# Electric circui parameters

1. May 2, 2006

### liucibegemoc

Hello.
I have an electric circuit that's made from conductors, resistors and coils.
I needed to find a voltage between two points and I did. Got answer that plot is:

I need to find electric circuit parameters like resonance, degression constant and other.
My teacher said something about finding zeros of current equation denominator.

2. May 2, 2006

### Staff: Mentor

It looks like you've plotted current versus time? What is the equation for the current versus time based on the circuit that you are testing? The parameters like resonant frequency and damping constant can be derived from the i(t) equation, and checked against the data plot.

3. May 2, 2006

### liucibegemoc

Hi.
Thanks. This is plot of voltage over time. And it's equation is very huge.
I also have current over time and plot:

How can I find all those circuit parameters?
And equtaion i(t) is:
funk := 0.5620773930e-4*Heaviside(t-0.4000000000e-5)*
exp(-3682527.090*t+14.73010836)-0.1174739794e-5*
exp(-3937.865780*t)*cos(133298.0502*t)-0.4341766870e-7*
exp(-3937.865780*t)*sin(133298.0502*t)-0.1429572824e-4*
exp(-571.4260766*t)*cos(35731.92305*t)+0.1268711907e-5*
exp(-571.4260766*t)*sin(35731.92305*t)-0.4451456129e-4*
Heaviside(t-0.4000000000e-5)*exp(-938125.1264*t+3.752500506)-
0.2695421453e-4*Heaviside(t-0.4000000000e-5)*
exp(-5398.616627*t+0.2159446651e-1)+0.1179385884e-5*
Heaviside(t-0.4000000000e-5)*exp(-3937.865780*t+0.1575146312e-1)*
cos(133298.0502*t-.5331922009)-0.5836283136e-6*
Heaviside(t-0.4000000000e-5)*exp(-3937.865780*t+0.1575146312e-1)*
sin(133298.0502*t-.5331922009)+0.1408171837e-4*
Heaviside(t-0.4000000000e-5)*exp(-571.4260766*t+0.2285704306e-2)*
cos(35731.92305*t-.1429276922)-0.3309067451e-5*
Heaviside(t-0.4000000000e-5)*exp(-571.4260766*t+0.2285704306e-2)*
sin(35731.92305*t-.1429276922)+0.4093686070e-5*
exp(-3682527.090*t)-0.1617240812e-4*
exp(-938125.1264*t)+0.2754912314e-4*exp(-5398.616627*t)

Last edited: May 2, 2006
4. May 2, 2006

### Staff: Mentor

The vertical scale of your first plot is in Volts? So your waveform is in the milliVolt range? And how many components are in the circuit? If it's just an RLC, the equation won't be huge.

5. May 2, 2006

### Curious3141

That equation looks like classic blind best curve fitting.:rofl:

Gosh, even the Heaviside function is inside!

6. May 2, 2006

### liucibegemoc

yeah.

it's RLC circuit and the Voltage source is dependent from time.
But how can I find circuit parameters from i(t) function?

7. May 2, 2006

### Staff: Mentor

When you solve the differential equation for i(t), the solution will include terms for things like the damping constant and resonant frequency. Can you write the homgenous differential equation for the circuit excluding the voltage source?

8. May 3, 2006

### liucibegemoc

yes of course, but it will be in laplace form. after making an inverce laplace transformation I get i(t). And I made voltage source 1000V. So there won't be any Heviside functions left.
Here you go:
I3(p) := 0.9090909090e14*p*(0.5946291561e23+0.2536345448e14*p^2+0.5477237852e17*p+12264000.*p^3+1134.*p^4)/
(0.1056757215e46+0.1413175209e37*p^2+0.1985730159e42*p+0.1663723689e33*p^3+0.3449827174e27*p^4+0.8832606692e22*p^5+0.1156357118e17*p^6+2494800000.*p^7)

9. May 4, 2006

### liucibegemoc

somebody please tell me how to find damping constant and resonance frequency from i(p) (laplace form of current).

Thanks

10. May 4, 2006

### Ouabache

Perhaps putting your equation in more compact form will make analysis easier. If it may be assumed that the first "open parenthesis" in the numerator (of your equation in #8) was misplaced, one form for your equation would be:

$$I(p) = \frac {\sum_{i=0}^{4} m_i p^i}{\sum_{j=0}^{7} n_j p^j}$$

Last edited: May 4, 2006
11. May 4, 2006

### liucibegemoc

yes.but that doesn't help me at all. i need theoretical equation of how can i find damping constant and resonance frequency. i have found some on www, but that was only second level equation like p^2a+pb+c=0. This have only two zeros and they can be used by calculating those constants. Now I have a lot of zeros.... don't know what to do.

12. May 6, 2006

### Ouabache

You're right, an RLC circuit (comprised of a resistor, capacitor and inductor) is represented by a 2nd order differential equation. The LaPlace transform of i(t) will have 2 zeros. Since you began with a circuit, you will know how many capacitive and inductive elements you have and the denominator of your equation should reflect that.

Since you're expressing the equation with 10 decimal precision, it appears you are using software to generate your equation. If that's true, I would explore the help files in your software toolkit, it may give you the format of the parameters you're looking for, as defined functions. Or it may indicate a pieces of code you can use to calculate them.

Last edited: May 6, 2006
13. May 7, 2006

### liucibegemoc

Oh. Thanks for a repy! Yes, I'm using Maple. Will try