Question E9G06:
On the Smith chart shown in Figure E9-3, what is the name for the large outer circle on which the reactance arcs terminate?  

Choices:  
A: Prime axis  
B: Reactance axis  
C: Impedance axis  
D: Polar axis    

Correct Answer is  B: Reactance axis  

Correct choice: Reactance axis

Why it’s correct:
- On a Smith chart, the large outer circle is the locus of points where the reflection coefficient magnitude is 1: $|\Gamma|=1$.
- Purely reactive impedances ($r=0$, $z=jx$) lie on this circle. Constant-reactance arcs end on it, so it’s called the reactance axis.
- The top semicircle corresponds to inductive reactance ($+jx$); the bottom semicircle corresponds to capacitive reactance ($-jx$).

Why the others are incorrect:
- Prime axis: Not a standard Smith chart term for any boundary or axis.
- Impedance axis: The Smith chart represents normalized impedance everywhere, but the named axes are the resistance axis (horizontal centerline) and reactance axis (outer circle). There isn’t a specific “impedance axis.”
- Polar axis: While the Smith chart uses a polar mapping of $\Gamma$, “polar axis” refers to a direction, not the outer circle.

Useful formulas and rules:
- Normalize impedance: $z = \dfrac{Z}{Z_0} = r + jx$.
- Reflection coefficient: $\Gamma = \dfrac{z - 1}{z + 1}$.
- For pure reactance ($z = jx$), the magnitude is unity:
  $$\left|\Gamma\right| = \left|\frac{jx - 1}{jx + 1}\right| = \frac{\sqrt{x^2 + 1}}{\sqrt{x^2 + 1}} = 1,$$
  placing these points on the outer circle (the reactance axis).
- Horizontal centerline ($x=0$) is the resistance axis (purely resistive points).
- Rightmost point (open circuit): $\Gamma = +1$. Leftmost point (short): $\Gamma = -1$.