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Electrical Engineering Challenge #2

Cornel
19-Tanzanite

Electrical Engineering Challenge #2

Hello,

The problem is as following:
Find currents through R3 and R1 and voltages of R2, R1 and C1 in below circuit:

Cornel_5-1712569372845.png

Cornel_8-1712569562580.png


when:

a) 

Cornel_3-1712568938162.png

 


b) 

Cornel_2-1712568852677.png

11 REPLIES 11
Fred_Kohlhepp
23-Emerald I
(To:Cornel)

Do you REALLY mean this: 

Fred_Kohlhepp_0-1712576498984.png

Or is mW to be megohms?

 

Cornel
19-Tanzanite
(To:Fred_Kohlhepp)

Its ok as in yellow. Not megohms. 

-MFra-
21-Topaz II
(To:Cornel)

Isn't there a switch right after the generator? Or, since it is not there, should we consider the circuit for an indeterminate time in such conditions, i.e. in the state in which the transient was completed? 

Cornel
19-Tanzanite
(To:-MFra-)

In principle no, we should not consider that transient was completed.  You can try doing so If you want, but that will be not the complete solution. 

 

 

LucMeekes
23-Emerald III
(To:Cornel)

What do you define as 'the voltage of R1'?

LucMeekes
23-Emerald III
(To:Cornel)

Anyway, with V2 the voltage across R2 and V3 the voltage across C1, we get:

LucMeekes_0-1712611800497.png

gives:

LucMeekes_2-1712611852152.png

so:

LucMeekes_3-1712611908845.png

Now:

LucMeekes_4-1712611954086.png

so:

LucMeekes_5-1712612016887.png

And we find the time functions with:

LucMeekes_6-1712612058710.png

Enter component values and plot:

LucMeekes_7-1712612111591.png

When R1=200 mOhm:

LucMeekes_8-1712612821621.png

 

For case b:

LucMeekes_11-1712613872261.png

 

LucMeekes_12-1712613879894.png

 

Following the same procedure as for case a:

LucMeekes_13-1712613954357.png

And with R1=200 mOhm:

LucMeekes_14-1712614008055.png

Success!
Luc

 

 

 

 

ttokoro
20-Turquoise
(To:Cornel)

image.pngimage.pngimage.png

Cornel
19-Tanzanite
(To:ttokoro)

Now, lets say that someone wants to express voltage across R2 to be function of voltage across C1 and current through L1/R3. Could give the desired equation for this?

ttokoro
20-Turquoise
(To:Cornel)

Using laplace we get same results by using IR3(s) and also by using VC1(s).

image.pngimage.png

But you want to express vR2(t) to be the function of vC1(t) and iR3(t). So the rest part of s regions of above are used to evaluate their time functions. They are include delta(t) function, therefore, some techniques are used evaluate the combolution integrals.

 

image.png

image.png

image.pngimage.png

image.png

image.png

Finally, we get the same results for all equations.

 

image.png

Second one is using digital convolution by * . At first digitize all signals of time domain. Also needs some treatment to the delta(t) function.

image.png

image.png

image.pngimage.pngimage.png

image.pngimage.pngimage.pngimage.png

Finally, also get same results. So, this is the answers of your questions.

image.png

-MFra-
21-Topaz II
(To:Cornel)

Cornell 1.png

Cornell 2.pngCornell 3.pngCornell 4.pngCornell 5.pngCornell 6.pngCornell 7.pngCornell 8.pngCornell 9.pngCornell 10.pngCornell 11.png

-MFra-
21-Topaz II
(To:Cornel)

The network analysis (first case only) can also be done on the basis of the theory of network topology (see: Applied graph theory - W. K. Chen - North Holland ) and the formation of the TABLEAU for the node voltage method (see: Linear and non-Linear Circuits - L. O. Chua, C. A. Desoer, E. S. Kuh - Mc Graw Hill), see following photos:

Cornell Top 1.pngCornell Top 2.pngCornell Top 3.pngCornell Top 4.pngCornell Top 5.pngCornell Top 6.pngCornell Top 7.pngCornell Top 8.pngCornell Top 9.pngCornell Top 10.pngCornell Top 11.pngCornell Top 12.pngCornell Top 13.pngCornell Top 14.pngCornell Top 15.png

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