in which Julia realizes the limitations of op amps
The two golden rules detailed before are not entirely accurate.
Golden Rule I*: Under negative feedback, the op amp will do everything it can to make V+ - V- = 0, but this will never truly be the case--there will always be a small offset voltage, Vos, between these two inputs.
Golden Rule II*: The op amp draws a tiny amount of current through its inputs (~pA).
Golden Rule II*: The op amp draws a tiny amount of current through its inputs (~pA).
Lab 9-1: Op Amp Limitations
A) Slew rate
Part I: Square wave input
We drove the 411 with a 1 kHz square wave and did not observe slew with this excellent op amp, which has a slew rate of 15 V/μs.
The circuit diagram for measuring slew rate in a 411 or 741 op amp (H&H). |
We drove the 411 with a 1 kHz square wave and did not observe slew with this excellent op amp, which has a slew rate of 15 V/μs.
The slew of a 411 op amp is quite small, not visible for 1 kHz input frequencies. (Here purple is input, yellow is op amp output; the DC offset was added by the function generator and removed from input by AC coupling.) |
A 411 (yellow) accurately follows an input square wave (purple); the offset was caused by a DC offset from the function generator, removed by the AC-coupled oscilloscope. |
If we drive with a high enough frequency, we expect the output to greatly decrease (but maintain the same input frequency), as the finite slew rate of the 411 would prevent a rapid climb to the wave's amplitude. We expect this effect to occur where:
omega*amplitude = 2*pi*f*Vin = 12 x 10^6 V/s
Vin(max) = 5
fmax = 382 kHz
So, for a 5 V input sine wave, we expect the 411 to accurately follow waves of up to 382 kHz frequencies, but to lag behind at greater frequencies.
The circuit can accurately reproduce quite high frequencies (158 kHz here) with no observable phase shift. |
Driving the circuit with a sine wave of higher frequency (619 kHz here) causes a larger phase shift, but also a comparable decrease in amplitude of both input (yellow) and output (purple) signals. |
We repeated the experiments with a 741 op amp, which has a "typical" slew rate of 0.5 V/us. While the 411's slew rate was difficult to perceive, the 741's was quite clear at standard driving frequencies.
The falling slew rate of the 741 (yellow) was not high enough to accurately reproduce a square wave input (purple) at 1.9 kHz. |
The falling slew rate is 2.88 V/4.680 us = 0.615 V/us. This is slightly higher than the expected slew rate.
The rising slew rate was slightly higher. |
Measuring the slew rate from a 741 driven with a 1.9 kHz sine wave. |
Calculation for the frequency at which a 741 would no longer accurately follow a sine wave:
max: omega*amplitude = 2*pi*f*Vin = 0.6 x 10^6 V/s
Vin(max) = 5
fmax = (0.6 x 10^6)/(31.4) = 86 kHz
This was in accordance with our experimental findings.
At 86 kHz input sine wave (purple), the 741 produces a triangle wave (yellow). |
Part B) Offset voltage (Vos)
A railing op amp (yellow) from a large input signal (purple). |
Shorting the input (yellow) allowed for measurement of the offset voltage (purple). |
Part II: Minimize the effect of Vos
Upon viewing a flatline at -10.4 V no matter the input, we assumed our op amp was no longer operating. A new 741 showed a reasonable signal, and we adjusted the potentiometer so Vout = 0, thus minimizing the offset voltage between V- and V+.
C) Bias Current
Now we removed the extra 10 kΩ resistor to see Ibias.
Suddenly we measured a -0.384 V line with no Vin (measured -384 mV output).
Thus we expect -0.384/(10 kΩ) = -3.8 x 10^-8 = -38 nA, in reasonable agreement with the 741's specs of 80 nA.
Lab 9-2: Op amp integrator
The integrator makes a nice integrating triangle wave when driven with square wave.Driving with a 1 kHz, 1 Vpp square wave (yellow) causes a triangle wave output (purple), as expected with an integrator. |
500 Hz square wave input (yellow) makes less frequent, larger-amplitude oscillations in the output (yellow). |
Removing the 10 MΩ resistor makes the output voltage steadily increase, as the capacitor charges.
Lab 9-4: AC Amplifier: microphone amplifier
To conclude our experiments in electronics, Kathryn and I build an AC amplifier to amplify sound signals--to act as a microphone. We used a single-supply op amp here (the LM358) so we could easily power it with three AA batteries. Our circuit amplified signals of less than 20 mV to a maximum of +4.5 V; the input bias voltage goes directly to the output, without amplification, so the DC gain is unity so the signal should be clearly evident over the DC offset.
We tried whistling into the microphone and observed higher pitches produced higher-frequency waves (generally they appeared to be sine waves, as expected when whistling), and louder noises increased the amplitude.
We tried whistling into the microphone and observed higher pitches produced higher-frequency waves (generally they appeared to be sine waves, as expected when whistling), and louder noises increased the amplitude.