VCO Gain and Injection-Locking to Measure Inductor Coupling on ICs

The theoretical behavior of oscillators is explored using the gm model. Mathematical derivations based on the model show that the frequency response of an LC oscillator resembles that of a high-Q bandpass filter with exceptionally high, but finite, pass-band gain. The linear derivations predict a 20 dB/decade roll-off beyond the loaded 3 dB corner frequency which is consistent with the accepted phase noise model of the oscillator. The demonstrated oscillator gain shows how oscillators can be used in non-traditional roles such as active filters or amplifiers. As an oscillator has gain within a determinable bandwidth and an injection-locked oscillator has the same output power as an identical oscillator operated free-running, on-chip inductor coupling can easily be measured using oscillators. The design, implementation, and measurements of a unique experimental test chip and PCB for measuring on-chip inductor coupling easily and accurately are presented. The experiment requires no calibration, matching, or probe de-embedding and makes use of an injection-locked bipolar oscillator acting as a transmitter and a free-running bipolar oscillator behaving as a receiver.