# Trouble with First Order circuits

#### Vanush

Joined Apr 19, 2008
46
Hi all, I'm trying to relate input source current x(t) to output current y(t) in the following first order circuit. I've attempted a solution, but I don't think it's correct. Where is the error in this analysis?

#### Ratch

Joined Mar 20, 2007
1,068
Vanush,

Where is the error in this analysis?
First of all, since you are not combining the two storage elements L1 and L2, you have a second order circuit analysis instead of a first order circuit like you claim.

Since this circuit comprises storage elements, you cannot just find a general function of the current in Y(t) depending of the current X(t) as if it were an all resistance network. The function of X(t) determines greatly what Y(t) will look like.

Specifically, if the current function is a step function with a value of A at t>0, then by using Laplace transforms and the current division rule.

http://www.intmath.com/Laplace-transformation/Intro.php

I get as a solution, I of L2 = A*(L1/(L1+L2))(1-exp(-R(L1+L2)/L2L2)*t) .

Ratch

#### Vanush

Joined Apr 19, 2008
46
So you're saying there's no way to determine the DE that relates x(t) to y(t)?

#### Ratch

Joined Mar 20, 2007
1,068
Vanush,

I just gave you a solution for a step function. If X(t) were sinusoidal, then the solution would be different. Also the solution would be different for a square wave, triangle wave, or a pulse wave. So you tell me, how would you relate X(t) to something like that?

Ratch

#### Vanush

Joined Apr 19, 2008
46
They were able to do it here

From your circuits course, you can determine that the differential equation describing the current flowing across the second inductor is given by:

y(2)(t) + (10/3 + 10/2)y(1)(t) = -10/2 sin(t)
Rewrite this as a system of 1st-order differential equations.
http://www.ece.uwaterloo.ca/~ece204/TheBook/14IVPs/higher/complete.html, under "RLL Circuit"

I don't get it though, and I can't solve it in matlab.

#### Ratch

Joined Mar 20, 2007
1,068
Vanush,

They were able to do it here
I am not seeing it. You specified a general waveform x(t). They specified a specific sinusoidal waveform cos(t). How were they able to do it with a general waveform?

Ratch