Feedback Network Analyzer — Control Loops

Part 8 · Control Loops

Feedback network

Key point: \(T=P\cdot C\cdot F\) in dB. Last page built Type II (\(C\)). Here the plant can be fast or slow, Type II may be yours to retune or frozen inside an IC, and \(F\) is \(C_{\mathrm{ff}}\) (zero) and \(C_{\mathrm{filt}}\) (pole). Read PM and BW on loop gain.

Each case: the condition moves first (watch PM), then compensation. Red PM is in trouble.

1
Goal: \(F\) flat, Type II at ~60°.
Default plant. Compensator is the Type II you just built. Feedback is 0 dB — no \(C_{\mathrm{ff}}\), no \(C_{\mathrm{filt}}\). \(T\) is the dB sum. Read BW and PM.
2
Slow plant — retune Type II.
Plant LF pole drops. Crossover moves. You still own \(C\): walk the Type II zero (and a bit of gain) until PM comes back.
3
Fast plant — retune Type II.
Plant poles move out. Zero stays near 50 kHz — same neighborhood as the original Type II — and PM comes back.
4
Same plant, faster loop.
Leave the fast plant. Raise Type II gain: \(f_c\) walks out (PM sags). Then slide the zero and high pole to buy the margin back at the new bandwidth.
5
Type II is frozen — internal compensation.
Slow plant again, but \(C\) is locked. You do not get those Type II knobs. PM and BW sit wherever the IC left them.
6
Feedforward (\(C_{\mathrm{ff}}\)) with frozen Type II.
The FB zero is \(C_{\mathrm{ff}}\) across the divider. You cannot retune \(C\), so you buy phase in \(F\). Watch the FB sketch light up.
7
\(C_{\mathrm{filt}}\) wrecks the loop.
Back to a healthy Type II. Enable the FB pole — that is \(C_{\mathrm{filt}}\) on the FB node — near crossover. PM collapses.
8
You cannot Type-II your way out of a bad \(C_{\mathrm{filt}}\).
Pole still sitting on the loop. Walk the Type II zero anyway. The extra lag is still in \(F\). Dock stays sick.
9
Park \(C_{\mathrm{filt}}\) above the loop.
Same pole, 400 kHz — well above BW. Type II back to the 60° network. The filter is still there; it is just out of the way.

FB Enable Zero is \(C_{\mathrm{ff}}\). Enable Pole is \(C_{\mathrm{filt}}\). If Type II is inside the IC, those two knobs are what you have left.

Plant + \(C\) + \(F\)

Four Bodes · hover syncs frequency · gray line is loop \(f_c\)

fc — kHz PM —°

Gain (dB):

LF Pole (kHz):

Zero (kHz):

HF Pole (kHz):

Plant

At \(f_c\) — dB —°

X: — kHz | Mag: — dB | Phase: — °

Feedback

At \(f_c\) — dB —°

X: — kHz | Mag: — dB | Phase: — °

Gain (dB):

Enable Zero Zero (kHz):

Enable Pole Pole (kHz):

Gain (dB):

LF Pole (kHz):

Pole (kHz):

Zero (kHz):

Type II frozen — internal compensation

Compensator

At \(f_c\) — dB —°

X: — kHz | Mag: — dB | Phase: — °

Loop gain

Phase margin —°

Crossover \(f_c\) — kHz

T(s) = P + C + F: —

X: — kHz | Mag: — dB | Phase: — °

Loop-gain notes & slider limits

Adjust slider limits

Plant Parameters

Gain Min (dB): Max (dB):

LF Pole Min (kHz): Max (kHz):

Zero Min (kHz): Max (kHz):

HF Pole Min (kHz): Max (kHz):

Compensator Parameters

Gain Min (dB): Max (dB):

LF Pole Min (kHz): Max (kHz):

Pole Min (kHz): Max (kHz):

Zero Min (kHz): Max (kHz):

Feedback Parameters

Gain Min (dB): Max (dB):

Zero Min (kHz): Max (kHz):

Pole Min (kHz): Max (kHz):

Reading loop gain

A Bode plot shows how each pole and zero contributes magnitude (dB) and phase (degrees) versus frequency. Loop gain here is P + C + F in dB — the open-loop product split into plant, compensator, and feedback. Hover any chart to sync crosshairs at the same frequency. The gray line marks loop bandwidth (0 dB crossover). The @BW readouts show each block's contribution there.

In most textbooks, phase margin is the distance from −180° at crossover — the stability line for negative feedback. You read how much phase headroom remains above that line (e.g. 60° margin means loop phase is −120° at crossover).

The loop-gain chart defaults to the standard textbook view: phase is P + C + F with the −180° stability line on the plot. Use Folded (−360° view) to include the feedback inversion in the trace (axis −360° to −180°) — same phase margin, different bookkeeping.

Practical targets:

45–60° — common for power-supply loops; stable without being sluggish
Below ~30° — expect ringing or bench instability
Very high PM — often a low crossover; transients may be slow

Bode analysis is fast for compensation, but it focuses on crossover and assumes linear behavior. Use Bode to get close, then confirm with a load step in simulation or on the bench.