Hi,
Basically I have circuit with an input Vi (s) across a capacitor C which is in parallel with a resistor R1. And these 2 components are in series with another resistor R2 (please see attached drawing).
The question states:
Show that the transfer function of the circuit is:
Vo/Vi = (s + (1/(R1.C))) / (s + (R1+R2)/(R1.R2.C)) (Hope thats clear)
Where the laplace voltage (drop) across each individual component is as follows:
V(s) = I(s) / sC [laplace of capacitor]
V(s) = I(s) . R [laplace of a resistor]
In a previous worked example, the Transfer function was found by using mesh analysis and Kirchhoff's second law to find an equivalent equation for Vi and Vo. Therefore I thought I could use that here.
In the attachment I've redrawn the circuit given in the question (which is on the left labeled (1)), so that there are 2 clear loops to use mesh analysis on (the right labeled (2)). Is this correct?
(1) is the diagram given in the question
and (2) is what I've redrawn (1) as.
(This is the first time I've come across a resistor in parallel with a capacitor and I'm guessing they both have the same voltage drop across them).
Anyway so what I did was as follows (using my attached equivalent drawing (2):
loop 1) Vi (s) = [I1(s) . R1] + [I1(s) . R2] - [I2(s) . R1]
loop 2) 0 = [I2(s) . R1] + [I2(s) / sC] - [I1(s) . R1]
I rearranged loop 2 equation to get I2(s) in terms of I1(s) and substituted that into loop 1 equation. I think this would be Vi. As for Vo I assumed that would just be the voltage drop across R2 which is I1(s) . R2.
However, I could not simplify my answer (whatsoever) to what the question gave, making me think that I've done something wrong.
Any help would be much appriciated. I hope everything above makes sense.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
Basically I have circuit with an input Vi (s) across a capacitor C which is in parallel with a resistor R1. And these 2 components are in series with another resistor R2 (please see attached drawing).
The question states:
Show that the transfer function of the circuit is:
Vo/Vi = (s + (1/(R1.C))) / (s + (R1+R2)/(R1.R2.C)) (Hope thats clear)
Where the laplace voltage (drop) across each individual component is as follows:
V(s) = I(s) / sC [laplace of capacitor]
V(s) = I(s) . R [laplace of a resistor]
In a previous worked example, the Transfer function was found by using mesh analysis and Kirchhoff's second law to find an equivalent equation for Vi and Vo. Therefore I thought I could use that here.
In the attachment I've redrawn the circuit given in the question (which is on the left labeled (1)), so that there are 2 clear loops to use mesh analysis on (the right labeled (2)). Is this correct?
(1) is the diagram given in the question
and (2) is what I've redrawn (1) as.
(This is the first time I've come across a resistor in parallel with a capacitor and I'm guessing they both have the same voltage drop across them).
Anyway so what I did was as follows (using my attached equivalent drawing (2):
loop 1) Vi (s) = [I1(s) . R1] + [I1(s) . R2] - [I2(s) . R1]
loop 2) 0 = [I2(s) . R1] + [I2(s) / sC] - [I1(s) . R1]
I rearranged loop 2 equation to get I2(s) in terms of I1(s) and substituted that into loop 1 equation. I think this would be Vi. As for Vo I assumed that would just be the voltage drop across R2 which is I1(s) . R2.
However, I could not simplify my answer (whatsoever) to what the question gave, making me think that I've done something wrong.
Any help would be much appriciated. I hope everything above makes sense.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
via Physics Forums RSS Feed http://www.physicsforums.com/showthread.php?t=703439&goto=newpost
0 commentaires:
Enregistrer un commentaire