Question E9G02:
What type of coordinate system is used in a Smith chart?  

Choices:  
A: Voltage circles and current arcs  
B: Resistance circles and reactance arcs  
C: Voltage chords and current chords  
D: Resistance lines and reactance chords    

Correct Answer is  B: Resistance circles and reactance arcs  

Correct answer: B — Resistance circles and reactance arcs

1) Why this is correct
- A Smith chart is a plot of the complex reflection coefficient that maps normalized impedance $z = r + jx$ onto the unit disk.
- Its coordinate grid consists of:
  - Constant-resistance loci: complete circles (centered on the horizontal axis).
  - Constant-reactance loci: arcs of circles (inductive above the axis, capacitive below).
- Thus, the chart uses resistance circles and reactance arcs.

2) Why the other choices are incorrect
- A: Voltage circles and current arcs — The Smith chart does not use voltage/current as its coordinate axes; it uses normalized impedance/admittance via reflection coefficient.
- C: Voltage chords and current chords — Not a feature of Smith chart geometry; “chords” are not the coordinate lines.
- D: Resistance lines and reactance chords — The resistance and reactance coordinates are not straight lines or chords; they are circles and arcs.

3) Useful formulas and rules of thumb
- Normalize impedance:  
  $$z = \frac{Z}{Z_0} = r + jx$$
- Reflection coefficient mapping:  
  $$\Gamma = \frac{z - 1}{z + 1}, \quad z = \frac{1 + \Gamma}{1 - \Gamma}$$
- Constant SWR circles:  
  $$|\Gamma| = \text{constant}$$
- Inductive reactance ($+jx$) plots above the horizontal axis; capacitive ($-jx$) below.
- Match point (center of chart): $z = 1 + j0$.
- Move toward the generator along a lossless line: rotate clockwise along a constant $|\Gamma|$ circle by the electrical length.
- For constant resistance $r$, the circle in the $\Gamma$-plane has center and radius:  
  $$\text{center} = \left(\frac{r}{1+r},\,0\right), \quad \text{radius} = \frac{1}{1+r}$$
- Admittance view: rotate 180°; then you have conductance circles and susceptance arcs for $y = g + jb = 1/z$.