Thevenins Theorem on AC Analysis

           Solving on Thevenins theorem in ac anaylsis, is just the same process in dc analysis, which we've  done to tackle. The difference is in ac, there's a presence of impedance which involve in solving series-parallel combination.

Thevenins Theorem states that:

            Any combination of sinusoidal AC sources and impedances with two terminals can be replaced by a single voltage source  e and a single series impedance z. The value of e is the open circuit voltage at the terminals, and the value of z is e divided by the current with the terminals short circuited. In this case, that impedance evaluation involves a series-parallel combination.

Summary of Thevenin's Theorem

    Remember that the Thevenin equivalent circuit is always a voltage source in series with a resistance regardless of the original circuit that it replaces. The significance of Thevenin's theorem is that the equivalent circuit can replace the original circuit as far as any external load is concerned. Any load connected between the terminals of a Thevenin equivalent circuit experiences the same current and voltage as if it were connected to the terminals of the original circuit.

A summary of steps for applying Thevenin's theorem follows.


Step 1. Open the two terminals between which you want to find the Thevenin circuit, This is done by removing the component from which the circuit is to be viewed.


Step 2. Determine the voltage across the two open terminals.

Step 3. Determine the impedance viewed from the two open terminals with ideal voltage sources replaced with shorts and ideal current sources replaced with opens (zeroed).

Step 4. Connect Vr7, andZ,Tinseies to produce the complete Thevenin equivalent circuit.

Here are some example of solving thevenins theorem(note that they are the same process on solving the thevenins theorem through ac analysis in a dc analysis):

Insight Learnings:

       Remember that the Thevenin equivalent circuit is always a voltage source in series with a resistance regardless of the original circuit that it replaces. The significance of Thevenin's theorem is that the equivalent circuit can replace the original circuit as far as any external load is concerned. Any load connected between the terminals of a Thevenin equivalent circuit experiences the same current and voltage as if it were connected to the terminals of the original circuit.

Source Transformation on AC Analysis

The source transformation in ac analysis involves transforming a voltage source in series with an impedance to a current source in parallel with an impedance.


where:

Vs = Zs Is       <--->      Is = Vs / Zs


as a recall to the dc analysis :

 DC Source transformation Source transformation is the process of replacing a voltage source vs in series with a resistor R by a current source is in parallel with a resistor R, or vice versa.

but in AC Source transformation A voltage source with impedance Z in series is the same as a current source with an impedance Z in parallel.

Here are some examples of source transformation solving in dc analysis( note that they are the same on solving in ac analysis):

Insight Learnings:

In dc analysis:

Source transformation is the process of replacing a voltage source vs in series with a resistor R by a current source is in parallel with a resistor R, or vice versa.

In ac analysis:

A voltage source with impedance Z in series is the same as a current source with an impedance Z in parallel.

Transform a voltage source in series with an impedance to a current source in     parallel with an impedance for simplification or vice versa.

Superposition Theorem On AC Analysis

   
       The superposition theorem in ac circuit is just the same on dc circuits. What is add on ac is just there's a presence of Impedance which are the conductor and capacitor. They had a variable and value. But the process is just the same, which all sources (except dependent sources) other than the one being considered are eliminated and then replace current sources with opens, replace voltage sources with shorts. Based on the book, The superposition theorem can be stated as follows:

        The current in any given branch of a multiple-source circuit can be found by determining the currents in that particular branch produced by each source acting alone, with all other sources replaced by their internal impedances. The total current in the given branch is the phasor sum of the individual source currents in that branch.

The procedure for the application of the superposition theorem is as follows:

Step 1. Leave one of the sources in the circuit, and replace all others with their internal impedance. For ideal voltage sources, the internal impedance is zero. For ideal current sources, the intemal impedance is infinite. We will call this procedure zeroing the source.

Step 2. Find the cunent in the branch of interest produced by the one remaining source.

Step 3. Repeat Steps 1 and 2 for each source in turn. When complete, you will have a number of current values equal to the number of sources in the circuit.

Step 4. Add the individual current values as phasor quantities.


Here are an example of Superpostion Theorem, but these videos are just in dc circuit, as like what I've said earlier in ac circuit there's a presence of impedances and solving these are just the same in dc analysis.

Insight Learning:

To calculate the contribution of each source independently, all the other sources must be removed and replaced without affecting the final result.

When removing a voltage source, its voltage must be set to zero, which is equivalent to replacing the voltage source with a short circuit.

When removing a current source, its current must be set to zero, which is equivalent to replacing the current source with an open circuit.