Question E9E01:
Which matching system for Yagi antennas requires the driven element to be insulated from the boom?  

Choices:  
A: Gamma  
B: Beta or hairpin  
C: Shunt-fed  
D: T-match    

Correct Answer is  B: Beta or hairpin  

For E9E01, the matching system that requires the driven element to be insulated from the boom is the Beta (hairpin) match.

Why “Beta or hairpin” is correct:
- A hairpin (beta) match is a parallel, inductive shorted stub placed directly across the split driven element’s feedpoint.
- The driven element must be split and both halves “hot,” so the element must be insulated from the boom to avoid shorting the feedpoint to ground.
- Typical practice: shorten the driven element to make it slightly capacitive, then use the inductive hairpin to cancel that capacitive reactance and raise the resistance to the feedline value (often 50 Ω).

Why the other choices are incorrect:
- Gamma (A): Designed specifically to allow a grounded (uninsulated) driven element. It feeds one side of the element via a series capacitor and a parallel rod, with the other side bonded to the boom/shield.
- Shunt-fed (C): By definition uses a grounded element with a shunt feed; does not require insulating the element from the boom.
- T-match (D): A balanced “dual-gamma”-style match that can be used with a grounded (uninsulated) element; it does not inherently require insulation from the boom.

Useful formulas and rules of thumb:
- For a beta/hairpin match, if the driven element’s feedpoint impedance (with the element slightly shortened) is $Z_a = R_a - j|X_a|$, choose the shunt inductive reactance $X_L$ so the net susceptance is zero:
  - Admittance of the element: $Y_a = \dfrac{1}{Z_a} = \dfrac{R_a + j|X_a|}{R_a^2 + X_a^2}$
  - Set $B_L = -\dfrac{1}{X_L} = -\Im(Y_a)$, giving:
    $$X_L = \frac{R_a^2 + X_a^2}{|X_a|}$$
  - Inductance value:
    $$L = \frac{X_L}{2\pi f}$$
- If using a shorted transmission-line “hairpin” stub of characteristic impedance $Z_0$ and length $\ell$:
  $$X_{\text{stub}} = Z_0 \tan\!\left(\frac{2\pi \ell}{\lambda}\right) \quad (\ell < \lambda/4,\ \text{inductive})$$
- Rule of thumb: Hairpin/beta matches require a split, insulated driven element. Gamma and T-matches are commonly used when you want to avoid insulating the element from the boom.