Output impedance

Part 3 · Voltage Regulation

Key point: the load only sees \(Z\) at its pins. Series \(R\) and \(L\) raise it. Local ceramic and bulk bring it down, and \(L\) with those caps can peak near \(f_0\).

3.3 V, 100 mA ↔ 500 mA. The ±5% window is ±165 mV. Rose marker on \(|Z|\) is the load rate.

1
Series \(R\) is a flat floor.
10 mΩ, no \(L\), no caps. \(|Z_o|\) is 10 mΩ at every frequency. The 500 mA plateau drops 5.0 mV. In spec.
2
Series \(L\) hits the edge.
200 nH. Same 50 kHz steps. \(L\,di/dt\) lifts the peak to 105 mV, still inside ±165 mV. \(|Z|\) at 50 kHz is 63.6 mΩ and still rising.
3
Ceramic drops the high-frequency floor.
10 µF, 5 mΩ. \(f_0\) is 112.5 kHz. At 50 kHz you are under it: peak \(|\Delta V|\) falls to 55.7 mV. The \(|Z|\) peak is 1.335 Ω, up at \(f_0\).
4
Park the load rate on that peak.
112 kHz. \(|Z_o|\) there is 1.332 Ω. Peak \(|\Delta V|\) is 232.6 mV. That leaves the ±5% band.
5
Bulk damps the peak.
47 µF at 40 mΩ. \(f_0\) moves to 47.1 kHz, and the load rate moves with it. Peak \(|Z|\) is 109.9 mΩ. Peak \(|\Delta V|\) is 30.8 mV. Back in spec. Ceramic is still the high-frequency floor.

\(Z_o\) is at the load pins. Each cap is ESR \(+ 1/(j\omega C)\), in parallel with \(R_s + j\omega L\). The .asc uses C1 ceramic, C2 bulk.

What the load sees

Series \(R\) always on · tick \(L\), ceramic, bulk

Series L Local ceramic Local bulk

Series R (mΩ) Series L (nH) Ceramic C (µF) Ceramic ESR (mΩ) Bulk C (µF) Bulk ESR (mΩ) Load rate (kHz) Light (mA) Heavy (mA)

\(V_{\mathrm{OUT}}\) · blue inside ±5% · red outside

\(I_{\mathrm{LOAD}}\)

\(|Z_o(f)|\) · rose = load rate · amber ≈ \(f_0\)

Network—

Status—

Peak \(|\Delta V|\)—

\(|Z_o|\) @ rate—

\(f_0\)—

Load rate—

Peak \(|Z_o|\)—

\(Z_{\mathrm{series}} = R_s + j\omega L\)

→ —

\(Z_o = Z_{\mathrm{series}} \,\|\, Z_{\mathrm{bulk}} \,\|\, Z_{\mathrm{cer}}\)

→ —