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Operational Amplifier Frequency Response Lab

Objectives:

To become familiar with the frequency response of a typical operational amplifiers in both open loop and closed loop opamp configurations, and to model the frequency response of an op‑amp using PSpice.

Materials List:
1.
741 Op‑Amp
2. Assorted Resistors
3. Dual Power Supply
4. Function Generator
5. Dual Channel Oscilloscope
6. DMM
7. Seven cycle Semilog Graph Paper



Procedure:

A. Unity Gain Bandwidth, UGBW, or Gain Bandwidth Product, GBWP

1. Determine the UGBW for a typical 741 from the specification sheet.

2. Assemble your operational amplifier in a closed loop unity gain, voltage follower configuration. Use ±15V supplies and use 10μF bypass capacitor on your protoboard.

3. Keeping the output swing at or below 100mVpp, determine the upper cutoff frequency, ff, for your voltage follower circuit. Measure the magnitude of the gain as a function of frequency out to 10MHz.

4. Remember, that the product of the gain times the bandwidth remains constant for the non-inverting amplifier, Aofo = Af ff = GBWP since Af = 1 for the follower, ff = UGBW = GBWP.


B. Transient Response

1. Considering that the frequency response of your voltage follower circuit can be approximated as a single pole response at ff = UGBW (i.e. a low pass RC filter with ff = 1/(2 π τ)), derive the following relationship, BW ≈ 0.35/tr, where t, is the rise time of the output voltage in response to a step function of input voltage, defined as the time between the 10% and 90% of final steady state value of output voltage.

2. Drive your voltage follower circuit with a 0 to 80mV square wave at 1kHz, and measure the rise time.

3. Compute the BW from your measured value of tr and compare to ff = UGBW.


C. Slew Rate

1. Determine a typical value for the slew rate of your 741 op amp from the specification sheet.

2. Drive your voltage follower with a 10VPP square wave at 10kHz. Measure and record the output waveform on graph paper and calculate the slew rate. Compare to specification sheet values.

3. From your measured value of slew rate, use differential calculus to determine the maximum value of the sinusoidal peak to peak output voltage without being slew rate limited as a function of frequency. Complete Table 1.

Table 1: Maximum Peak to Peak Output Voltage without Slew Rate Limiting


4. Measure the maximum output without slew rate limited distortion of your voltage follower and complete Table 1, and compare results.


D. Open Loop Frequency Response

1. Consider the circuit shown below in Figure 1.


Figure 1: Circuit for Measuring Open Loop Gain

vo = Ao v3

v3 = va( R3 / (R3 + R2))

vo = - AovRa(R3 / (R3 + R2))

Ao = -((R3 + R2) / R3) • vo / va = -1001(vo / va)

Therefore, by simultaneously measuring vo and va we can determine Ao as a function of frequency.

2. Assemble the circuit shown in Figure 1. At each frequency, select vg to obtain measurable values of both vo and va, but do not exceed the maximum output voltages determined previously in Table 1. For frequencies below 10kHz, use R2 = 100kΩ, R3 = 100 Ω. For frequencies of 10kHz and above, use R2 = 0, R3 = ∞, resulting in Ao = vo / va. Complete Table 2.

Table 2: Open Loop Frequency Response


3. Plot | Ao | dB versus frequency on Semilog paper. Draw straight line approximation to the data (i.e. Bode Plot), and determine the low frequency open loop gain Ao and the open loop bandwidth in fo.

4. Compare in Aofo to the GBWP found in Step A, Part 4.




E. Closed loop Frequency Response Non-inverting

1. Based on the open loop gain as a function of frequency, predict the Bode Plots for the magnitude of the closed loop gain as a function of frequency for closed loop non-inverting gains of 1000, 100, 10, and I for frequencies between 1Hz and 10MHz. Plot the results on the same sheet of semilog graph paper as you plotted the open loop response.

2. Build the circuits for the above conditions and measure the frequency response. Plot the data on your predicted Bode Plots from step above. (Note: There is no need to repeat the gain= 1 voltage follower measurements. Use your data from Step A, Part 3).


F. Closed Loop Frequency Response Inverting

1. Based on the open loop frequency response, predict the inverting closed loop voltage gain magnitude as a function of frequency for inverting closed loop gains of -1000, -100, -10, and -1. Bode plot the magnitude of the gains on one piece of semilog graph paper with the open loop response for frequencies between 1Hz and 10MHz.

2. Build the circuits for the above conditions and measure the magnitude of the voltage gains as a function of frequency. Plot the data on your predicted Bode Plots. Compare results.

3. Compare the actual gain bandwidth product for your inverting and non-inverting configurations for the different values of Af.


G. PSpice Simulations

1. Build a pSpice model of your 741 op amp that includes the dominant pole. One possible configuration is shown in Figure 2. Pick any reasonable value for CDP (say 1μF) and calculate RDP to give desired fDP = fo.


Figure 2: Simplified Model of Op Amp Including Dominant Pole Frequency Response

2. Plot the magnitude (in dB) and phase angle (degrees) on PSpice for the open loop response, and non-inverting closed loop gains of 1000, 100, 10, and 1 for frequencies between 1Hz and 10MHz. Plot all the magnitudes on one page and all the phase angles on another page. Compare with previous predicted and experimental results.

3. Repeat Step 2 above for inverting configuration.


Lab Notes

Lab Data


Electrical Engineering lab key words: OpAmp, open loop, dominant pole, response, inverting, non-inverting, bode plot, gain, closed loop response, bandwidth, operational amplifier, frequency response, DC circuit analysis, AC circuits.

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