Why Close the Loop

Along the way

1
Green is the spec. 3.3 V ±5% here. The load does not care how you got there — only that you stay in the band.
2
Open loop droops \(ΔI\,R_{\mathrm{out}}\). Drive is trimmed at idle. Extra load current through the plant’s \(R_{\mathrm{out}}\) is volts you lose, and nothing pulls them back.
3
Close it: error drives the plant. \(e = V_{\mathrm{ref}} - F\,V_{\mathrm{out}}\). Compensator \(C\) (here a gain \(K\)) and plant \(P\) sit in the forward path.
4
\(K\) divides the droop. Closed-loop, \(ΔV = ΔI\,R_{\mathrm{out}}/(1+K)\). Weak \(K\) still leaves the ±5% window.
5
Hard load is a bigger \(ΔI\). Same \(K\) and \(R_{\mathrm{out}}\), more amps → more volts. Red = left the window.

Try it: Open loop (full \(ΔI R_{\mathrm{out}}\)). Weak loop — same current, smaller droop, still red. Tight loop stays blue. Hard load keeps a moderate \(K\) and raises \(ΔI\) until you leave the band again.

What we ignored: stability, phase margin, and a real compensator network. This \(K\) is a number, not yet Type II. Next: loop gain \(T=PCF\).

Open vs closed · load step

Top: \(V_{\mathrm{OUT}}\) vs ±5% window · Bottom: \(I_{\mathrm{LOAD}}\)

Loop gain K

droop \(ΔI R_{\mathrm{out}}/(1+K)\) → —

vs open-loop \(ΔI R_{\mathrm{out}}\) → —

Load step ΔI (A) Plant Rout (Ω)

K = 0 is open loop: idle is trimmed to 3.3 V. The step drops Vout by ΔI·Rout. Nothing pulls it back.

Block diagram: Vref into summing junction, through Compensator and Plant to Vout, Feedback returning to the summer — Forward: \(C\) then \(P\). Return: \(F\). Here \(C\) is a gain \(K\).

Vout · blue in-spec · red out · green = ±5%

Iload · step up, then release

Vout in spec Vout out of spec Vref Iload

Dig deeper — the circle in algebra

Error at the summer is \(e = V_{\mathrm{ref}} - F V_{\mathrm{out}}\). The forward chain is \(L = C P\). Then

\[ ΔV = \frac{ΔI\,R_{\mathrm{out}}}{1+K} \]

Idle is trimmed to \(V_{\mathrm{ref}}\). Extra load current through the plant’s \(R_{\mathrm{out}}\) is a disturbance. Closed-loop it is divided by \(1+K\). Open loop (\(K=0\)) takes the full \(ΔI R_{\mathrm{out}}\) hit. A later page puts a pole at the origin so even the leftover DC error goes to zero, and asks whether a large \(K\) is still stable.

Analog Intuition

Open vs closed · load step