PROBLEM 036 · Medium · The basic differential pair
Two's Company
Differential pair with resistor loads
The problem
Build a differential pair: two matched NMOS transistors whose sources join at a tail node, which a current source pulls to ground. Each drain has a load resistor to VDD. The two drains are the differential output, named “outp” (from the transistor whose gate is “inp”) and “outn” (from the one whose gate is “inn”).
Drive each gate with its own Input source: one named “inp” and one named “inn”, both at the same DC common-mode level. A differential pair rejects what the inputs have in common and amplifies what differs. The tail current splits between the two sides, so each side carries half.
The test bench
- Supply: VDD = 1.8 V.
- The test bench hangs a 200 fF load capacitor from each of “outp” and “outn” to ground.
- It applies the AC stimulus to the source named “inp” only, and measures the differential output, the difference “outp” minus “outn”.
Numbers to hit
- Differential gain at least 12 dB
- Bandwidth (−3 dB) at least 40 MHz
- Output common-mode level between 0.8 V and 1.5 V
- Output DC imbalance at most 20 mV
- Power at most 250 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.
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- Pair, FlippedFlip the pair upside down: PMOS inputs, a tail current from VDD, loads to ground. It works with inputs near ground.
- Tail RiskAn ideal tail current source rejects everything the inputs share. A transistor tail only does so if its output resistance is high.
- Slow DownAdd a resistor in each source: the gain drops, but the pair stays linear for a much larger input.
- LimboA pair only works while its tail transistor stays saturated. Find how much common-mode range your design really has.
- Load BearingUse PMOS diodes as the loads: the gain is no longer a resistor ratio but a transistor ratio.
- Mirror TailReal tails come from mirrors. Take a 25 µA reference, scale it to 100 µA, and use it to bias the pair.