Question E7C03:
What is the purpose of adding an inductor to a Pi-network to create a Pi-L-network?  

Choices:  
A: Greater harmonic suppression  
B: Higher efficiency  
C: To eliminate one capacitor  
D: Greater transformation range    

Correct Answer is  A: Greater harmonic suppression  

Correct answer: A — Greater harmonic suppression

Why A is correct:
- A Pi-network (C–L–C) is a 3-element low-pass filter. Adding a series inductor to make a Pi-L-network turns it into a 4-element low-pass filter. Increasing the filter order increases out-of-band attenuation (steeper roll-off), so harmonics are reduced more effectively.
- Filter roll-off increases by roughly 20 dB/decade (≈6 dB/octave) per reactive element. Thus:
  - Pi (3 elements): about −60 dB/decade (−18 dB/octave)
  - Pi-L (4 elements): about −80 dB/decade (−24 dB/octave)
- This extra attenuation is why many HF amplifiers use a Pi-L output network to meet harmonic emission limits without overly high Q in the Pi.

Why the other choices are incorrect:
- B: Higher efficiency
  - Adding components generally adds loss. While a Pi-L can allow using a slightly lower loaded Q (which can help efficiency marginally), the primary reason for the extra inductor is improved harmonic suppression, not efficiency.
- C: To eliminate one capacitor
  - A Pi-L adds an inductor; it does not remove a capacitor from the Pi. The network still uses both capacitors of the Pi section.
- D: Greater transformation range
  - A standard Pi already provides a wide impedance transformation range. The added inductor is not primarily for extending matching range; it is for enhanced low-pass filtering of harmonics.

Useful formulas and rules of thumb:
- Roll-off with N reactive elements:
  $$\text{Roll-off} \approx -20N \text{ dB/decade} \approx -6N \text{ dB/octave}$$
  So moving from a Pi ($N=3$) to a Pi-L ($N=4$) increases harmonic attenuation slope by about 20 dB/decade (≈6 dB/octave).
- Practical rule: A Pi-L output network in a power amplifier typically yields noticeably better 2nd/3rd harmonic suppression compared to a Pi of similar loaded Q.