Question E5D04:
Why are short connections used at microwave frequencies?  

Choices:  
A: To increase neutralizing resistance  
B: To reduce phase shift along the connection  
C: To increase compensating capacitance  
D: To reduce noise figure    

Correct Answer is  B: To reduce phase shift along the connection  

Correct answer: B — To reduce phase shift along the connection

Why B is correct:
- At microwave frequencies, wavelengths are very short, so even millimeter-long leads become a noticeable fraction of a wavelength and introduce significant phase shift.
- Phase shift along a line of length $l$ is:
  $$\phi = \beta l = \frac{2\pi}{\lambda} l \text{ radians} = 360^\circ \frac{l}{\lambda}$$
- Example: at 10 GHz, $\lambda \approx 3$ cm. A 5 mm lead gives $\phi \approx 360^\circ \times 5/30 \approx 60^\circ$ — large enough to detune circuits and cause unintended impedance transformations.

Why the other choices are incorrect:
- A: Increase neutralizing resistance — Neutralization in RF amplifiers is done with capacitive networks to cancel interelectrode capacitance; “neutralizing resistance” is not the goal, and shortening leads does not “increase” a resistance.
- C: Increase compensating capacitance — Short connections reduce stray capacitance and inductance; they do not aim to increase any “compensating” capacitance. Any required capacitance is added deliberately with components.
- D: Reduce noise figure — While minimizing preamp input loss can help noise figure, the primary reason for short connections at microwave frequencies is to control phase and avoid transmission-line effects, not noise figure.

Useful formulas and rules of thumb:
- Phase shift: $$\phi = 360^\circ \frac{l}{\lambda} = 360^\circ \frac{f\,l}{v_p}$$ where $v_p$ is phase velocity on the medium.
- Impedance transformation of a line section:
  $$Z_\text{in} = Z_0 \frac{Z_L + j Z_0 \tan(\beta l)}{Z_0 + j Z_L \tan(\beta l)}$$
  Even small $l$ at high $f$ can significantly change $Z_\text{in}$.
- “Lumped” rule of thumb: keep interconnects shorter than about $0.05\lambda$ (preferably) and no longer than $0.1\lambda$ to limit phase error.
- Parasitics grow with frequency:
  - Lead inductance ≈ 1 nH/mm, so $X_L = 2\pi f L$ gives about 63 Ω per mm at 10 GHz.
  - Any stray C has $X_C = 1/(2\pi f C)$, which becomes small at microwave frequencies, further disturbing matching.

Bottom line: Short connections keep the electrical length small to minimize phase shift and unintended transmission-line effects at microwave frequencies.