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A transmitter's phase modulator gives an index of \( 0.4 \) at \( 400 \ \mathrm{kHz} \). To reach an index of \( 5 \), the multiplication factor needed is

  • A.20
  • B.12.5
  • C.5
  • D.2

Answer: B

Dividing the required index by the available one:

\[ n = \frac{5}{0.4} = 12.5 \]

so about 12.5, which in practice would be built from a chain of doublers and triplers giving twelve or sixteen. The carrier goes to 5 MHz at the same time, and a mixer then shifts it to the operating frequency without further scaling the deviation. 5 and 20 are the index and a plausible chain factor rather than the ratio, and 2 is a single doubler. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

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