---
title: "Direct FM generation using varactor diode"
subject: "Communication Systems"
chapter: 3
key: "semester_6/communication_systems:direct-fm-varactor"
source: https://www.bctengineer.com/q/semester_6/communication_systems/direct-fm-varactor
site: BCT Engineering
---

# Direct FM generation using varactor diode

Communication Systems · Chapter 3: Angle Modulation

- Asked in: 2064 Shrawan (CS I), 6+2 marks
- Video: [Communication Engineering - FM Generation: Direct Method (Varactor Diode Method)](https://www.youtube.com/watch?v=5W2JUlq3Srs) — Dr. Sapna Katiyar
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/direct-fm-varactor
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-3

## Question

Explain how frequency modulated signals can be generated by direct method using a varactor diode. What are the disadvantages of such a method?

## Short answer

A reverse‑biased varactor diode in an LC oscillator tank changes its capacitance with the modulating voltage, directly shifting the oscillator frequency to produce FM. Disadvantages include poor carrier stability (requires AFC), nonlinear capacitance causing distortion, temperature drift, and inability to use a crystal oscillator directly.

## Answer

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

```text
           +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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How does a varactor produce FM in the direct method?
   A. Its resistance varies with the message
   B. Its reverse-biased junction capacitance changes with the message voltage, varying the LC oscillator frequency
   C. Its gain changes the carrier amplitude
   D. It multiplies the frequency
   Answer: B. The reverse-biased p-n junction capacitance depends on voltage; in parallel with the tank it varies the oscillator frequency with m(t). (Key point: Varactor principle)

2. For small DeltaC << C0, how does the frequency change with C(t) = C0 - DeltaC cos 2π fm t?
   A. fi = fc [1 + DeltaC/(2C0) cos 2π fm t], giving delta f = DeltaC fc/(2C0)
   B. fi = fc DeltaC/C0
   C. fi is constant
   D. fi = fc [1 - DeltaC/C0]^2
   Answer: A. Using (1 - x)^(-1/2) ~ 1 + x/2, frequency varies linearly with the message, so delta f = (DeltaC/2C0) fc. (Key point: Deviation result)

3. Why is carrier stability poor in the direct method?
   A. The varactor is a crystal
   B. The message is too large
   C. An LC oscillator drifts with temperature and supply, so AFC is needed
   D. Frequency multipliers are used
   Answer: C. An LC oscillator (not crystal controlled) drifts, so an AFC loop is required. (Key point: Stability disadvantage)

4. Why must only small DeltaC/C0 be used?
   A. Large deviation reduces power
   B. Cv varies non-linearly with voltage, so large deviations cause distortion
   C. The oscillator would stop
   D. The approximation of AM fails
   Answer: B. Junction capacitance is Cv = K/(V0 + VR)^n, non-linear in voltage, so linear FM holds only for small swings. (Key point: Non-linearity)

## Related in Communication Systems

- [Angle modulation; single tone FM time and frequency domain](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aangle-mod-single-tone-fm-time-freq) — Communication Systems, chapter 3
- [Armstrong (indirect) FM generation; pre-emphasis](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aarmstrong-indirect-pre-emphasis) — Communication Systems, chapter 3
- [Armstrong's method of FM generation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aarmstrong-fm) — Communication Systems, chapter 3
- [Angle modulated signal 12 sin(10⁶t + 5 sin10⁴t)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aangle-mod-12sin-numerical) — Communication Systems, chapter 3
- [Angle modulated signal 20cos(6×10⁸t + 7sin1250t)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aangle-mod-20cos-6e8t) — Communication Systems, chapter 3
- [Modulated signal Z(t) = 50cos{98.6×10⁶×2πt + 15sin(2×10³×2πt)}](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aangle-mod-50cos-98-6mhz) — Communication Systems, chapter 3

## Related in other subjects

- [Short note: Varactor diode](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Ashort-note-varactor) — Basic Electronics Engineering, chapter 2
- [Modulation; AM and FM modulated waves](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Amodulation-am-fm-wave) — Basic Electronics Engineering, chapter 5
- [Direct sequence and frequency hopped SS](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adsss-fhss-techniques) — Wireless Communication, chapter 4
- [Derive 4-hr UH from triangular direct runoff hydrograph](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Atriangular-dro-4hr-uh) — Engineering Hydrology, chapter 5