Analytical solution for Gaussian pulse in RC circuit

Charles C. Kim

doi:10.1117/12.2586257

12 April 2021 Analytical solution for Gaussian pulse in RC circuit

Charles C. Kim

Proceedings Volume 11740, Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXXII; 117400F (2021) https://doi.org/10.1117/12.2586257
Event: SPIE Defense + Commercial Sensing, 2021, Online Only

Abstract

The output voltage of the capacitor (C) and resistor (R) is subject to a low and high pass filter in a RC circuit, respectively. When the input voltage is sinusoidal over time its output voltage is obtained analytically. Its magnitude and phase are determined as a function of the input frequency and the time constant RC. When the input voltage is a Gaussian pulse the RC circuit is no longer a simple low and high pass filter. No analytical solution for the output voltage exists due to the lack of the analytical solution for the integral of the Gaussian function. This makes it cumbersome to predict the output voltage as the ratio of its pulse width to RC. I present an analytical solution in two ways; by using an error function and by approximating the Gaussian function. The latter solution provides the magnitude of the output voltage as a function of the ratio. This is useful in designing a RC circuit for the Gaussian pulse. For example, it can be applied to a pulse detector made of the photoconductor PbSe (Thorlab, PDA20H). An example illustrates such benefit.

Conference Presentation

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Charles C. Kim "Analytical solution for Gaussian pulse in RC circuit", Proc. SPIE 11740, Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXXII, 117400F (12 April 2021); https://doi.org/10.1117/12.2586257

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