---
title: "AM vs FM efficiency and complexity; coherent ASK error"
subject: "Communication Systems"
chapter: 9
key: "semester_6/communication_systems:am-fm-bw-efficiency-ask-error"
source: https://www.bctengineer.com/q/semester_6/communication_systems/am-fm-bw-efficiency-ask-error
site: BCT Engineering
---

# AM vs FM efficiency and complexity; coherent ASK error

Communication Systems · Chapter 9: Noise in Communication Systems

- Asked in: 2070 Asar (CS II), 3+4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/am-fm-bw-efficiency-ask-error
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-9

## Question

Compare AM and FM in terms of power efficiency, band width efficiency and system complexity. Calculate the error probability of coherent ASK.

## Short answer

AM (DSB-FC) has poor power efficiency (γ ≤ 1/3) and narrow bandwidth 2W, while FM has good efficiency (γ = 1.5β² for tone), uses wider bandwidth 2(β+1)W, and has higher complexity (limiter/discriminator). Coherent ASK error probability is Q(√(E_b/N_0)).

## Answer

#### AM vs FM

| Point | AM (DSB-FC) | FM |
|---|---|---|
| Power efficiency | Poor: carrier carries $\ge 2/3$ of power; $\gamma = \mu^2/(2+\mu^2) \le 1/3$ | Good: constant envelope; $\gamma = \tfrac32\beta^2$ (tone), can be $\gg 1$ |
| Noise performance | Noise adds directly to amplitude | Limiter removes amplitude noise; SNR rises with $\beta^2$ |
| Bandwidth | $2W$ (narrow) | $2(\beta+1)W$ (Carson), much wider |
| Bandwidth efficiency | Better | Poorer; trades bandwidth for SNR |
| Threshold | Envelope detector threshold at low SNR | Sharper threshold (~10 dB CNR) |
| Transmitter | Needs linear power amplifier at high level | Class C amplifiers usable (constant envelope) |
| Receiver complexity | Simple (diode envelope detector) | More complex (limiter, discriminator/PLL, de-emphasis) |

#### Error probability of coherent ASK

Signals over a bit: $s_1(t) = A\cos\omega_c t$ for "1", $s_0(t) = 0$ for "0"; AWGN of PSD $N_0/2$; equal priors.

Correlator output $y = \int_0^{T_b} r(t)\cos\omega_c t\,dt$ has mean $AT_b/2$ for "1" and 0 for "0", with Gaussian noise variance

$$
\sigma^2 = \frac{N_0}{2}\cdot\frac{T_b}{2} = \frac{N_0T_b}{4}
$$

Optimum threshold is midway, $AT_b/4$, so

$$
\begin{aligned}
P_e &= Q\!\left(\frac{AT_b/4}{\sqrt{N_0T_b/4}}\right) = Q\!\left(\sqrt{\frac{A^2T_b}{4N_0}}\right)
\end{aligned}
$$

With average bit energy $E_b = \tfrac12\cdot\tfrac{A^2T_b}{2} = \tfrac{A^2T_b}{4}$:

$$
P_e = Q\!\left(\sqrt{\frac{E_b}{N_0}}\right)
$$

This is 3 dB worse than coherent BPSK, $Q(\sqrt{2E_b/N_0})$.

## Check yourself

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

1. Which is true about the power efficiency of AM (DSB-FC) and FM?
   A. AM gamma can exceed 1, FM gamma is at most 1/3
   B. FM has constant envelope and gamma = 1.5 beta^2, can be much greater than 1
   C. Both have the same figure of merit
   D. AM is better because its envelope varies
   Answer: B. FM's limiter removes amplitude noise and the tone-modulation gain is 3/2 beta^2, while AM gamma is at most 1/3. (Key point: Power efficiency of FM vs AM)

2. FM bandwidth by Carson's rule is 2(beta + 1)W, compared with AM's 2W. This means FM is
   A. more bandwidth efficient than AM
   B. less bandwidth efficient but trades bandwidth for SNR
   C. equal in bandwidth efficiency
   D. unaffected by beta
   Answer: B. FM uses much more bandwidth and in return gets an SNR improvement growing with beta^2. (Key point: Bandwidth trade-off)

3. The error probability of coherent ASK in terms of average bit energy is
   A. Q(sqrt(2E_b/N_0))
   B. Q(sqrt(E_b/N_0))
   C. Q(sqrt(E_b/(2N_0)))
   D. 0.5 exp(-E_b/N_0)
   Answer: B. With threshold A T_b/4 and sigma^2 = N_0 T_b/4, P_e = Q(sqrt(A^2 T_b/(4N_0))) = Q(sqrt(E_b/N_0)). (Key point: Coherent ASK error probability)

4. Which item makes an FM receiver more complex than a simple AM receiver?
   A. Diode envelope detector
   B. Limiter, discriminator or PLL and de-emphasis
   C. Linear power amplifier
   D. Single IF filter only
   Answer: B. FM needs a limiter and a frequency discriminator/PLL plus de-emphasis, whereas AM uses a simple diode envelope detector. (Key point: Receiver complexity)

## Close variants set in other exams

- [AM vs FM; error probability of coherent ASK](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aam-fm-compare-ask-error) — Communication Systems, chapter 9, asked 2×

## Related in Communication Systems

- [Error probability of coherent ASK](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aask-coherent-error-probability) — Communication Systems, chapter 9, asked 2×
- [Coherent ASK and PSK error; ASK needs double power](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aask-psk-error-double-power) — Communication Systems, chapter 9
- [Threshold effect in FM; error probability of coherent PSK](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Athreshold-effect-psk-error) — Communication Systems, chapter 9
- [Error probability of binary ASK extended to M-ary](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aask-error-prob-mary) — Communication Systems, chapter 9
- [Bit error probability for binary ASK](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Abinary-ask-ber) — Communication Systems, chapter 9
- [M-ary error probability; binary vs M-ary](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amary-error-compare-binary) — Communication Systems, chapter 9