Time-Domain and Frequency-Domain Mappings of Voltage-to-Charge and Charge-to-Voltage in Capacitive Devices

TL;DR

This paper explores the mathematical mappings between voltage and charge in capacitive devices across time and frequency domains, revealing conditions under which these mappings simplify to a constant capacitance.

Contribution

It identifies eight possible mapping functions between voltage and charge in capacitive devices and analyzes their relationships using Fourier transforms.

Findings

Eight mapping functions are identified for voltage- and charge-based inputs.

All functions coincide under constant capacitance conditions.

Dual relationships are expressed via Fourier transforms.

Abstract

In this work, we aim to show that there are generally four possible mapping functions that can be used to map the time-domain or frequency-domain representations of an applied voltage input to the resulting time-domain or frequency-domain electrical charge output; i.e. when the capacitive device is voltage-charged. Alternatively, there are four more possible combinations when the device is current-charged. The dual relationship between each pair of functions for the case of voltage or charge input are provided in terms of single or double Fourier transforms. All eight system functions coincide with each other if and only if a constant time- and frequency-independent capacitance is considered.