Walter Maxwell wrote in
:

Summarizing reflection coefficient values at stub point with stub in
place: Line coefficients: voltage 0.5 at +120°, current -60° (y = 1
+ j1.1547) Stub coefficients: voltage 0.5 at -120°, current +60° (y
= 1 - j1.1547) Resultant coefficients: voltage 0.5 at 180°, current
0.5 at 0° WRONG Resultant coefficients: voltage 1.0 at 180°, current
1.0 at 0° CORRECT

Walt,

Though admittance or impedance at a point on the mismatched line are
calculated from the underlying Zo and the reflection coefficient
corrected for line loss, they are easier to work in than the raw
reflection coefficient.

It is easier to explain why the stub is located at a position where Yn'=1
+jB than where Gamma=0.5120 (assuming lossless line). It is relatively
obvious that where Yn'=1+jB, a shunt reactance of -jB from a s/c or o/c
stub will leave Yn=1 which is the matched condition.

Re your worked solution (above), I agree that the normalised admittance
looking into 30deg of line with load 16.667+j0 is about 1-j1.1547 (not
the different sign).

I make the normalised admittance looking into the stub about 0+j1.15 (and
the reflection coefficient about 0.5-98, how do you get 1+j1.15?

The addition of the two normalised admittances 1-j1.15 + 0+j1.15 gives 1
+j0 which is the matched condition.

The design is correct, the stub results in a match at the stub connection
point (irrespective of what is connected on the source side of the
point), but I can't understand your maths above (allowing for the sign
error that I think you have made).

Is the reflection coefficient explanation a clearer explanation than
using admittances?

Owen

BTW, my line loss calculator solutions (http://www.vk1od.net/tl/tllc.php)
for Belden 8262 RG58 (you said RG53, but you probably meant RG58) a

(Note some symbols arent supported by plain ascii and appear as '?'.)

Load to Stub connection:

Parameters
Transmission Line Belden 8262 (RG-58C/U)
Code B8262
Data source Belden
Frequency 16.000 MHz
Length 1.030 metres
Zload 16.67+j0.00 ?
Yload 0.059999+j0.000000 ?
Results
Zo 50.00-j0.54 ?
Velocity Factor 0.660
Length 29.97 ?, 0.083 ?
Line Loss (matched) 0.059 dB
Line Loss 0.149 dB
Efficiency 96.63%
Zin 22.12+j24.55 ?
Yin 0.020258-j0.022480 ?
Gamma, rho, theta, VSWR (source end) -2.44e-1+j4.29e-1, 0.493,
119.6?, 2.950
Gamma, rho, theta, VSWR (load end) -5.00e-1+j4.03e-3, 0.500, 179.5?,
3.000
? 6.54e-3+j5.08e-1
k1, k2 1.30e-5, 2.95e-10
Loss model source data lowest frequency 1.000 MHz
Correlation coefficient (r) 0.999884

Stub:

Parameters
Transmission Line Belden 8262 (RG-58C/U)
Code B8262
Data source Belden
Frequency 16.000 MHz
Length 1.685 metres
Zload 100000000.00+j0.00 ?
Yload 0.000000+j0.000000 ?
Results
Zo 50.00-j0.54 ?
Velocity Factor 0.660
Length 49.02 ?, 0.136 ?
Line Loss (matched) 0.096 dB
Line Loss 40.574 dB
Efficiency 0.01%
Zin 0.50-j43.44 ?
Yin 0.000265+j0.023019 ?
Gamma, rho, theta, VSWR (source end) -1.37e-1-j9.69e-1, 0.978, -
98.0?, 90.720
Gamma, rho, theta, VSWR (load end) 1.00e+0+j1.07e-8, 1.000, 0.0?, inf
? 6.54e-3+j5.08e-1
k1, k2 1.30e-5, 2.95e-10
Loss model source data lowest frequency 1.000 MHz
Correlation coefficient (r) 0.999884