Day: July 27, 2013

First, with a dummy load. This seems to be quite reasonable. Almost no reflection (green), and V1 (red) and V2 (yellow) are almost the same.

Then, my 17m band full-size dipole, which is far from satisfactory.

The voltage ratio V2/V1=0.9085/2.259=0.402, and the delay of V2 against V1 is 41.7deg (=360deg*6.40nS/55.2nS).

The magnitude of the reflection coefficient is 0.749, which corresponds to the VSWR of 6.98.

(%i) V1:1.0+%i*0.0;
(%i) t:2.0*3.1416*(-41.7/360.0);
(%i) V2:0.402*(cos(t)+%i*sin(t));
(%i) Vr:2*V1-V2;
(%i) z:50.0*V2/Vr;
(%i) realpart(z);
(%o) 7.407809291003613
(%i) imagpart(z);
(%o) -9.031478001791401
(%i) abs(z);
(%o) 11.68089180622445
(%i) g:(z-50)/(z+50);
(%i) abs(g);
(%o) 0.74920478622757
(%i) SWR:(1+abs(g))/(1-abs(g));
(%o) 6.974633845344225

The cable length is, if I remember correctly, around 20m, so the antenna impedance should be 17.8+i59.4 ohm, but this is not very likely from the simulation below.

The same 9m coax cable but with its far end terminated with 100ohm.

At 1910kHz (T=523.6nS) the delay of V2 (yellow) against V1 (red) is +19.00nS (=+13.1deg) and V2-V1 (green) +91nS (=+62.6deg), whereas V1=2.939V and V2=3.463V (V2/V1=1.18).

Theoretically, the magnitude of the reflection coefficient in this case is (ZL-Zs)/(ZL+Zs)=1/3, and its phase is 61.6deg (=2.0*360.0*(9/0.67)/(300/1.91)), which gives the relationship between the incident wave (=V1, red) and the reflected wave (=V2-V1, green).

From the figure, you can see that V2 (yellow) should be mag=1.19 and phase=14.1 deg, both in good agreement with the measurement.

gnuplot> set object 1 rectangle from screen 0,0 to screen 1,1 fillcolor rgb "#f0f0f0" behind
gnuplot> set size square
gnuplot> set xrange[-0.5:2.5]
gnuplot> set yrange[-1.5:1.5]
gnuplot> set zeroaxis
gnuplot> set parametric
gnuplot> plot [0:2*pi] 1+cos(t)/3,sin(t)/3 lw 2 lt -1
gnuplot> set arrow 1 from 0.0 to 1.0 lw 2 lt -1
gnuplot> set arrow 2 from 1,0 to 1+cos(1.07)/3,sin(1.07)/3 lw 2 lt 2
gnuplot> set arrow 3 from 0,0 to 1+cos(1.07)/3,sin(1.07)/3 lw 2 lt 6
gnuplot> set arrow 4 from 0.0 to 2,0 lw 1 lt -1
gnuplot> set arrow 5 from 1+cos(1.07)/3,sin(1.07)/3 to 2,0 lw 2 lt 3
gnuplot> replot

The same configuration, but at 18100kHz. The phase of the reflection coefficient in this case becomes 583.5deg, or 223.5deg by subtracting 360deg.

From the figure, it is expected that V2 (yellow) is mag=0.79 and phase=-16.8 deg.

From the measurement, we see that V2 (yellow)/V1 (red)=2.334/2.560=0.911 and the phase of V2 relative to V1 is -19.6deg.