---
title: "PLL lock and capture range; FM demodulation"
subject: "Communication Systems"
chapter: 3
key: "semester_6/communication_systems:pll-lock-capture-fm-demod"
source: https://www.bctengineer.com/q/semester_6/communication_systems/pll-lock-capture-fm-demod
site: BCT Engineering
---

# PLL lock and capture range; FM demodulation

Communication Systems · Chapter 3: Angle Modulation

- Asked in: 2072 Magh (CS I), 2+4 marks
- Video: [PHASE LOCKED LOOP - Concept, Block Diagram Of PLL, Need of PLL, Capture range, Lock range - ENGLISH](https://www.youtube.com/watch?v=YeMt4Q2FYow) — Electronics Subjectified
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/pll-lock-capture-fm-demod
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-3

## Question

Define lock range, capture range in PLL. Explain the demodulation of FM using PLL.

## Short answer

Lock range is the frequency range over which a locked PLL stays locked; capture range is the range over which an unlocked PLL can acquire lock (capture ≤ lock). For FM demodulation, the PLL phase detector compares input FM with VCO output; the error voltage after the loop filter forces the VCO to track the input phase, producing a control voltage proportional to the message.

## Answer

#### Lock range and capture range

- **Lock range (tracking range):** the range of input frequencies over which a PLL that is **already locked** stays in lock as the input frequency is slowly changed. It is set mainly by the VCO range and loop gain.
- **Capture range (acquisition range):** the range of input frequencies over which an **unlocked** PLL can **acquire** lock. It is limited by the loop filter bandwidth.

Capture range is always less than or equal to lock range: $2f_{capture} \le 2f_{lock}$, both centred on the VCO free-running frequency $f_0$.

#### FM demodulation using PLL

```text
 FM in   +-------+  e(t)  +------+  v(t) = output
 ------->| Phase |------->| Loop |----+---------->
 s(t)    | det.  |        | LPF  |    |
         +-------+        +------+    |
             ^                        |
             |        +-------+       |
             +--------|  VCO  |<------+
              r(t)    +-------+
```

**Working:**

1. Input FM: $s(t) = A_c \sin[2\pi f_c t + \phi_1(t)]$, where $\phi_1(t) = 2\pi k_f \int_0^t m(\tau)d\tau$.
2. The VCO free-running frequency is set to $f_c$. Its output is $r(t) = A_v \cos[2\pi f_c t + \phi_2(t)]$ with $\phi_2(t) = 2\pi k_v \int_0^t v(\tau)d\tau$.
3. The phase detector (multiplier) output, after the loop filter removes the $2f_c$ term, is

$$
e(t) \approx \tfrac12 A_c A_v \sin[\phi_1(t) - \phi_2(t)] = \tfrac12 A_c A_v \sin\phi_e(t)
$$

4. This error voltage drives the VCO so that its phase follows the input phase. When the loop is locked, $\phi_e$ is small and $\phi_2(t) \approx \phi_1(t)$.
5. Hence

$$
2\pi k_v \int_0^t v(\tau)\,d\tau \approx 2\pi k_f \int_0^t m(\tau)\,d\tau \;\Rightarrow\; v(t) \approx \frac{k_f}{k_v}\, m(t)
$$

So the VCO control voltage $v(t)$ is directly proportional to the message. The PLL demodulator needs no tuned circuits, is linear, and gives good threshold performance, so it is widely used in IC FM receivers.

## Check yourself

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

1. What is lock range?
   A. Range of input frequencies over which an already-locked PLL stays locked
   B. Range over which an unlocked PLL acquires lock
   C. Bandwidth of the VCO output
   D. Range of the loop filter cutoff
   Answer: A. Lock (tracking) range applies once the loop is locked. (Key point: Lock range)

2. How are capture and lock ranges related?
   A. Capture range > lock range
   B. Capture range <= lock range
   C. They are always equal
   D. Capture range is unrelated to loop filter
   Answer: B. Capture is limited by loop filter bandwidth. (Key point: Capture vs lock)

3. To what is the VCO free-running frequency set?
   A. Zero
   B. 2 fc
   C. The carrier frequency fc
   D. The message frequency
   Answer: C. So the loop can lock onto the FM carrier. (Key point: VCO free-run)

4. What is the PLL demodulator output when locked?
   A. The phase detector product at 2fc
   B. A constant DC
   C. The integral of m(t) squared
   D. v(t) = (kf/kv) m(t), the VCO control voltage
   Answer: D. VCO phase follows the input phase so its control voltage is proportional to m(t). (Key point: Demodulated output)

## Related in Communication Systems

- [FM demodulation using PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afm-demod-pll) — Communication Systems, chapter 3, asked 2×
- [Amplitude limiter; FM demodulation using PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Alimiter-discriminator-pll-fm) — Communication Systems, chapter 3, asked 2×
- [Phase error in coherent DSB-SC detection; AM demodulation by PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aphase-error-dsbsc-am-pll) — Communication Systems, chapter 2
- [PLL as FM demodulator; uses of PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apll-fm-demod-uses) — Communication Systems, chapter 3
- [PLL components and AM demodulation using PLL](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apll-components-am-demod) — Communication Systems, chapter 2, asked 3×
- [Limiter-discriminator FM demodulation; need for pre-emphasis](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Alimiter-discriminator-pre-emphasis) — Communication Systems, chapter 3