This
lab served as an introduction to Operational Amplifiers and their
finite gain-bandwidth product as well as their slewing properties.
Ideally, we can assume that an op-amp can operate the same under all
frequencies, however this is not the case, like at all. We can find
that under gains such as 10 will cause a massive decrease of usable
bandwidth. The slew rate is another issue to consider: Things cannot
change instantly.
Experiment 1 - Bandwidth of 1x, 5x, and 10x ACL for non-inverting config
Above are the hand calculations used to determine the usable
bandwidths of different non-inverting configurations with different
close loop gains (ACLs). Below are the varying frequencies at which we
found our output to be 0.707*Vout (that's the expected Vout).
Experiment 2 - Bandwidth of 1x, 5x, and 10x ACL for inverting config
ACL
= 1x (Unity)
ACL = 5x
ACL = 10X
Above
are the scope waveforms and pictures of the function generator for each
different ACL for the inverting configurations. We can see that the
unity gain is experimentally determined to be 400kHz, however this
should be equal to 1.3MHz which is the gain-bandwidth product. The hand
calculations should be the same for this configurations.
Experiment 3 - Slewrate
To
find the slew rate of this particular op-amp, I decided to use a high
gain configuration at a frequency low enough to allow the voltages to
reach steady state. We can use the oscilloscope to conviniently measure
the rise time and peak to peak voltage: 1.78V in 5.64us which makes for
a slew rate of 0.136V/us which is close to the datasheet value of 0.4V/us.
Using
a sine wave instead of a pulse for the second part of this portion of
the lab. I figured, since this waveform is continuous, the output will
never reach steady state, however we can observe a phase shift. In an
inverting configuration, we should see a perfect 180 degrees of phase
shift (inverted), however we can see a slight difference above. If we
take this phase: (2 Pi) * (Delta t) / (period) will give us the period.
Cos(0) will give us the maximum value (peak), and if we subtract the
value of a Cos(0 + Phase) will give us the difference in voltages. That
(Delta V) / (Delta t) should result in the proper slew rate of around
0.4 V/us. Delta t is 2.3us and Delta V is 1.28V - 0.7V will result in a
slew rate of 0.252V/us.
Conclusion
We explored the real
characteristics of this LM324 op-amp such as its gain-bandwidth product
and slew rate. Assuming that an op-amp can work at about any frequency
is a terrible assumption and this information should be taken into
serious consideration. The slew rate will be important if we are using
our op-amps for higher gains or frequencies since it takes a decent
amount of time to rise the voltage.
