Good Day all,
I hope you are well, please can you assist me with the following I attempted the homework question but I am still not able to understand how to get the transmission matrix. I really appreciate all your help. thanks

Assume the two-port shown in Fig 5 is the sinusoidal steady state at frequency ω; calculate the
transmission matrix of this two-port.

 

How are the transmission parameters defined?

The most common way uses I2 as the current OUT of the network (this makes using the parameters for cascaded networks more straight forward).

Most network parameters are obtained by doing a sequence of analyses under different combinations of leaving ports open or short-circuiting them in order to remove terms from the expressions.

So start with the two defining equations for your parameters and go from there with that in mind.

 

You will also need to do something with ω.

 

Look at your units.

What are the units on CV (capacitance multiplied by voltage)? It's charge, which is NOT current. So you can't add a current to the product CV.

 

How are the transmission parameters defined?

The most common way uses I2 as the current OUT of the network (this makes using the parameters for cascaded networks more straight forward).

Most network parameters are obtained by doing a sequence of analyses under different combinations of leaving ports open or short-circuiting them in order to remove terms from the expressions.

So start with the two defining equations for your parameters and go from there with that in mind.

Hello Sir this is what I currently have done, But how do we work out the rest for B and D since if we make V2= 0 then the capacitor become short circuited?

V1 = L.I1 + C.I1
= 1.I1 + 1.I1
= 2I1 (using I2=0 as open circuit and adding V1 source)

V2 = (I1+I2).C (KCL)
= (I1 +0).C
= I1.C
= I1


A = V1/V2 = 2I1/I1 = 2

C = I1/V2 = I1/I1 = 1

 

Again, start with the definitions of the transmission parameters.

You still don't have the units correct.

L*I1 is NOT a voltage.

C*I1 is NOT a voltage.

 

Again, start with the definitions of the transmission parameters.

You still don't have the units correct.

L*I1 is NOT a voltage.

C*I1 is NOT a voltage.

Hi Sir, Please find my attached working. I am really trying hard with this homework and exam prep example.
thank you.

 

naickej4, you're getting your units right, and those are correct equations, but you need to relate them to the "transmission matrix", correct?

We don't really know how your transmission matrix is defined. Could be admittance parameters, impedance parameters, hybrid parameters, or something else we're unaware of. Ask your instructor. It's a smart question, so be not afraid.

You have good equations for the voltages and currents of your 2-port network. Finding your transmission matrix involves algebraic manipulation of those equations to find particular ratios of those voltages and currents.

For example, if you are using hybrid parameters, here's the transmission matrix:
h11 = V1/I1 (V2 held to zero) -- short circuit input impedance
h12 = V1/V2 (I1 held to zero) -- open circuit reverse voltage gain
h21 = I2/I1 (V2 held to zero) -- short circuit forward current gain
h22 = I2/V2 (I1 held to zero) -- open circuit output admittance
Take your equations and alternately hold V2 or I1 to zero, and solve for the ratios.

The procedure is similar for impedance and admittance parameters, but you have to know which ones you are being asked for.
Regards

 

Hi Sir, Please find my attached working. I am really trying hard with this homework and exam prep example.
thank you.

Again, for the umpteenth time, start with what you are trying to find. If you are planning a trip to New York, how can you do so without first figuring out what the general direction it is from where you are to New York. Start with the goal and work back.

You want the transmission parameters. Fine. So start with the definition of the transmission parameters in terms of the port voltages and currents. That gives us the overall roadmap and also makes sure that we are on the same page.

 

Good Day all,
I hope you are well, please can you assist me with the following I attempted the homework question but I am still not able to understand how to get the transmission matrix.

It would be well worth your time to study this web page: https://en.wikipedia.org/wiki/Two-port_network

 

Again, for the umpteenth time, start with what you are trying to find. If you are planning a trip to New York, how can you do so without first figuring out what the general direction it is from where you are to New York. Start with the goal and work back.

You want the transmission parameters. Fine. So start with the definition of the transmission parameters in terms of the port voltages and currents. That gives us the overall roadmap and also makes sure that we are on the same page.

Hi Sir, I am really sorry for annoying if I have.
I have now found and read the article on Transmission parameters, since the book I am using does not help much with regards to this topic, I have more light in this matter.
this is the transmission parameters
V1=A×V2+B×I2
I1=C×V2+D×I2

this another working using KCL
V1=jωL×I1+1jωC×(I1+I2)

V2=1jωC×(I1+I2)

and my final in terms of V1 and I1:

V1 = (j^2ω^2L.C+1).V2 –jωL.i2

I1= jωC.V2 – I2

I hope this is finally correct. So after this is in a scalar form I need to put in a matrix form.
thanks.

 

It would be well worth your time to study this web page: https://en.wikipedia.org/wiki/Two-port_network

thank you I read this and it helped me understand more.