Use of Thevenin Equivalent Circuit In Transient Calculations

Prerequisite Knowledge:

You should understand Thevenin's theorem and know how to calculate time constants and plot the transient response of single time constant circuits.

Objectives:

At the end of this session you should know how to apply the Thevenin equivalent circuit to the solution of transient problems.

Theory:

In a single time constant circuit, the voltage across a capacitor changes exponentially according to the equation
where vi is the initial voltage on the capacitor, vt is the target voltage, t and is the time constant. A second equation used to find the time t1 taken to reach a voltage v(t1) is

In a given circuit, it is not always obvious what values t, vi, vt, have. In many such circuits, the Thevenin equivalent circuit can be used to simplify the evaluation of these quantities. The key to this method is to take the Thevenin equivalent circuit at the terminals of the capacitor to evaluate t, vi, vt as seen by the capacitor.

References:

Chapter 2 Fundamentals of Electronic Circuit Design.

Demonstration Problem:

Circuit 1:.

Circuit 2:.
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Click to see the respective transient responses.

Transient Response of Circuit 1

Transient Response of Circuit 2

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Exercises:

  1. Compare the transient responses for the two circuits.

  2. Determine if the second circuit is derived from the first circuit by taking a Thevenin equivalent of the circuit seen by the capacitor in Circuit 1.

  3. Calculate the time required for the voltage to reach 4 V by equations above Compare to the value derived from the waveform.