Q.Describe basic operation of a reactance FM modulator.

A reactance modulator is a transistor (FET or BJT) stage connected across the oscillator tank that is made to behave as a variable inductance or capacitance. The modulating signal changes its effective reactance, which changes the tank resonant frequency and hence produces FM. …

[!TLDR]

A transistor with a 90 degree phase-shift network acts as a variable reactance across the oscillator tank; varying the modulating voltage varies that reactance and hence the oscillator frequency, producing FM.

A reactance modulator uses an active device (commonly a FET or BJT) connected in parallel with the tank circuit of the carrier oscillator. A phase-shifting network of a resistor and capacitor (or inductor) is arranged so that the alternating current drawn by the device is 90 degrees out of phase with the voltage across it. A current that leads or lags the applied voltage by 90 degrees is exactly what a capacitor or inductor produces, so as seen by the tank the transistor behaves like a pure reactance rather than a resistance.

The value of this effective reactance depends on the transconductance $g_m$ of the device. When the modulating (audio) signal is applied to the gate or base, it changes the operating point and therefore $g_m$. Consequently the reactance presented to the tank varies in step with the message. Since this reactance is effectively in parallel with the tank capacitance (or inductance), the resonant frequency of the oscillator,

$f = \frac{1}{2\pi\sqrt{LC}},$ …