On Thu, Oct 10, 2019 at 08:44 AM, alan victor wrote:
If it is available on line see hp application note 117-1.
Alan, thank you very much for mentioning the HP app note!
I've taken a look at its figure 8-13 as well as another S11 plot of a resonant circuit, and I now believe that the earlier-mentioned SWR threshold of 2.618:1 for BW calculation is only valid if, at resonance, the SWR is 1:1.
I'll explain my rationale, but please note, THIS IS NOT A PROOF! It's more of an intuitive insight...
If you look at the attached image, it shows two different Smith chart plots. The left plot is figure 8-13 from the App note and the right plot is from a Simulink-generated model of a resonant circuit (which I've also attached).
Looking at these two plots, it occurred to me that if HP's plot were shrunk (keeping the left-hand side "pinned" at the left-hand side of the Smith Chart) until the right-hand side of the plot intersected the x-axis at "1" (i.e. 50 ohms), then this plot would intersect the Q-curve at reflection coefficients equal to Z = 25 +/- j25 ohms (in other words, the S11 plot would overlay the "circle of constant conductance" where conductance equals 0.02).
What this means is that the S11 plot of the resonant circuit would intersect the Q-curves at the same point where the "circle of constant SWR" for an SWR of 2.618, also intersects the same Q curves. (These two intersections are highlighted with the yellow circles in the right-hand plot).
And, because the S11 plot passes through the x-axis (i.e. resonance) at "1" (which corresponds to 50 ohms), the SWR at resonance must be 1:1.
You can picture the same for the right-hand plot, but rather than shrinking the circle, grow it to the right, keeping the left-hand side pinned to the far left side of the Smith Chart. When the circle has grown to the point where its diameter equals the radius of the Smith Chart, it will intersect the Q-curves at the same points where it intersects the SWR = 2.618 circle, and, again, the SWR is 1:1 at the resonant frequency (i.e. coincident with the point "1" on the x-axis of figure 8-13).
So, it would seem that the BW corresponds to an SWR threshold of 2.618 only when the SWR at resonance is 1:1.
Again, let me stress that this is NOT a proof. Please feel free to shoot it down (anyone).
(The other attached image is the Simulink model used to S11 data plotted on the right-hand Smith Chart).
- Jeff, k6jca
