Data Communication · Lecture 8

Analog-to-Analog Conversion

AM, FM and PM: putting voice and music onto a carrier

Md Mahbub E Noor · Assistant Professor, Department of CSE, University of Barishal

Course: Data Communication · 2nd Year, 2nd Semester

Analog signals on a carrier: today's goals

Explain why analog signals are modulated onto a high-frequency carrier
Describe AM, its modulation index, spectrum, bandwidth and power
Describe FM and PM, and apply Carson's rule for their bandwidth
Calculate how many stations fit in the AM and FM broadcast bands
Compare AM, FM and PM for bandwidth, noise and uses

The four conversions

Lecture	Conversion	Example
5	Analog → digital	PCM
6	Digital → digital	Line coding
7	Digital → analog	ASK, FSK, PSK, QAM
8 · today	Analog → analog	AM, FM, PM

Reading: Forouzan, Section 5.2

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

2 / 26

Why put an analog signal on a carrier?

Radio and many cables are band-pass: they carry only a band far from 0 Hz
Antennas must be roughly a quarter-wavelength long, impossible for audio frequencies
Each sender needs its own band so many can share one medium
So the message (low-frequency, baseband) modulates a high-frequency carrier

Antenna for 1 kHz audio sent directly

λ = 3×10⁸ / 10³ = 300 km → λ/4

75 km long!

Antenna for a 100 MHz FM carrier

λ = 3×10⁸ / 10⁸ = 3 m → λ/4

75 cm

Every station's audio uses the same 0 to 15 kHz range. Shifting each to its own carrier frequency lets them share the air without colliding.

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

3 / 26

Three ways to carry an analog message

Amplitude modulation (AM): the carrier's height follows the message
Frequency modulation (FM): the carrier's frequency follows the message
Phase modulation (PM): the carrier's phase follows the message
The carrier's other two properties stay constant in each case

Message · a voice tone

AM · amplitude follows the message

FM · frequency follows the message

PM · phase follows the message

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

4 / 26

Amplitude modulation (AM)

The carrier's amplitude varies with the message; its frequency and phase stay fixed
s(t) = Ac [1 + m·cos(2πfm t)] · cos(2πfc t)
The outline of the peaks, the envelope, is a copy of the message
Implemented by multiplying the carrier by (1 + message)

Message m(t)

Carrier

AM signal · dashed blue = envelope = message

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

5 / 26

The modulation index m

m measures how deeply the message changes the carrier's amplitude
0 < m < 1: normal AM; the envelope is a faithful copy
m = 1: 100% modulation; the envelope just touches zero
m > 1: overmodulation; the envelope folds over and the message is distorted

m = 0.5

m = 1 (100%)

m = 1.4: overmodulated

m = (Amax − Amin) / (Amax + Amin)

Example: Amax = 10 V, Amin = 2 V → m = 8 / 12 = 0.67 (67% modulation)

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

6 / 26

AM spectrum and bandwidth

AM shifts the message's spectrum up to the carrier and mirrors it
Upper sideband (fc to fc + B) and lower sideband (fc − B to fc)
So an AM signal needs twice the message's bandwidth: B(AM) = 2B
Both sidebands carry the same information; single-sideband (SSB) sends only one to halve the bandwidth

message: 0 to B

LSB

USB

B(AM) = 2B

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

7 / 26

Worked example: planning the AM band

Audio for AM broadcasting is limited to about 5 kHz
Each station needs 2 × 5 = 10 kHz (the FCC allocation in Forouzan)
Carriers must be at least 10 kHz apart so neighbours do not overlap
The AM band, 530 to 1,700 kHz, fits 117 such channels

Bandwidth per station

audio 5 kHz → 2 × 5 kHz

10 kHz

Station on 1,000 kHz occupies

1,000 ± 5 kHz

995 to 1,005 kHz

Stations in 530 to 1,700 kHz

(1,700 − 530) / 10

117 channels

Asia, including Bangladesh, and Europe use 9 kHz spacing on medium wave (531 to 1,602 kHz): 119 channels.

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

8 / 26

AM power: most of it is in the carrier

The carrier itself carries no information; only the sidebands do
Total power Pt = Pc (1 + m²/2)
Even at m = 1, the sidebands get only one third of the power
This waste is why AM is inefficient, and why SSB and FM were developed

Pt = Pc (1 + m² / 2)

Pc = carrier power · the extra Pc·m²/2 is shared equally by the two sidebands

Pc = 100 W, m = 0.8

100 × (1 + 0.64/2) = 100 × 1.32

Pt = 132 W

Useful (sideband) power, same example

32 W of 132 W

≈ 24%

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

9 / 26

Checkpoint 1 · 3 minutes

Check your understanding

Q1

An AM signal's peaks measure 12 V at most and 4 V at least. What is m?

Q2

A 6 kHz audio signal is sent by AM on a 900 kHz carrier. Which band does it occupy, and how wide is it?

Q3

What happens if m is set to 1.3, and why must broadcasters avoid it?

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

10 / 26

Frequency modulation (FM)

The carrier's frequency varies with the message's value; amplitude and phase stay fixed
The frequency swings by up to Δf (the peak deviation) either side of fc
The modulation index is β = Δf / fm
Implemented with a voltage-controlled oscillator (VCO): the message voltage sets the frequency

Message m(t)

FM signal · crowded where the message is high

f(t) = fc + Δf · m(t)

Δf = peak frequency deviation · β = Δf / fm = modulation index

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

11 / 26

FM spectrum and bandwidth: Carson's rule

FM produces many sidebands at fc ± fm, ± 2fm, …
Their strengths follow Bessel functions of β; beyond about β + 1 they become tiny
Carson's rule: B(FM) ≈ 2(1 + β)B
Larger β: better noise immunity, but more bandwidth

β = 4: lines at fc ± n·fm; shaded = Carson's bandwidth

B(FM) = 2(1 + β)B = 2(Δf + B)

Carson's rule: contains about 98% of the power. Forouzan uses β = 4 for broadcasting.

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

12 / 26

Worked example: planning the FM band

FM stereo audio extends to about 15 kHz
With β = 4: B = 2(1 + 4) × 15 = 150 kHz; the allocation is 200 kHz per station
The FM band 88 to 108 MHz holds 20 / 0.2 = 100 channels
Only alternate channels are used in one area, to avoid interference: about 50

Stereo audio 15 kHz, β = 4 (Forouzan)

2(1 + 4) × 15 kHz

150 kHz

Real broadcast: Δf = 75 kHz, fm = 15 kHz

β = 5 → 2(75 + 15) kHz

180 kHz

Channels in 88 to 108 MHz at 200 kHz

20 MHz / 0.2 MHz

100 (50 per area)

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

13 / 26

Why FM sounds cleaner than AM

Most noise (thermal, impulse, lightning) changes the signal's amplitude
AM carries the message in the amplitude, so the noise goes straight into the audio
FM carries it in the frequency, so a limiter can strip amplitude changes away
The price: much more bandwidth (200 kHz vs 10 kHz)

AM + amplitude noise · the noise changes the envelope itself

FM + amplitude noise · the information is in the zero crossings

An FM receiver first clips the signal to a constant height (a limiter), discarding amplitude noise, then reads the frequency.

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

14 / 26

Phase modulation (PM)

The carrier's phase varies with the message's value; amplitude stays fixed
s(t) = Ac cos(2πfc t + kp·m(t))
PM of a message = FM of its derivative: the frequency shifts where the message changes
Same bandwidth formula as FM, but a smaller β in practice

Message · a smoothed square wave

FM · frequency follows the message's value

PM · phase follows the value; frequency changes only where the message changes

B(PM) = 2(1 + β)B, with β ≈ 1 (narrowband) to 3 (wideband): smaller than FM's

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

15 / 26

AM, FM and PM compared

	AM	FM	PM
Changes	amplitude	frequency	phase
Bandwidth	2B	2(1 + β)B, β ≈ 4	2(1 + β)B, β ≈ 1–3
Noise immunity	poor	good	good
Power efficiency	low (carrier wastes power)	high (constant amplitude)	high (constant amplitude)
Receiver	very simple (envelope detector)	limiter + discriminator	phase detector
Uses	MW/SW broadcast, aircraft radio	FM broadcast, two-way radio, TV sound	basis of PSK and QAM; some radios

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

16 / 26

Try it: AM, FM and PM side by side

Interactive

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

17 / 26

Checkpoint 2 · 3 minutes

Check your understanding

Q1

A 5 kHz voice signal is modulated. Find the bandwidth for AM, FM with β = 5, and PM with β = 1.

Q2

FM: peak deviation 50 kHz, message 10 kHz. What are β and the Carson bandwidth?

Q3

Why does an FM receiver use a limiter before demodulating?

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

18 / 26

Getting the message back: demodulation

The receiver reverses the modulation to recover the message
AM: a diode and an RC filter follow the envelope; the simplest radio receiver
FM: limit the amplitude, then convert frequency changes into voltage
Real radios first shift the chosen station to a fixed intermediate frequency (superheterodyne)

AM: envelope detector

Diode: keep the top half

RC filter: follow the peaks

Audio out

FM: limiter, then discriminator

Clip to constant height, then turn frequency changes into voltage (a frequency-to-voltage converter or a phase-locked loop).

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

19 / 26

Try it: get the message back from AM

Interactive

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

20 / 26

Many stations, one medium: the bridge to multiplexing

Each station

modulates its own carrier, placed in its own slot of the band

Guard bands

small gaps between slots stop neighbours from overlapping

Lecture 9

this is frequency-division multiplexing (FDM)

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

21 / 26

Try it yourself: Analog Modulation Lab

1 · AM: change m; watch the envelope, sidebands and power
2 · FM: change Δf and fm; see β, the Bessel lines and Carson's band
3 · FM vs PM: same message, two waveforms
4 · Band planner: how many AM or FM stations fit

Scan to open the lab on your phone

Open the lab ↗

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

22 / 26

See it in action: voice on a carrier

Watch the AM envelope follow the message, then fold when m > 1
See the carrier and two sidebands appear in the AM spectrum
Watch FM bunch and stretch the carrier, and its sidebands spread with β
When a “Pause & predict” card appears, answer before the video moves on

Click the video to play or pause · Press → for full screen

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

23 / 26

Checkpoint 3 · 3 minutes

Check your understanding

Q1

How many AM stations (10 kHz each) fit between 600 kHz and 1,000 kHz?

Q2

An FM station broadcasts 12 kHz audio with β = 4. Find its Carson bandwidth.

Q3

AM transmitter: carrier power 400 W, m = 1. What are the total and sideband powers?

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

25 / 26

Key takeaways

Analog messages ride on a carrier for antenna size, band-pass media and sharing
AM: envelope follows the message; m = (Amax − Amin)/(Amax + Amin); B = 2B; Pt = Pc(1 + m²/2)
FM: frequency follows the message; β = Δf/fm; Carson B = 2(1 + β)B
PM: phase follows the message; same formula with smaller β; FM of the derivative
Broadcast plans: AM 10 kHz per station (9 kHz in Asia); FM 200 kHz per station

Next lecture

Lecture 9 · Multiplexing and Spread Spectrum

FDM, WDM and TDM: sharing one link among many signals; then spreading a signal on purpose with FHSS and DSSS.

Reading: Forouzan, Chapter 6 · Practise in Analog Modulation Lab

Md Mahbub E Noor

Lecture 8: Analog-to-Analog Conversion

University of Barishal

26 / 26