Question E8B06:
What is the deviation ratio of an FM phone signal having a maximum frequency swing of plus or minus 7.5 kHz if the highest modulation frequency is 3.5 kHz?  

Choices:  
A: 2.14  
B: 0.214  
C: 0.47  
D: 47    

Correct Answer is  A: 2.14  

To find the deviation ratio, use the definition: the ratio of maximum frequency deviation to the highest modulating (audio) frequency.

Formula:
$$D = \frac{\Delta f}{f_m}$$
where:
- $\Delta f$ = peak deviation (one-sided), not peak-to-peak
- $f_m$ = highest modulating frequency

Compute:
$$D = \frac{7.5\ \text{kHz}}{3.5\ \text{kHz}} = 2.142857... \approx 2.14$$

Why A is correct:
- Using the correct formula and treating “±7.5 kHz” as a peak deviation of 7.5 kHz gives $D \approx 2.14$.

Why the others are incorrect:
- B: 0.214 — off by a factor of 10; likely from misplacing a decimal (e.g., using 0.75 kHz) or mixing units.
- C: 0.47 — equals $3.5/7.5$; this is the inverse of the correct ratio.
- D: 47 — far too large; would imply an unrealistically low $f_m$ for the given deviation.

Rules of thumb:
- Deviation ratio: $$D = \frac{\Delta f}{f_m}$$
- “±” value is the peak deviation, not double it.
- Carson’s Rule for FM bandwidth (useful related concept): $$B \approx 2(\Delta f + f_m)$$