Total posts : 45366
Rich,
Since we both agree that the antenna capacitance is about 30 pF, the graphs for the input impedance and the VSWR can be calculated by hand. This is important for this discussion, because the differences in the RF bandwidth we calculated are not due to differences in definition, but brcause of some error in calculation. Now we can eliminate the computer program from the discussion, and just determine if the results obtained are correct or not.
Your link gives two graphs: One is the input impedance of the antenna vs. frequency. The other is VSWR vs. frequency. The VSWR plot follows directly from the input impedance, so we only need to determine if the input impedance plot is correct or not.
I will demonstrate that that the reactance shown on your input impedance plot for 5 kHz below resonance (which is about 10 ohms of capacitive reactance) is incorrect. It should actually be about 20 ohms of capacitive reactance, as I claimed in a previous post.
As is well-known, inductive reactance is proportional to frequency. Capacitive reactance is inversely proportional to frequency. 5 kHz is 5/1610 = 3.1056(10^-3) of the resonant frequency of 1610 kHz. The inductive reactance has the same absolute value at resonance as the capacitive reactance (3136 ohms). At 5 kHz below resonance, the inductive reactance is
3136(3.1056)(10^-3) = 9.74 ohms less than the inductive reactance at resonance. Because 5kHz is much smaller than 1610 kHz, it can be estimated that the capacitive reactance is very nearly 9.74 ohms more than the capacitive reactance at resonance. By algebraically adding the inductive and capacitive reactances, we get the input reactance of the antenna. The inductive reactance at 5 kHz below resonance is
j(3136-9.74) ohms. The capacitive reactance at 5 kHz below resonance is -j(3136+9.74) ohms. Algebraically adding these two reactances gives: -j(3136+9.74) + j(3136-9.74) =
j3136-j3136 -j9.74-j9.74 = -j19.48 ohms.
So, the capacitive reactance at the antenna input at 5 kHz below resonance is not about 10 ohms, as your plot shows, but about 20 ohms, as I claimed. There is some error in your calculations that doubles the frequency shift from resonance over what it should be. Because of this error, the VSWR values you reported are also incorrect. The correct VSWR values are more like the ones I gave in a previous post.
