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Phase modulation causes instantaneous frequency to vary according to modulating signal. In the same way does Frequency modulation by direct method causes any phase variation in proportion to modulating signal?

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Yes. Frequency is the derivative of phase over time. So you can't modulate one without changing the other.

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  • $\begingroup$ Thank you marcus $\endgroup$
    – sudheer
    Commented Jun 28, 2022 at 10:45
  • $\begingroup$ It seems from equations : FM by m(t) results in PM by 2*pi*m(t).t where as PM by m(t) results in FM by (1/(2*pi)) * d/dt(m(t)) $\endgroup$
    – sudheer
    Commented Jun 28, 2022 at 12:06
  • $\begingroup$ yes. again, frequency is the derivative of phase. No matter how you modulate a signal, you cannot effect one without affecting the other. $\endgroup$ Commented Jun 28, 2022 at 15:35

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