Lab 4 - EE 420L
reedj35@unlv.nevada.edu
For
the following questions and experiments assume VCC+ = +5V and VCC- = 0V.
Experiment 1:
To estimate the
bandwidth of an op-amp knowing its gain, we must first know about the Gain
Bandwidth Product (GBP). The GBP is going to be
, where fun is the unity frequency. Looking at the
datasheet, I obtain:
Using this data, I can
calculate the bandwidth given a specific gain.
We know that the gain of
an op-amp for a non-inverting topology (figure below) is 
Non-Inverting Op-Amp Topology
Therefore, my
theoretical bandwidth calculations are as follows:
|
Gain of 1:
|
Gain of 5:
|
Gain of 10:
|
Experiment 2:
- Experimentally verify these
estimates assuming a common-mode voltage of 2.5 V.
In order to
experimentally find what the bandwidth is for each gain, we will be sweeping
the frequency of the input signal until the resulting output voltage is 
.
The frequency at which
this is found is the 3dB bandwidth and this experimental frequency should
closely resemble the theoretical bandwidth calculated above.
The following are the
topologies for each circuit and includes the actual resistor values I used when
finding experimental results. The input voltage had a DC offset of 2.5V and
sinusoidal signal of 100mVpp starting at 1kHz. The frequency is then swept
until the desired output voltage of is attained:
|
Gain of 1:
|
Gain of 5:
|
Gain of 10:
|
|
|
|
|
|
Input and output
waveforms at a frequency of 1kHz |
Input and output waveforms at a frequency of 10kHz |
Input and output
waveforms at a frequency of 1kHz |
|
Experimentally
measured bandwidth of 900kHz; (Vout
* 0.707) |
Experimentally
measured bandwidth of 90kHz; (Vout *
0.707) |
Experimentally
measured bandwidth of 44kHz; (Vout *
0.707) |
|
Bandwidth |
Gain of 1 |
Gain of 5 |
Gain of 10 |
|
Theoretical |
1.3MHz |
260kHz |
130kHz |
|
Simulated |
1.28MHz |
257kHz |
129kHz |
|
Experimental |
900kHz |
90kHz |
44kHz |
These experimental
values are far off below the theoretical values. Referring to the datasheet image
above of the GBP, the manufacturer tested the device using a VCC of
30V and a Vin of 10mV. We used a VCC of 5V and a Vin
of 100mV and this could be a contribution as to why the experimental bandwidth
is far off from the theoretical values. Other reasons could be the measuring
equipment, the circuit build, or human error.
Experiment 3:
- Repeat these steps using the
inverting op-amp topology having gains of -1, -5, and -10.
We know that the gain of
an op-amp for an inverting topology (figure below) is 
, however, we only consider the absolute value, or magnitude of
calculating the GPB. Referring to page 1047 of Dr. Baker’s textbook, “CMOS: Circuit Design, Layout, and
Simulation” we find the GBP of the inverting op-amp is: 
.
Inverting Op-Amp Topology
|
Gain of -1:
|
Gain of -5:
|
Gain of -10:
|
Just like in Experiment
2, in order to experimentally find what the bandwidth is for each gain, we will
be sweeping the frequency of the input signal until the resulting output
voltage is . The frequency at which this is found is the 3dB bandwidth and
this experimental frequency should closely resemble the theoretical bandwidth
calculated above.
The following are the
topologies for each circuit and includes the actual resistor values I used when
finding experimental results. The input voltage had a DC offset of 2.5V and
sinusoidal signal of 100mVpp starting at 1kHz. Then the frequency is swept
until the desired output voltage of is attained:
|
Gain of -1:
|
Gain of -5:
|
Gain of -10:
|
|
|
|
|
|
Input and output waveforms at a frequency of 1kHz |
Input and output
waveforms at a frequency of 1kHz |
Input and output
waveforms at a frequency of 1kHz |
|
Experimentally
measured bandwidth of 650kHz; (Vout * 0.707) |
Experimentally
measured bandwidth of 120kHz; (Vout * 0.707) |
Experimentally
measured bandwidth of 44kHz; (Vout * 0.707) |
|
Bandwidth |
Gain of -1 |
Gain of -5 |
Gain of -10 |
|
Theoretical |
650kHz |
217kHz |
118kHz |
|
Simulated |
644kHz |
215kHz |
117kHz |
|
Experimental |
650kHz |
120kHz |
44kHz |
Again, the experimental
values are far below the theoretical values. As mentioned above, I believe this
is due to the manufacturer using a VCC of 30V and a Vin
of 10mV.
Experiment 4:
- Design two circuits for
measuring the slew-rate of the LM324. One circuit should use a pulse input
while the other should use a sinewave input.
As we can see above, the
typical slew rate for the LM324 is 0.4 V/µs. In order to experimentally measure
this, I will be using a non-inverting op-amp topology with a gain of 1;
otherwise known as a voltage follower. The reason for this design is because it
will be easy to measure the slew rate since there is no gain. Also, this is how
the manufacturer measured it according to the datasheet. The function generator
will have an input frequency starting at 1kHz for both the pulse input and
sinusoidal input; then I will increase the frequency until I notice that the
output takes time to reach what the input is. For the pulse input, I can find
the change in Vout by measuring how long
it takes to go from 10% of Vout to 90% of Vout. For the sinusoidal input, I will be able
to just simply measure the peak-to-peak voltage of the output and find the
slope.
|
Pulse Input:
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Sinusoidal Input:
|
The experimental values
for the slew rate with a pulse input and sinusoidal input are below the value
given in the datasheet. The slew rate values calculated between the pulse and
sinusoidal inputs match well and I can confidently say that this specific
op-amp’s slew rate is below 0.4 V/µs. The reason for this can be attributed to
the fact that the VCC used by the manufacturer to test was 15V. Since
we used 5V, this can be the contributor as to why the slew rate is lower. Other
reasons could be the measuring equipment, the circuit build, or human error.
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