Exactly why do some SWR meters give a changing reading depending on the length of coax used to connect to an antenna?

Question

Following is my understanding of some theory and the questions are at the end.

Is this right ? ...

A standing wave is an AC waveform oscillating at a particular frequency which has a varying amplitude as time progresses (only in a sinusoidal fashion if the AC source is emitting a sine wave, which in our case it hardly ever is), but has a fixed amplitude profile in space (or length) along say in this case the inside of some coax, and is the interference pattern created when two AC wave forms traveling in opposite directions cross paths (and the superposition theorem explains this).

And remembering that the AC wave forms in question are in reality just the movement of electrons (which is current which is coulombs per sec) in sympathy with the potential difference of the output of the AC source, which hardly ever is a sine wave, away from the antenna during the periods of source output which have a positive voltage with respect to the AC ground, towards the antenna during the negative periods, the whole thing moving in space away from the source at the speed of light x the velocity factor.

At any one particular point along a transmission line,

VSWR is the the ratio (one divided by the other) of two things :

1. The potential difference between the maximum value in volts of an existing oscillating standing wave on the outside of the inner conductor and the inside of the coax shield at that point.

2. The potential difference between the minimum value in volts of an existing oscillating standing wave on the outside of the inner conductor and the inside of the coax shield at that point.

I've noticed that there are a few different kinds of SWR meters, some use a Bridge and some use a Directional Coupler. The different kinds probably have advantages and disadvantages.

However i want to point out that no SWR meters measure the Standing Wave Ratio directly right ? They either measure the ratio of peak voltage for two wave forms traveling in opposite directions (directional coupler) or measure the apparent change in impedance inflicted upon the source by the presence of the standing waves (bridge) ... is that right ? So they indirectly measure SWR and even more indirectly measure the impedance match of the coax to the antenna. That's like a 3rd hand me downed measurement.

Also it's probably worth noting here that the VSWR on a transmission line, excluding I2R losses, is the same at every point along the transmission line.

If there is an error current flowing on the outside of the coax due to incorrect balancing of the coax to the antenna because the AC current flowing on the inside of the shield splits up between the antenna and the outside of the shield because the impedance that the outside of the coax presents to the AC signal is not negligible compared to the antenna impedance, then apparently according to various sources such as the ARRL Antenna Handbook this can affect a VSWR measurement because it results in a "Common Mode Impedance" which affects the measurement made by the SWR meter.

Can someone tell me EXACTLY how the presence of current on the outside of the coax changes the VSWR reading ?

Or, what are the other causes if any of a SWR meter changing it's reading as the length of coax is changed ?

Oh and btw the answer i'm looking for is not : SWR meters are designed to work with a specific feed line impedance and if that impedance isn't the correct value the SWR meter doesn't measure correctly.

Answer 1

The SWR is related to the reflection coefficient $\Gamma$:

$$ \Gamma = {Z_L - Z_0 \over Z_L + Z_0 } $$

$$ \text{VSWR} = {1+|\Gamma| \over 1 - |\Gamma|} $$

where:

• $Z_0$ is the feedline impedance, usually 50 ohms, and
• $Z_L$ is the load (nominally, the antenna) impedance.

The reflection coefficient is a complex number and thus takes into account the phase of the reflection, but the SWR depends only on the magnitude of the reflection coefficient. If the load impedance is held constant, then changing the feedline length (neglecting losses in the feedline) changes the phase but not the magnitude of the observed reflection at the source end of the feedline, due to the changing delay provided by the line. Because SWR by definition does not care about phase, SWR does not change.

If adding additional length increases losses, then the SWR will improve. Consider a feedline so long its loss is nearly infinite: it's indistinguishable from a dummy load. When the line loss is not substantially less than the return loss, the length of the line can be very significant.

But when there are common-mode currents, the feedline is effectively part of the antenna. So changing the feedline length is effectively changing the antenna, and thus changing the load impedance. Thus SWR changes.

Answer 2

Can someone tell me EXACTLY how the presence of current on the outside of the coax changes the VSWR reading ?

When RF current is flowing on the outside of a coaxial cable, the exterior shield has become part of the radiating antenna. The presence of the SWR meter disturbs this common mode current. Therefore relocating the meter changes the common mode current, thereby altering the antenna feed point impedance which alters the SWR.

Or, what are the other causes if any of a SWR meter changing it's reading as the length of coax is changed ?

The losses in the coax cable changes the SWR. The power traveling towards the load is reduced by the coaxial losses and the reflected power is again reduced by the coaxial losses. The longer the coaxial cable, the greater the losses and therefore the SWR is further reduced. While these losses are usually dominated by conductive I²R losses, dielectric and radiative losses contribute to the effect.

VSWR is the the ratio (one divided by the other) of two things :

1. The potential difference between the maximum value in volts of an existing oscillating standing wave on the outside of the inner conductor and the inside of the coax shield at that point.

2. The potential difference between the minimum value in volts of an existing oscillating standing wave on the outside of the inner conductor and the inside of the coax shield at that point.

Neither one of these is correct. The voltage and current between the inner braid and the center conductor at any point along the coaxial cable will be equal but opposite in phase. This is the required condition for a coaxial cable to function as a transmission line. When the load does not match the characteristic impedance of the coaxial cable, power will be reflected toward the source. If the source impedance does not match the characteristic impedance, some of the returned power will be reflected back to the load. These reflections combine to form a standing wave so named because there are observable minima and maxima voltages and currents at fixed points along the length of the coax. SWR can be defined as the ratio of an observed minima voltage or current to the nearest voltage or current maxima.

The voltage minima and maxima is measured across the two conductors at each point. The current minima and maxima can be measured in either conductor but both readings must be taken from the same conductor in order to properly cancel the sign due to the direction of the current.

A modern SWR meter does not measure the minima and maxima of voltage or current but instead relies on other observable effects caused by the standing wave. If you wish to understand how an SWR meter functions, check out How does an SWR Meter Really Work?.