Question E9D04:
Why should antenna loading coils have a high ratio of reactance to resistance?  

Choices:  
A: To swamp out harmonics  
B: To lower the radiation angle  
C: To maximize efficiency  
D: To minimize the Q    

Correct Answer is  C: To maximize efficiency  

Correct answer: C — To maximize efficiency

1) Why C is correct
- A shortened antenna needs an inductor (loading coil) to cancel its capacitive reactance. The coil’s inductive reactance is $X_L = 2\pi f L$, but the coil also has a series resistance $R_s$ from wire losses.
- Only resistance dissipates power. For a given antenna current $I$, coil loss is $P_{\text{loss}} = I^2 R_s$; the reactive part $X_L$ does not dissipate power.
- The coil’s quality factor is $Q = \dfrac{X_L}{R_s}$. A high $X_L/R_s$ ratio (high Q) means small $R_s$ for the required $X_L$, minimizing $I^2R$ losses and maximizing radiation efficiency:
  $$\eta \approx \frac{R_{\text{rad}}}{R_{\text{rad}} + R_s + R_{\text{other losses}}}$$
- In short antennas, $R_{\text{rad}}$ is already small (often just a few ohms), so keeping $R_s$ very small is critical to high efficiency.

2) Why the other choices are incorrect
- A: To swamp out harmonics  
  “Swamping” is done with resistors or filters, not with a high-Q loading coil. The loading coil primarily tunes the antenna; harmonic suppression is the job of output filters/traps.
- B: To lower the radiation angle  
  Takeoff angle is dominated by antenna height, geometry, and ground system, not the coil’s X/R ratio. The coil mainly impacts tuning, bandwidth, and efficiency.
- D: To minimize the Q  
  The ratio $X/R$ is the definition of series Q ($Q = X/R$). A high X/R increases Q. We want high Q to reduce loss; minimizing Q would increase loss (though it would broaden bandwidth).

3) Useful formulas and rules of thumb
- Inductive reactance: $X_L = 2\pi f L$
- Coil Q (series): $Q = \dfrac{X_L}{R_s}$
- Antenna efficiency (simplified): $\eta \approx \dfrac{R_{\text{rad}}}{R_{\text{rad}} + R_s + R_{\text{ground}} + R_{\text{other}}}$
- Practical tips to increase coil Q (reduce $R_s$): use large diameter coils, thick/low-resistance conductors, well-spaced turns, air cores (low-loss), and place the coil where antenna current is lower (e.g., higher on a vertical or use top-loading).
- Trade-off: Higher Q improves efficiency but narrows bandwidth.