Gael Hatchue

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Nov 2, 2013 (3 years and 5 months ago)

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Gael Hatchue

ENS 202

Fall 2005




Experiment:
Effect of an
A
ctive
L
oad on the
G
ain of a
D
ifferential
A
mplifie
r




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 in
side

the circuit is reduced.
However,
t
his 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 bipola
r
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 a
n 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:


,

where R
c

i
s

the collector resistance and
g
m

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 tra
nsistors have some fabrication constraints
that have the effect of
limiting the response of the amplifier



second order effects.

The base
-
emitter and base
-
collector capacitances

are
fabrication
characteristics of
each device, and
have the effect
of

narrow
ing down or expanding the bandwidth of the amplifier.

The

collector
-
emitter
resistance
r
0



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:



The purpose is to show that replacing the active load with a
re
sistive load results
in a significant increase in the open loop gain of the
differential
amplifier
.


Apparatus



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, d
igital
oscilloscopes are preferable because they
can display
voltage
s 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 volta
ge


of the bipolar transistor is exactly 10 volts.



A 10K

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
oth
er
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
10
KΩ resistors are used as our resistive load resistors.



Other less
re
levant
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 measur
ements 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 independen
t 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 load
s.

The closed loop gain of an amplifier is a
function of the exter
nal 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


Am灬ifier c潮fi杵ration use搠in
the
ex灥rime湴K






Calculating the open loop gain or common mode rejection ratio (
CMRR
) of an amplifier
is a two
-
step proc
ess; the first step consists of calculating the differential gain of the
amplifier,

A
d
, 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,
A
cm
, 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:

,

where A
d

is t
he differential gain, and A
cm

is the common mode gain.


Experimental
procedure



Th
e

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
gr
ound.

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
.










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:





Figure 2


oe灬aci湧 the resistive l潡搠with
an active l潡d

cigure ㌠


Ty灩cal 摩ffere湴ial 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.








Table 1 shows the results of our

measurements, as well as the calculated gain values for
each differential amplifier topology built.




Differential Mode

Common Mode


ΔV
OUT

ΔV
IN

A
d

ΔV
OUT

ΔV
IN

A
cm

Open Loop
Gain

Resistive
Load

-
6.02V

157mV

-
38.3V/V

-
31.2mV

967.5mV

-
0.0322V/V

1190V/V

(61.5dB)

Active
Load

-
6.03V

125mV

-
48.2V/V

-
31.2mV

7.52V

-
0.00415V/V

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 m
ultiplying
th
e 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
reason
s

why
active load circuit design has completely replaced the alternati
ve in commercial
applications.

Great: A


Figure 4


Ty灩cal c潭m潮 m潤o gain
transfer curve