Type II Compensator

Part 7 · Control Loops

Key point: Type II is an OTA into a three-corner network: an integrator pole \(f_{p0}\), a zero \(f_{z1}\) that buys phase back, and a higher pole \(f_{p2}\) that spends it. Place the parts or place the corners — \(A(s)\) is the same story.

Click a step, or Next, to set the lab. The sliders wait until you have walked it.

1
Start at ITH.
The triangle is \(g_m\): error becomes current. Everything on that pin is the compensator. Textbook 10×, parts knobs. Read the violet max-boost line.
2
You start as an integrator.
\(R_o\) and \(C_{\mathrm{TH}}\) set \(f_{p0}\). Slow integrator: large \(C_{\mathrm{TH}}\) and \(R_o\) push that pole down. Above \(f_{p0}\) the blue trace falls and phase sits near −90°.
3
The zero is the recovery.
\(R_{\mathrm{TH}}C_{\mathrm{TH}}\) places \(f_{z1}\). Wide boost: zero and high pole far apart. After the zero the slope flattens and phase climbs — that climb is the boost you came for.
4
The high pole ends the boost.
\(C_{\mathrm{THP}}\) places \(f_{p2}\). Almost no boost: \(f_{z1}\) and \(f_{p2}\) sit on top of each other and the hump disappears. Type II collapses toward Type I.
5
Parts vs frequencies.
Back to Textbook 10×, then flip to Frequencies. Same \(A(s)\). The grayed parts are what the network became. Lab chip More gm: corners stay, only gain moves.

Next page puts this \(C\) next to a plant and \(F\) — including a frozen Type II, \(C_{\mathrm{ff}}\), and \(C_{\mathrm{filt}}\).

Tune

\( f_{z1} = \dfrac{1}{2\pi R_{\mathrm{TH}} C_{\mathrm{TH}}} \)

\( f_{p0} = \dfrac{1}{2\pi R_{o} C_{\mathrm{TH}}} \)

\( f_{p2} = \dfrac{C_{\mathrm{TH}}+C_{\mathrm{THP}}}{2\pi R_{\mathrm{TH}} C_{\mathrm{TH}} C_{\mathrm{THP}}} \)

RTH (kΩ) CTHP (pF) gm (mS) Ro (kΩ) CTH (pF)

fz1 (kHz) fp2 (kHz) fp0 (kHz) Mid-band gain (dB)

Freeze traces

Compensator Bode · |A| blue · phase rose · violet is max boost

Hover the plot

max boost at — kHz phase boost —° |A| there — dB fp/fz — fz — fp0 — fp2 — gain —

A(s) = 60.0 dB · 1 + s / (2π · 15.92 kHz) (1 + s / (2π · 0.318 kHz)) (1 + s / (2π · 175.1 kHz))