# Frequency controlled energy absorption in parametric mixing

## TL;DR

This paper explores how energy is absorbed in circuits based on frequency control, with potential uses in filters and surfaces that select specific frequencies.

## Contribution

The study introduces a unified framework linking parametric mixing theory to energy absorption in circuits.

## Key findings

- A time-varying capacitance model explains energy exchange in parametric mixing circuits.
- A fabricated on-chip circuit validated energy transfer behavior between 1.3 and 2.3 GHz.
- Positive conductance at signal frequencies confirms frequency-controlled energy absorption.

## Abstract

This work presents the theory and experimental demonstrations of frequency-controlled energy absorption in parametric mixing circuits which may find applications in the design of tunable notch filters and frequency-selective surfaces. A time-varying capacitance model is used to describe the energy exchange among the pump, signal, and idler frequencies in parametric mixing circuits. Analytical derivations reveal that under specific frequency ordering, the system exhibits a positive conductance at the signal frequency that is correlated with the pump frequency, leading to measurable energy absorption. A fabricated on-chip circuit operating between 1.3 and 2.3 GHz serves as a physical representation of the theoretical model, experimentally validating the predicted energy transfer behavior. The results establish a unified framework linking circuit-level phenomena to the fundamental physics of energy redistribution in parametric systems.