Capacitance Multiplier

Use the Miller effect to make a small capacitor draw the current of a larger capacitance.

A1 is an inverting amplifier with R1 = 10 kΩ and RF = 90 kΩ, giving gain near −9. C1 = 100 nF connects the input port to the inverted output. The voltage change across C1 is about ten times the port-voltage change, so it draws the current of a larger grounded capacitor. RS = 1 kΩ exposes the charging response to a 0–0.5 V pulse.

$$C_{\mathrm{eff}}\approx C_1(1-A_V)=1\,\mathrm{\mu F}$$ $$\tau\approx(R_S\parallel R_1)C_{\mathrm{eff}}\approx0.91\,\mathrm{ms}$$

Drive is green, the capacitor-port voltage red and input current blue. R1 also loads the port, so the final voltage is about 10/11 of the drive. The amplifier output must remain within its limits; increasing effective capacitance increases the required internal swing. This active port is not an energy-storage substitute for a physical large capacitor.

Read the results. The saved transient chart uses separate voltage and current panels; the table provides numerical samples. The first voltage probe is green and the second red. The first current probe is blue; a second current probe is purple.

Model limits. The three-terminal op-amp model has implicit ±12 V output limits, 200,000 low-frequency gain and 10 MHz gain-bandwidth product. Supply pins are intentionally absent in this functional model. In Schmitt-trigger and relaxation/integrator oscillator examples, the switching amplifier uses a 100 kHz gain-bandwidth setting to resolve transitions cleanly at the saved time step. It omits detailed slew-rate, input common-mode, output-current and thermal limits.

Try it. Set RF to 190 kΩ; effective capacitance increases from about 1 µF to 2 µF. Restore the original values after comparing the results.