PROBLEM 066 · Medium · Feedback with a capacitor
Ramp Maker
An integrator with a 100 kHz unity-gain frequency
The problem
Build an inverting integrator. The signal “in” drives a resistor Rin to the inverting input “inn”; a capacitor Cf runs from “out” to “inn”; the non-inverting input is tied to a 0 V source named “inp”. Choose Rin and Cf so the gain magnitude is 1 (0 dB) at 100 kHz.
A capacitor’s impedance 1/(jωC) falls with frequency, so the gain Zf/Rin = 1/(jω·Rin·Cf) falls at 20 dB per decade, with a −90° phase: the output is the integral of the input. The unity-gain frequency is 1/(2π·Rin·Cf).
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 80 dB, one pole at 1 kHz (unity-gain frequency 10 MHz), output resistance 100 Ω.
- The test bench applies the AC stimulus to “in” (the source “inp” stays at 0 V).
Numbers to hit
- Frequency where the gain is 0 dB between 85 kHz and 118 kHz
- Gain at 10 kHz between 18 dB and 22 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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