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Gael Hatchue
ENS 202
Fall 2005
Experiment: Effect of an Active Load on the Gain of a Differential
Amplifier
Summary
Since the invention of CMOS circuits in 1963, active load amplifiers have
become more popular in circuit design than resistive load amplifiers. One advantage of
active load circuits is that the power dissipated inside the circuit is reduced. However,
this experiment focuses on a second advantage which is characteristic to a specific type
of active load circuits: differential amplifiers. The experiment shows that using an active
load differential amplifier over a resistive load amplifier results in a significant increase
in open loop gain.
Introduction
In this experiment, we build two topologies of differential amplifier using bipolar
transistors; one is the resistive load amplifier topology, and the other is the active load
amplifier topology. Replacing the resistive load with an active load has the effect of
eliminating the collector resistance in the amplifier — replacing it with an open circuit.
The gain of a typical differential amplifier — similar to the one used in this experiment
— is proportional to the collector resistance. The following formula is an expression of
the gain of the amplifier:
Gain  g m Rc ,
where Rc is the collector resistance and gm is BJT transconductance.
This means that in an ideal case, the open loop gain of an active load amplifier is infinite
as opposed to the open loop gain of a resistive load amplifier which is finite.
In reality, BJT transistors have some fabrication constraints that have the effect of
limiting the response of the amplifier — second order effects. The base-emitter and basecollector capacitances are fabrication characteristics of each device, and have the effect
of narrowing down or expanding the bandwidth of the amplifier. The collector-emitter
resistance r0 — also known as “Early” resistance — limits the mid-band gain of the
amplifier. This resistance is the reason why there can be no infinite gain in practice, not
even in the active load amplifier circuit, as shown in the below formula:
Gain  g m ( Rc || r0 )  g m ( || r0 ))  g m r0
The purpose is to show that replacing the active load with a resistive load results
in a significant increase in the open loop gain of the differential amplifier.
Apparatus
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The apparatus used in this experiment consists of:
An oscilloscope, used to plot the output versus input response — transfer curve — of
the amplifier and calculate its gain. In this experiment, both analog and digital
oscilloscopes were used. However, digital oscilloscopes are preferable because they
can display voltages on the plot, and users have the ability to export a picture of the
curves for further analysis.
A voltmeter, used for making sure that the operating point voltage — base voltage —
of the bipolar transistor is exactly 10 volts.
A 10KΩ potentiometer, used in a voltage divider configuration to create a 10 volts
source voltage from the 15 volts supply.
Four NPN Bipolar transistors: two transistors are used in a “current sink”
configuration to establish a stable collector current; two other transistors are the main
transistors of the differential amplifier circuit.
Two PNP Bipolar transistors are used to replace the resistive load and build an active
load amplifier.
Two 10KΩ resistors are used as our resistive load resistors.
Other less relevant circuit elements such as coupling and de-coupling capacitors and
bias resistors are also used to complete the amplifier circuit.
Experimental set-up
The experiment consists of building the amplifier circuit in Figure 1 and making
different measurements to calculate the open loop gain of the amplifier.
The open loop gain — or common mode
rejection ratio for a differential amplifier — is a
good measure of the performance of the
amplifier as opposed to the closed loop gain,
because it is independent of the external load
attached to the amplifier. In this experiment, by
resistive “load” and active “load”, we refer to
the amplifier’s internal loads which are different
from external loads.
The closed loop gain of an amplifier is a
function of the external load attached to the
system; it is thus less suitable to use the closed
loop gain of an amplifier to evaluate its general
gain efficiency.
Figure 1 – Amplifier configuration used in
the experiment.
Calculating the open loop gain or common mode rejection ratio (CMRR) of an amplifier
is a two-step process; the first step consists of calculating the differential gain of the
amplifier, Ad, which is obtained when the first input terminal of the amplifier is
connected to an AC voltage source, and the second input is connected to ground. In the
second step, we calculate the common mode gain, Acm, which is obtained when the two
input terminals are connected to the same AC voltage source. The formula below can be
used to calculate the open loop gain of the amplifier:
Open Loop Gain  CMRR 
Ad
,
A cm
where Ad is the differential gain, and Acm is the common mode gain.
Experimental procedure
The resistive load amplifier circuit of Figure 1 is first built, with the first input
terminal connected to an AC voltage source, and the second input terminal connected to
ground. Then, the transfer curve on the oscilloscope is used to calculate the differential
gain of the amplifier. Second, both input terminals are connected to the AC source, and
the transfer curve is used to measure the common mode gain. Finally, these two pieces of
information are used to evaluate the open loop gain of the amplifier.
The same procedure is repeated for the active load differential amplifier, which is
built by replacing the resistors R2 and R3 from Figure 1 with two transistors configured
as shown in Figure 2.
Figure 2 – Replacing the resistive load with
an active load
Results
Figure 3 shows a typical differential
gain transfer curve (second input terminal
connected to ground), obtained using a digital
oscilloscope. The differential gain can be
calculated using the following formula:
Ad 
VOUT
VIN
Figure 3 – Typical differential gain transfer
curve
Similarly, Figure 4 shows a typical common
mode gain transfer curve (both input terminals
connected to AC source signal). The common
mode gain is the slope of the linear curve in
the figure.
Figure 4 – Typical common mode gain
transfer curve
Table 1 shows the results of our measurements, as well as the calculated gain values for
each differential amplifier topology built.
Differential Mode
Resistive
Load
Active
Load
Common Mode
ΔVOUT
ΔVIN
Ad
ΔVOUT
ΔVIN
-6.02V
157mV
-38.3V/V
-31.2mV 967.5mV
-0.0322V/V
-6.03V
125mV
-48.2V/V
-31.2mV
-0.00415V/V
7.52V
Acm
Open Loop
Gain
1190V/V
(61.5dB)
11614V/V
(81.3dB)
Table 1 – Results of measurements
Conclusion
The purpose of the experiment was to show that in a typical differential amplifier
circuit, replacing the resistive load with an active load results in a significant increase in
open loop gain. We can see in Table 1 that the active load has the effect of multiplying
the gain by a factor of about 10. This proves that active loads provide much greater gain
than resistive loads, besides consuming less power. This is clearly one of the reasons why
active load circuit design has completely replaced the alternative in commercial
applications. Great: A