# HELP with sinusoidal/phasor analysis of a circuit

#### dacrazyazn

Joined Mar 30, 2009
22
Hey guys,

my goal for this problem, is to determine Vo(t) in the sinusoidal steady state.
Ive been working on this problem for quite awhile now and im still stuck.
So i started out by getting the impedance for the C and Rc because they are parallell, and i got Z=Rc/(jwRcC+1)

After this, i am stuck. i cant do KVL b/c i have a current controlled current source, i cant do voltage division because there is a ground right in the middle (does the ground in the middle mean anything?) also, i cant do KCL either because of that ground in the middle of the circuit again. Please help!

the picture is in the attachment.

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#### t_n_k

Joined Mar 6, 2009
5,447
Unfortunately there appears to be an error in the diagram - plus the current source has no parameter values marked. Where did this question come from?

#### dacrazyazn

Joined Mar 30, 2009
22
The parameter for the current source is B*iB(t) and iB(t) is the current of Rb. and that is the exact diagram from my review.. the problem was made up by my professor. What seem to be the error?

#### t_n_k

Joined Mar 6, 2009
5,447
OK - if the unmarked source is a controlled source then there is no issue. It seems the circuit may be modeling a transistor amplifier.

The solution should be relatively straightforward.

The controlled source has a value

I=β*Ib

Ib=(2/Rb)*cos(ωt)

I=β*(2/Rb)*cos(ωt)

This current I drives the parallel combination (Z) of RC & C - the equation you have derived for Z is correct.

So Vo(t)=Z*I

#### dacrazyazn

Joined Mar 30, 2009
22
hey t_n_k, i got what you are doing, but can you explained why you did the Vo(t)=Z*I at the end? it doesnt make sense to me that you are taking the voltage before Z. By doing what you did, doesnt that mean that the voltage is measured after Z?

im basing this off something i remember where z is replaced with R, and voltage is different before and after the resistor right?

#### t_n_k

Joined Mar 6, 2009
5,447
hey t_n_k, i got what you are doing, but can you explained why you did the Vo(t)=Z*I at the end? it doesnt make sense to me that you are taking the voltage before Z. By doing what you did, doesnt that mean that the voltage is measured after Z?

im basing this off something i remember where z is replaced with R, and voltage is different before and after the resistor right?
Perhaps you are thinking of a series connected circuit - I'm not sure.

It might help if you solve the problem another way ... rather longer though

1. Consider Rc and C as dividing the current from the source into 2 parts, Ir (the current in Rc) and Ic (the current in C).

2. Ir = I*(-jXc)/(Rc-jXc) where Xc = 1/(ωC) and I is the same as in the earlier post.

3. Vo(t)=R*Ir

Alternatively, you could use the same idea to find Ic and Vo(t)=Ic*(-jXc)