Z-Parameter Calculation for Circuit | Nodal Analysis Method

[CoolDude420]

Homework Statement

Calculate the z-parameters for this circuit.

Homework Equations

The Attempt at a Solution

I'm trying to apply Nodal Analysis in order to find V_1 and I'm not too sure where to go with this now.

 

[gneill]

For ##Z_{11}## I think my approach would be to assume ##V_1## as a source, then find the ##i_1## that results. Either nodal or mesh analysis looks promising. If you're familiar with the use of supermeshes, then one loop equation will suffice (along with whatever auxiliary equations are required to satisfy the current source constraint).

 

[CoolDude420]

For ##Z_{11}## I think my approach would be to assume ##V_1## as a source, then find the ##i_1## that results. Either nodal or mesh analysis looks promising. If you're familiar with the use of supermeshes, then one loop equation will suffice (along with whatever auxiliary equations are required to satisfy the current source constraint).

So I should put a V1 voltage source in parralel with the current source on the left?

 

[gneill]

So I should put a V1 voltage source in parralel with the current source on the left?

You want only one source there, so either leave the current source as is, or replace it with a voltage source. If you leave the current source, then that would fix the mesh current for its loop, or can be used as a branch current for nodal analysis. Then you'd need to find a way to determine the voltage across it. If you replace it with a voltage source, then you will solve for the mesh (or branch) current instead, giving you both the voltage and current needed for the Z-parameter.

If you're going to use nodal analysis, you'll want to define your reference node and solve for the voltage at node A, since that's where you're summing currents. Note that ##V_2## can be written in terms of ##V_A##, since ##V_2## appears along a single branch leading from node A.

 

[CoolDude420]

You want only one source there, so either leave the current source as is, or replace it with a voltage source. If you leave the current source, then that would fix the mesh current for its loop, or can be used as a branch current for nodal analysis. Then you'd need to find a way to determine the voltage across it. If you replace it with a voltage source, then you will solve for the mesh (or branch) current instead, giving you both the voltage and current needed for the Z-parameter.

If you're going to use nodal analysis, you'll want to define your reference node and solve for the voltage at node A, since that's where you're summing currents. Note that ##V_2## can be written in terms of ##V_A##, since ##V_2## appears along a single branch leading from node A.

Oh. I see. Just another thing, how would I change that current source into a voltage source. The way we usually did it was if there was a resistor in parallel with that current source but in this case there's no resistor.

 

[gneill]

Oh. I see. Just another thing, how would I change that current source into a voltage source. The way we usually did it was if there was a resistor in parallel with that current source but in this case there's no resistor.

In this case you don't have to transform the source as you might convert a Norton current source to a Thevenin voltage source. Simply swap the current source for a voltage source. There are two variables of interest here: the voltage and current produced by whichever source is in that place. Their ratio will determine the impedance you're seeking. You can specify either the current or the voltage, then determine the resulting value of the other quantity.

 

[CoolDude420]

In this case you don't have to transform the source as you might convert a Norton current source to a Thevenin voltage source. Simply swap the current source for a voltage source. There are two variables of interest here: the voltage and current produced by whichever source is in that place. Their ratio will determine the impedance you're seeking. You can specify either the current or the voltage, then determine the resulting value of the other quantity.

Ah. I don't seem to be getting anywhere. I have no idea why this isn't making sense to me. I'm going for the nodal analysis route.

I just ended up where i started..

 

[gneill]

Proceed step by step. For Nodal Analysis you need to first choose your reference node, then identify the essential nodes in the network. In your first post you identified node A, but didn't specify the reference node. You should label your drawing with your chosen reference node.

Next, don't be too quick to use variables that you want to disappear! When you're done you want to find the ratio ##V_1 / I_1## in terms of the fixed parameters of the circuit, namely the resistances and the amplification factor ##G_3##. So try to avoid using ##V_2## to specify the branch current; Branch currents should be written in terms of the node potentials, and ##V_2## is not at an essential node! Instead, write that term as though ##V_2## was not labelled on the diagram.

You'll need to define an "auxiliary" equation to write ##V_2## in terms of its branch current in order to "disappear" the ##V_2## in the ##G_3 V_2## branch