PSS + PAC analysis of a parametric amplifier

Hi everyone,

I am designing a parametric amplifier based on a time-varying capacitor. The operating principle is that an AC pump signal causes the capacitance to vary in time (implemented using a varactor in TSMC 65 nm technology).

The pump signal has a frequency fp = 10.3 GHz and an amplitude Vp = 1.2 V. In addition, there is an input port with an AC signal at fs = 5 GHz and amplitude Vs = 1 mV, and a passive output port with a 50 Ohm load.

The three ports are isolated using a circulator: the input signal goes from port 1 to port 2, and from port 2 to port 3 (output), preventing reflections in the opposite direction. The idea is to transfer power from the pump signal to the input signal by exploiting the nonlinearity of the varactor.

Using transient analysis and FFT of the signals, I observe multiple tones at the output. The dominant one is at 10.3 GHz with a level of -12 dB, but there is also a component at 5 GHz at -35 dB, whereas at the input the same tone is at -60 dB. Therefore, there is indeed amplification of the 5 GHz signal.

My goal is now to obtain the gain versus input frequency, and for that I am using a PSS + PAC analysis. The procedure I follow is:

1. I disable the input source and keep only the pump signal.

2. In the PAC analysis, I set an amplitude of 1 V.

3. In this way, the PSS analysis contains only one tone (10.3 GHz), and the simulator finds the periodic steady state while accounting for the nonlinear element.

4. Then, with PAC, I inject a small-signal excitation from 1 to 15 GHz at the input port to see how the nonlinear system processes it.

The issue is that when I observe the output signal using Direct Plot -> Voltage in dB, I obtain values close to -1 dB, approaching 0 dB. However, I would expect positive values, at least around the 5 GHz input frequency, where amplification was already observed in the transient analysis.

Could this be a configuration issue in the PSS/PAC analysis, or am I misinterpreting the results?

Thanks a lot.