Newton Raphson Method

Newton Raphson is a powerful technique used to solve equations for finding successively better approximations to the roots of a real-valued function.

The formula used is :

v_{j+1 =} v_j – f(v_j)/f’(v_j)

 Here we have used matlab to solve the circuit using Newton Raphson Method

Now the diode equation for current is,

i = (10)^ (-15) (e^38v-1)

Applying KCL at the node,

(v-0.1/2000) + i + (v/4000) = 0

 Substituting the value of i we get,

((v-0.1)/2000) + (10)^ (-15) (e^38v-1) +(v/4000) = 0

By Newton Raphson method Formula,

v^((j+1)) = v^((j)) - (6000v -400+8000*(10)^(-15) (e^38v-1))/(6000 +8000*38*(10)^(-15) (e^38v-1))

According to the code,

First the values of x and temp are compared and if they’re not equal, we enter the while loop,

The Newton Raphson method is applied therein, where

 num = f(v_j)

den = f’(v_j)

We observe that if the value of temp is way different from the answer expected then the program performs many iterations which is very inefficient.

Experiment performed by Krish Matrja and Melita Benn