Finding Thevenin's equivalent circuit for AC network

In summary, the conversation discusses finding the value of the variable resistor Z in an AC circuit in order to deliver maximum power. The approach of using nodal analysis, KVL, and KCL to find Vth and Isc is suggested, but it is noted that finding the Thevenin equivalent of a network with controlled sources may not be straightforward. Instead, it is recommended to replace the load with a voltage source and use KVL mesh equations to solve for the current in the loop containing the load resistance. The maximum power can then be found by maximizing the expression for power delivered to the load with respect to the load resistance. This may involve some algebraic manipulation.
  • #1
nicky_2793
1
0
1. Hi everyone, i was given an AC circuit (capture.png) and am required to find the value of the variable resistor Z so that average maximum power is delivered to it.
To solve this i am trying to find the thevenin equivalent circuit but i am stuck and unable to figure it out. Any help would be much appreciated


Homework Equations


Rth=Vth/Eth


The Attempt at a Solution


I think i need to use nodal analysis, KVL and KCL to find Vth
then find short circuit current across Vth in order to get Rth = Vth/Isc
 

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  • #2
Finding the Thevenin equivalent of a network with controlled sources is not always simply a matter of finding the open circuit impedance and voltage in the usual fashion -- the controlled sources can make the impedance vary with the load conditions.

In such cases one way to proceed is to replace the load (Zo) with a voltage source (introducing a new variable, say vo). The Thevenin impedance will be given by the ratio of the voltage vo to the current that it drives into the circuit (be careful with the current direction -- the impedance definition assumes that the current is flowing out of the voltage source and into the circuit).

For this circuit I would be tempted to write KVL mesh equations for the bottom two loops assuming that the current in the top loop is already "solved" since that loop's mesh current is determined by the controlled source which is strictly dependent upon the other two mesh currents that flow through the inductive impedance (in other words, if i3 is the top loop's mesh current, then you replace i3 with i3 = (i1 - i2)*(j5Ω)*(1/10)[A] where i3 would appear in the two bottom loop equations. The resulting expression must have units of Amps [A], so adjust as required).

After solving for the current in the loop containing the load resistance you can use it to write a suitable expression for the power delivered to the load. Maximize this relationship with respect to the load resistance (a touch of calculus).

The algebra may not be pretty...
 

What is Thevenin's equivalent circuit?

Thevenin's equivalent circuit is a simplified representation of a complex AC network, which includes a voltage source and a series impedance. It is used to analyze the behavior of a network and calculate the voltage and current at any point in the circuit.

Why is Thevenin's equivalent circuit important?

Thevenin's equivalent circuit allows for easier analysis and calculation of a complex AC network. It can also help in determining the most efficient way to transfer power from one part of the circuit to another.

How is Thevenin's equivalent circuit calculated?

Thevenin's equivalent circuit is calculated by first removing the load from the original circuit and determining the open-circuit voltage at the load terminals. Next, the internal impedance of the network is calculated by short-circuiting all voltage sources and calculating the resulting current. The Thevenin voltage source is then placed in series with the Thevenin impedance to create the equivalent circuit.

What are the assumptions made in Thevenin's equivalent circuit analysis?

Thevenin's equivalent circuit assumes that the network is linear and time-invariant, meaning that the behavior of the circuit does not change over time. It also assumes that the load is resistive and that there are no dependent sources in the network.

What are some applications of Thevenin's equivalent circuit?

Thevenin's equivalent circuit is commonly used in circuit analysis and design, as well as in electronic device modeling. It is also used in power systems to determine the maximum power transfer and in telecommunications to analyze signal transmission and reception.

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