# Zin of 3 Lossless Transmission Transmission Lines

Discussion in 'Homework Help' started by Jess_88, May 25, 2011.

1. ### Jess_88 Thread Starter Member

Apr 29, 2011
174
1
Hi guys

I'm having a little difficulty determining the input impedances for the circuit

I need to determine, when the lines are disconnected
1)Zin looking into line 1 towards the 200Ω load.
2)Zin looking into Line 2 towards the short circuit
With lines RECONNECTED
3) Zin looking into line 3.

For question 1 I have
Zin = Zo[(ZL + jZotanβl)/(Zo + jtanβl)]

and l = λ/4 and β = 2π/λ
βl = π/2

or (Zo^2)/ZL
but I don't know what Zo is???

For question 2 I have.
Zin = Zo[(ZL + jZotan(π/2))/(Zo + jtan(π/2))]
ZL = 0
Zi = Zo[(jZotan(π/2))/Zo]
=jZotan(π/2) = ∞
so it appears as an open circuit

I have no idea how to approach question thee .
would it be λ/2 wave length for both line one and line two?
how on earth do I fined Zo for my calculations???

thanks guys

Last edited: May 25, 2011
2. ### Jess_88 Thread Starter Member

Apr 29, 2011
174
1
I just noticed I have a typo in the thread title... sorry :S

So doing a little more looking around and this is what I have.
It appears to be a dipole antenna feed configuration. right??
And for part three of my question (impedance input at line 3) it looks like some similar questions I found online, which used line one and line two in parallel.
Would I also do this for my circuit configuration?

I'm still lost when it comes to the line impedances Zo.

Last edited: May 26, 2011
3. ### Jess_88 Thread Starter Member

Apr 29, 2011
174
1
Is this question even possible without the transmission line impedance or a operating frequency???

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
Yes it is possible.

The quarter wave line (or quarter wave transformer) has the well known property you noted - Zin=(Zo^2)/ZL.

The shorted quarter wave line has infinite impedance. This part of the circuit will therefore have no effect on the rest of the circuit.

Zin for the quarter wave line 1 terminated in 200Ω will be (Zo^2)/200.

This impedance will be the load referred to the input quarter wave line 3.

So what impedance will you see with a quarter wave line [with characteristic impedance Zo] terminated in [(Zo^2)/200]?

Jess_88 likes this.
5. ### Jess_88 Thread Starter Member

Apr 29, 2011
174
1
nice!

so Zin on line 3 = ((Zo^2)/ZL) where ZL = (Zo^2)/200
so Zin(line 3) = 200 ohms right?

but how can you determine the input impedance of line 1 without Zo

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
Yes 200Ω is correct.

You can't find the actual numerical value of impedance for line 1 - you can only state the impedance in terms of Zo.

7. ### Jess_88 Thread Starter Member

Apr 29, 2011
174
1
ah ok, thanks