Why Isn't My Coax Capacitance Per Foot Linear?

[dnyberg2]

So I left a thread of posts about this new coax I had made, trying to understand its electrical characteristics such as velocity factor and so on... Then I had an occasion to exchange emails with the MFG asking what the capacitance was per foot. The answer was something like 30pF per foot. The operating frequency is 49MHz. When I use the same VNA I posted about last time, the capacitance at 36" @ 49MHz rose to 5.1nF before it flipped to inductive! Why isn't the capacitance per foot exactly that? Why isn't it linear? One would think if a MFG told you our new coax design had 30pF per foot that three feet would yield 90pF, not 5100! Whats going on? By the way, this new coax is being measured open ended as this config presents an issue so that's the way we are testing. The same 36" coax lead terminated with a 50 Ohm terminator yields about 10pF@ 36"! Makes no sense to me whatsoever. The dielectric constant of this stuff is very close to 2.03 with a Vf of .7 Anybody understand why my VNA single port S-Param measurements are so wacky when it comes to this coax? I've tested multiple assy's on two different VNA's and get the same data.

Thanks.

 

[berkeman]

So I left a thread of posts about this new coax I had made, trying to understand its electrical characteristics such as velocity factor and so on... Then I had an occasion to exchange emails with the MFG asking what the capacitance was per foot. The answer was something like 30pF per foot. The operating frequency is 49MHz. When I use the same VNA I posted about last time, the capacitance at 36" @ 49MHz rose to 5.1nF before it flipped to inductive! Why isn't the capacitance per foot exactly that? Why isn't it linear? One would think if a MFG told you our new coax design had 30pF per foot that three feet would yield 90pF, not 5100! Whats going on? By the way, this new coax is being measured open ended as this config presents an issue so that's the way we are testing. The same 36" coax lead terminated with a 50 Ohm terminator yields about 10pF@ 36"! Makes no sense to me whatsoever. The dielectric constant of this stuff is very close to 2.03 with a Vf of .7 Anybody understand why my VNA single port S-Param measurements are so wacky when it comes to this coax? I've tested multiple assy's on two different VNA's and get the same data.

Thanks.

Stop trying to measure a DC/geometric parameter with a high frequency source. I believe that you were told that in the previous thread at some point.

Use a low-frequency LCR meter to measure the capacitance of a piece of cable.

 

[Bob S]

Any time a transmission is open ended (unterminated), signals will reflect back to the source. This makes the input impedance vary, depending on the length of the transmission line. When the transmission is a quarter wave long, for example, the input impedance of an unterminated line is a short. Read about quarter wave transformers at

http://en.wikipedia.org/wiki/Quarter-wave_impedance_transformer

At different frequencies, the input impedance will flip from capacitive to inductive.

Bob S

 

[jim hardy]

Have you ever used a "Smith Chart" ?

This would be a good time to get familiar with that handy tool.

 

[sophiecentaur]

Oh boy, Jim. I was there too.
The antenna engineer's sliderule!

 

[jim hardy]

Oh boy, Jim. I was there too.
The antenna engineer's sliderule!

Thanks Sophie !

I shouldn't admit i used to be good with them. Somebody might think i still am !

They are a remarkable tool, helps one visualize those long transmission line equations.

 

[dnyberg2]

Thanks for all your help. The VNA is being used in the Smith chart mode and yes, I understand Smith charts. The explanation from Bob S. was very helpful, unlike Berkmans. If I wanted to know what was going on at low frequencies, I would have used a $5 capacitance meter @ 100KHz. Whats going on at those frequencies is painfully obvious on the Smith chart of the VNA. Sweeping the open ended coax from 1 to 100 MHz moves the response form a few pF to way over the inductive line as the transmission line approaches resonance as one would expect. At the frequency of interest, this coax sucks, and THAT is what I'm trying to understand and come to grips with. When a MFG tells someone what the characteristic impedance and capacitance of a coax design is, they MUST be doing that magic thing where they test at some outrageous low frequency that has nothing to do with where the end user intends to use the wire. This stuff is only .100" in DIA. Something I can not control. Wish i could replace it with a huge chunk of RG-8! Thanks guys!

 

[sophiecentaur]

Thanks for all your help. The VNA is being used in the Smith chart mode and yes, I understand Smith charts. The explanation from Bob S. was very helpful, unlike Berkmans. If I wanted to know what was going on at low frequencies, I would have used a $5 capacitance meter @ 100KHz. Whats going on at those frequencies is painfully obvious on the Smith chart of the VNA. Sweeping the open ended coax from 1 to 100 MHz moves the response form a few pF to way over the inductive line as the transmission line approaches resonance as one would expect. At the frequency of interest, this coax sucks, and THAT is what I'm trying to understand and come to grips with. When a MFG tells someone what the characteristic impedance and capacitance of a coax design is, they MUST be doing that magic thing where they test at some outrageous low frequency that has nothing to do with where the end user intends to use the wire. This stuff is only .100" in DIA. Something I can not control. Wish i could replace it with a huge chunk of RG-8! Thanks guys!

If you understand the Smith Chart and it implications then why are you surprised that the Capacity you measure is not pro-rata per foot at high frequencies?.
In what way does this coax "suck" at only 100MHz? 100MHz is a low frequency for coax cable spec. Is it high loss or, perhaps full of water?

The characteristic impedance of a cable can be (and is) measured over a range of frequencies (10GHz is no problem). There is no need to measure it at an "outrageous low frequency" if you know what you are doing.

PS if you want a good response from people then, if I were you, I should avoid making personal remarks about the quality of answers. Your original question fully deserved Berkeman's response.

 

[berkeman]

@sophiecentaur -- thanks!

@dnyberg2 -- My point was that you are not measuring "capacitance" with your high frequency measurement. Capacitance is defined by the geometry of the cable. The complex impedance is what you are measuring with the Smith Chart, so it is important for you to get your terms correct, IMO. It does seem like the coax would have a large loss issue, as well as a high capacitance problem. Does the manufacturer specify loss as a function of frequency for this cable? Are you constrained to using such small coax in your project?

 

[dnyberg2]

Unfortunately yes, marketing has a big hand in the aesthetics of this coax and it has to be tiny and flexible which doesn't make a nice coax for 50MHz. The power level we're putting through it doesn't help things either and the fact that its REALLY harmonic rich makes it all the worse.

 

[berkeman]

Unfortunately yes, marketing has a big hand in the aesthetics of this coax and it has to be tiny and flexible which doesn't make a nice coax for 50MHz. The power level we're putting through it doesn't help things either and the fact that its REALLY harmonic rich makes it all the worse.

Could you use twisted pair instead? At those dimensions, you would probably get a lot better RF characteristics.

 

[sophiecentaur]

@sophiecentaur -- thanks!

@dnyberg2 -- My point was that you are not measuring "capacitance" with your high frequency measurement. Capacitance is defined by the geometry of the cable. The complex impedance is what you are measuring with the Smith Chart, so it is important for you to get your terms correct, IMO. It does seem like the coax would have a large loss issue, as well as a high capacitance problem. Does the manufacturer specify loss as a function of frequency for this cable? Are you constrained to using such small coax in your project?

In as far as measurement at a high frequency will give you an Impedance value then this value may give a Capacitative or Inductive value. That is just as valid a Capacitance value as the LF- measured value. If it is 50Ω coax then it doesn't matter what the capacity is, for most purposes, because the diameter of the inner will be appropriate to keep Z₀ at 50Ω.

The only time that Capacity per Metre is relevant is when the length of cable is short in wavelengths (<λ/8, say). Longer than that and the cable's behaviour as a transmission line will dominate.

If this cable is impracticably thin then you will have problems with resistive losses and uniformity when it is bent. The only really small diameter coax I was ever involved with was dead expensive and very highly spec'd. "Marketing" are probably fuller carp as usual.

 

[Bob S]

The only time that Capacity per Metre is relevant is when the length of cable is short in wavelengths (<λ/8, say). Longer than that and the cable's behaviour as a transmission line will dominate.

The capacitance per meter C and the inductance per meter L of a transmission line are both related to both the signal propagation velocity and the characteristic impedance, for any length cable. See equations (11), (19) and (21) in http://cnx.org/content/m1045/latest/

Bob S

 

[Windadct]

Wouldnt the Cap per meter -also be critical in Time Domain Reflectometer (sp?) (TDR)- which could help the OP determine if the cable is good or bad as well.

 

[sophiecentaur]

Most of these replies relate our own personal usr of coax. If the original application could be spelled out then the responses could be more useful.

 

[jim hardy]

Sorry Dynberg i didnt know your level.
No offense meant.

Somebody said wet co-ax.

I learned hard way to check the simple things first.
Water has dielectric constant around 80?

Slap a kilovolt on that sample and listen for corona.
I walked around the powerplant with a cheap AM radio
and you can really tell when a big motor needs insulation work.

 

[vk6kro]

Sweeping the open ended coax from 1 to 100 MHz moves the response form a few pF to way over the inductive line as the transmission line approaches resonance as one would expect. At the frequency of interest, this coax sucks, and THAT is what I'm trying to understand and come to grips with.

Do you know that ALL coax and ALL transmission lines behave like this?

It is due to the reflected wave from a previous cycle coming back to the input end and interfering with the new input signal. Depending on the load, the length of cable, the velocity factor and the frequency, the exact phase relationship between the incoming signal and the reflected signal can make the input look like a resistor, a capacitor or an inductor.

This is not some sort of poor quality coax causing this.

If the cable was twice as long as this, the load seen at the input is the same as the load on the output. This may be the effect you are looking for.

A true measure of how good the coax is would be to measure the resistive component at resonance. With an open circuit at the far end, the input resistance at resonance will approach zero ohms. The closer it gets to zero, the lower the losses in the coax.

 

[sophiecentaur]

In what respect does this cable "suck"? I have asked before, I think.

I suspect that your problem could just be mis-termination, unless you are dealing with a very long length of cable. 50MHZ is nearly DC fagodssake.