Question E7E02:
What is the function of a reactance modulator?  

Choices:  
A: Produce PM or FM signals by varying a resistance  
B: Produce AM signals by varying an inductance  
C: Produce AM signals by varying a resistance  
D: Produce PM or FM signals by varying a capacitance    

Correct Answer is  D: Produce PM or FM signals by varying a capacitance  

A reactance modulator varies the reactive part of an oscillator’s tuned circuit so the oscillator’s frequency or phase follows the modulating signal. In practice, this is usually done by making the circuit look like a voltage-controlled capacitor (often with a varactor diode), which shifts the tank resonance and creates FM or PM.

Why D is correct (Produce PM or FM signals by varying a capacitance):
- The oscillator’s resonant frequency is set by its LC tank:  
  $$f_0 = \frac{1}{2\pi\sqrt{LC}}$$
- If the modulator varies the effective capacitance $C \to C + \Delta C(t)$, then the instantaneous frequency varies, producing FM (or PM with appropriate audio pre-/de-emphasis).
- For small changes:  
  $$\frac{\Delta f}{f_0} \approx -\frac{1}{2}\frac{\Delta C}{C}$$
- Practical circuits use a varactor (voltage-variable capacitor), which is exactly “varying a capacitance.”

Why the other choices are incorrect:
- A: Produce PM or FM by varying a resistance  
  Varying resistance mainly changes amplitude or loading (AM), not the resonant frequency. Not a reactance (capacitive/inductive) modulator.
- B: Produce AM by varying an inductance  
  Varying inductance changes the resonant frequency (FM/PM), not amplitude. Also, the exam-standard reactance modulator is capacitive.
- C: Produce AM by varying a resistance  
  While varying resistance can produce AM, that is not a reactance modulator (reactance means capacitive or inductive, not resistive).

Useful formulas and rules of thumb:
- LC resonance:  
  $$f_0 = \frac{1}{2\pi\sqrt{LC}}$$
- Small-signal sensitivity to capacitance:  
  $$\frac{\Delta f}{f_0} \approx -\frac{1}{2}\frac{\Delta C}{C}$$
- Capacitive reactance:  
  $$X_C = \frac{1}{2\pi f C}$$
- PM and FM relations (conceptual):  
  PM: $$\phi(t) = k_p\,m(t)$$  
  FM: $$f_i(t) = f_c + k_f\,m(t)$$
- A reactance modulator can be configured for PM or FM by adding an integrator or differentiator in the audio path.