How to find Thevenin Equivalent using Thevenin Theorem : Complete Guide

How to find Thevenin Equivalent using Thevenin Theorem

Thevenin theorem is one of the handiest tools for the analysis of a network. It can be used to find the Thevenin equivalent of a complicated network without much effort. Let us discuss the various aspects of Thevenin theorem step by step.


Where to use Thevenin Theorem

Thevenin theorem is applicable on a linear and bilateral network with two terminals. The network can have both independent sources as well as dependent sources. Before applying the theorem, one must very carefully understand where it can be used along with each and every term stated above.

What is a Linear Network

A network having its characteristics in the form of a straight line and passing through the origin is the necessary and sufficient condition for being linear. These characteristics are usually Voltage (V) vs Current (I) for a resistor, Flux (ψ) vs Current (I) for an inductor and Charge (Q) vs Voltage (V) for a capacitor. Some linear characteristics have been shown below.

Thevenin Equivalent Linear Resistance Plot
Thevenin Equivalent Linear Inductor Plot
Thevenin Equivalent Linear Capacitor Plot
Thevenin Equivalent Non Linear

Note: The characteristics must be straight line throughout with no constant in it (y= mx). A few non- linear characteristics of a network are shown below with proper indication.

Thevenin Equivalent Non Linear I-V Plot
Thevenin Equivalent Non Linear V-I_2 Plot
Thevenin Equivalent Non Linear V-I Plot
Thevenin Equivalent Non Linear

What is a Bilateral Network

A network having its characteristics symmetric about origin is a bilateral network. These characteristics can also be Voltage (V) vs Current (I) for a Resistor, Flux (ψ) vs Current (I) for an inductor and Charge (Q) vs Voltage (V) for a capacitor. Some characteristics of a bilateral network have been stated below.

Thevenin Equivalent Non Linear V-I_2 Plot
Thevenin Equivalent Linear and Bilateral

Note: All linear networks are bilateral however, all bilateral networks may or may not be linear. The above note can be justified from the following characteristics which are bilateral but non-linear.

Thevenin Equivalent Bilateral but Non Linear
Thevenin Equivalent Non Linear

What are Independent Sources

There are two types of independent sources commonly used in a network namely voltage source and current source. Both voltage and current sources can be ideal as well as practical. These sources are independent of any other network parameters and continue to supply constant voltage or current to a network at any point of time.

Thevenin Equivalet Dependent Sources
independent sources

What are Dependent Sources

These sources are usually dependent on any one parameter of the network. The parameters can be current through an element or voltage across it. Based on this, there are four dependent sources seen in a network:

  • Voltage Controlled Voltage Source (VCVS)
  • Voltage Controlled Current Source (VCCS)
  • Current Controlled Voltage Source (CCVS)
  • Current Controlled Current Source (CCCS)
Thevenin Equivalet Dependent Sources
dependent sources

Where to apply Thevenin Theorem

Thevenin theorem can be used to find out the Thevenin equivalent of a linear and bilateral network. Besides, the above theorem can be best used to find the current or voltage across an element by following the same number of steps. This reduces the overall complexity of the network thereby making Thevenin theorem useful. A very basic misconception about Thevenin theorem is that it can only be used when asked for whereas it is best utilized when used instinctively. We shall be learning about it here.


What is Thevenin Equivalent

The Thevenin equivalent of a linear and bilateral network across a load is basically a Thevenin voltage (Vth) in series with Thevenin resistance (Rth) and load as shown in the figure below:

Thevenin Equivalent Circuit 1
linear bilateral network
Thevenin Equivalent Circuit 2
corresponding thevenin equivalent

How to find Thevenin Equivalent

As per the explanation above it is quite obvious that a network can have both independent and dependent sources present simultaneously or one at a time. This Thevenin equivalent is found using a series of simple steps based on the type of network given.

If the network consists of only Independent Sources

Thevenin Equivalent Independent Sources Only

We shall be finding the Thevenin voltage across the load at first. This can be done by:

  1. Disconnecting the load from the circuit given and finding the open circuit voltage across the two terminals. In technical terms, we need to find the respective voltage across the load while it is open circuited. This voltage is called Thevenin voltage.
    (Open Circuit implies that the current through an element is zero however, there exists an open circuit voltage across the same)
Thevenin Equivalent for Vth_1
  1. Secondly, we need to find the Thevenin resistance for the network which is done by disabling all the independent sources in it. While getting rid of independent sources one needs to be very careful because the independent voltage sources are made short circuited however, the independent current sources are made open circuited. Once all the independent sources have been disabled, we can find the equivalent resistance of the left network which is nothing but the Thevenin resistance.
Thevenin Equivalent Independent Sources Only for Rth_1
  1. Lastly, connecting the Thevenin voltage in series with Thevenin resistance and load yields us the Thevenin equivalent.
Thevenin Equivalent Circuit 2

If the network consists of both Dependent and Independent Sources

We shall be finding the Thevenin voltage across the load again as stated above:

  1. Disconnecting the load from the circuit given and finding the open circuit voltage across the two terminals. In technical terms, we need to find the respective voltage across the load while it is open circuited. This voltage is called Thevenin voltage.
  1. Secondly, we need to find the Thevenin resistance for the network which is done by disabling all the independent sources and leaving the dependent sources untouched. Once all the independent sources have been disabled, one needs to connect a test voltage source across the load (let’s say V) and also assume the current coming from ‘V’ is ‘I’. In such circuits, the Thevenin resistance is the ratio V/I.
  1. Lastly, connecting the Thevenin voltage in series with Thevenin resistance and load yields us the Thevenin equivalent.
Thevenin Equivalent Circuit 2

If the network consists of Only Dependent Sources

Thevenin Equivalent dependent Sources Only

We shall be finding only the Thevenin resistance using the below steps:

  1. For finding the Thevenin resistance of the network, one needs to connect a test voltage source across the load (let’s say V) and also assume the current coming from ‘V’ is ‘I’. Thus, the Thevenin resistance is the ratio V/I.
Thevenin Equivalent dependent Sources Only for Rth
  1. Thevenin voltage for such circuits is always zero.

The Thevenin equivalent of a circuit can now be conveniently found by following the above steps carefully. However, one must not be confined to use Thevenin theorem only when asked for. In other words, if in a given complicated circuit with various dependent and independent sources, voltage across a resistor is required one can use Thevenin theorem. In such a case, consider that corresponding element as the load and find the Thevenin equivalent accordingly.

Last but not the least connecting the Thevenin equivalent in series with load can help us find any parameter of the load such as current and voltage for the load. Another commonly used application of Thevenin theorem can be seen while finding the maximum power absorbed by the load.


Special use of Thevenin Theorem: Norton Theorem

Norton theorem is quite similar to Thevenin theorem with just minor changes in the Thevenin equivalent. Norton equivalent consists of Norton current or short circuit current with Norton resistance in shunt with the load. This Norton resistance is nothing but the Thevenin resistance found using the aforementioned steps. However, the short circuit current or Norton current is the ratio of Thevenin voltage and Thevenin resistance (also Norton resistance).

Last but not the least, connecting this Norton current (Isc) in shunt with Norton resistance (Rth) and load gives us the Norton’s equivalent of the network as shown below.

Thevenin Equivalent-Norton

  • Circuit diagrams created using LTspice
MORE FROM INKCUE
READ MORE
Gopesh Shukla Profile Image

About author

Gopesh Shukla

An Electronics engineer with a flair for Mathematics. He is a hardcore techie who is always on the lookout for products packed with innovation.