Laboratory 1
Operational Amplifier-Based Integrators
OBJECTIVE
To construct an op-amp based integrator and investigate its characteristics.
PRELAB
The schematic of an op-amp based integrator is depicted in Fig. 1-1 below.
Fig. 1-1: An operational amplifier-based integrator
1. Use ideal op-amp analysis to obtain an expression for the output voltage of the circuit
and demonstrate that it behaves as an integrator. What is the input resistance of the
integrator?
2. What is the output vo of the integrator if the input signal vi has a dc component? What
could be done to avoid this problem?
3. Let the input vi to the integrator be a 50% duty cycle square wave of period T that
switches between the voltage levels V and -V. Assume that the square wave begins at
t = 0 at a level of V volts. Also assume that the initial voltage of the capacitor is zero.
Sketch the waveform of the resulting output signal vo. What is the peak-to-peak
voltage of vo?
4. Design an op-amp based integrator that has an input resistance of l0kΩ. The
integrator should produce a 5V peak-to-peak output voltage when the input signal is a
1kHz square wave varying between -2.5 and +2.5V. Simulate your integrator using
PSpice and verify that it works as expected.
5. Assume that the input to the integrator is a sinusoid of frequency ω. Use phasor
analysis to obtain an expression for the output phasor V0 in terms of the input phasor
Vi. The ratio Vo/Vi is a function of ω that is called the frequency response H(ω) of the
circuit. Obtain an expression for the frequency response of the integrator. Your
frequency response expression will be in terms of R, C. and ω. At what frequency F
(in Hz) is the magnitude of the frequency response equal to 1?
6. Use PSpice to obtain a plot of the magnitude response |Vo/Vi| of the integrator
designed in part 4. Use cursors to determine the frequency at which the gain of the
integrator is 1. Compare this with your theoretical prediction from part 5. Hint: Use a
sinusoidal input signal of amplitude 1V and then perform a frequency sweep over the
appropriate frequency range.
IN LAB
1. Construct the integrator that you designed in part 4 of the prelab. Test it with the
square-wave input of part 4 and verify that the circuit works as expected. Obtain a
printout of the oscilloscope screen with traces of both vi and vo. What is the peak-topeak voltage of the output waveform? Compare with the expected peak-to-peak
voltage.
2. Apply a sinusoidal input to the integrator. Experimentally determine the frequency at
which the integrator has unity gain. Make comparisons with your prelab results.
3. Using a sinusoidal input, obtain data that will help you generate a plot of the
magnitude response of the integrator (over the range 100Hz to 10kHz). Tabulate your
data in your lab notebook. Use appropriate computer software to obtain a semilog
plot of the magnitude response of the integrator. How do your measurements
compare with the prelab predictions? Note: If you use Matlab, you can use the
sernilogx command to obtain the desired semilog plot.
4. Apply a sinusoidal input to the integrator and observe both the input and output
signals on the oscilloscope. What is the phase difference between the input and output
signals? Does the output lag or lead the input? Does the phase difference change as
the frequency of the input signal changes? Compare your observations with the
phasor analysis in your prelab. Do the results make sense? Explain.
5. Experiment with feeding different waveforms into your integrator and observe the
corresponding output waveforms. Comment on your observations.