PROBLEM 004 · Easy · Output resistance and intrinsic gain
Long Story Short
Intrinsic gain: how long should the channel be?
The problem
Connect one NMOS with its source at ground and its gate driven by an Input source named “in”. Its drain is the net “out”, which the test bench holds at a fixed voltage so you can see the current the transistor delivers.
The current of a real transistor still creeps up as the drain voltage rises (channel-length modulation). The slope of that curve is 1/ro. A transistor used as an amplifier cannot have more gain than gm·ro, its intrinsic gain, and the main way to raise ro is a longer channel.
The test bench
- Supply: not needed.
- The test bench holds “out” at 0.9 V with a voltage source and sweeps it from 0.1 V to 1.7 V. It reports the transistor’s gm and output conductance at 0.9 V.
Numbers to hit
- Drain current at 0.9 V between 45 µA and 55 µA
- Intrinsic gain gm/gds at least 40 dB
- Efficiency gm/Id at least 10 1/V
- 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.
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