Question E9G01:
Which of the following can be calculated using a Smith chart?  

Choices:  
A: Impedance along transmission lines  
B: Radiation resistance  
C: Antenna radiation pattern  
D: Radio propagation    

Correct Answer is  A: Impedance along transmission lines  

Correct Answer: Impedance along transmission lines

Why A is correct:
- A Smith chart is a graphical tool for transmission-line problems. You plot the normalized load impedance $z_L = Z_L/Z_0$, then “rotate” along the chart by the electrical length to read the normalized impedance (or admittance) at any point on the line.
- It directly yields impedance, admittance, reflection coefficient, and SWR along a line.

Why the others are incorrect:
- B: Radiation resistance is an antenna property derived from its geometry and current distribution, not something computed with a Smith chart. You can plot a known feedpoint impedance on the chart, but the chart doesn’t determine radiation resistance.
- C: Antenna radiation pattern (field strength vs. angle) is unrelated to the Smith chart; it requires modeling or measurement, not transmission-line plotting.
- D: Radio propagation depends on ionospheric/terrestrial media and frequency; the Smith chart does not model propagation paths.

Useful formulas and rules:
- Normalize impedance: $z = \dfrac{Z}{Z_0}$; admittance: $y = \dfrac{1}{z}$.
- Reflection coefficient at the load:
  $$\Gamma_L = \frac{Z_L - Z_0}{Z_L + Z_0}$$
- VSWR:
  $$\text{SWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|}$$
- Input impedance of a lossless line of length $l$:
  $$Z_{\text{in}} = Z_0 \,\frac{Z_L + j Z_0 \tan(\beta l)}{Z_0 + j Z_L \tan(\beta l)}$$
  where $\beta = 2\pi/\lambda$.
- On the Smith chart, moving toward the generator is a clockwise rotation along a constant-SWR circle; a full circle corresponds to $\lambda/2$ of line length (perimeter scales are labeled in wavelengths toward load/generator).
- For lossy lines: $|\Gamma(z)| = |\Gamma_L| e^{-2\alpha z}$, so SWR decreases toward 1 as you move toward the generator.