PROBLEM 058 · Expert · Driving a capacitive load
Heavy Cap
Stable into 10 pF
The problem
The load is now 10 pF: five times heavier than in the previous problem. Build the two-stage Miller OTA: an NMOS pair with a PMOS mirror load and a tail from a bias mirror, a PMOS common-source second stage with an NMOS current-source load, and a series Rz + Cc compensation network from the first stage’s output to “out”. Mark the non-inverting input with an Input source named “inp”, the other gate with a Net label “inn”, and the output “out”.
Two poles are enough to make a loop unstable, so the point of this problem is where they fall. The first pole (the dominant one) is made low by Miller multiplication of Cc; the second sits at about gm2/C_L and must be well above the unity-gain frequency. The resistor Rz moves the right-half-plane zero.
The test bench
- Supply: VDD = 1.8 V.
- The test bench adds a 10p load capacitor on “out”, and a 1 GΩ feedback resistor from “out” to “inn” (with a 1 F capacitor from “inn” to a quiet source) so the amplifier biases itself but is open-loop for AC.
- It applies the AC stimulus to “inp” only.
Numbers to hit
- DC gain at least 55 dB
- Unity-gain bandwidth at least 6 MHz
- Phase margin at least 55 °
- Power at most 600 µW
- Every transistor in saturation
Design it yourself
Draw the circuit on a schematic canvas, size every transistor, and see it simulated in your browser with ngspice and the SkyWater SKY130 models. Every transistor lights up green, gold or red by operating region as you move the sliders.
Sign in or create a free account →More on frequency response
- Miller's TaxA small capacitor from drain to gate looks 10 times larger at the input. Find out how much bandwidth it costs.
- Zero HeroBypass part of the degeneration resistor with a capacitor: a zero that cancels the output pole and extends the bandwidth.
- Seventy DegreesA comfortable margin keeps a closed-loop amplifier from ringing. Tune the compensation until the margin is at least 70°.
- Two-Stage TurboUnity-gain bandwidth of 100 MHz with a safe margin: raise gm1 and shrink Cc, but watch the second pole.
- Penny PincherBandwidth is cheap when power is free. Reach a respectable gain and margin on a very small budget.
- Peak PerformanceAn inductor in series with the load resistor cancels some of the load capacitance’s effect at high frequency: more bandwidth for the same gain.