transmission lines

[Kevin Weddle]

Corroboration on a few things would be appreciated.

A transmission line can appear to the source as a parallel resonant circuit, a series resonant circuit, a capacitor, or an inductor.

When constructed correctly, the source only sees a very high resistive impedance.

 

[audioguru2]

My cable TV is fed from a 75 ohms coax cable. It isn't a very high resistance. Some coax transmission lines are 50 ohms.

 

[Kevin Weddle]

What about the parallel resonance and things?

 

[AN920]

There are a few conditions of importance. Example:
1) for lines < 1/4 wavelength
50Ohm source into 50 ohm (Zo) line, OC at the end appears (capacitive)
50Ohm source into 50 ohm line, SC at the end appears (inductive)
50Ohm source into 50 ohm line, Rl at the end (Rl> Zo)appears (cap//resistance)
50Ohm source into 50 ohm line, Rl at the end (Rl< Zo)appears (ind + resistance)
2) for lines = 1/4 wavelength
50Ohm source into 50 ohm (Zo) line, OC at the end appears (SC)
50Ohm source into 50 ohm (Zo) line, SC at the end appears (OC)
50Ohm source into 50 ohm (Zo) line, Rl at the end appears (Zo*Zo/Rl)
3) for lines > 1/4 wl and < 1/2 wl
50Ohm source into 50 ohm (Zo) line, OC at the end appears (inductive)
50Ohm source into 50 ohm (Zo) line, SC at the end appears (capacitive)
50Ohm source into 50 ohm (Zo) line, Rl at the end (Rl>Zo) appears (ind + res)
50Ohm source into 50 ohm (Zo) line, Rl at the end (Rl<Zo)appears (cap//res)

where OC :-open circuit
SC :-short circuit
Rl :-Rload
cap//res :-cap and resistor in parallel
ind + res :-ind and resistor in series

 

[Kevin Weddle]

You know, I thought a tuning stub was to be shorted, instead I've seen it open.

 

[AN920]

It all depends what you want to do.

 

[audioguru2]

Coax cable has series inductance and capacitance between conductors. If it is terminated with an incorrect resistance like a short or an open, then it resonates as a series resonanlt circuit with a very low resistance or as a parallel resonant circuit with a high impedance. You tune the resonant frequency by changing its length which might be 1/4 wavelength.

In "the good old days" we used to notch out interference from a very strong local TV station with a piece of coax cable hanging at the antenna terminals.

 

[AN920]

The resonance conditions in the coax will happen only at a 1/4 wavelength (when the coax cable is 1/4 wl long)

 

[Kevin Weddle]

Isn't a 50 ohm termination much like a short?

 

[audioguru2]

Coax cable is 50 ohms or 75 ohms. A short is zero ohms, a big difference.

 

[Kevin Weddle]

Audioguru,

We'll set the line, load, and source impedances properly for argument sake. As far as I know, the source sees parallel resonance, series resonance, a capacitor, or inductor. And since these conditions are determined by the load value and length of the line, these four conditions are all it sees.

Why not parallel resonance? Or series resonance?

 

[audioguru2]

A 75 ohm source connected to a 75 ohm coaxial cable that is terminated by a 75 ohm resistor does not resonate, even though the transmission line has inductance and capacitance. The circuit is purely resistive.

The source and cable's output will be messed up if the termination resistance doesn't match.

 

[Kevin Weddle]

A series resonant circuit looks only to be the resistance of the coil. Outside the resonant frequency, it looks to be a capacitor or inductor, whichever takes precedence. It would seem to be the same with a cable. Add any reactive element, they call it a resonant line. A non resonant line would be a resistor circuit, or a cap/ind operated at the resonant frequency.

 

[Kevin Weddle]

If you took a 50 ohm source, a 50 ohm cable, and a 50 ohm load and did not operate on the conditions of resonance, you would have a VERY LOW impedance as seen by the signal source. They say 200 KHz is the leveling frequency, but you would have to have a cable a mile long to not see a 50ohm source,line,load combination. You HAVE to resonate. It would be the same with high frequency, but luckily the cable length is reasonable. If it were not, you would be driving a virtual short just like at 200 KHz.

 

[AN920]

Specify if you are talking about ideal cases or practical cases. If we know what you are talking about then we can give answers, otherwise it becomes confusing! At the moment I can't follow your reasoning.

 

[audioguru2]

My cable TV company has many miles of 75 ohm coax around my city and has signals from 50MHz to 900MHz in it. It is 75 ohms everywhere and nothing resonates. In my home the 75 ohm coax cable from outside is connected to a 75 ohm splitter which feeds 75 ohm coax to my 75 ohm cable-modem and feeds 75 ohm coax cable to my 75 ohm TV.
It is a 75 ohm transmission line!

The signal source has a 75 ohm impedance, is perfectly matched to the 75 ohm transmission line which is perfectly matched to the 75 ohm load. Nothing resonates.

 

[Kevin Weddle]

My cable TV has a wide bandwidth too. Because the frequencies are realtively high, I could get the transmission line length perfect for one station if a wanted to. I could add a reasonable tuning stub, or even cut the line to the exact length.

I don't think the TV is a good indicator of the quality of cable line signal transmission anyway.

 

[audioguru2]

Because the source has a 75 ohm impedance and it matches the 75 ohm impedance of the transmission line and the 75 ohm impedance of the TV also matches the impedance of the transmission line, the response is pretty flat on a cable TV system from 50Mhz to 900MHz. The length of the line doesn't matter because the impedances match.

 

[ante1]

Coax cable is 50 ohms or 75 ohms. A short is zero ohms, a big difference.

Hi AG,

At which frequency is it a short (zero ohms)? How many meters (or feet) is 50/75Ohms? Are you talking resistance or impedance here and what frequency?