# transmission: two-port circuit

Discussion in 'Homework Help' started by naickej4, Sep 13, 2015.

1. ### naickej4 Thread Starter Member

Jul 12, 2015
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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.

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2. ### WBahn Moderator

Mar 31, 2012
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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.

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3. ### The Electrician AAC Fanatic!

Oct 9, 2007
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You will also need to do something with ω.

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4. ### WBahn Moderator

Mar 31, 2012
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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.

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5. ### naickej4 Thread Starter Member

Jul 12, 2015
188
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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

6. ### WBahn Moderator

Mar 31, 2012
18,079
4,917

You still don't have the units correct.

L*I1 is NOT a voltage.

C*I1 is NOT a voltage.

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7. ### naickej4 Thread Starter Member

Jul 12, 2015
188
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Hi Sir, Please find my attached working. I am really trying hard with this homework and exam prep example.
thank you.

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8. ### Russmax Member

Sep 3, 2015
81
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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

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9. ### WBahn Moderator

Mar 31, 2012
18,079
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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.

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10. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,300
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It would be well worth your time to study this web page: https://en.wikipedia.org/wiki/Two-port_network

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11. ### naickej4 Thread Starter Member

Jul 12, 2015
188
10
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.

Jul 12, 2015
188
10