Question E9E08:
What is a use for a Wilkinson divider?  

Choices:  
A: To divide the operating frequency of a transmitter signal so it can be used on a lower frequency band  
B: To feed high-impedance antennas from a low-impedance source  
C: To divide power equally between two 50-ohm loads while maintaining 50-ohm input impedance  
D: To divide the frequency of the input to a counter to increase its frequency range    

Correct Answer is  C: To divide power equally between two 50-ohm loads while maintaining 50-ohm input impedance  

To divide power equally between two 50-ohm loads while maintaining 50-ohm input impedance is correct.

1) Why the correct answer is correct
- A Wilkinson power divider is a 3-port passive RF network that:
  - Splits input power equally between two outputs (each ideally gets $P_\text{in}/2$, i.e., −3 dB).
  - Presents a matched input impedance of $50\,\Omega$ when both outputs are terminated in $50\,\Omega$.
  - Provides high isolation between the two output ports via an isolation resistor.
- It uses two quarter-wave transmission line sections and a resistor between the outputs to achieve equal split, good match, and isolation.

2) Why the other choices are incorrect
- A: Frequency division is done by digital prescalers or regenerative dividers, not by a passive RF power divider. A Wilkinson does not change frequency; it only splits power.
- B: Feeding high-impedance antennas from a low-impedance source is an impedance matching task (e.g., L-network, transformer, or quarter-wave transformer), not the purpose of a Wilkinson. While it uses quarter-wave lines, its goal is equal power split into matched loads.
- D: Dividing the input frequency for a counter is again a frequency divider/prescaler function. A Wilkinson divider does not divide frequency.

3) Useful formulas and rules of thumb
- For a 2-way equal-split Wilkinson designed for system impedance $Z_0$:
  - Quarter-wave line impedance: $$Z_q = Z_0\sqrt{2}$$
  - Isolation resistor between outputs: $$R = 2Z_0$$
  - Ideal output power per port: $$P_\text{out} \approx \frac{P_\text{in}}{2} \quad (\text{−3 dB})$$
  - Quarter-wave physical length in a medium with phase velocity $v_p$: $$\ell = \frac{v_p}{4f} = \frac{c \cdot VF}{4f}$$
- Key properties:
  - Input match: $Z_\text{in} = Z_0$ with matched loads.
  - Outputs are isolated; imbalance power is absorbed by the resistor.