Authored by Your Name, Cody McDonald
Today's date 2/27/19
E-mail: mcdonc4@unlv.nevada.edu
This lab will contain:
0. Pre-lab work
1. Integrator circuit hand calculations
2. Integrator circuit demonstration
3. Integrator circuit design and analysis
Part 0: Pre-lab Work
- Watch the video op_amps_III, review op_amps_III.pdf (associated
notes), and simulate the circuits in op_amps_III.zip.
- Read the write-up seen below before coming to
lab.
Again, this lab will utilize the LM324 op-amp (LM324.pdf).
For the following questions and experiments assume VCC+ = +5V and
VCC- = 0V.
Part 1: Integrator Circuit Hand
Calculations
Calculate the frequency response of the following
circuit. Ensure you show your clear hand calculations. What can you neglect to
simplify the calculation? Does the circuit work if you remove the 100k? Why or
why not? Does the 100k have much of an effect on the frequency response?
Figure 1:Given integrator circuit
Hand
calculations for gain:
Hand
calculations for unity gain and phase:
Since resistor R2 is much
larger than resistor R1, we were able to neglect the 
term from the equation.
Building off the
above equation, we can see that resistor R2 is integral towards eliminating
that term in the gain equation. Without the R2 resistor the result would be a
circuit with too much DC offset as well as clipping at one of the rails.
Part 2: Integrator circuit demonstration
Verify your calculations with experimental
results.
Show, at the unity-gain frequency of the
integrator, that the input and the output have the same peak values. Is the
phase shift between the input and the output what you expect? Why or why not?
Referring again
to the calculations in Part 1, my hand calculations are located again below for
reference in regard to calculations for unity gain and
phase. Note that phase is calculated from the gain equation below.
Hand
calculations for unity gain and phase:
We can continue
by running an AC sweep simulation on the circuit in part 1:
Figure 2:LTSpice simulation of the circuit in Part 1
We can see that the simulation
confirms our calculation for the unity frequency. The gain is roughly 1 (0dB)
at approx. 159Hz.
We will now
implement the integrator circuit onto a breadboard and measure the results. We will
be expecting that the input and output of the circuit will reflect a gain of 1
as well as a phase shift of 90 degrees.
Here is our
implemented integrator circuit:
Here is our
measured result from the replicated integrator:
Figure 3:Input(blue) and output(yellow) of the integrator circuit in Part 1
This confirms our calculation
as the gain is also 1 at 159Hz
Upon further observation we
measured the time delay between the two waveforms to calculate the phase
difference
Here we have a
time delay of 1.6ms, so we will use this to calculate the phase
This calculation
confirms our phase estimation of 90 degrees.
Part 3: Integrator Circuit Demonstration
Next, design, simulate, and build a square-wave
to triangle wave generation circuit.
Assume the input/output frequency is 10
kHz and the output ramp must swing from 1 to 4 V centered around 2.5 V.
Show all calculations and discuss the
trade-offs (capacitor and resistor values, input peak, min, and average, etc.)
The design
parameters of this experiment required us to weigh the tradeoffs between the variables
we could choose for the integrator circuit. This involved the selection of input
voltage, VCM, resistor value, and capacitor value. There is a direct
correlation between selecting a resistor and capacitor as selecting a smaller
capacitor results in requiring larger resistor and vice-versa.
We must also be
careful in choosing our input voltage and common-mode voltage as an incorrect
selection will cause clipping at one of the rails. In the parameters given to
us, the wave must swing from 1v to 4v while centered at 2.5v. This makes sense
since if we were to choose a Vcm that was a greater
distance from the swings, we risk clipping the output of the circuit.
Here is our circuit
design created in LTSpice:
Figure 4:Designed integrator circuit
We chose a
smaller capacitor so we wouldn’t need a very large resistor. Given the capacitor
we were able to select a proportional resistor using the following calculation
for integrator circuits:
After running
our integrator circuit design, we obtained the following input and output:
Figure 5:LTSpice integrator
simulation
Our implemented
circuit should reflect a similar wave form.
Here is our
implementation of the circuit onto a breadboard:
Figure 6:Our integrator design on a breadboard
By measuring the output
against the input for our circuit, we obtained the following waveforms:
Figure 7:Integrator circuit measurements
We
can observe that we were able to successfully transform our square wave input
into a triangle wave given the design parameters we were given and chose. We
also avoided clipping by utilizing the same parameters given to us.