The Capacitor Buys Microseconds, the Regulator Owns Milliseconds

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

The Capacitor Buys Microseconds, the Regulator Owns Milliseconds

An ESP32 prototype resets exactly when its Wi-Fi radio keys up to transmit: idle draw is only 20-80 mA, but the power amplifier spikes current to roughly 300-500 mA in microseconds, and the brownout detector trips near ~2.7 V. The chapter sizes the fix from a worked example — a 300 mA surge, a ~10 us regulator response, and a tolerated 0.1 V droop — landing on a 47-100 uF bulk capacitor. This audit asks the question that sizing exercise invites: does that capacitor actually stop the reset, or only if the regulator itself can supply the sustained peak?

Companion to the chapter Hardware Prototyping Case Studies — every number here comes from that chapter.

Ada: The sizing math here is short enough to check by hand, and worth checking because it hides a second condition the headline number can obscure. The chapter takes a 300 mA surge, a 10 microsecond regulator response, and a tolerated droop of 0.1 V.

• Charge the transient demands: Q = I x dt = 0.3 x 10e-6 = 3.000e-6 C, that is 3 uC
• Capacitor to hold the droop: C = Q / dV = 3e-6 / 0.1 = 30e-6 F, that is 30 uF

Both match, and the recommended 47-100 uF adds margin. Let me confirm that margin by running the droop backwards for the recommended parts, using dV = I x dt / C:

• 47 uF: 0.3 x 10e-6 / 47e-6 = 0.063830 V, about 64 mV
• 100 uF: 0.3 x 10e-6 / 100e-6 = 0.030000 V, exactly 30 mV

So 47-100 uF holds the sag to 30-64 mV, comfortably under the 100 mV budget. But now the hidden condition. That whole calculation only covers the roughly 10 microseconds until the regulator catches up. If the regulator itself cannot supply the sustained peak — the chapter’s 250 mA LDO facing a 400 mA burst leaves a 400 - 250 = 150 mA deficit — the capacitor is merely bridging until it drains. How long can even 100 uF cover a continuous 150 mA shortfall within the same 0.1 V budget? t = C x dV / I = 100e-6 x 0.1 / 0.15 = 66.7e-6 s, about 67 microseconds.

That is the audit’s real lesson: the capacitor answers a microsecond question and the regulator answers a millisecond one. A TX burst that lasts milliseconds will brown out a rail behind an under-rated regulator no matter how large the bulk cap — which is exactly why the chapter insists the supply be rated for the peak, not the average.

Every number above is taken from the chapter’s own material and re-derived step by step.