Question E7E01:
Which of the following can be used to generate FM phone signals?  

Choices:  
A: Balanced modulation of the audio amplifier  
B: Reactance modulation of a local oscillator  
C: Reactance modulation of the final amplifier  
D: Balanced modulation of a local oscillator    

Correct Answer is  B: Reactance modulation of a local oscillator  

To generate FM directly, you vary the oscillator’s frequency in step with the audio. That’s done by changing the oscillator’s tank reactance (C or L) with the audio signal.

Why the correct answer (B) is correct
- Reactance modulation of a local oscillator: An active device (e.g., varactor diode or FET as a “reactance modulator”) varies the LC tank reactance, so the oscillator frequency shifts with the audio:
  - Oscillator: $f=\dfrac{1}{2\pi\sqrt{LC}}$
  - Small change: $\dfrac{\Delta f}{f}\approx -\dfrac{1}{2}\dfrac{\Delta C}{C}$
  - FM definition: $f_i(t)=f_c+k_f m(t)$, with deviation $\Delta f = k_f V_m$
  - This is a standard direct-FM method; the FM can then be amplified and, if desired, frequency-multiplied (deviation scales by the multiplier).

Why the other choices are incorrect
- A: Balanced modulation of the audio amplifier
  - Balanced modulators produce double-sideband suppressed-carrier (AM/SSB) at RF/IF, not FM. Doing this at audio doesn’t create RF frequency deviation.
- C: Reactance modulation of the final amplifier
  - The PA is not an oscillator; changing its tuning mostly causes AM and distortion. FM must be created in an oscillator or VCO stage, not in the final amplifier.
- D: Balanced modulation of a local oscillator
  - A balanced modulator by itself yields DSB-SC (an AM process). Without additional 90° phase-shift and integration networks (Armstrong method), it does not produce FM.

Useful formulas and rules
- Modulation index: $\beta=\dfrac{\Delta f}{f_m}$
- Carson’s rule (occupied bandwidth): $B \approx 2(\Delta f+f_m)$
- Frequency multipliers: multiplying by $N$ multiplies both $f_c$ and $\Delta f$ by $N$, so $\beta$ scales by $N$.