Output Impedance

Along the way

1
Low impedance is the goal. An ideal rail has \(Z_o \approx 0\): load steps do not move \(V_{\mathrm{out}}\). Here a small series \(R\) is always present (wiring / residual) so DC \(|Z_o| \approx R_s\).
2
The load only cares about its pins. Anything between the ideal source and the load — series \(R\), series \(L\), local caps — is part of \(Z_{\mathrm{out}}\) as the load sees it.
3
Series \(L\) grows with frequency. Wire, bead, connector, or filter inductor: \(Z_L = j\omega L\). Fast \(\Delta I\) (sharp load edges) is where that series impedance hurts most.
4
Repeating load steps have a rate. Set light/heavy current and the step rate (kHz). The waveform is square-ish, not a pure sine, but much of the energy sits near that rate and its harmonics — watch the rose line on \(|Z_o|\).
5
Ceramic first, then bulk. Local ceramic: smaller \(C\), low ESR — holds high-frequency \(|Z_o|\) down. Local bulk: larger \(C\), often higher ESR — mid-band energy and damps the peak.
6
Resonance & damping. Series \(L\) with the local caps peaks \(|Z_o|\) near \(f_0 \approx 1/(2\pi\sqrt{L\,C_{\mathrm{tot}}})\). Ceramic alone still leaves a peak; add bulk and raise its ESR to damp. Keep ceramic for the high-\(f\) floor.

Build the network · watch Zo and the load step

Series \(R\) always on · tick L / bulk / ceramic · green ±5% · rose = load rate on |Zo|

Series L Local ceramic Local bulk

Series R (mΩ) · always on Series L (nH) Local ceramic C (µF) Local ceramic ESR (mΩ) Local bulk C (µF) Local bulk ESR (mΩ) Load-step rate (kHz) Load light (mA) Load heavy (mA)

Series \(R\) is always in the path (min 0.5 mΩ). Tick L / bulk / ceramic to insert them. Load steps light↔heavy at the rate you set. Charts: \(I_{\mathrm{LOAD}}\), \(V_{\mathrm{OUT}}\) (±5% band), \(|Z_o(f)|\).

\(I_{\mathrm{LOAD}}(t)\) · repeating steps at the chosen rate

\(V_{\mathrm{OUT}}(t)\) · blue in-spec · red out · green = ±5%

\(|Z_{\mathrm{out}}(f)|\) · rose = load rate · amber ≈ \(f_0 = 1/(2\pi\sqrt{L C_{\mathrm{tot}}})\)

Network—

Status—

Peak |ΔV|—

|Zo| @ load rate—

Approx \(f_0\)—

Load rate—

Peak |Zo|—

\[ Z_{\mathrm{ideal}} \approx 0 \]

→ low-impedance rail

\[ Z_{\mathrm{series}} = R_s + j\omega L \]

→ —

\[ Z_o = (R_s + j\omega L) \,\|\, Z_{\mathrm{bulk}} \,\|\, Z_{\mathrm{cer}} \]

→ —

Each enabled cap branch is \(\mathrm{ESR}+1/(j\omega C)\). Series path is always \(R_s\) and optional \(L\). Load-step rate near the |Zo| peak is the stress case.

Try it: (1) Series \(R\) only — flat \(|Z_o| \approx R_s\), small \(\Delta V\). (2) Add series \(L\) — edges on \(V_{\mathrm{out}}\) spike; \(|Z_o|\) rises with \(f\). (3) Add local ceramic only — high-\(f\) floor drops, but the LC peak can still be sharp. (4) Add local bulk, set load rate near \(f_0\); raise bulk ESR and watch the peak dampen.

Analog Intuition

Build the network · watch Zo and the load step