Question E9D02:
How can two linearly polarized Yagi antennas be used to produce circular polarization?  

Choices:  
A: Stack two Yagis to form an array with the respective elements in parallel planes fed 90 degrees out of phase  
B: Stack two Yagis to form an array with the respective elements in parallel planes fed in phase  
C: Arrange two Yagis on the same axis and perpendicular to each other with the driven elements at the same point on the boom and fed 90 degrees out of phase  
D: Arrange two Yagis collinear to each other with the driven elements fed 180 degrees out of phase    

Correct Answer is  C: Arrange two Yagis on the same axis and perpendicular to each other with the driven elements at the same point on the boom and fed 90 degrees out of phase  

To get circular polarization, you must combine two orthogonal linear fields of equal amplitude with a 90° phase difference.

Why the correct answer is correct (Choice C)
- Two Yagis mounted on the same axis and physically perpendicular (e.g., one horizontal, one vertical) create orthogonal linear polarizations.
- Feeding them with equal power and a 90° phase shift produces a rotating E-field, i.e., circular polarization.
- Co-locating the driven elements at the same point on the boom keeps the phase centers aligned, minimizing ellipticity.

Mathematically:
- Condition for circular polarization:
  $$|E_x| = |E_y| \quad \text{and} \quad \phi_x - \phi_y = \pm 90^\circ$$
- Example fields:
  $$E_x = E_0 \cos(\omega t), \quad E_y = E_0 \cos(\omega t \pm 90^\circ)$$
  This yields constant magnitude:
  $$E_x^2 + E_y^2 = E_0^2$$
- Axial ratio:
  $$AR = \frac{E_{\max}}{E_{\min}} = 1 \; (0\ \text{dB}) \text{ for ideal circular}$$

Why the other choices are incorrect
- A: “Stack two Yagis in parallel planes fed 90° out of phase”
  - Both Yagis have the same polarization; 90° phase only steers/tilts the beam or changes pattern, not polarization. Result remains linear, not circular.
- B: “Stack two Yagis in parallel planes fed in phase”
  - Same polarization and phase → more gain/directivity, but still linear polarization.
- D: “Arrange two Yagis collinear and feed 180° out of phase”
  - Antiphase feeding shapes/nulls the pattern but doesn’t create orthogonal components. Polarization remains linear.

Useful implementation notes and rules of thumb
- Use a 90° hybrid coupler or a quarter-wave phasing line to get the required phase shift and equal amplitudes.
- The sense (RHCP vs LHCP) depends on which antenna leads by +90° when looking in the direction of propagation.
- Keep phase and amplitude balance tight (within a few degrees and ~1 dB) and align phase centers to avoid ellipticity.