The widespread takeup of the NanoVNA has given new life to the resonance myth. Heard on air some years ago was this enlightenment:
anyone who has blown across the top of an empty milk bottle and observed resonance knows that you really need a resonant antenna to fairly suck the power out of the transmitter.
Phase of s11
Let’s divert to the new pitch that phase of s11 equal to 0° is a key optimisation target.
Adapted to the NanoVNA is this capture from an instructional video:
The voice over is explaining that the (load) voltage and current are in phase at the cursor in this phase of s11 chart (check the axis title). The discussion asserts that phase=0° is goodness.
Well, the first thing to note is that the apparent discontinuity at the cursor is actually an artifact of phase wrapped presentation (ie wrapping phase to be in the range -180° to 180°), phase is not 0° or anywhere near it at the cursor.
Next thing is that if the reference impedance for measurement / calculation of s11 is purely real (eg 50+j0Ω) as is common, then it is true that if phase of s11 is zero, that the associated impedance is purely real (ie the X component is zero which some people assert to mean resonance in the general case).
That so, is using phase of s11 to indicate resonance a good metric… or is it a really poor metric that works some of the time, but is not a reliable metric?
In fact s11 measurements are adversely affected by measurement noise when the magnitude of s11 is very small (ie when VSWR is very close to unity), and that noise is manifest as very high phase jitter, the phase value becomes worthless.
The location of the reference plane is critical to rational interpretation of s11 phase.
Doubling down
Proponents of the magic of s11 phase double down insisting that X=0 when phase of s11=0.
There is no doubt that that is true (though it ignores the R dimension of Z), but measuring phase is adversely impacted by measurement noise as magnitude of s11 becomes small.
Some measurements of a near ideal load
For many modern applications, users seek a low VSWR50 (to mean VSWR wrt Z=50+j0Ω).
Above is a VSWR plot from a VNA sweep of a nearly ideal load. Maximum VSWR is less than 1.001.
Above is the calculated R and X components of Z from the same measurement. X is relatively very small, <0.01Ω at 10MHz.
You might think this is a model load… and it is, but lets look at the magic phase metric.
The first observation is that the plot is of 101 points, and NONE of the points lie near phase=0°, they all lie around phase just less than 180° or just more than -180°.
So much for the phase = 0° optimisation target!
Some measurements of an example non-ideal resistive load
Above is measurement of a nominally 200+j0Ω load. As expected, VSWR50 is 4.
This is not a good load if the object is low VSWR50, it is not a good load for most transceivers designed for a nominal 50Ω load.
Yet, the phase of s11 is the magic 0°, and it is a jitter free plot.
Whilst it is true that if phase of s11 is zero, that X=0, it speaks nothing of the value of the R component of impedance, except that R>50Ω (and in this case it is 200Ω).
The reason the plot is jitter free is that the magnitude is quite high (around 0.6 or -2.8dB), way above the instrument noise floor.
The resonance myth
I wrote on the resonance myth a long time ago at The importance (or not) of being resonant. The article gives example of non-resonant antennas that are widely employed and have high radiation efficiency.
Resonance is not a necessary condition for high radiation efficiency, nor is it sufficient condition to assure high radiation efficiency.
Nevertheless, in this day when popularity is held to determine fact, the resonance myth is popular (as demonstrated in the referenced video).
What is wrong with optimising for VSWR?
If we go back to the 1960s when optimising VSWR50 became more popular, it was driven partly by the movement to coax fed antennas.
With time, the development of transceivers designed for a load specified in terms of VSWR50 (eg VSWR<2.0), then optimising for VSWR is optimising to suit the transmitter’s rated load for power, distortion etc. A side benefit is that it also optimises feed line loss where the feed line is 50Ω coax.
Optimising for VSWR50 remains the best choice for a lot of common antenna systems (including the dipole that was the subject of the Youtube presentation quoted above).
Conclusions
- The notion that a resonant radiator naturally has high radiation efficiency, and that a non-resonant radiator does not is ill founded, and not borne out by real antennas.
- Phase of s11 can be used to indicate X=0 at the reference plane (irrespective of R), but it is adversely affected by measurement noise when magnitude of s11 is small (ie VSWR close to 1).
- Phase of s11 says nothing of the R component of Z.
- Phase of s11 says nothing of VSWR50 which is calculated solely from the magnitude of s11.