6 Spectacular Facts about Norton’s Theorem (Circuit Lover Should Know)

Circuit analysis knows a number of analytical methods to define voltages and currents in a specific circuit. Among the most popular is Norton’s Theorem that works effectively to simplify a complex circuit into a simple, equivalent circuit.

This theorem is considered similar to Thevenin’s theorem which can also alternate a complex circuit into a simple one. Both of them can help find the values of current and voltages without involving complex calculations. And yet, Norton’s have some advantages compared to other methods.

Norton's Theorem

Norton’s Theorem Explanation

Norton’s Theorem is known as a simplification in DC circuit theory which can be applied to linear networks. The theorem states that any linear circuit can be changed into a simple equivalent circuit, no matter how complex the circuits are. The equivalent consists of parallel resistance and a current source.

As with Thevenin’s, Norton has a specific qualification of linear term that it uses. The linear circuit must be the same as of the Superposition theorem. It means the underlying equations must not include exponents or roots.

Aside from being used in direct-current circuit, the theorem can also be applied for alternating-current (AC) circuit, particularly to resistances and reactive impedance.

Since the principle of this method is to simplify the circuit, Norton’s method reduce the network to have a single current source, load, and parallel resistance. Unlike Thevenin’s theorem which has an equivalent voltage source, Norton’s has the equivalent current source. In other words, Norton is the converse of Thevenin.

Norton Equivalent Circuit

Norton equivalent circuit is the simplification of a complex circuits. For instance, a circuit has two current sources, series resistors and a parallel resistor. After Norton conversion, the circuit has a current source and parallel resistance which is known as Norton equivalent circuit.

Current source is the component that provides a constant current. The constant current is one that flows if two output terminals are shorted. The load resistance needs to be short-circuited to define the current. Equation is also needed to find the current flowing in the circuit.

Much like Thevenin’s method, Norton also offers advantages for circuit analysis. The theorem simplifies electrical circuit analysis which helps save time and effort to calculate. As the equivalent circuit comes with simpler components, it can reduce the complexity of analysis.

Once the value is obtained, the load resistance can be reconnected to the circuit. This is how to make Norton equivalent circuit even to the complex one.

How to Analyze a Circuit using Norton’s Theorem

Find the right way to solve the right thing. If you follow the previous saying, you will be able to resolve almost anything the right way. When it comes to analyzing a circuit using Norton’s method, there are several steps that you need to do.

It is necessary to understand the step by step instruction in order that the analytical method can be well-conducted. As with maximum power transfer theorem, Norton’s theorem can work well in linear circuits, either DC or AC. Follow the general steps below:

  • Identify a load resistance of the circuit then remove it.
  • Deactivate the constant source in order to find the internal resistance (Rint).
  • Next, short the load terminals. Continue the next step by finding the short circuit current (Isc) which flows through the load terminals which have been shorted previously. You can use any network analysis method for this.
  • To draw the equivalent circuit, make sure the circuit current is parallel with the resistance.
  • Next, reconnect the load resistance. It should be located in the opposite of the load terminals.
  • Now, find the load current through the load terminals.

This how you can analyze a circuit using Nortons theorem. This method is way simpler to reduce a complex network into an equivalent circuit that consists of a current source, parallel load, and parallel resistance.

Finding Norton Current and Resistance

Equivalent circuit’s current source or also known as Norton current can be found by placing a direct wire connection between the load points. Instead of replacing the load resistor with an open circuit as of Thevenin’s, you need to define the resultant current.

After finding the current source, you also need to find Norton resistance. How to calculate the resistance? It is actually the same as calculating Thevenin resistance. First, remove the load resistor as well as the the power sources and calculate total resistance from one point of load connection.

The style of Superposition theorem can be used to remove the power source. Wire and breaks can be used to replace the voltage source and current source respectively.

Norton’s and Thevenin’s Theorem

What is the relation between Thevenin’s and Norton’s theorem? Both theorems are widely used to simplify circuit analysis. These methods are commonly used to study the initial condition as well as steady-state response of a circuit.

When you compare equivalent circuits from both methods, you will find out that Norton current source is in parallel with Thevenin resistance. Given that, performing a source transformation is possible.

You can use Norton’s equivalent to get Thevenin’s equivalent or vice versa. Besides, it means the two methods can be used to analyze any linear circuits.

Additionally, Thevenin’s advantages also prevail to Norton’s. With this method, you can determine the values of voltage and current of any linear circuits without involving complex calculations. Not to mention both of them are easy to apply.

Theorem Limitations

Norton’s theorem has a few limitations that should be taken into consideration. First, the analytical method is not applicable to nonlinear elements. Whenever the circuit consists of unilateral elements, the theorem cannot be applied. Besides, it is not applicable to the circuits with dependent sources.

Any circuits consisting of magnetic locking or coupling between loads cannot be analyzed using Norton’s. Additionally, the power dissipation which across the equivalent circuit is not identical with ones across in real system.

All in all, Norton’s theorem is an analytical method to simplify linear circuits, either AC or DC. No matter how complex a circuit is, the theorem can create an equivalent circuit that works really like the original one. However, the theorem is only applicable to linear networks and inapplicable to nonlinear circuits.

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