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Lab 04: Feedback Amplifier (20 points)
NOTE:
1) In this lab, we will use quad opamp to build the feedback amplifier. The feedback
topology and concepts apply to both BJT-based and MOSFET-based op amps.
Objectives
The purpose of this lab is to
(1) demonstrate the effect of negative feedback on amplifier performance and
(2) a method of frequency compensation.
The lab is divided into three parts. Part 1 involves the construction and characterization of an
amplifier whose poles are accurately set by discrete resistors and capacitors. In Part 2, we will
close the feedback loop and measure the effect on the amplifier. In Part 3, we will use dominant
pole compensation to stabilize the system.
A major benefit of using a feedback amplifier is to make the gain independent of load,
fabrication process, and environmental conditions such as temperature. Additionally, the
feedback amplifier enhances bandwidth and is more effective at rejecting noise.
For the experiments, you can use the quad op amp LM348N (datasheet at the bottom of labs
page). Connect the positive and negative power supplies of the op-amps to 10 V and -10 V,
respectively. In addition the components shown in Fig. 1, you will need more resistors to
complete the feedback amplifier shown in Fig. 2 and a capacitor for compensation.
Fig. 1: Open-loop amplifier made with three amplifier stages and discrete components
As discussed in the class, the high-frequency response (poles and zeros) of an amplifier is
primarily due to the internal capacitors (e.g. between gate and drain, base and collector etc). The
high-frequency poles and zeros result from the internal capacitances of the transistors. These
poles occur at frequencies too high to be measured using a breadboard (the poles of the
breadboard wiring appear at lower frequencies than the amplifier poles). To avoid this problem,
we will deliberately and accurately set these poles to relatively low frequencies by external
resistors and capacitors (using R3, R4, R5, R6 and C1,C2,C3 in Fig. 1).
Weber State University
EE3120 Microelectronics II
Suketu Naik
2
Fig.1 shows the open-loop schematic of the amplifier using three different op-amps1. Note that
the first amp in the chain is the non-inverting op-amp, the second amp is the buffer, and the third
amp is the inverting op-amp. This circuit models an op-amp on IC with multiple gain stages,
where vin is the positive input, and the negative input is implicitly grounded. The above circuit
has a high input resistance, low output resistance, and high gain. The capacitors C1, C2, and C3
limit the high-frequency response of this amplifier and emulate the role that internal transistor
parasitic capacitances which are inherent in the actual IC. The resistors R3, R4, R5, and R6 shape
the high-frequency response as well as provided matching to the input/output resistances at the
individual amplifier stages. Again, note that the entire circuit shown in Fig. 1 will act as a single
op-amp.
You can skip to the simulation or you can do the calculation first before proceeding. For the
simulation and experiment, we will first build the circuit, verify gain at each stage. Next, we will
do AC simulation on the open-loop circuit shown in Fig. 1. Next we will close the loop by
adding the feedback network and do AC simulation. After that, we will compensate the amplifier
to increase its stability.
1.0 (Optional) Low-frequency gain, upper 3-dB cutoff frequency, and dominant pole
calculation
Calculate the low frequency gain for this circuit (Hint: open circuit all capacitors and
consider each of the three gain stages in isolation). Next, estimate the upper 3-dB cutoff
frequency for this circuit using the method of Open Circuit Time Constants (Hint: op-amp
outputs are assumed to be connected to the ground in the analysis. Same is true for the op-amp
inputs that are driven to be virtual grounds by feedback).
From the relative values of the time constants associated with each capacitor, which capacitor do
you expect to contribute the dominant pole? Note that this is the capacitor we will focus on for
the frequency compensation.
L1: What are the low-frequency gain, 3-db cutoff frequency, and the dominant pole
capacitor of the amplifier?
2.0 Simulation
Before we do the simulation, we need to make sure that the parts library has LM348 model.
Otherwise we will need to add LM348 subcircuit. To do so, first download the subcircuit file for
LM348 from the lab page and place it in same directory as your circuit file. Choose opamp2 in
LTSpice (Multisim should also have a generic op-amp symbol in its library). Now right click on
the symbol and change Value to LM348. Click ok. Now go to your schematic editor and click
on .op (all the way on the right on top). Type in “.include LM348.sub” and then left click on
place it in the schematic (e.g. right below the opamp symbol). Now connect resistors and the
positive and negative power supplies to the first opamp.
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Ref: Dr. Charles Cameron, U.of. U., ECE 3110: Engineering Electronics II, Fall 2008.
Weber State University
EE3120 Microelectronics II
Suketu Naik
3
2.0.1 Transient Simulation
Run the transient simulation with appropriate resistor values, input voltage set to a small
amplitude at 300 Hz and verify that the op-amp shows the gain around 11. Similarly, add more
op-amps and the circuit components as shown in the Fig. 1 and verify the gain at each step (for
both the simulation and experiment, the input signal amplitude should be small enough such that
the output does not saturate). You don’t have to include the .include statement for each op-amp
symbol; one statement is enough. Note that the gain will drop as the signal passes through the
passive components R3-C1-R4-C2 and R5-C3. In order to bring the signal level up again, we will
use the third op-amp with gain≈20 V/V. Make a note of the open-loop gain from the transient
simulation |Vo|/|Vin|.
2.1 Open-loop
(1) Run an AC simulation on the open loop amplifier in Fig. 1 (set the AC amplitude=1) and plot
the magnitude and phase response. Optionally, you can save the data points for the magnitude
and phase so they can be plotted in Matlab or Excel along with the measured data. The value of
the gain at low frequency should be similar to what you obtain before in the transient simulation.
L2: Simulate and provide the magnitude and phase response plots of the open-loop
amplifier in Fig. 1.
(2) Using the bode plot of the open-loop amplifier, we can predict the stability of different
closed-loop configurations. For a feedback factor of β = 1/4.3 (i.e. Ra= 1kΩ and Rb=3.3 kΩ in
Fig. 2), determine whether or not you expect the closed-loop system to be stable. Stability of an
amplifier can be determined by observing its phase margin (see section 10.12.3 pp. 881-882).
Record the phase margin as follows: check where the magnitude crosses 20 log(1/β). Note the
the value of the phase at that crossing. This is the phase margin2. If this value is negative then the
closed-loop amplifier will be unstable. As a rule of thumb, phase margin of 60-70 deg allows
stable operation with acceptable gain.
(3) Repeat the previous step for a feedback factor of β = 1/16.
L3: What is the phase-margin of the amplifier at the feedback factor of β = 1/4.3 and β =
1/16?
Fig. 2: Closed-loop amplifier with the feedback network and the open-loop amplifier (-A(s)) shown in Fig. 1
Normally, when visualizing phase margin, we look at the difference between the phase at the cross point and -180 deg but here
we use 0 deg as the reference point because we have the third stage that inverts the output of the second stage.
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Weber State University
EE3120 Microelectronics II
Suketu Naik
4
2.2 Closed-loop
We will now close the feedback loop. At this point, it is beneficial to run transient simulation to
predict stability. You can create a symbol representing the schematic in Fig. 1 and use it for the
closed-loop simulation. Or you can create a separate file for the closed-loop simulation. It is
important to save the open-loop schematic separately as we will use it for the compensation in
2.3.
Let’s select Ra = 1kΩ. We will adjust the value of Rb to give feedback values of β = 1/4.3 and β
= 1/16 (recall that β=Ra/(Ra+Rb)).
(1) For the feedback factor of β = 1/4.3, select Rb = 3.3 kΩ. First ground the input node (where
Vin is connected). Run a transient simulation for about 10-30 ms. Observe whether the feedback
amplifier oscillates or not. Does it oscillate?
(2) Repeat the above step for the feedback factor of β = 1/16, by selecting Rb = 15 kΩ.
L4: Provide the transient plots for the closed-loop amplifier with the feedback factor of β =
3.3/4.3 and β = 1/16 while grounding the input node.
(3) With the above value of Rb = 15 kΩ, connect a 100 mVamp (or smaller), 100 Hz square wave
at the input. Run the simulation for about 2 periods of the input wave. Do you see any ringing in
the output signal? Optionally, you can also save the data points for so they can be plotted in
Matlab or Excel along with the measured data.
L5: Provide the transient plots for the closed-loop amplifier with the feedback factor of β =
1/16 with 100 Hz square wave at the input node.
2.3 Compensation
With the above value of Rb = 15 kΩ for feedback factor of β = 1/16, we will now compensate the
feedback amplifier to increase its stability to reduce the ringing observed in the previous section.
We will use the dominant pole compensation as described in the last few sections in Ch. 10.
(1) Open up the open-loop amplifier schematic. We will run AC simulation and look at the
magnitude and phase responses. Adjust the value of C2 and run the AC simulation until the
amplifier shows a phase margin of about 70 deg. Record the value of C2.
(2) Open up the closed-loop amplifier schematic. Use the new value of C2. Run the transient
simulation with 100 mVamp (or smaller), 100 Hz square wave. Do you see any ringing in the
output signal? Note that the ringing should either eliminated or reduced.
L6: With the feedback factor of β = 1/16, provide the magnitude and phase plots, and the
transient plot with square wave for the closed-loop amplifier.
Note that the IC design of a multi-stage amplifier involves compensation to stabilize the circuit
and to ensure that the circuit will work as expected post-fabrication.
Weber State University
EE3120 Microelectronics II
Suketu Naik
5
3.0 Experiment
Build the open-loop amplifier circuit on your board. Make sure to use short wires as much as
possible. Take care in placing the resistors and capacitors. Again, clip the resistors and capacitors
and use short leads whenever possible.
Check the operation of the circuit in steps. First build the first stage and verify the gain≈11. Next,
build the buffer stage (second stage) and verify that the gain is 1 and the overall gain drops
below 11 (due to the external resistors R3, R4 and capacitors C1 , C2). Now add the third stage and
verify that the gain goes up as determined by Ro/R6. Lower the input amplitude such that the
output signal looks sinusoidal and that there are no distortions present.
3.1 (Repeat 2.1)
Perform a frequency sweep but you don’t have to record values for magnitude and phase. Note
the upper 3-dB cutoff frequency (observe at which frequency the output signal drops to 0.707 x
input signal).
3.2 (Repeat 2.2)
Ground the input node and observe ringing in the output. Similarly, connect square wave and
observe ringing. Perform a sinusoidal frequency sweep and observe the upper 3-dB cutoff
frequency.
3.3 (Repeat 3.3)
Use the value of the compensation capacitor as determined in the simulation. Observe that
ringing reduces (perhaps diminishes with an appropriate capacitor) with square wave input.
Connect the sinusoidal input signal and perform a quick frequency sweep. Note the value of the
upper 3-dB cutoff frequency. How does it compare to the uncompensated feedback amplifier in
3.2?
L7: Report the upper 3-dB frequency for the open-loop amplifier, the closed-loop amplifier,
and the compensated closed-loop amplifier. Also comment on the ringing for the three
cases.
Weber State University
EE3120 Microelectronics II
Suketu Naik