Three-stage op amp, reversed active feedback

How it works

A three-stage op amp with the nesting reversed: an inverting second stage carries the inner Miller capacitor, a non-inverting output stage drives the load, and the outer capacitor returns to the first stage through its cascode - a current buffer, which removes that capacitor's feedforward. What is left is the inner capacitor's own path from o1 to o2 and on to the output, which the feedforward device M14 must outweigh.

The testbench draws Ib (2.5 µA) out of MB; MT is two copies of it, the sinks M3/M4 two copies of M21, and Rb (116 kΩ) lifts the cascode gate vbc above vbn. The sink M12, one copy of M21, sets the second stage at Ib; M15, four copies of MB, feeds 10 µA into the mirror diode M16, and M13 - four copies of it - sinks the 40 µA that M14, sixteen copies of M9, sources.

Signal path

• First stage (M1, M2, MT, M3, M4, M5, M6, M7, M8): The PMOS pair M1/M2 on the tail MT folds into the sinks M3/M4 and the cascodes M5/M6; the mirror M7/M8 turns the two halves into one output, o1, which falls as inp rises.
• Second stage (M9, M12): Common-source M9 against the sink M12 inverts o1 onto o2.
• Output stage (M15, M16, M13, M14): M15 on o2 drives the NMOS mirror M16/M13: a non-inverting stage onto out. M14, on o1, feeds forward and makes the output push-pull.
• Compensation (Cm1, M6, Cm2): Cm1 (4.5 pF) senses out and injects into f2, the source of the cascode M6, which carries the current to o1; Cm2 (2 pF) across the inverting second stage is the inner Miller capacitor. Increasing Cm1 from 3.5 pF lowers crossover to recover phase-margin headroom without changing the current ratios.

Key relations

• DC gain: A_0 ≈ g_m1 R_o1 · g_m9 R_o2 · (g_m15/g_m16) g_m13 R_o3. The output stage is a transconductance M15 into a mirror of gain N3: its gain is that of M15 times the mirror ratio, into the output's resistance.
• Unity-gain frequency: ω_u ≈ g_m1/C_m1. About 2.85 MHz at tt with Cm1 at 4.5 pF and Cm2 at 2 pF. The larger outer capacitor gives more phase margin at the cost of bandwidth and capacitor area; the 1.5 MHz minimum and 60° phase-margin requirement are unchanged.
• Inner capacitor's path: i_out/v_o1 → −g_m14 + g_m15 N_3 C_m2/(C_o2 + C_m2). At high frequency Cm2 carries o1 onto o2 in phase; M14 must win, which M15's long, low-g_m/I_D units ensure.
• Current-buffer zero: ω_z ≈ g_m6/C_m1. The cascode passes Cm1's current without its feedforward: no right-half-plane zero from the outer capacitor.

Trade-offs

• Cm2: too small and the loop through the current buffer peaks; larger lowers ω_u and raises the gain margin.
• Cm1: larger lowers ω_u and raises the phase margin; the buffer's corner g_m6/C_m1 falls with it.
• M15's units: shorter or wider, their g_m approaches M14's and the zero from Cm2's path turns right-half-plane.
• Kf: more output current raises every non-dominant pole, at the cost of supply current.

Testbenches and limits

• Operating point: The amplifier as a unity-gain buffer at its input common mode: the current it draws and where its output settles.
• Open-loop gain: Gain and phase with the loop closed only at DC, through a 1 TH inductor, so the operating point is the buffer's and every frequency sees the open loop.
• Step response: A 200mV step into the unity-gain buffer. Settling requires an output change of 90–110 % of the input step; static offset is reported separately. The 1 % dynamic settling band is around the final output, not a claim of 1 % DC accuracy.
• Supply rejection: A ripple on V_DD, and how much of it reaches the unity-gain buffer's output.
• Common-mode rejection: Equal AC sources on both inputs, one in the feedback path, measure closed-loop common-mode leakage. Its inverse approximates CMRR only where differential loop gain is large.
• Noise: Noise referred to the input of the unity-gain buffer: its density at 1 kHz and its total from 1 Hz to 1 MHz.

Design variables and defaults

Ports

• inp input
• inn input
• out output
• vdd supply
• vss ground
• ib bias: the reference current, drawn out of this pin

Reference

A. D. Grasso, G. Palumbo, S. Pennisi, Advances in Reversed Nested Miller Compensation, 2007. IEEE Transactions on Circuits and Systems I: Regular Papers, 54(7):1459-1470.

The reversed active-feedback frequency compensation (RAFFC): the inner capacitor across the second stage, the outer capacitor through a current buffer, a feedforward device from the first stage's output to the output, and the condition that the feedforward outweigh the inner capacitor's own path. The core amplifier, its bias and every size are this library's, for SG13G2 at 1.2 V.