PROBLEM 064 · Easy · Gain error from finite loop gain
Short on Gain
Hit 14 dB with only 40 dB of op-amp gain
The problem
Build a non-inverting amplifier with a closed-loop gain of 14 dB (5.0×). This time the op amp is weak: only 40 dB of open-loop gain. The ideal formula 1 + R1/R2 is no longer exact: the real gain is A/(1 + A·β).
Choose R1 and R2 so that the real closed-loop gain is within 0.4 dB of 14 dB. A designer picks the ratio from the exact formula, not from the ideal one.
The test bench
- The test bench supplies the op amp as a ready-made block with terminals on the nets named “inp”, “inn” and “out”: DC gain 40 dB (100×), one pole at 100 kHz (unity-gain frequency 10 MHz), output resistance 100 Ω.
- The test bench applies the AC stimulus to “inp”.
Numbers to hit
- Closed-loop gain between 13.6 dB and 14.4 dB
- Bandwidth (−3 dB) at least 1 MHz
- Peaking at most 0.5 dB
Design it yourself
Draw the circuit on a schematic canvas, size every transistor, and see it simulated in your browser with ngspice and the SkyWater SKY130 models. Every transistor lights up green, gold or red by operating region as you move the sliders.
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