I'm trying to figure out what I did wrong...

Is the circuit attached to this post correct? (See figure)

Should I be able to derive the transfer function from this representation of the circuit?

What did I do wrong previously?

You can use the mesh method to solve this. Once you get a solution for i1 and i2, then Vo is given by Vo = i2*Rc. The expression for i2 will involve Vin and then Vo/Vin can be determined.

You have two meshes here, but the currents i1 and i2 aren't independent; in fact, i2 = -β*i1, so you really have only one mesh equation; the other equation needed is a constraint equation.

The first (and only) mesh equation is (rp1+Z)*i1 - (Z)*i2 - Vin = 0
The constraint equation is (β)*i1 + (1)*i2 = 0

You should be able to solve those and get an expression for Vo/Vin.

Later you can give the nodal method a go.

 

You can use the mesh method to solve this. Once you get a solution for i1 and i2, then Vo is given by Vo = i2*Rc. The expression for i2 will involve Vin and then Vo/Vin can be determined.

You have two meshes here, but the currents i1 and i2 aren't independent; in fact, i2 = -β*i1, so you really have only one mesh equation; the other equation needed is a constraint equation.

The first (and only) mesh equation is (rp1+Z)*i1 - (Z)*i2 - Vin = 0
The constraint equation is (β)*i1 + (1)*i2 = 0

You should be able to solve those and get an expression for Vo/Vin.

Later you can give the nodal method a go.

I've managed to successfully derive the transfer function using both nodal and mesh analysis. The next part of the question states,

"Using Laplace transform method find \(V_{o}(t), \quad t>0,\) if \(V_{in}(t) = 0.001V u(t)\)"

Can I simply using the transfer funcition I derived in the previous questions?

If so, then I will take the \(L\left{V_{in}\right}\) and with this multiply both sides of my transfer function, giving me \(V_{o}\).

Should that work?

(Also is that the, "Laplace transform method"? We've never done this before)

 

It seems strange to me that you would be asked to use a method (Laplace transform method) that you haven't been taught. It it explained in your textbook?

Anyway, give it a try and show us your work; then we can help if need be.

 

It seems strange to me that you would be asked to use a method (Laplace transform method) that you haven't been taught. It it explained in your textbook?

Anyway, give it a try and show us your work; then we can help if need be.

Alrighty, here's my attempt at it so far, I've gotten \(V_{o}(s)\) now I'm just gotta figure out how I can get the inverse laplace of this.

It's of the form, \(\frac{a + bs}{c + ds}\). Is there an easy way of getting this done? Note that we've got access to Laplace Transform tables.

Thanks again!

 

I would think that one thing you could do would be to remove Rb1 & Rb2 from the analysis as both are simply in parallel with the the source voltage Vin. If the source included a series resistance you could not do this.

Let me see if l got this right ,so if a resistor is in parallel with a voltage source, you can simply remove the resistor from your analysis ? I haven't heard about this technique before so l just want to be sure before l start using it.

 

Let me see if l got this right ,so if a resistor is in parallel with a voltage source, you can simply remove the resistor from your analysis ? I haven't heard about this technique before so l just want to be sure before l start using it.

The only current it changes is the current the voltage source is supplying. The currents (and thus voltages) are the same in the rest of the circuit.

The difference in the two currents(i.e. circuit with the resistors and without resistors) is the current being sucked across those resistors.

But that aside, let's stay on topic. I'd still like to know how I'm supposed to finish my Laplace Transform attempt.

Does anyone have any suggestions?

 

The only current it changes is the current the voltage source is supplying. The currents (and thus voltages) are the same in the rest of the circuit.

The difference in the two currents(i.e. circuit with the resistors and without resistors) is the current being sucked across those resistors.

But that aside, let's stay on topic. I'd still like to know how I'm supposed to finish my Laplace Transform attempt.

Does anyone have any suggestions?

You can finish your Laplace Transform using the same method which was employed by the prof in that example yesterday in class.

 

You can finish your Laplace Transform using the same method which was employed by the prof in that example yesterday in class.

I need to know how to deal with the inverse laplace transform of that form.

 

I need to know how to deal with the inverse laplace transform of that form.

I used both nodal and mesh analysis without removing those two resistors, l got the same answer as you on both occasions. But now, just like you, l am stuck on how to find the inverse of the Laplace transform for Vo(s).

 

In the attachment to post #24 you have an error. In line 3 you have an expression "where Z= (Re2+Re1+1+Re1Re2CbS)/(1+Re2CbS)".

This should be Z= (Re2+Re1+Re1Re2CbS)/(1+Re2CbS)

This error is propagated into the rest of your calculations.

The inverse Laplace transform of \((\frac{1}{s})\frac{a + bs}{c + ds}\)
can be found in various ways. You could use tables or various mathematical software programs. Even my HP50 calculator can find it:

\((\frac{a}{c})- (\frac{a*d-b*c}{c*d})exp(-\frac{c}{d}t)\)

 

In the attachment to post #24 you have an error. In line 3 you have an expression "where Z= (Re2+Re1+1+Re1Re2CbS)/(1+Re2CbS)".

This should be Z= (Re2+Re1+Re1Re2CbS)/(1+Re2CbS)

This error is propagated into the rest of your calculations.

The inverse Laplace transform of \((\frac{1}{s})\frac{a + bs}{c + ds}\)
can be found in various ways. You could use tables or various mathematical software programs. Even my HP50 calculator can find it:

\((\frac{a}{c})- (\frac{a*d-b*c}{c*d})exp(-\frac{c}{d}t)\)

Thank you very much for pointing this error out, for I would have never had caught it.

I fixed my work due to this error and posted the new results. I'm going to see if I can find a way of solving this laplace transform on my calculator. I'll post again if I run into troubles.

Thanks again!