Performance-Based Assessments for Analog Integrated Circuit Competencies

Use a dual-voltage, regulated power supply to supply power to the opamp. I recommend using a “slow” op-amp to make the slewing more easily noticeable. If a student chooses a relatively fast-slew op-amp such as the TL082, their signal frequency may have to go up into the megahertz range before the slewing becomes evident. At these speeds, parasitic inductance and capacitance in their breadboards and test leads will cause bad “ringing” and other artifacts muddling the interpretation of the circuit’s performance.

I have had good success using the following values:

V = 12 volts

-V = -12 volts

V_in = 4 V peak-to-peak, at 300 kHz

U₁ = one-half of LM1458 dual operational amplifier

An extension of this exercise is to incorporate troubleshooting questions. Whether using this exercise as a performance assessment or simply as a concept-building lab, you might want to follow up your students’ results by asking them to predict the consequences of certain circuit faults.

The purpose of this exercise is to empirically determine the gain-bandwidth product (GBW) of a closed-loop opamp amplifier circuit by setting it up for three different closed-loop gains (A_CL), measuring the cutoff frequency (f_−3dB) at those gains, and calculating the product of the two (A_CL f_−3dB) at each gain. Since this amplifier is DC-coupled, there is no need to measure a lower cutoff frequency in order to calculate bandwidth, just the high cutoff frequency.

What GBW tells us is that any opamp has the tendency to act as a low-pass filter, its cutoff frequency being dependent on how much gain we are trying to get out of the opamp. We can have large gain at modest frequencies, or a high bandwidth at modest gain, but not both! This lab exercise is designed to let students see this limitation. As they set up their opamp circuits with greater and greater gains ([(R₂)/(R₁)] 1), they will notice the opamp “cut off” like a low-pass filter at lower and lower frequencies.

For the “given” value of unity-gain frequency, you must consult the datasheet for the opamp you choose. I like to use the popular TL082 BiFET opamp for a lot of AC circuits, because it delivers good performance at a modest price and excellent availability. However, the GBW for the TL082 is so high (3 MHz typical) that breadboard and wiring layout become issues when testing at low gains, due to the resulting high frequencies necessary to show cutoff. The venerable 741 is a better option because its gain-bandwidth product is significantly lower (1 to 1.5 MHz typical).

It is very important in this exercise to maintain an undistorted opamp output, even when the closed-loop gain is very high. Failure to do so will result in the f_−3dB points being skewed by slew-rate limiting. What we’re looking for here are the cutoff frequencies resulting from loss of small-signal open-loop gain (A_OL) inside the opamp. To maintain small-signal status, we must ensure the signal is not being distorted!

Some typical values I was able to calculate for GBW product are 3.8 ×10⁶ for the BiFET TL082, 1.5 ×10⁶ for the LM1458, and around 800 ×10³ for the LM741C.

An extension of this exercise is to incorporate troubleshooting questions. Whether using this exercise as a performance assessment or simply as a concept-building lab, you might want to follow up your students’ results by asking them to predict the consequences of certain circuit faults.

I recommend setting the function generator output for 1 volt, to make it easier for students to measure the point of “cutoff”. You may set it at some other value, though, if you so choose (or let students set the value themselves when they test the circuit!).

For capacitors, I recommend students choose three (3) capacitors of equal value if they wish to build the Sallen-Key circuit with a Butterworth response (where C₂ = 2 C₁). Capacitor C₁ will be a single capacitor, while capacitor C₂ will be two capacitors connected in parallel. This generally ensures a more precise 1:2 ratio than choosing individual components.

I also recommend having students use an oscilloscope to measure AC voltage in a circuit such as this, because some digital multimeters have difficulty accurately measuring AC voltage much beyond line frequency range. I find it particularly helpful to set the oscilloscope to the “X-Y” mode so that it draws a thin line on the screen rather than sweeps across the screen to show an actual waveform. This makes it easier to measure peak-to-peak voltage.

Values that have proven to work well for this exercise are given here, although of course many other values are possible:

V = 12 volts

-V = -12 volts

R₁ = 10 kΩ

R₂ = 10 kΩ

R_comp = 20 kΩ (actually, two 10 kΩ resistors in series)

C₁ = 0.001 μF

C₂ = 0.002 μF (actually, two 0.001 μF capacitors in parallel)

U₁ = one-half of LM1458 dual operational amplifier

This combination of components gave a predicted cutoff frequency of 11.25 kHz, with an actual cutoff frequency (not factoring in component tolerances) of 11.36 kHz.