What does SWR and reflected power mean in terms of power actually dissipated in a load?

Question

I'm struggling to understand the "meaning" of VSWR in the context of power delivered to a load.

Say I have a transmitter operating at 10MHz, a short (~1m) piece of assumed-lossless transmission line, and a load whose impedance is not well-matched to the line.

If I measure forward and reflected power at the transmitter, I'll see some reflected power due to the impedance mismatch. But I understand this gets reflected "again" at the transmitter back to the load and is eventually transferred to the load (it does not get dissipated in the transmitter). So for a lossless transmission line, what measurement is the power dissipated by the load? It is simply the forward power? It would seem like it's not the (forward minus reflected) power, so does that quantity (forward minus reflected) have any physical meaning?

Ultimately, I'm trying to measure the power delivered to this load at 10MHz, and don't quite understand if I can just measure voltage and current and multiply them (accounting for any phase shift), of it I need to account for SWR and/or reflected power in some way...

Answer 1

Power transmission in a cable:

You have a 2 parallel wire cable between the signal source and the load. You can have power meter inserted at some point of the cable (practically it's at the source or the load end of the cable). It gives to you 2 numbers: Power towards the load and power towards the source. The first one can have text label "transmitted" and the second one can have text label "reflected". But those labels are only text, the measured things are net power flow towards the load and net power flow towards the source.

The momentary energy flow direction through the meter can change during the AC cycle. The direction is always the direction of the current in that wire which has the +polarity of the voltage. If voltage and current have phase difference there is a part of the time energy flow towards the load and a part of the time towards the source

Your bidirectional power meter calculates separately the average power when the flow is towards the load and when the flow is towards the source. There are numerous analog circuit constructions which can make it. At low frequencies, like at 10 MHz you can use transformers and rectifiers to make the separation. At microwaves you must use directional couplers to separate the waves which propagate to different directions.

If it happens that your load is mismatched, but the transmitter reflects back all of what returns from the load you have succesful or lucky matching circuit in the transmitter. Then your meter shows nothing coming back from the load because the net energy flow summed from the multiple reflections is only towards the load. Practical transmitters absorb a part of the returning signal. It's either dissipated in the transmitter circuit or directed back to the power supply through protection diodes.

VSWR is not practical thing to be measured directly as the voltage ratio Vmax/Vmin at 10 MHz because one needs a half wavelength piece of open cable where the voltage amplitude between the wires is possible to measure at every point. In shorter cables one cannot reliably detect a standing wave.

But it's common to calculate the theoretical VSWR from the reflection factor (=the VSWR which could be detected in a line which is at least half wavelength long and with the same mismatch as the actual line) because radio engineers and hobbyists are used to talk of VSWR as a measure for how well matching has succeeded. It's done even in cases when the cables are so short that no standing wave could be noticed. There's simple formula between that calculated VSWR and the ratio of powers to different directions.

The powers themselves cannot be decided from VSWR - only their ratio, the power reflection factor. It has formula Preflected/Pforward/=((VSWR-1)/(VSWR+1))^2 That formula isn't valid if there's nonlinearity which generates harmonic components that contain tens of percents of the power. That's because the reflection happens differently in different frequencies and the standing waves of the harmonic components are generally placed differently.

ADD: Practical transmitters have often non-linearly working output amplifier. The amp can be linear in cases it must be able to handle AM or SSB signal. Even a linear amp starts in practice to behave non-linearly with mismatched reactive-looking load because the voltage or current limits of the linear operating range are exceeded or some protection circuits can start to rectify excessive voltage and direct it back to power supply or a dummy load. The exact behaviour can be analyzed by making simulations. Ideal AC voltage source is poor model for real transmitter which has reactive load because it totally skips nonlinear effects in the amp.

BTW. In microwaves we can have circulators and isolators, special ferrite components which really can see the propagation direction of a wave. The reflected wave can be simply stopped and dissipated before it enters back to the transmitter, it can be reflected back to the load or directed to a dummy load where it dissipates. But these components are not practical below 1GHz. They are common for ex. in measurement instruments and radars.

Answer 2

There are two distinct parameters critical to transmitting square edge pulses that are affected by Return Loss at source and load.

1. MPT max power transfer. This is the criteria often used for RF and matched impedance at both ends implies 50% loss which sounds bad but is necessary if power gain is the primary goal with signal integrity.

2. Signal Integrity with voltage shape of harmonics that define the edge. (Rise time, ringing overshoot , ISI (INTERSYMBOL INTERFERENCE) group delay distortion,jitter, etc)

   • Here the mismatch of the harmonics is more critical than the fundamental which might only be 10% or <1% depending on the application. It is not about getting total power transfer perhaps with a high impedance load, getting full no load voltage amplitude with the same signal integrity that you expect or need from a square pulse. We may call this baseband data or SPI or with a need to extract clock from data or have low jitter or minimal edge ringing. But for USB it must be matched at both ends for integrity not power efficiency.

3. thus consider the rise time *f ratio product you need which defines the harmonic number roughly, and decide what is the phase shift , or ISI or return loss YOU NEED in order to define the Return loss at that harmonic. The simplest solution is to use the Vol/Iol=Zol of the driver and the Zo of the transmission line or cable and simply add a series R to match the source to cable impedance, then minimize the parasitic load capacitance (pf) that acts as a short lived short- circuit to 5ns/m edges. These will echo only once if your source is matched.

But driving with ARM 22 OHM DRIVERS into 220 ohm twisted pair will cause ringing with 2ns risetime on 5ns per meter cable with some known computed decay time on the ringing. The signal integrity is a matter of noise margin. Logic in theory, has infinite SNR, just clipped, but in practice it's lower. BER (bit error rate) then is a probability of errors you must avoid than depends on SNR.

Consider > =500MHz HDMI IC's is even harder to do for signal integrity so Broadcom chips do a spectral analysis and equalization or to predistort and compensate these signals to equalize the spectrum. Then add SMT CMchokes in order to get the signal integrity just for a 1m cable. This is transparent to you the PC user. Ethernet must reduce the BW by using long Run LENGTH LIMITED (RLL) TO narrow the BW used in order to reduce the group delay distortion by limiting the low f and also upper f in this modulation scheme.

Conclusion.

Spectral Return Loss (RL) or s11 is more than just about s21 transmission function response, but also about signal integrity from a skewed ratio with phase and amplitude response on harmonics or side bands.

Correlation into the time domain depends on the application, and experience in writing specs.

E.g. once I had a requirement for 50% duty cycle from an RF limiter to within 0.05%. getting a scope to measure this was hard. Using a spectral analyzer on 2f suppression was trivial. Data is often analyzed with time domain eye patterns, yet group delay distortion and s11, s21 amp/phase response can tell the story as well, how to improve it.

Answer 3

As others have pointed out, if the transmission line is "short" relative to the signal wavelength, then one can usually ignore transmission line effects.

However there is a point you raised that I would like to address.

I'll see some reflected power due to the impedance mismatch. But I understand this gets reflected "again" at the transmitter back to the load and is eventually transferred to the load

Suppose the transmission line is sufficiently long that we must consider transmission line effects. If the transmission line is not balanced, say it is coaxial, then it is not true that all, or essentially all, of the power of the transmitter will eventually make it to the load.

Some, perhaps a substantial fraction, of the reflected energy will be radiated from the coaxial cable's shield. As an antenna might be very directional, and as this radiated power is likely not oriented in the desired direction, it represents a loss.