Transmission line and cable specifications

[DragonPetter]

Are the R,L,C specifications for a cable to be taken as the lumped circuit model paramters, or can I use the dimensions to actually calculate the cable's total R,L, and C?

Say a cable has a specification of "capacitance = 10pF/m", then is it safe to say that if I have 10 meters of the cable, its total capacitance is 100pF? If I take a capacitance meter and put it on the inner and outter conductors of the cable, will it read, ideally, 100pF? Or is this spec only meant to be used in the transmission line equations for calculating characteristic impedance? Or is the spec valid for both?

 

[berkeman]

Are the R,L,C specifications for a cable to be taken as the lumped circuit model paramters, or can I use the dimensions to actually calculate the cable's total R,L, and C?

Say a cable has a specification of "capacitance = 10pF/m", then is it safe to say that if I have 10 meters of the cable, its total capacitance is 100pF? If I take a capacitance meter and put it on the inner and outter conductors of the cable, will it read, ideally, 100pF? Or is this spec only meant to be used in the transmission line equations for calculating characteristic impedance? Or is the spec valid for both?

The capacitance per unit length is a real quantity, and the datasheet number (plus tolerance) should match what you measure with your capacitance meter.

 

[Antiphon]

The reading will depend on the capacitance meter.

If it uses DC you would read C times the length. If it uses AC and the line is really long or really short but terminated in the characteristic impedance, you will read zero capacitance.

Similar remarks for inductance.

 

[yungman]

For low frequency that the λ of the frequency is way over 20 times the length of the cable, you can treat the capacitance of the cable as pF/ft times the length in ft.

At λ comparable to the length, then you need to treat is as tx line.

 

[Antiphon]

For low frequency that the λ of the frequency is way over 20 times the length of the cable, you can treat the capacitance of the cable as pF/ft times the length in ft.

At λ comparable to the length, then you need to treat is as tx line.

Yungman this is not correct.

If it is terminated in the characteristic impedance R then the length of the line doesn't matter and the input always looks like a resistor of R ohms. It can be .001 or 1000 wavelengths long.

If it is terminated in another impedance (including an open or short) then the impedance will depend on the length periodically. It may vary between inductive and capacitive as the length changes.

 

[vk6kro]

You would measure the capacitance of a cable with the cable open circuited at each end.

Yungman correctly cautioned that this would become inaccurate if the wavelength of the testing instrument's output and the length of the cable were comparable or even if the length of the cable was greater than 0.05 of a wavelength of the testing signal.

He was quite right to do this.

 

[yungman]

Yungman this is not correct.

If it is terminated in the characteristic impedance R then the length of the line doesn't matter and the input always looks like a resistor of R ohms. It can be .001 or 1000 wavelengths long.

If it is terminated in another impedance (including an open or short) then the impedance will depend on the length periodically. It may vary between inductive and capacitive as the length changes.

But if you are not terminated with the characteristic impedance, it behave like a cap. I am in the process of writing a paper on musical instrument with high impedance circuit. The instrument is connected to an amp with a coax cable. The input impedance of the amp is over 1M and the output impedance of the circuit that drive the coax can be in over 100K. I consider the coax is a capacitance of about 30pF per ft as the load.

In this kind of circuit, you don't match the terminating resistance with the impedance of the coax. Question is how do you unify the answer with the given question.

 

[jim hardy]

yungman is right.

sit down with a very long roll of coax and a multimeter.
or a short piece of coax, it doesn't matter.

set multimeter to ohms.

check resistance between center lead and shield, you'll read infinite.

set multimeter to capacitance
and you'll read some picofarads or if a long cable some nanofarads.

now short circuit the far end and repeat ohm check. you'll read the round trip resistance of the two conductors - maybe a couple ohms.
short far end and repeat capacitance check and cap meter is confused - it can't read cable capacitance when cable is shorted.



yungman is right.
two wires in proximity to one another don't make a transmission line at low frequency.
they act like a transmission line only when their length approaches a quarter wave.
which is to say when the frequency gets high enough that the wires are a significant fraction of a wavelength.

that can get interesting on really long power lines.

that is why when you drive a long way beside a large cross-country power line
you'll see the order of the wires swapped at intervals of several miles.
a quarter wave at 60 hz is like 775 miles.
so, to prevent transmission line effects and radiation of power into the aether, the utility makes it into a twisted trio by rolling the phases .

more practical - notice telephone lines.(if there's still any in your part of country)
they are rolled every few poles, same reason.

 

[Antiphon]

I agree with everyone here, including Yungman. I misread his original post thinking he meant 20 wavelengths rather than 1/20th of a wavelength which is correct. My bad.

 

[DragonPetter]

Thanks for all the replies. This question came up when a cable isn't being used for anything close to what it was designed for.

 

[jim hardy]

yes, you can wire boat trailer lights with co-ax if center conductor is big enough.

 

[yungman]

And in my case, a guitar can have varying resistance between 6K to over 100K source and driving an amplifier with input impedance of 1M. The line has been shown to behave like a cap. Actually for over 20pF per ft, it can get quite large a cap!