- Review properties of operational amplifier.
- Investigate properties of integrator and differentiator circuits.
- Investigate properties of a passband Sallen-Key active filter.
- Investigate the use of frequency sweeps to analyze filter characteristics.

Download lab5 materials

The pin layout of the LM1458 Dual Operational Amplifier (datasheet) used in this lab is shown in Figure 1 below.

Figure 1. LM1458 Pin Diagram |
Figure 2. Inverting amplifier |

An ideal (inverting) Integrator can be build using the schematic in Figure 3 below.

Figure 3. Ideal integrator circuit |
Figure 4. Improved integrator circuit. |

The ideal integrator suffers from two main limitations. One comes
from the fact that the output voltage of the opamp can not exceed the
supply voltage. The output of the integrator is inversely proportional
to the time constant *τ* = *R _{s}C_{f}*. The
larger the time constant

An ideal (inverting) Differentiator can be build using the schematic in Figure 5 below.

Figure 5. Ideal differentiator circuit |
Figure 6. Improved differentiator circuit. |

Like the integrator before, the ideal differentiator has some
limitations. The output is limited to the supply voltages, and since
the differentiator is a noise-amplifying device, it suffers from
excessive response to high-frequencies. Generally a practical
differentiator is combined with a low-pass filter to smooth the
high-frequency noise effects. Figure 6 shows some possible
modifications to the ideal circuit. A large (over 1 MΩ) resistor
*R _{x}* may be inserted in parallel with

Figure 7. Sallen-Key active filter

It can be shown that the transfer function of the filter is

Observe that the transfer function shown in equation above is quite
complex. The analysis can be greatly simplified, however, if all
frequency-determining capacitors are set equal to each other, as well
as all frequency-determining resistors. That is, let
*R*_{1} = *R*_{2} = *R*_{3}/2
= *R* and *C*_{1} = *C*_{2} =
*C*.
The original transfer function then simplifies to

A second order band-pass transfer function can written in the following standard form

Comparing coefficients of the last two equations, we see that

An example Sallen-Key bandpass filter, analyzed using MATLAB nodal equations and the symbolic toolkit, is shown the following MATLAB script.

You learned how to set the function generator to do a frequency sweep in lab 1. It is tempting to analyze an active filter by setting the function generator to sweep through a frequency range of interest and see how the output waveform changes.

An attempt to predict the results of such a measurement resulted in the following MATLAB script. The results were less than satisfactory. The filter examined was a passband filter with center frequency of 1200 Hz and 100 Hz bandwidth. The calculated waveform showed a center frequency of about 1000 Hz and some unexpected structure in the envelope. Either there is a problem with the script or the measurement itself is more complicated than anticipated.

As part of this lab, perform the measurement and report on the results. See if you can find a problem in the MATLAB script.

- Characterize your operational amplifier by doing the following.
- Construct the inverting amplifier circuit shown in Figure 1,
with a gain of -10. Suggested resistances are R
_{f}= 470 kΩ, R_{s}= 47 kΩ, and R_{C}= 10 kΩ. - Measure the gain and phase shift from 100 Hz to 100 kHz. Use a MATLAB script to make the measurements. Plot the results and tabulate values at decade intervals (100 Hz, 1 kHz, 10 kHz, and 100 kHz).
- Measure the saturation (clipped) peak-to-peak level at 1 kHz. Set the input so that the ideal output value would be 25 volts peak-to-peak. Attach an image of the oscilloscope output to the report.
- Measure the slew rate by using a square-wave at a frequency that clearly shows slew-limited behavior. Measure the rise and fall times and the peak-to-peak output voltage. Attach an image of the oscilloscope output to the report.
- Find the frequency at which the gain drops to 0.707 of its ideal value. Measure the phase shift at that frequency.
- Ground the input of the OpAmp and measure the output voltage (offset voltage).

- Construct the inverting amplifier circuit shown in Figure 1,
with a gain of -10. Suggested resistances are R
- Build an integrator circuit as shown in Figure 3. Suggested values
are 40-100 kΩ for
*R*, 100 nF to 0.01 μF for_{s}*C*, and 10-20 kΩ for_{f}*R*. Try the ideal circuit first and determine the effects of offset voltage by measuring the rate of change of the output voltage with the input grounded. You may need to short the integrating capacitor before starting your measurement. If the output is unstable, insert a large resistor in parallel with the capacitor, as shown in Figure 4. Then characterize the system as follows:_{c}- Measure the frequency response (magnitude and phase) of the system. Compare the results to theoretical expectations.
- Show that the output of the integrator is a triangle wave if the input is a square wave. Capture a demonstration oscilloscope trace showing the frequency and peak-to-peak magnitude of input and output.
- Capture an oscilloscope image showing the output and input of the integrator if the input is a noise signal from the signal generator.

- Build an differentiator circuit as shown in Figure 5. Suggested values
are 40-100 kΩ for
*R*, 100 nF to 0.01 μF for_{f}*C*, and 10-20 kΩ for_{s}*R*. Try the ideal circuit first and determine the effects of noise by evaluating the output for a variety of input signals. If the output noise levels are unacceptable, modify the circuit by the addition of_{c}*R*and/or_{x}*C*, as shown in Figure 6. Then characterize the system as follows:_{x}- Measure the frequency response (magnitude and phase) of the system. Compare the results to theoretical expectations.
- Show that the output of the differentiator is a square wave if the input is a triangle wave. Capture a demonstration oscilloscope trace showing the frequency and peak-to-peak magnitude of input and output.
- Capture an oscilloscope image showing the output and input of the differentiator if the input is a noise signal from the signal generator.

- Build a Sallen-Key circuit as shown in Figure 7. Design the
filter for a center frequency of 1500 Hz and a
*Q*of 4. Keep resistor values above 1 kΩ and capacitance values above 100 pF. Then characterize the system as follows:- Measure the frequency response (magnitude and phase) of the system. Compare the results to theoretical expectations.
- Calculate the observed values of gain, center frequency, and Q.
- Capture an oscilloscope image showing the output and input of the filter if the input is a noise signal from the signal generator.

- Simulate your passband filter in SPICE and compare the results to your measured frequency response above. Adjust the circuit parameters of your SPICE model to match the measured values of your circuit components.
- Capture an oscilloscope image showing the input and output of the filter above with the function generator set to sweep from 1 kHz to 2 kHz, assuming your passband filter is centered at 1500 Hz. Discuss the resulting image. Does the modulated sweep have its peak value at a time for which the input is the center frequency of the filter? Is the bandwidth of the modulated sweep what you expected? Are there any unexpected structures?

Maintained by John Loomis,
last updated *25 October 2010 *