Please... I need to know if the length is lamda/4 ???

[juanma21]

Hello! I need quick help with one exercise that I have to do for tomorrow. Please?

I have a microwave generator, an isolator, two transmission lines, and a load. Both transmission have air as dielectric filling material. Ohmic losses can be neglected. The left transmission line has a charectiristic impedance of Zo=100 ohm, and the load that is after the second T.L. has Zl=400 ohm. We don't know the characteristic impedance of the second line. and the generator supplies fo=600Mhz.

a)What is the wavenumber, beta, for both transmission lines?Determine the characteristic impedance Z1 and the lenght l of the right transmission line such that the left transmission line is impedance matched to the load. What do you call the right transmission line?

Is this the case the one of the quarter-wave transformer?????

 

[streamlet]

Yes, a quarter-wavelength TL of a characteristic impedance 200 ohm can fulfill such a task.

 

[vfone]

If the left TL is quarter wavelength (beta = pi/4), using the formula Zo = SQRT(Zin*Zload), the impedance of the right quarter wavelength TL (Zo) should be 282 ohms to match the left TL to the 400 ohms load.

 

[biff44]

You can read the problem a number of ways, leading to different answers! I would begin the answer by STATING my initial assumptions:

Assumption: The signal generator/isolator is impedance matched to the 100 ohm transmission line. (If it were a 50 ohm isolator, this would not be true and lead to a different answer).

So you then have a matched generator driving a 100 ohm transmission line. There is no standing wave on that line, and the driving impedance at the end of the 100 ohm line is 100 ohms!

So you now have another legth of transmission line on the right and a 400 ohm load. An obvious solution is to make the right hand transmission line a "quarter wave transformer". Such a transformer has a electrical length of 90 degrees at 600 MHz, and an impedance of Zc = √(100*400) = 200 ohms.

 

[vfone]

Hard to believe that there is a 100 ohms isolator, without a clear specification.

 

[biff44]

Yeah, I know, but if it was a 50 ohm isolator, then they would have had to give the length of the left 100 ohm transmission line, as the 50 ohm source impedance would immediately become a complex impedance as the line length grew from 0 degrees. Since they did not give the line length, you can not compute the impedance at the far end of the 100 ohm line. That is why I had to assume a matched generator.

Now, maybe this guy left out an important detail that the prof. wrote into the problem?

We normally think in terms of 50 ohm test equipment, but there is plenty of 75 ohm stuff out there, and even some 120 ohm stuff out there. Like I said, state your assumption right at the front and then you can argue with the prof. if he dings you.