and
design. For all of the problems in Homework #5 use the following parameter values
unless otherwise instructed otherwise (i.e., parameters stated directly in the problem).
parameter
nCOX
Channel length L

VTH
n-channel value
0.1 mA/volt2
0.18 m
-1
0.1 V unless  = 0 stated
+ 0.4 volt
p-channel value
0.04 mA/volt2
0.18 m
-1
0.1 V unless  = 0 stated
 0.4 volt
Problem 1 (20 points)
A student builds builds a common-source cascoded amplifier – Circuit “A” as shown
below. The bipolar transistors all have the same parameter values: current gain  =
100, saturation current IS = 1  10-15 A, and Early voltage VA = 20 volts. The ideal
current source IO is set at 2 mA. Hint: If you need to review the parameters used in the
bipolar small-signal model, refer to Example 4.14 of Razavi, on page 155.
(b) (8 points) Next, the student reverses the constant base bias voltage V B and the input
terminal Vin as shown in Circuit “B.” Now the amplifier is no longer in the cascode
configuration. Calculate the voltage gain of Circiut “B.”
(c) (4 points) How do the voltage gains of Circuits “A” and “B” compare?
Homework 5
(a) (8 points) Calculate the voltage gain AV for Circuit “A.”
1
Problem 2 (10 points)
In the cascode-connected n-MOSFET circuit below, you are to determine what gate
width-to-length ratio (W/L) gives a voltage gain of 200. Assume both MOSFETs have
identical gate widths and use nCOX = 0.1 mA/volt2 and  = 0.1 volt-1 for parameter
values (both M1 and M2).
Problem 3 (15 points)
Homework 5
The figure below shows a cascoded MOSFET pair used to achieve higher output
resistance ROUT. We want to obtain ROUT = 200 k using this cascode pair operating at
drain current ID = 0.5 mA. Assuming that (W/L)1 = (W/L)2 = (W/L), nCOX = 0.1 mA/volt2,
and  = 0.1 volt-1; what is the required (W/L) for this circuit?
2
Problem 4 (10 points)
In this problem we have a bipolar transistor current mirror driven with a current source
IREF. One small source of error in current mirroring is the presence of base currents in
the bipolar transistors. In a prefect current mirror current IC would precisely equal
reference current IREF. Both transistors have a current gain = . This is the simplest
current mirror one can make using only two transistors. Neglect the Early effect.
(a) (4 points) Derive an expression for the ratio of (IREF/IC).
(b) (6 points) At what value of  is the mirrored current IC within 1% of the reference
current IREF?
Problem 5 (10 points)
Homework 5
George Wilson (an IC designer at Tektronix who lead a highly productive bipolar IC
design group that made many contributions to Tektronix oscilloscope products)
proposed an improved current mirror over the basic current mirror circuit in Problem 4
above. What is now known as the “Wilson current mirror” adds a transistor Q 3 to the
basic current mirror. This is shown in the figure below.
3
(a) (6 points) Derive an expression for the ratio of (IREF/IC).
(b) (4 points) Compare the (IREF/IC) ratio for the Wilson current mirror to the (IREF/IC) ratio
you found for the basic current mirror in Problem 4. How much better is it?
Problem 6 (10 points)
Homework 5
Consider again the basic current source from Problem 4 above. Now we have a small
resistance RE in series with the emitter of transistor Q2 – see the schematic below. For
this problem assume you can neglect base currents (that is, assume infinite ),
saturation current IS = 1  10-15 A, and both transistors are identical. When resistor RE
is zero, then IREF = IC. But the presence of RE reduces IC. Let IREF = 1 mA. If IC = 0.75
IREF, what is the value of RE?
4
Problem 7 (10 points)
Consider the current mirroring circuit used in an analog IC where current scaling is
achieved by varying the (W/L) MOSFET parameter. What is the current IP relative to
IREF (i.e., IP to IREF ratio)?
Homework 5
Problem 8 (15 points)
We have considered current mirrors for DC biasing in integrated circuits. But they can
also be used as signal-current amplifiers. Transistor M1 acts as the input current source
(driven by voltage VIN). What is the voltage gain using the parameters in the Table at
the beginning of this homework along with the (W 2/L) and (W 3/L) parameters?
5