# Laplace Transform Finding Open-Circuit Voltage

• willDavidson
In summary, Laplace is a mathematical tool that can be used to model the small signal response of a system, such as the charge and discharge curve of a battery. However, I think it would be best suited for a time domain model rather than an open circuit voltage model.
willDavidson
TL;DR Summary
I am trying to determine how to represent open circuit voltage during laplace transform
I am interested in modeling a battery charging/discharging. I am starting off with a simple model using a voltage source in series with a parallel RC branch which is in series with a resistor. I will be measuring the open circuit voltage between the last series resistor and the bottom of the source. In the past when I've done Laplace, it was never looking at open circuit voltage but voltage across an element. For this, I'm wondering if I represent the open circuit voltage as a simple voltage source when doing the Laplace transform or is it something more?

I should've posted a sample of the circuit schematic. I've attached it here.

#### Attachments

• battery model.png
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The Laplace transform of a constant, say c, is c/s.

But I think really the answer to your question depends on what the model is for. i.e. If you're looking to model the transient response of a system upon battery insert (or removal) I would just use the standard technique of modeling the source as a step function and put your impedance model in series with that source.

I don't think the impedance would matter since it's just an open circuit? There's no current. If I got that question on an exam I would likely say the transform is whatever the source is.

willDavidson said:
I am interested in modeling a battery charging/discharging. ... For this, I'm wondering if I represent the open circuit voltage as a simple voltage source when doing the Laplace transform or is it something more?

I should've read your question more closely. Because of your description of the independent voltage source and the resistor, etc. I assumed your were looking for the small signal response of the battery so you could asses the stability (or general response) of a circuit while charging, or something, at a given operating point.

If you're just looking to model the charge and discharge curve (i.e. charge stored vs open circuit voltage) then I am not sure Laplace is the right mathematical tool for that. I'm confident one could jury rig a model to make it fit but I think it would be pretty unwieldy. I could be wrong though.

If it was limited to a certain range then it could be linear enough where perhaps you could just model it as a capacitor with an initial condition, and that would work well with Laplace. But over the entire operating range batteries are fairly non-linear which makes me think you're probably going to be best off with a time domain model. It still boils down to what question you're asking of the model and what accuracy you require, as always.

https://www.richtek.com/Design Support/Technical Document/AN024

## What is a Laplace transform?

A Laplace transform is a mathematical tool used in engineering and science to convert a function of time into a function of complex frequency. It is often used to simplify the analysis of linear systems.

## How is a Laplace transform used to find open-circuit voltage?

In order to find the open-circuit voltage of a system using a Laplace transform, the system's transfer function must first be determined. This transfer function can then be multiplied by the input function, and the inverse Laplace transform can be taken to obtain the time-domain output, which will include the open-circuit voltage.

## What is the difference between open-circuit voltage and short-circuit voltage?

Open-circuit voltage refers to the voltage across a circuit when there is no current flowing through it, while short-circuit voltage refers to the voltage across a circuit when there is a direct connection between the two terminals. Open-circuit voltage is typically higher than short-circuit voltage.

## What are some applications of Laplace transform in finding open-circuit voltage?

Laplace transform is commonly used in electrical and electronic engineering to analyze and design circuits, control systems, and filters. It is also used in physics, particularly in studying the behavior of mechanical systems.

## Are there any limitations to using Laplace transform to find open-circuit voltage?

While Laplace transform is a powerful tool for analyzing linear systems, it may not be applicable to non-linear systems. Additionally, the accuracy of the results depends on the assumptions made about the system and the accuracy of the transfer function used.

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