Question E9A09:
What is antenna efficiency?  

Choices:  
A: Radiation resistance divided by transmission resistance  
B: Radiation resistance divided by total resistance  
C: Total resistance divided by radiation resistance  
D: Effective radiated power divided by transmitter output    

Correct Answer is  B: Radiation resistance divided by total resistance  

To define antenna efficiency, use the ratio of radiated power to power accepted by the antenna, which maps to resistances in the antenna model.

Correct concept:
- Antenna efficiency, η:
  $$\eta = \frac{P_{\text{radiated}}}{P_{\text{input}}} = \frac{R_{\text{rad}}}{R_{\text{total}}}$$
- Total resistance at the feedpoint:
  $$R_{\text{total}} = R_{\text{rad}} + R_{\text{loss}}$$
  where:
  - $R_{\text{rad}}$ = radiation resistance (power that becomes RF radiation)
  - $R_{\text{loss}}$ = all loss resistances (ohmic conductor loss, ground loss, loading coil/trap loss, etc.)

Why B is correct (Radiation resistance divided by total resistance):
- By the power-divider model of a series resistance, the fraction of input power that is radiated is the fraction of the total resistance that is radiation resistance:
  $$\eta = \frac{R_{\text{rad}}}{R_{\text{rad}} + R_{\text{loss}}}$$

Why the others are incorrect:
- A: Radiation resistance divided by transmission resistance  
  “Transmission resistance” is not a standard term here, and this ignores other loss components. Efficiency must compare $R_{\text{rad}}$ to the sum of all resistive components, not just a subset.
- C: Total resistance divided by radiation resistance  
  This is the reciprocal of efficiency and would often exceed 1, which is impossible for efficiency.
- D: Effective radiated power divided by transmitter output  
  ERP includes antenna directivity and reference gain; it mixes pattern gain with efficiency and also includes feedline/matching losses relative to the transmitter. Antenna efficiency is strictly about the antenna’s radiated vs accepted power, independent of directional gain.

Useful rules of thumb:
- If $R_{\text{rad}} = R_{\text{loss}}$, then $\eta = 0.5$ (50% efficiency, 3 dB loss).
- If $R_{\text{rad}} = 9 R_{\text{loss}}$, then $\eta \approx 0.9$ (90% efficiency, ~0.46 dB loss).
- Half-wave dipole: $R_{\text{rad}} \approx 73\,\Omega$; quarter-wave vertical over good ground: $R_{\text{rad}} \approx 36.5\,\Omega$. Short/loaded antennas have very small $R_{\text{rad}}$ so losses dominate and efficiency drops.