Direct FM generation using varactor diode

In the direct method, the frequency of an LC oscillator is varied directly by the message, using a voltage-variable reactance. A varactor diode is a reverse-biased p-n junction whose depletion capacitance changes with reverse voltage.

Varactor diode FM generator

           +Vcc (bias)
             |
            RFC                  +-----------+
             |                   |  LC tank  |
m(t) --||--+-+---||----+---------|  L || C0  |--> FM out
      Cc        Cb     |         | Hartley / |
                      ---  Cv    | Colpitts  |
                      /\ varactor|  osc.     |
                       |         +-----------+
                      GND

• A DC reverse bias $V_0$ sets the operating point; the message $m(t)$ is added through a coupling capacitor and RF choke.
• The varactor capacitance is in parallel with the tank capacitor, so it changes the total tank capacitance.

Analysis. The junction capacitance is $C_v = \frac{K}{(V_B + V_R)^{n}}$, where $V_B$ is the barrier potential, $V_R = V_0 + m(t)$ is the total reverse voltage and $n = 1/2$ for an abrupt junction. For a small message, the total tank capacitance varies nearly linearly about its rest value $C_0$:

$$C(t) = C_0 - \Delta C\cos 2\pi f_m t$$

The oscillator frequency is

$$f_i(t) = \frac{1}{2\pi\sqrt{L C(t)}} = \frac{1}{2\pi\sqrt{LC_0}}\left[1 - \frac{\Delta C}{C_0}\cos 2\pi f_m t\right]^{-1/2}$$

For $\Delta C \ll C_0$, using $(1-x)^{-1/2} \approx 1 + x/2$:

$$f_i(t) \approx f_c\left[1 + \frac{\Delta C}{2C_0}\cos 2\pi f_m t\right] = f_c + \Delta f\cos 2\pi f_m t$$

with $f_c = \frac{1}{2\pi\sqrt{LC_0}}$ and $\Delta f = \frac{\Delta C}{2C_0}f_c$. The instantaneous frequency varies linearly with the message, i.e. FM.

Disadvantages

1. Poor carrier stability: an LC oscillator (not crystal) drifts with temperature and supply; an AFC loop is needed.
2. Non-linearity: $C_v$ varies non-linearly with voltage, so large deviations cause distortion; only small $\Delta C/C_0$ is usable.
3. Varactor capacitance is temperature-sensitive.
4. A crystal oscillator cannot be used directly, since its frequency can be pulled only slightly.