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0

$begingroup$

so I am trying to solve an RC circuit problem that represents the square wave. Which I have already done on paper and now I am trying to plot it. So for this problem, we solved it using two methods, one using a Fourier series and another using the Laplace transformation method. When I solved for this method I got the following equation:

$$ e^{-tover CR} bigg( e^{Tover CR} Theta(t-T) - e^{Tover 2CR} Thetabig(t-frac{T}{2}big) + i_0 *Rbigg ) over R$$

Where $Theta$ is the Heaviside function and is periodic about $T$ and $i_0 = frac{e^{Tover 2CR}}{(1+e^{Tover 2CR})R} $

My problem is that when I try to plot this I only know of one way to plot that and it doesn't give me a periodic plot. So what I am wondering is how would you implement this?

This is currently the chunk of code I am working with:

time = np.linspace(0,5e-3,100000)

i0 = (np.exp(T/(2*C*R)))/((1+np.exp(T/(2*C*R)))*R)

I = (np.exp(-time/(C*R))*(np.exp(T/(C*R))*np.heaviside(time-T,1) - np.exp(T/(2*C*R))*np.heaviside(time-T/2,1)+ i0*R))/R

plt.plot(time,I)

This is being done in python and the libraries I have imported are:

• matplotlib.pyplot


• numpy


• math

My thoughts were possibly having my variable I be a nested list or maybe a matrix, and then insert loop over a variable n (which would be inside the Heaviside function to get the periodicity) but I wasn't sure if this would be an ideal way to do this. Any assistance would be greatly appreciated.

EDIT #1: So what I did was this

i0 = (np.exp(T/(2*C*R)))/((1+np.exp(T/(2*C*R)))*R)

I = []

for n in range(1,6):



    i = (np.exp(-time/(C*R))*(np.exp(T/(C*R))*np.heaviside(time-n*T,1) - np.exp(T/(2*C*R))*np.heaviside(time-n*T/2,1)+ i0*R))/R

    I = np.concatenate((I,i),axis=None)

This gave me something similar to what I was expecting but I am not sure if there would be a better way to do this.

graphing-functions laplace-transform python

share|cite|improve this question

edited Mar 10 at 23:25

Robert

asked Mar 10 at 22:32

RobertRobert

16212

$endgroup$

add a comment | 

0

$begingroup$

so I am trying to solve an RC circuit problem that represents the square wave. Which I have already done on paper and now I am trying to plot it. So for this problem, we solved it using two methods, one using a Fourier series and another using the Laplace transformation method. When I solved for this method I got the following equation:

$$ e^{-tover CR} bigg( e^{Tover CR} Theta(t-T) - e^{Tover 2CR} Thetabig(t-frac{T}{2}big) + i_0 *Rbigg ) over R$$

Where $Theta$ is the Heaviside function and is periodic about $T$ and $i_0 = frac{e^{Tover 2CR}}{(1+e^{Tover 2CR})R} $

My problem is that when I try to plot this I only know of one way to plot that and it doesn't give me a periodic plot. So what I am wondering is how would you implement this?

This is currently the chunk of code I am working with:

time = np.linspace(0,5e-3,100000)

i0 = (np.exp(T/(2*C*R)))/((1+np.exp(T/(2*C*R)))*R)

I = (np.exp(-time/(C*R))*(np.exp(T/(C*R))*np.heaviside(time-T,1) - np.exp(T/(2*C*R))*np.heaviside(time-T/2,1)+ i0*R))/R

plt.plot(time,I)

This is being done in python and the libraries I have imported are:

• matplotlib.pyplot


• numpy


• math

My thoughts were possibly having my variable I be a nested list or maybe a matrix, and then insert loop over a variable n (which would be inside the Heaviside function to get the periodicity) but I wasn't sure if this would be an ideal way to do this. Any assistance would be greatly appreciated.

EDIT #1: So what I did was this

i0 = (np.exp(T/(2*C*R)))/((1+np.exp(T/(2*C*R)))*R)

I = []

for n in range(1,6):



    i = (np.exp(-time/(C*R))*(np.exp(T/(C*R))*np.heaviside(time-n*T,1) - np.exp(T/(2*C*R))*np.heaviside(time-n*T/2,1)+ i0*R))/R

    I = np.concatenate((I,i),axis=None)

This gave me something similar to what I was expecting but I am not sure if there would be a better way to do this.

graphing-functions laplace-transform python

share|cite|improve this question

edited Mar 10 at 23:25

Robert

asked Mar 10 at 22:32

RobertRobert

16212

$endgroup$

add a comment | 

$begingroup$

so I am trying to solve an RC circuit problem that represents the square wave. Which I have already done on paper and now I am trying to plot it. So for this problem, we solved it using two methods, one using a Fourier series and another using the Laplace transformation method. When I solved for this method I got the following equation:

$$ e^{-tover CR} bigg( e^{Tover CR} Theta(t-T) - e^{Tover 2CR} Thetabig(t-frac{T}{2}big) + i_0 *Rbigg ) over R$$

Where $Theta$ is the Heaviside function and is periodic about $T$ and $i_0 = frac{e^{Tover 2CR}}{(1+e^{Tover 2CR})R} $

My problem is that when I try to plot this I only know of one way to plot that and it doesn't give me a periodic plot. So what I am wondering is how would you implement this?

This is currently the chunk of code I am working with:

time = np.linspace(0,5e-3,100000)

i0 = (np.exp(T/(2*C*R)))/((1+np.exp(T/(2*C*R)))*R)

I = (np.exp(-time/(C*R))*(np.exp(T/(C*R))*np.heaviside(time-T,1) - np.exp(T/(2*C*R))*np.heaviside(time-T/2,1)+ i0*R))/R

plt.plot(time,I)

This is being done in python and the libraries I have imported are:

• matplotlib.pyplot


• numpy


• math

My thoughts were possibly having my variable I be a nested list or maybe a matrix, and then insert loop over a variable n (which would be inside the Heaviside function to get the periodicity) but I wasn't sure if this would be an ideal way to do this. Any assistance would be greatly appreciated.

EDIT #1: So what I did was this

i0 = (np.exp(T/(2*C*R)))/((1+np.exp(T/(2*C*R)))*R)

I = []

for n in range(1,6):



    i = (np.exp(-time/(C*R))*(np.exp(T/(C*R))*np.heaviside(time-n*T,1) - np.exp(T/(2*C*R))*np.heaviside(time-n*T/2,1)+ i0*R))/R

    I = np.concatenate((I,i),axis=None)

This gave me something similar to what I was expecting but I am not sure if there would be a better way to do this.

graphing-functions laplace-transform python

share|cite|improve this question

edited Mar 10 at 23:25

Robert

asked Mar 10 at 22:32

RobertRobert

16212

$endgroup$

time = np.linspace(0,5e-3,100000)

i0 = (np.exp(T/(2*C*R)))/((1+np.exp(T/(2*C*R)))*R)

I = (np.exp(-time/(C*R))*(np.exp(T/(C*R))*np.heaviside(time-T,1) - np.exp(T/(2*C*R))*np.heaviside(time-T/2,1)+ i0*R))/R

plt.plot(time,I)

i0 = (np.exp(T/(2*C*R)))/((1+np.exp(T/(2*C*R)))*R)

I = []

for n in range(1,6):



    i = (np.exp(-time/(C*R))*(np.exp(T/(C*R))*np.heaviside(time-n*T,1) - np.exp(T/(2*C*R))*np.heaviside(time-n*T/2,1)+ i0*R))/R

    I = np.concatenate((I,i),axis=None)

share|cite|improve this question

edited Mar 10 at 23:25

Robert

asked Mar 10 at 22:32

RobertRobert

16212

share|cite|improve this question

edited Mar 10 at 23:25

Robert

asked Mar 10 at 22:32

RobertRobert

16212

asked Mar 10 at 22:32

RobertRobert

16212

asked Mar 10 at 22:32

RobertRobert

16212