Question E9C13:
How does the radiation pattern of a horizontally polarized antenna vary with increasing height above ground?  

Choices:  
A: The takeoff angle of the lowest elevation lobe increases  
B: The takeoff angle of the lowest elevation lobe decreases  
C: The horizontal beamwidth increases  
D: The horizontal beamwidth decreases    

Correct Answer is  B: The takeoff angle of the lowest elevation lobe decreases  

Correct answer: B — The takeoff angle of the lowest elevation lobe decreases

1) Why B is correct
- A horizontal antenna over ground forms its elevation pattern from the direct wave and the ground-reflected wave. As you raise the antenna (in wavelengths), the path-length difference changes so that the first constructive-interference maximum occurs at a lower elevation angle.
- For a horizontal radiator over good ground, the first elevation maximum occurs approximately at:
  $$\sin\theta_0 \approx \frac{\lambda}{4h}$$
  where:
  - $\theta_0$ = takeoff angle of the lowest lobe
  - $h$ = height above ground
  - $\lambda$ = wavelength
- As $h$ increases, $\lambda/(4h)$ gets smaller, so $\theta_0$ decreases (lower takeoff angle).
- Quick examples:
  - $h = 0.5\lambda \Rightarrow \sin\theta_0 = 0.5 \Rightarrow \theta_0 \approx 30^\circ$
  - $h = 1\lambda \Rightarrow \sin\theta_0 = 0.25 \Rightarrow \theta_0 \approx 14.5^\circ$
  - $h = 2\lambda \Rightarrow \sin\theta_0 = 0.125 \Rightarrow \theta_0 \approx 7^\circ$

2) Why the other choices are incorrect
- A: “The takeoff angle increases” — Opposite of what happens. Raising a horizontal antenna lowers the takeoff angle.
- C and D: “Horizontal beamwidth increases/decreases” — Height above ground mainly alters the elevation (vertical) pattern. The azimuthal (horizontal) beamwidth of a simple horizontal antenna (e.g., a dipole) is largely unchanged by height; it remains a broadside figure-eight.

3) Useful formulas and rules of thumb
- First elevation-lobe angle for a horizontal antenna over ground:
  $$\sin\theta_0 \approx \frac{\lambda}{4h}$$
  More generally, the elevation maxima for a horizontal radiator over good ground occur at:
  $$\sin\theta_m \approx \frac{(2m+1)\lambda}{4h}, \quad m=0,1,2,\dots$$
- Rule of thumb: Raise a horizontal antenna (in wavelengths) to lower the takeoff angle and improve DX performance; lower heights favor higher-angle radiation (good for NVIS).