Norton's Theorem
Norton’s theorem states, “Any linear electrical network containing only voltage sources, current sources, and resistances can be replaced by a single constant current source (Inorton) in parallel with a single resistor (Rnorton).”
![norton_theorem-1 norton theorem](https://analogcircuitdesign.com/wp-content/uploads/elementor/thumbs/norton_theorem-1-e1703347251372-qh8pm58tbb0ivlk5atmwmn3k5f2becqzjnegy9aciw.png)
Using Norton theorem to simplify circuits
Norton’s theorem is a fundamental principle in electrical engineering that simplifies complex linear circuits to a simpler equivalent circuit. An example to simplify circuits is shown below using a well-defined procedure:
Identify the load and the network
![thevenin_step_1-1 norton theorem procedure step 1.](https://analogcircuitdesign.com/wp-content/uploads/elementor/thumbs/thevenin_step_1-1-e1703347309855-qh8pnnrdvzjfa5q2astuhbblas2r12acij1yjf50sc.png)
Find the short circuit current by shorting nodes A and B
![norton_step_2-1 norton theorem procedure step 2. Finding norton current.](https://analogcircuitdesign.com/wp-content/uploads/elementor/thumbs/norton_step_2-1-e1703347332307-qh8poabig0eb0stan2kw55mnk0zk5srwlmpm227klc.png)
Using the superposition theorem,
$$I_{norton}=\cfrac{V_1}{R_1}+I_1\cfrac{R_4}{R_2+R_4}+\cfrac{V_2}{R_2+R_4}$$
Find the equivalent resistance
The equivalent Rnorton is the resistance the circuit between terminals A and B would have if a short circuit replaced all ideal voltage sources and an open circuit replaced all ideal current sources.
$$R_{norton}=R_1||(R_2+R_4)$$
The method of finding the resistance is identical to Thevenin resistance.
![norton_step_3-1 finding norton equivalent resistance](https://analogcircuitdesign.com/wp-content/uploads/elementor/thumbs/norton_step_3-1-e1703347412910-qh8pqckrfx7yhztflgof44w2hgtk1vyp7u8yyx5h00.png)
Create the Norton network
![norton_equivalent-1 norton_equivalent-1](https://analogcircuitdesign.com/wp-content/uploads/elementor/thumbs/norton_equivalent-1-e1703347693669-qh8pxpn75f50pww8hdz59thj0vvx9qc7atkw4ab2ki.png)
Step 5: Find the voltage across the load
The current through the load,
$$I_{load}=I_{norton}\cfrac{R_{norton}}{R_{norton}+R_{load}}$$
The voltage across the load,
$$V_{load}=I_{norton}\left(R_{norton}||R_{load}\right)$$