Question E9E11:
What is the purpose of using multiple driven elements connected through phasing lines?  

Choices:  
A: To control the antenna’s radiation pattern  
B: To prevent harmonic radiation from the transmitter  
C: To allow single-band antennas to operate on other bands  
D: To create a low-angle radiation pattern    

Correct Answer is  A: To control the antenna’s radiation pattern  

Correct answer: A — To control the antenna’s radiation pattern

Why A is correct:
- Multiple driven elements fed through phasing lines let you set specific amplitude and phase relationships between element currents. This shapes and steers the array’s pattern (gain, beam direction, front-to-back ratio, sidelobes).
- Examples: broadside (max perpendicular to the line of elements), end-fire (max along the line), and cardioid (deep null in one direction).

Key ideas and formulas:
- Phase shift introduced by a phasing line of length ℓ and velocity factor VF:
  $$\Delta\phi = \frac{2\pi\,\ell}{\lambda_{\text{line}}} = \frac{2\pi\,\ell}{\text{VF}\,\lambda_0}$$
- Two equal elements separated by distance $d$ with phase difference $\alpha$ have array factor:
  $$AF(\theta) = 2\cos\left(\frac{\beta d\cos\theta + \alpha}{2}\right),\quad \beta=\frac{2\pi}{\lambda_0}$$
  - Broadside: $\alpha = 0$
  - End-fire (unidirectional): $\alpha \approx \beta d$
- Rules of thumb:
  - Typical spacing: $0.2\lambda$ to $0.5\lambda$
  - Feed the element “farther along” the desired beam direction with a phase lag so fields add in that direction.

Why the other choices are incorrect:
- B: Prevent harmonic radiation from the transmitter
  - Harmonics are controlled with transmitter/line filtering (e.g., low-pass filters), not by phasing driven elements.
- C: Allow single-band antennas to operate on other bands
  - Multiband operation uses traps, parallel elements, tuners, or log-periodic designs—not phasing lines among multiple driven elements.
- D: Create a low-angle radiation pattern
  - While certain phased arrays (especially verticals) can produce low-angle radiation, phasing lines are used to control the overall pattern (which could be high or low angle). Low-angle specifically depends heavily on height above ground, ground conductivity, and geometry; it’s not the universal purpose.