Greetings.

I am a computer science major, but I recently started a Circuit-related course. I have only basic knowledge of the field, and I fear I might be in a bit over my head. I hope I can get some good pointers from you all!

The problem I'm asking for help with in this post is worded as follows:

Obtain the transfer function Vout / Vin of the circuit shown in Fig. 1 where R1 = R2 = 1KOhm, C1 = C3 = 1 / 2 000 000 pi) microFarad, and L2 = 1 / 2pi H.



What I've tried so far:

I figured the main gist of this problem is to apply regular techniques like Kirchofs circuit and voltage laws. So I did:

V1 = V2 - Vin
V2 = I2 / s*C1
V3 = V4 - V2
V4 = I4 / s*C2
Vout = V4

I1 = V1 / Rs
I2 = I1 - I3
I3 = V3 / s*L2
I4 = I3 - I5
I5 = V4 / R2

Given this set if equations I started solving for V4, as that would give me the desired Vout. But either I'm bad or it's hard, because it took me an unreasonable amount of steps to get there. I eventually ended up with an answer, but a very ugly one containing many factors containing s, up to the 4th power. It's been a while since I learned about Laplace transform and I haven't gone to check how hard the reverse transform would be, but I have a feeling it's harder than this assignment was supposed to be. To be honest, I don't even know if a "transform function" is supposed to be in the s-realm or not.

Where I tried to find the answer on my own

I first checked the learning materials on this site. What I was able to find was this: https://www.allaboutcircuits.com/textbook/alternating-current/chpt-5/series-parallel-r-l-and-c/

However, I am not sure if regular circuits and the ones in my problem with everything grounded are equivalent, so I didn't dare follow the same pattern.

After some google, I found this slide: https://inst.eecs.berkeley.edu/~ee247/fa05/lectures/L4_f05.pdf
Page 5 of that has essentially the same problem, and I used it as a reference when applying KCL and KVL. However, it doesn't finish the calculations, and I struggled with even that much.

I know we aren't supposed to say "Newbie needs help!" and such, but I would like to emphasize that I feel slightly out of my depth here, and I would really appreciate it if any explanations you'd be so kind as to offer would assume that I knew very little more advanced than KCL / KVL and how the different components work.

 

Actually you have 3 reactive components,. so max S power is 3.

Also several expressions have the wrong sign for element V.
You must have consistent signs for the element when a current
enters them, so in your case sign V2 correct for I2 entering C1,
but V1 not correct for I1 entering R1. Eg. Vin = V1 + V2 or
V1 = Vin - V2

KVL states that sum off all voltages around a loop = 0.

KCL states sum of all currents entering and leaving a node = 0
(electrons do not pile up over time and dribble onto the floor).


Regards, Dana.

 

Thank you, Dana! I'll make sure to correct the drawing.

Unfortunately, I'm afraid that doesn't bring me much closer to finding out whether my answer strategy is solid and I just need to take another look at the equations, or if I'm misunderstanding something more fundamental.

 

Thank you, Dana! I'll make sure to correct the drawing.

Unfortunately, I'm afraid that doesn't bring me much closer to finding out whether my answer strategy is solid and I just need to take another look at the equations, or if I'm misunderstanding something more fundamental.

Try searching for "derive transfer function" within this forum; also search on Google.

 

Greetings.

I am a computer science major, but I recently started a Circuit-related course. I have only basic knowledge of the field, and I fear I might be in a bit over my head. I hope I can get some good pointers from you all!

The problem I'm asking for help with in this post is worded as follows:

Obtain the transfer function Vout / Vin of the circuit shown in Fig. 1 where R1 = R2 = 1KOhm, C1 = C3 = 1 / 2 000 000 pi) microFarad, and L2 = 1 / 2pi H.

View attachment 160763

What I've tried so far:

I figured the main gist of this problem is to apply regular techniques like Kirchofs circuit and voltage laws. So I did:

V1 = V2 - Vin
V2 = I2 / s*C1
V3 = V4 - V2
V4 = I4 / s*C2
Vout = V4

I1 = V1 / Rs
I2 = I1 - I3
I3 = V3 / s*L2
I4 = I3 - I5
I5 = V4 / R2

Given this set if equations I started solving for V4, as that would give me the desired Vout. But either I'm bad or it's hard, because it took me an unreasonable amount of steps to get there. I eventually ended up with an answer, but a very ugly one containing many factors containing s, up to the 4th power. It's been a while since I learned about Laplace transform and I haven't gone to check how hard the reverse transform would be, but I have a feeling it's harder than this assignment was supposed to be. To be honest, I don't even know if a "transform function" is supposed to be in the s-realm or not.

Where I tried to find the answer on my own

I first checked the learning materials on this site. What I was able to find was this: https://www.allaboutcircuits.com/textbook/alternating-current/chpt-5/series-parallel-r-l-and-c/

However, I am not sure if regular circuits and the ones in my problem with everything grounded are equivalent, so I didn't dare follow the same pattern.

After some google, I found this slide: https://inst.eecs.berkeley.edu/~ee247/fa05/lectures/L4_f05.pdf
Page 5 of that has essentially the same problem, and I used it as a reference when applying KCL and KVL. However, it doesn't finish the calculations, and I struggled with even that much.

I know we aren't supposed to say "Newbie needs help!" and such, but I would like to emphasize that I feel slightly out of my depth here, and I would really appreciate it if any explanations you'd be so kind as to offer would assume that I knew very little more advanced than KCL / KVL and how the different components work.

Hello,

DId you try Nodal Analysis? That is a very general method that approaches every network in the same way so you can apply it to any network using the same technique each time.

The result, provided you simplify, will be of the form:
Vout/Vin=R2/(a3*s^3+a2*s^2+a1*s+a0)

Note i gave you the numerator solution but left out the four constants a0 through a3 for you to find.