EE 420L – Engineering Electronics II Lab – Lab 4
Due: February
27, 2019
Pre-Lab
·
Watch the op-amps II discussion video.
·
Simulate the op-amp circuits found in the op-amps II zip file.
·
Read the lab write-up before coming to lab.
Lab Tasks
This lab will
utilize the LM324 op-amp (LM324.pdf).
For this lab, VCC+
= 5V and VCC- = 0V.
- Estimate, using the datasheet,
the bandwidths for non-inverting op-amp topologies having gains of 1, 5,
and 10.
- Experimentally verify these
estimates assuming a common-mode voltage of 2.5 V.
- Your report
should provide schematics of the topologies you are using for
experimental verification along with scope pictures/results.
- Associated
comments should include reasons for any differences between your
estimates and experimental results.
- Repeat these steps using the
inverting op-amp topology having gains of -1, -5, and -10.
- 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.
- Provide
comments to support your design decisions.
- Comment on any
differences between your measurements and the datasheet’s specifications.
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Part 1: Non-Inverting Topology GBW Product
From the datasheet for the LM324, we obtain the typical G*BW of
the op-amp: 1.3 MHz at nominal operating temperature.
Also from the datasheet, we can read from this plot to
determine the expected typical
gain bandwidth product and unity gain frequency of
the LM324 op-amp.
Note that in the plot, the rightmost trace gives
the GBW product for VCC+ greater than
30 V, where the leftmost trace gives the GBW
product for VCC+ between 10V and 15V.
We are using a VCC+ of 5V, so we should expect our
values to fall left of both of the traces in the plot,
and expect a unity gain frequency of just below 800 kHz.
Breadboard Setup
Inverting Non-Inverting
Estimated Gain Bandwidth Product From Datasheet
The equation used to calculate gain, bandwidth,
and unity gain frequency is shown below.
For Gain of 1:
For Gain of 5:
For Gain of 10:
Unity Gain (Gain of 1) Frequency Response
Simulations
Here we can observe the unity
gain frequency from simulation results to be 1.15 MHz.
Experimental
From the figure above, the oscilloscope
could not measure the frequency directly from the function generator.
Instead, using cursors, we can
measure the period of the signal to be 920ns – 120ns = 800ns.
Since frequency is the inverse
of the period, our measured unity gain frequency is 1/800ns = 1.25 MHz.
Notice that the waveforms above
are out of phase by 180 degrees. This is because at 100 mVpp,
the op-amp can
not keep up with the input
because the input signal is too fast. The slew rate, or the maximum output rate
of change,
for the LM324 is 400mV/µs. A
100mV sine wave at its maximum slope at a frequency of 1 MHz is trying to
change at
a rate of (2∏*100mV)/µs =
or 628mV/µs. Since the slew rate of the op-amp is slower than the output is trying
to change,
we get a phase shift in our waveform.
Regardless, the unity gain frequency is 1.25 MHz. This
is very close to the datasheet
typical value for unity gain frequency for VCC+ = 30V. Since we estimated for our
VCC+ = 5V, our estimate is off by a bit.
Gain of 5 Frequency Response
Simulations
Here we can observe that the -3dB frequency for a
gain of 5 is around 181 kHz.
Experimental
Note that in the figure above, for a gain of 5,
the -3db frequency should yield an output of roughly 0.7 times the
output, which, with a 100mVpp input signal, should
be around 350mVpp. The output here is 356mV, so we can conclude
that the experimental -3dB frequency for a gain of
5 is 200kHz, which is roughly one fifth of the unity gain frequency.
Gain of 10 Frequency Response
Simulations
Here we can observe that the -3dB frequency for a
gain of 10 is around 79 kHz.
Experimental
For a gain of 10, the -3dB
frequency is assumed by noting where the output is around 700mVpp for an input
signal of 100mVpp.
In the above waveform, the output
reads 716mVpp, so we can conclude that our experimental -3dB frequency for gain
of 10 is
around 96kHz.
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Part 2: Inverting Topology GBW Product
Estimated Gain Bandwidth Product By Calculation
The equation used to calculate gain, bandwidth,
and unity gain frequency is shown below.
For the inverting op-amp topology, gain is known
to be equal to -R2/R1. However, in order to
calculate bandwidth, we need to use the non-inverting
gain equation, since the unity gain frequency
is measured using the non-inverting topology. The
non-inverting gain equation is given by
For Gain of 1:
For Gain of 5:
For Gain of 10:
Gain of 1 Frequency Response
Simulation
Here we can observe that the op-amp unity gain
frequency for non-inverting topology
is around 675 kHz.
Experimental
For a gain of 1, we simulated
to get 675 kHz for our -3dB frequency. Experimentally, observing the
frequency when the output is
roughly 0.7 times the input, we see our -3dB frequency is 660 kHz. This
is very close to the simulated
value for the bandwidth of the inverting topology for unity gain.
Gain of 5 Frequency Response
Simulation
Here, we see that from simulation
results for the inverting topology with a gain
of 5, the output falls off (the
-3dB frequency) at around 150 kHz.
Experimental
For a gain of 5, experimentally
we measure the -3dB frequency when the output is 0.7 times 500 mVpp for
an input signal of 100 mVpp. Here we measure the -3dB frequency to be 200 kHz.
Gain of 10 Frequency Response
Simulation
For a gain of 10, we observe
the -3dB frequency to be around 76 kHz for the
inverting topology.
Experimental
Above, we can observe the -3dB
frequency of the inverting topology to experimentally measure roughly 66 kHz,
not far off from our simulated
bandwidth for a gain of 10.
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Part 3: Slew Rate Measurement
Unity Follower Breadboard
Circuit
·
To measure slew
rate for both a sinusoidal wave and a square wave input, a unity follower or
voltage
follower circuit was used. With a gain of one, we can simply turn up the
frequency of the
input signal until
the output slews, and once it slews, we can measure the slope of the output
signal.
This slope, in
V/s, will give the experimental slew rate.
From the datasheet, the typical slew rate is 400 mV/µs.
Sinusoidal Input Signal
Sinusoidal signals can be represented by
where the slope is given by the
derivative,
Since cos(2πft) = 1, the slope can be
represented as Vo * 2π * f.
The slew rate must be less than the slope for
operation. But, at the point where
the output is a triangle wave, the output is
completely slewing, and we can write
To obtain slew rate in V/µs,
This value is reasonably close
to the typical value given in the datasheet.
Square Wave Input Signal
Using the cursors to measure
the rise time of the output signal, we can obtain the slew rate.
This value is also reasonably
close to the typical value given in the datasheet.