Newton Raphson Method

In numerical analysis, Newton's method or Newton–Raphson method is named after Isaac Newton and Joseph Raphson. It is a method for finding successively better approximations to the roots or zeroes of a real-valued function.The method can also be extended to complex functions and to systems of equations.

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.

- Rujuta Gokhale (17) and Sameeran Karpe (25)