Help with functions for my circuit

[RichardS]

Hi,

I need help with calculating my circuit, I've done something but not sure if that is correct. Any help or direction where to look at is welcome. In the end I need transfer function of the circuit.

The first circuit is the one I start with, the second picture is "simplified" circuit with impedance for easier calculation.
Where
Z1=(1/Cin*s) + R1 + R2 + L1*s
Z2 = R3+L2*s
Z3 = L3*s
Zload = Rload + (1/C2*s) ? Zload = (Rload) / (1 + (Rload*C2*s))

What I need is
uout/uin =
i1/uin =
i2/uin =
i2/i1 =

where uout is voltage on load and uin is entry voltage u1

 

[Harald Kapp]

Start by correcting the expression for Zload. Rload and C2 are in parallel, not in series.

Also show some effort in setting up the necessary equations. We will not provide complete solutions for your homework, but we will happily guide you through the process of finding the solution yourself. This will be more of a permanent help than a quick solution that's valid just for this single case.

 

[RichardS]

Thank you for fast response, what you mentioned is what I'd like to get here, explanation and help how to solve this because I need to understand this and not just have the solution.

Zload = (Rload) / (1 + (Rload*C2*s))

I'm a bit stuck at the point I came so far. There are now 2 branches, first one with i1 and second one with i2 and when writing the equation for first one the i2*z3 has to be subtracted from first one?

uin = i1*(Z1+Z3) - i2*z3
and
uout = i2*(Z2+Zload+Z3) - i1*Z3 ?

 

[duke37]

Am i seeing things, or do you have a capacitor in series with a battery?

 

[RichardS]

Am i seeing things, or do you have a capacitor in series with a battery?

Actually that's not a battery it's A source, I used wrong symbol. fixed the picture.

 

[RichardS]

Wouldn't the second branch actually be
i2 * ( Z2 + Z3 + Zload ) - i1 * Z3 = 0
and
uout = i2*Zload ?

 

[Ratch]

Wouldn't the second branch actually be
i2 * ( Z2 + Z3 + Zload ) - i1 * Z3 = 0
and
uout = i2*Zload ?

You are going about solving the problem all wrong. You are trying to solve for the loop currents when you want to find the voltage transfer (TF) function, right? Your method will work, but it is a lot simpler to use node equations instead. You can solve for Vout directly, and find the TF by Vout/Vs. If you insist on finding the loop currents above, you need another equation for i1.

Ratch

 

[RichardS]

Ok,

You are going about solving the problem all wrong. You are trying to solve for the loop currents when you want to find the voltage transfer (TF) function, right? Your method will work, but it is a lot simpler to use node equations instead. You can solve for Vout directly, and find the TF by Vout/Vs. If you insist on finding the loop currents above, you need another equation for i1.

Ratch

I wanted to do mesh analysis thinking it would help me out calculate TF.

Uout/Uin=(Z3*ZL) / [ZL*(Z1+Z3)+Z3*(Z1+Z2)+Z1*Z2] ?

=(L3*RL*s)/((C2*RL*s + 1)*((R3 + L2*s)*(R1 + R2 + R3 + L1*s + L2*s + 1/(C1*s)) + L3*s*(R3 + L2*s) + (RL*(R1 + R2 + L1*s + L3*s + 1/(C1*s)))/(C2*RL*s + 1)))

 

[Ratch]

Ok,


I wanted to do mesh analysis thinking it would help me out calculate TF.

Uout/Uin=(Z3*ZL) / [ZL*(Z1+Z3)+Z3*(Z1+Z2)+Z1*Z2] ?

=(L3*RL*s)/((C2*RL*s + 1)*((R3 + L2*s)*(R1 + R2 + R3 + L1*s + L2*s + 1/(C1*s)) + L3*s*(R3 + L2*s) + (RL*(R1 + R2 + L1*s + L3*s + 1/(C1*s)))/(C2*RL*s + 1)))

I get the feeling that you don't understand the big picture. Find the i2 loop current first. That is going to take two equations and two unknows (i1 and i2). Then multiply i2 by Zload to get the output voltage. Finally, divide the output voltage by Vsource to get the transfer function.


Ratch

 

[RichardS]

I get the feeling that you don't understand the big picture. Find the i2 loop current first. That is going to take two equations and two unknows (i1 and i2). Then multiply i2 by Zload to get the output voltage. Finally, divide the output voltage by Vsource to get the transfer function.
View attachment 27207

Ratch

i1 = -(uin*(z3 - (z1 + z3)*(z2 + z3 + zL)))/((z1 + z3)^2*(z2 + z3 + zL))
i1/uin=-(z3 - (z1 + z3)*(z2 + z3 + zL))/((z1 + z3)^2*(z2 + z3 + zL))

i2 = (uin*z3*(- z3^2 + z3 + z2 + zL))/(z2 + z3 + zL)^2
i2/uin = (z3*(- z3^2 + z3 + z2 + zL))/(z2 + z3 + zL)^2

i2/i1 = -(z3*(z1 + z3)^2*(- z3^2 + z3 + z2 + zL))/((z3 - (z1 + z3)*(z2 + z3 + zL))*(z2 + z3 + zL))

uout/uin = (z3*zL*(- z3^2 + z3 + z2 + zL))/(z2 + z3 + zL)^2

 

[Ratch]

i1 = -(uin*(z3 - (z1 + z3)*(z2 + z3 + zL)))/((z1 + z3)^2*(z2 + z3 + zL))
i1/uin=-(z3 - (z1 + z3)*(z2 + z3 + zL))/((z1 + z3)^2*(z2 + z3 + zL))

i2 = (uin*z3*(- z3^2 + z3 + z2 + zL))/(z2 + z3 + zL)^2
i2/uin = (z3*(- z3^2 + z3 + z2 + zL))/(z2 + z3 + zL)^2

i2/i1 = -(z3*(z1 + z3)^2*(- z3^2 + z3 + z2 + zL))/((z3 - (z1 + z3)*(z2 + z3 + zL))*(z2 + z3 + zL))

uout/uin = (z3*zL*(- z3^2 + z3 + z2 + zL))/(z2 + z3 + zL)^2

How on Earth are you getting a quadradic trinomial in the denominator of your solution for i2 ? Perhaps more practice in solving for two unknowns with two equations is in order.

Ratch

 

[RichardS]

How on Earth are you getting a quadradic trinomial in the denominator of your solution for i2 ? Perhaps more practice in solving for two unknowns with two equations is in order.
View attachment 27222
Ratch

You are correct, this calculation is way off. I realized too late the mistake I did. After fixing the mistake I again get same thing from post #8
so correct final thing is Uout/Uin=(Z3*ZL) / [ZL*(Z1+Z3)+Z3*(Z1+Z2)+Z1*Z2]

Thanks for help everyone.

 

[Ratch]

You are correct, this calculation is way off. I realized too late the mistake I did. After fixing the mistake I again get same thing from post #8
so correct final thing is Uout/Uin=(Z3*ZL) / [ZL*(Z1+Z3)+Z3*(Z1+Z2)+Z1*Z2]

Thanks for help everyone.

Now, do it by node analysis.

Ratch