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Chapter 6: AC Circuit Analysis Back To Chapter

6.11: Source Transformation for AC Circuits

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Source Transformation for AC Circuits

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Consider a circuit composed of a current source and a combination of resistors, capacitors, and inductors with known impedance values.

The aim is to utilize the source transformation technique to determine the voltage drop across the circuit's right-most branch.

Using source transformation, a current source in parallel with an impedance can be converted into a voltage source in series with the same impedance or vice-versa.

By applying Ohm's law, the source voltage is calculated. This value can then be expressed in terms of phasor.

In the transformed circuit, the impedance is in series with the voltage source, along with the other two elements of the top branch. The equivalent series impedance is obtained.

Now, the source transformation technique is applied again to convert the voltage source back into a current source.

Next, the impedance of the new parallel combination is obtained, which is utilized to transform the current source back into a voltage source.

Finally, the voltage division rule determines the voltage drop across the right-most branch.

6.11: Source Transformation for AC Circuits

The process of source transformation in the frequency domain entails the conversion of a voltage source, positioned in series with an impedance, into a current source that is parallel to an impedance, or the other way around. It is essential to maintain the following relationships while transitioning from one source type to another.

Equation1

Equation2

In order to determine the unknown voltage for a circuit composed of a current source and a collection of resistors, capacitors, and inductors - each with their distinct known impedance, a series of steps are followed. Initially, the voltage source is converted into a current source, and the values of the source current (I_s) and impedance (Z_s) are established.

Subsequently, transforming the current source back to a voltage source results in a different circuit. From this derived circuit, the source voltage (V_s) is calculated using the previously determined values. Finally, by applying the voltage division rule, the unknown voltage across the resistance can be identified.

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