[chris (OP)]

I was asked by a listener to one of our radio programmes why the measured impedance of a section of coaxial cable should change when he stood on it?

I speculated that perhaps the pressure was exaggerating a defect in the conductor, reducing the cross-sectional area for current flow and hence increasing the impedance. But have I missed something? Does anyone else have any bright ideas?

Chris

[syhprum]

I would depend on the type of cable, cable with a solid core would be largely unaffected but some aerial cable is semi air spaced and quite easily crushed this type would be much affected. 

[evan_au]

It's not clear what type of cable is being described, but the impedance is determined by the material and its geometry - usually a copper conductor with plastic insulation. The capacitance, resistance and inductance determines the impedance of the cable.

When you stand on the cable, the plastic deforms a fair amount, and the copper would deform a small amount, which changes the geometry. Depending on the way the wire is crushed, you would expect that the two conductors are pushed closer together, with any airspace being eliminated, and the plastic insulation being squeezed and stretching out of the way.

The capacitance is determined by the distance between the wires and the nature of the dielectric (insulator) between them. When crushed, this distance is reduced, increasing the capacitance, which changes the impedance. To some extent, the capacitance of your foot would also change the impedance to the outside world by a small amount.

Stretching the copper by a significant amount would decrease its area, and increase its resistance, but I expect that this effect would be small compared to the compression of the dielectric.

[RD]

I was asked by a listener to one of our radio programmes why the measured impedance of a section of coaxial cable should change when he stood on it?

I speculated that perhaps the pressure was exaggerating a defect in the conductor, reducing the cross-sectional area for current flow and hence increasing the impedance. But have I missed something? Does anyone else have any bright ideas?

Chris

Deforming the  coaxial cable, (including the dielectric material), would change the capacitance of the cable, comparable to reducing the gap between the plates of a capacitor. Changing the capacitance would change the capacitive reactance : the impedance to an AC signal.

[RD]

If the the outer braid on the coax is a bit sparse (cheapo) there could also be capacitive coupling.
Deforming the cable would not be necessary though, it may not actually be necessary to touch it, just to come close ... https://en.wikipedia.org/wiki/Capacitive_proximity_sensor .

[yor_on]

Yes RD, that was what I thought too. That you don't need to change somethings geometry to get it, just be grounded and in contact versus the EM field of whatever capacitance you change. But reading further it seems as if they mean that you have to be in direct contact some way, so the question becomes how 'isolated' this coaxial cable is? Or, what is a 'direct contact' here?

[SeanB]

You do not need to crush the cable, just bend it. This will change the dielectric constant of the insulation and thus change the impedance of the cable. It can be measured, but for most uses it is not significant. It has been used to make sensors though, with the most common use being the 2 coaxial cables used in certain Gatsometer devices where the dielectric is a plastic that generates a piezoelectric voltage in response to stress, and when a tyre hits it it is used to measure the speed of a vehicle to determine if you are exceeding the speed limit, mostly with a camera that takes a photo of the vehicle wheel in contact with the second cable ( and thus 2 pics of you exceeding the limit) At high power levels in radio transmitters this will have a big effect on the system, a crimped or kinked cable there can burn out quite spectacularly.

[evan_au]

Coaxial cables (as used on Cable TV and UHF antennas) and shielded cables (like balanced microphone cables) normally have the shield earthed, which isolates the wire(s) inside from capacitance changes due to nearby conductors like the ground, a hand or a foot. The impedance of these cable types should not change due to proximity.

300Ω ribbon cable used on VHF television antennas have the conductors about 7.5mm apart, and no shield. Placing an earthed object like your hand within 1mm of the conductors is likely to change the impedance significantly.

Cat 5 cable used for Ethernet has the conductors only 0.5mm apart, so placing your hand 1mm away would have a much lower impact on the impedance.

The impedance only changes in the segment you are touching/crushing with your hand or foot, and then it returns to normal in the undisturbed part of the cable. However, these changes in impedance cause signal reflections which reduce the signal level, and can cause ghosting on analogue TV (fortunately, digital TV has processing to hide this). In extreme cases, reflection of the high power levels found in a transmitter can damage the transmitter electronics.

The impact of the impedance change on the application depends on how the cable is connected to the driving electronics. The use of differential signals or an isolating transformer, or how the shield is connected can make a difference to how sensitive the cable is to proximity of external conductors.

Air-insulated cable could be permanently deformed if you stood on it, producing a large change in impedance.

[yor_on]

Very nice reading .

[chris (OP)]

Thank you, all, for your insights.

So it seems the consensus is that squashing the cable will alter the capacitance because it brings the two conductors closer together; a change in the capacitance will have a corresponding effect on the cable impedance.

What would be the magnitude of this effect, do you think?

[evan_au]

Looking up some cable impedance formulas, it looks like both the inductance and the capacitance changes if you change the size or spacing of the conductors, or the nature of the dielectric.

Assuming a twin-lead cable, if you crushed it so the wire separation were halved, the impedance would change from the usual 300Ω to about 220Ω (assuming the wire thickness and dielectric permittivity are unchanged).

• This would cause some of the signal voltage to be reflected, about 15% in this case.
  
• A similar amount of voltage would be reflected from the far end of the crushed section.
  
• Together, this reduces the forward signal strength.
  
• Depending on the length of the crushed section, this would cause constructive & destructive interference at different frequencies, causing some channels to be more affected than other channels.

The calculations for coaxial cable are more complex, since crushing it would make it elliptical rather than the usual circular cross-section - in some directions the wires would be closer and other parts would be further away (and the simple tables only give formulas for a circular cross-section).