# Can we measure reflected power in a transmission line?

This is a question related to radio transmission, I hope this is the proper forum to ask it. It relates to transmission lines connecting a radio transmitter to its antenna.

In his book "Reflections", at the start of Chapter 8, M. Walter Maxwell says "Energy reflected by a mismatched line termination can be entirely separated from the forward-travelling wave, and then be dissipated in a temperature calibrated resistor, and accurately measured as I^2R heat."

He later says "I have performed these measurements many times"

Now I find this book long-winded and too assertive, so I haven't read it all. Is he right? How can we do this measurement? What does it really measure?

I believe that forward and reflected power are mathematical artifacts used to make the calculations possible, and do not exist as separate physical entities. Am I right?

• Reflected power is not merely a mathematical construct any more (or less) than a sine wave or a square wave is a mathematical construct. It represents an actual physical wavefront traveling in the opposite direction to the excitation wave. This becomes more evident as trace length increases, and is made use of very effectively for various instrumentation design purposes. May 21, 2013 at 11:44
• I just cannot agree with @Anindo Ghosh on that. There is only one electromagnetic field on the line, in a standing wave formation, which can be resolved, mathematically and physically into two waves travelling in opposite directions, but these waves do not exist separately from the standing wave. May 21, 2013 at 12:53
• What about a long spring anchored at one end and plucked? You can physically see the energy pulse (as is evident from the compression) travel to the anchored end and return, and you will feel the returned energy. Similarly if you applied a voltage impulse to one end of a very long lossless open circuit (or short circuit) transmission line, you could disconnect the source, replace it with a 'scope and wait for the reflected pulse to return - and you would detect it. However I agree with your linked article about the common misunderstanding in regard to amplifier loads. May 21, 2013 at 13:52
• Harry, it's equally valid to think of the wave as counter-propagating (input and reflection) waves, and to say that the standing wave is "only" a mathematical construct that is created by summing the two waves. After all, if you took away the reflecting element, the forward-propogating wave would still be there, but the standing wave would be gone. May 21, 2013 at 14:42
• Interesting but heavy reading: g3ynh.info/zdocs/bridges/reflectom/part1.html May 21, 2013 at 17:07

Energy reflected by a mismatched line termination can be entirely separated from the forward-travelling wave, and then be dissipated in a temperature calibrated resistor, and accurately measured as I^2R heat.

This is more or less correct, with a couple of caveats.

First, it is possible to mostly, but not entirely separate the reflected wave. This is done a directional coupler. Practical directional couplers have isolation error, which causes a small portion of the input signal to appear at the measurement port, in addition to the reflected signal that is intended to be measured.

Second, the measurement is not typically done by heating a resistive element. This can be done and it is called a bolometric power sensor. However it's more common in my experience to use an rf detector based on a diode. The nonlinear response of the diode converts some of the rf energy to a dc voltage, which is read with a voltmeter.

Bolometric sensors might be used for very high power conditions, or when calibration to a non-electrical standard is required (e.g. a thermometer).

Edit Replying to your comment, "the generator supplies only the actual power that is transmitted to the load."

This depends a lot on the details of the generator. You refer to a white paper that suggests the following scenario:

Suppose a lossless line is terminated by a pure open circuit, and suppose the the line is exactly one wavelength long at the operating frequency. In this case the current at the generator will be zero, and so the current in its internal impedance will be zero, so there is no power dissipated in it.

This is correct if the generator is actually a perfect voltage source with a 50-ohm series resistance. But an actual benchtop generator might contain other circuits like a levelling circuit or power monitor between the actual generator and the front panel port. Also you rarely know the actual line length to the load --- maybe there is some internal transmission line between the actual source and its front-panel port. If you don't know you have perfectly tuned the transmission line length, then the reflected power is the power you should be prepared to absorb at the generator, even if you don't have to absorb that much in every case.

Also, the case of an open circuit termination and half-wavelength line means that the generator sees an effective open-circuit load (that's why the current is 0). But not every type of generator is designed to work correctly with an open circuit load. A practical circuit could end up demanding more power from other elements within it, or generating more harmonic content when incorrectly terminated. This could still damage the generator even if the ideal components view of the circuit says there's no power transferred in the standing wave.

Finally, if you did insert a directional coupler into this scenario, you would transfer power through the coupled port and into whatever terminates that port (assuming it's not a perfect open or short). This means you would have "separated the forward and reverse waves" as suggested by the author you quoted, even though you did it in a system that was not transferring power before you inserted the directional coupler.

• +1, "Bolometer", that's the word that was tickling the back of my mind! Haven't heard the term in two decades! May 21, 2013 at 14:46
• This is ok, however there is a "Yes but ..." to it. In a poorly terminated line, the generator supplies only the actual power that is transmitted to the load. See the reference I quoted above by [Scholl].(advanced-energy.com/upload/File/White_Papers/…) In analysis this is the difference between the power that would be carried by the notional forward and reverse waves. So, if this measurement is done on an actual transmission line, what power is being measured, and how does it relate to the power coming out of the generator? May 21, 2013 at 15:18
• Sorry I got two comments almost the same -- the first can be deleted or ignored May 21, 2013 at 15:19
• @HarryWeston, you or a mod can delete the duplicate comment, but I can't. Look for the little "x" icon when you wave your mouse around near the post time. May 21, 2013 at 15:34
• Thanks @Photon, there's a lot more to this mark up language than I've yet discovered. May 21, 2013 at 16:22

Yes you can. SWR meters can be made and the traditional way amateur radio operators do this is by inserting two lengths of enamelled copper wire between the braid and conductor insulation of a length of coaxial cable. These wires are terminated at one end and a peak detector is fitted at the opposite end.

Commercial units are more likely to use a carefully manufactured PCB.

• What would the test signal on the TX line have to look like for this to work? - Am I correct in understanding that it must have only a single transition to which the reaction is then measured? May 21, 2013 at 12:19
• @HannoBinder - No, it will work with a continuous sinusoidal signal - although I confess I am a little vague on the physics of why the reverse detection diode does not 'see' the forward component. May 21, 2013 at 12:31
• No, @MikeJ-UK, sorry, SWR meters separate out the in-phase and out of phase components of the standing wave, and use these to calculate a measure of the amplitudes of the notional forward and reflected waves. In all the directional couplers I have seen the diodes are simply to convert the oscillations to D.C. to operate a moving coil meter. For a good discussion see (advanced-energy.com/upload/File/White_Papers/…) May 21, 2013 at 12:48
• The circuit shown by @MikeJ-UK is a basic "micromatch", and, I believe, will work without the diodes, which are there to rectify the signal so that a D.C. meter can be used, not to determine the directional properties of the couplers. This is achieved by the orientation of the capacitive and resistive arms relative to the line, i.e why one goes left to right and the other right to left. The diagram is from the Wikipedia article, which says the FWD and REV labels are reversed. May 21, 2013 at 14:10

There is nothing wrong with the method described in the book, although it would only work well for relatively high powers.

Arguably the most widely used instrument in RF/antenna engineering is a Vector Network Analyzer which can accurately measure the reflected power down to a fraction of a mW. For example, a simple method of tuning a monopole is accomplished by connecting the antenna (slightly longer than 1/4 wavelength) to the VNA and measure the reflected power. Keep trimming the antenna until the reflected power is minimized (should say reflected coefficient, ie normalized reflected power). http://en.wikipedia.org/wiki/Vector_network_analyzer#VNA

There are a number of RF devices (directional couplers, isolators, etc) which discriminate the waves based on the direction of propagation. Of course nothing is perfect, but it is quite common to see 20-30 dB of isolation.

MikeJ-UK is quite right - it works and works with a continuous sinewave signal. If you are intent on understanding the theory there is a decent article called "Analysis of a portable Wattmeter by Frederick Glenn, K9SO". Here is a link to his website. It does cover all the necessary information for understanding SWR meter theory.

• Thanks, @Andy ala, but I think that like the Bible, one can find a reference to support any point of view you like. I prefer the approach in Bruene, and his basic directional coupler has no diode. May 21, 2013 at 13:04
• @HarryWeston - The diode is there (as you said yourself above) as a detector for the meter. May 21, 2013 at 13:55
• @HarryWeston The Frederick Glenn link I provided didn't have a diode - the diode is a refinement but not necessary to understand the basic function. May 21, 2013 at 13:59

First I would like to thank all who contributed to the question, in particular The Photon, who led me to articles that gave a resolution of the problem.

Here is my take on the idea of forward and reflected waves on a feeder from an r.f. generator to a load.

I will use "c" for the speed of electromagnetic waves along the feeder.

I think the clue to reconciling the apparently different views on this is to consider what happens when a sine wave is initially applied by the transmitter to the feeder. The front travels down the line at c, with voltage and current in phase. What happens next depends on the termination of the line. If it is the characteristic (resistive) impedance Z0 of the line then there is no phase change, and the energy conveyed by the line is dissipated as heat, or radiated from the antenna (or a bit of both?) and this situation continues indefinitely.

If the line is not terminated in Z0 then there is a phase change due to this mismatch, and the effect of this travels back at c as the front of a reverse, reflected wave. Until this front reaches the transmitter, energy is still being sent into the feeder as a sine wave with voltage and current in phase.

When this returning front reaches the transmitter, the line impedance is no longer seen as Z0 because of this phase change. So there is a further reflection forward down the feeder, which is reflected back again at the load, and so on. This eventually results in a steady state, with a reduced forward flow of energy towards the load, and (in principle) an infinite number of counter-travelling waves. The only observable effect of this summation of forward and reflected waves is to change the input impedance of the line. The process is analysed and explained in: http://www.qsl.net/zl1an/Downloads/Bruene_explanation_V13.pdf. Overall this is an excellent, fairly mathematical, article that dispels a lot of the myths and misconceptions common for this subject.

To quote from this article, for a normal, inevitably lossy, line "This derivation shows that the “standard” forward and reflected waves take a finite, though small, time to form, since energy has to travel up and down the line to create the wave assemblages that are summed. However, this process can be pretty well considered “instantaneous” at h.f., since typically a maximum of 10 or so line-lengths are travelled before contributions become vanishingly small - about half a microsecond on a typical 10 metre length of coax having a velocity factor of 66%."

In the resulting steady state, no further energy flows in the reverse direction, from load to transmitter. If we do think of there being a reflected wave then we can say that the energy it carries is subtracted from the forward energy that would have flowed, if the line was terminated in Z0, to give the net flow, which is always from transmitter to load. The transmitter never sends out more than the difference between the notional forward and reflected powers.

The steady state has a standing wave established on the feeder, governed by the situation at the load end. What the transmitter sees is determined by the length of the feeder, and depends on the phase relation at that point. At a voltage node the voltage is high and the current is low, and the transmitter sees the line as a high impedance. At a voltage anti-node it is the opposite, low voltage and high current, so the line is seen as a low impedance. We note that the standing wave is of average, usually r.m.s., values.

The standing wave can be resolved mathematically into forward and reflected components, also in the form of waves. In the forward component the voltage and current are in phase, and in the reverse component they are 180 degrees out of phase.

The current in the r.f. wave travelling forward can be analysed using phasors, into two components, that part (forward) in phase with the voltage, and that part (reflected) 180° out of phase. By sampling these currents they can be measured as voltages, and a calculation made of energy flow, i.e. forward and reflected powers, which can be displayed on moving coil meters with suitable calibrated scales. In order to use d.c. meters to measure the r.f. voltages, rectifying diodes are commonly found in SWR meters, nothing to do with separating the forward and reflected components. There area number of caveats to the power calculation, but for all practical purposes it is near enough.

To go further, for a less mathematical approach, I refer you to this article by Bruene, which nicely explains it all using graphical phasors: http://kambing.ui.ac.id/onnopurbo/orari-diklat/teknik/arrl/using-equipment/5904024.pdf

Note: My references worked on 23rd May 2013. I have found that some other references to these articles are no longer valid.