PROBLEM 094 · Expert · The LC oscillator
Tank Circuit
A cross-coupled LC oscillator near 2 GHz
The problem
Build a cross-coupled LC oscillator. Two NMOS have their sources joined and pulled to ground by a Current source (the tail). The gate of each is on the other’s drain: the drains are the nets “outp” and “outn”. An inductor from VDD to each drain, and a capacitor between “outp” and “outn”, form the tank. Choose L and C for an oscillation frequency between 1.6 GHz and 2.6 GHz.
The cross-coupled pair looks like a negative resistance, −2/gm, across the tank; when gm is large enough it cancels the tank’s losses and the oscillation grows until the transistors limit it. The frequency is 1/(2π√(L_diff·C)), with L_diff the sum of the two inductors. An inductor’s Q and the transistors’ gm decide the amplitude: more tail current gives more swing.
The test bench
- Supply: VDD = 1.8 V.
- The test bench injects a short current pulse into “outp” at 0.1 ns to start the oscillation, runs for 10 ns, and measures the frequency and the peak-to-peak swing of “outp” after the first 4 ns.
Numbers to hit
- Oscillation frequency between 1.6 GHz and 2.6 GHz
- Peak-to-peak swing at “outp” at least 1 V
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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