Finding h parameters when capacitors and inductors involved with resistors

[sns]

Homework Statement

Find the h parameters of the following systems:-

---L---------C--
:
:
R
:
:
----------------​

L= j5 ohm
C=-j5 ohm
R=1 ohm

Homework Equations

The above questions has to be solved manually as well as simulated (Matlab-simulink).
If anybody can please give a detailed solution explaining all the steps used I will be very grateful.
I only need the manual solution then obviously I can simulate the circuit. Also please explain the significance of giving L and C in ohms without specifying the frequency of supply to be used. Is this circuit only for an a.c. source? Can h parameters vary with time?

Thanks.

 

[Su3liminal]

Well, first write the h-parameters equations:

V1 = h11*I1 + h12*V2
I2 = h12*I1 + h22*V2

And to find the parameters follow the formal procedure:

First, by shorting V2 (that is, making V2 = 0), you can find:
h11 = V1/I1
h12 = I2/I1

Then, by opening the first port (that is, making I1 = 0), you can find:
h12 = V1/V2
h22 = I2/V2

And then after writing the equations, things going to be clear to you. Of course, I would like to help and solve all the project for you, but this isn't how it supposed to be. You have to work out the rest by yourself

 

[sns]

Well, first write the h-parameters equations:

V1 = h11*I1 + h12*V2
I2 = h12*I1 + h22*V2

And to find the parameters follow the formal procedure:

First, by shorting V2 (that is, making V2 = 0), you can find:
h11 = V1/I1
h12 = I2/I1

Then, by opening the first port (that is, making I1 = 0), you can find:
h12 = V1/V2
h22 = I2/V2

And then after writing the equations, things going to be clear to you. Of course, I would like to help and solve all the project for you, but this isn't how it supposed to be. You have to work out the rest by yourself

Well I had done the same and when I do it I start getting the same problems all over again.. Firstly please clear my concepts:
Can h parameters vary with time? Because if we supply voltage V1 ie sinusoidal then currents flowing will not be constant.. thus ratios wouldn't be constant.. Am I correct? Thus will h-parameter be an equation eh?
But if supply d.c. voltage and wait for circuit to be stable... then capacitor ultimately blocks current and inductor just passes current through.. then definitely h-parameters are constant. It'll just be a resistor circuit finally? Is this evaluation correct?

Please help..

 

[rude man]

Well I had done the same and when I do it I start getting the same problems all over again.. Firstly please clear my concepts:
Can h parameters vary with time? Because if we supply voltage V1 ie sinusoidal then currents flowing will not be constant.. thus ratios wouldn't be constant.. Am I correct? Thus will h-parameter be an equation eh?
But if supply d.c. voltage and wait for circuit to be stable... then capacitor ultimately blocks current and inductor just passes current through.. then definitely h-parameters are constant. It'll just be a resistor circuit finally? Is this evaluation correct?

Please help..

1. Your h parameters are not time-variant. They are defined solely by your component values, which are presumably constant. Almost by definition, 2-ports are restricted to ac signals.

2. I'm not going to try to solve the h parameter equations as suggested by su3liminal. That's because they may lead to singularities (& I'm too lazy to find out). In which case what you need to do is rewrite the 2-port equations in terms of a different parameter set. Try the z and the y parameters. Then get a table that gives you the h parameters given the z or y parameters.

 

[DeeNos]

To find the h parameters for this circuit, we need to first understand what h parameters are. h parameters are a set of four parameters that represent the relationship between voltage and current in a linear circuit. They are defined as follows:

h11 = input impedance (Zin)
h12 = reverse voltage gain (Av)
h21 = forward current gain (Ai)
h22 = output admittance (Yout)

In this circuit, we have a combination of resistors, inductors, and capacitors. To find the h parameters, we will use the following steps:

1. Convert the inductance and capacitance values to their respective impedances, using the formula Z = jωL for inductors and Z = 1/(jωC) for capacitors. In this case, we have L = j5 ohm and C = -j5 ohm, so their corresponding impedances are ZL = jω(5) = j5ω and ZC = 1/(jω(5)) = -jω/5.

2. Replace the inductors and capacitors with their respective impedances in the circuit. This will give us a circuit with just resistors and impedances.

3. Apply the voltage divider rule to find the voltage across the input impedance (h11). In this case, the input impedance is just the resistor R, so the voltage across it will be equal to the input voltage.

4. Apply the current divider rule to find the current through the output impedance (h22). In this case, the output impedance is just the parallel combination of the resistor R and the impedance ZC, so the current through it will be equal to the output current.

5. Use Kirchhoff's current law (KCL) at the input and output nodes to find the other two h parameters (h12 and h21).

The final h parameters for this circuit will be:

h11 = R
h12 = -ZC/(R+ZC)
h21 = -R/(R+ZC)
h22 = 1/(R+ZC)

Now, to address your questions about the circuit:

- The values of L and C given in ohms do not specify a particular frequency for the supply. This is because h parameters are independent of frequency. They represent the linear relationship between voltage and current in a circuit, regardless of the frequency of the input signal. However, the