Journal
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
Volume 70, Issue 2, Pages 801-805Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSII.2022.3174965
Keywords
Time-domain analysis; Capacitance; Capacitors; Mathematical models; Time-frequency analysis; Voltage measurement; Fourier transforms; Capacitve devices; circuit theory; capacitance; Fourier transform
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This paper aims to demonstrate the four possible mapping functions for voltage or charge inputs and their corresponding time-domain or frequency-domain electrical charge outputs when a capacitive device is voltage-charged. Similarly, there are four more possible combinations when the device is current-charged. The dual relationship between each pair of functions is established using single or double Fourier transforms. All eight system functions align only if a constant time- and frequency-independent capacitance is assumed.
In this brief, 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.
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