W2L1-communications

NIE2226 – Communications

(2023-2024)

AM and FM Modulation

Dr Qiang Hua

School of Computing and Engineering

February 2024

Multiple Choice

Where are you from?

• UK

• China

• USA

• Canada

Introduction – Amplitude Modulation

• Easily made
• High frequency carrier, say 1 MHz
• Audio frequency, say 1kHz
• Audio frequency applied to the control input

of a voltage controlled amplifier amplifying
the carrier

• Amplitude of carrier varies according to the

change in gain due to audio signal

AM modulation – time domain

AM modulation - Oscilloscope

AM modulation-theory

•The carrier amplitude can be written as:

Vc + Vmcosmt

•Thus the modulated carrier is:

(Vc + Vmcosmt) cosct

•Multiplying out the bracket gives:

Vccosct + Vmcosmtcosct

•The product of two cosines is half cos of the sum plus half cos of the
difference. So the AM signal is:

Vccosct + Vm ((cos(c+m)t +cos(c-m)t)

2

AM modulation-Frequency Domain

fc
fc + fm

fc - fm

Vc

(m/2)Vm

(m/2)Vm

AM modulation-Spectrum Analyser

AM modulation

• There are three components to the AM signal

– the original carrier (1MHz)

- the upper side frequency (1.001MHz)
- the lower side frequency (0.999MHz)
• The amplitude of the carrier is the same as the

original

• The amplitude of the side frequencies is HALF

the original audio amplitude

• The MODULATION DEPTH, m, is Vm/VC

AM modulation

• The carrier amplitude is fixed and so does not convey

any information – all the useful power is in the
sidebands

• Carrier power is Vc

2/2 (The rms amplitude is used here.

Hence the factor of 2)

• One sideband power is Vm

2/8

• Total power is Vc

2/2 + 2 x Vm

2/8 using a 1  resistor

• Broadcasters use an m of 30% to avoid overmodulating

the carrier.

• EXERCISE Determine the ratio of useful power (power

in the sidebands) to the TOTAL power for m = 30%.

AM modulation-DSBSC

Double Sideband Suppressed Carrier

• DSBSC is very simple to produce – you simply

multiply the carrier and audio together

• As the product of two cosines is ½ SUM and

DIFFERENCE only the sidebands are produced

• THERE IS NO CARRIER
• DSBSC is used to carry Radio Data Service (RDS) at 57

kHz in the baseband FM signal

Single Sideband modulation-SSB

• SSB is produced by filtering out the unwanted

sideband of a DSBSC signal

• Either the UPPER (USB) or LOWER (LSB) sideband can

be produced

• As both sidebands carry the same information,

transmission of both is rather a waste

• SSB is the best in terms of bandwidth and is 100%

power efficient

Single Sideband modulation-SSB

• Sideband filters are expensive
• Receivers are in general much more expensive than

AM-DSB receivers. Usually, SW world-receivers.

AM Demodulation

• The simple diode demodulator can be used for

AM demodulation

• The IF for AM detection is 455 kHz
• This is beyond the range of hearing
• PROBLEM – the diode is non-linear and so

produces distortion

• This is generally why AM sounds worse than

FM even if the audio is the same

AM Demodulation

• An alternative is to mix the signal back to baseband
• The received signal is mixed with 455 kHz
• Sum and difference signals are produced
• Sum is at 910 kHz, difference is at DC and so the

baseband is produced

• DANGER If there is an offset in the local 455kHz the

baseband will be distorted

• The same goes for phase
• EXERCISE. Confirm distortion for AM, DSBSC and SSB

with frequency offset AND phase.

AM Demodulation – Crystal Radio

AM Demodulation – Crystal Radio

Crystal Radio Circuit

https://www.electronics-notes.com/articles/history/radio-receivers/crystal-radio-set-
circuits.php

In this circuit the combination L1 with the range of VC1 would have been chosen to cover
the required frequency range, typically the medium wave band. Originally the diode
detector, D1, would have been a Cat’s Whisker assembly, but today a simple signal diode
would suffice. Either a germanium diode or a Schottky diode would be ideal as these types
have a lower turn on voltage than silicon devices. (silicon diode turn on voltage is around
0.6 V whereas both the germanium and Schottky diodes are around 0.2 – 0.3V).

Frequency modulation - FM

• Amplitude is FIXED
• FREQUENCY is varied by the modulating signal
• Easy to produce using a Voltage Controlled

Oscillator (VCO)

• Demodulation is easy with a Phase Lock Loop

(PLL)

• 100% power efficient
• The bandwidth is large (later)

Frequency modulation - FM

• VCO constant of proportionality: kf kHz/Volt
• So, the deviation is kfVmcosmt kHz
• This needs to be converted into rad/s
• So, the deviation becomes 2kfVmcosmt rad/s
• We need to convert this to an angle so that we

get Vccos(ct + offset)

• The conversion from rad/s to radians is done

by integrating the deviation

• Thus deviation becomes:

Frequency modulation - FM

2

cos

2

sin

2

sin

sin
2

fm

fm

fm

fm

m

m

m

m

m

m

m

k V

k V

k V
k V

t

t

t

t
f

f
















=

=

=



Frequency modulation - FM

• Definitions
• The maximum frequency deviation is f=kfVm
• The modulation index (not to be confused with

modulation depth in AM) is, mf, f/fm

• We now have FM given by

Vccos(ct + mfsinmt)

• The expansion of this is difficult...
• It is cos(A + B) but we end up with cos of a sine and

sine of a sine

• ‘Fortunately’ the solution is Bessel Functions

FM – Frequency Domain

frequency

fc
fc +
fm

fc +
2fm

fc +
3fm

fc -
3fm

fc -
2fm

fc -
fm

J0 (m)

J1 (m)

J2 (m)

J3 (m)

J1 (m)

J2 (m)

J3 (m)

Figure 5 – Spectrum of an FM signal.

FM – Spectrum Analyser

Frequency modulation - FM

• What we end up with are harmonics (infinite number

of sidebands)

• So, we get frequency components as:
J0(mf)Vccosct+
J1(mf)Vccos(c+m)t - J1(mf)Vccos(c-m)t
+ J2(mf)Vccos(c+2m)t + J2(mf)cos(c-2m)t
+ J3(mf)Vccos(c+3m)t - J3(mf)cos(c-3m)t
+ etc.
• Note that the minus sign is only a phase shift of 180o

• You should have a table of Bessel function coefficients

Frequency modulation - FM

• All the power is used so it is 100% efficient (useful if

battery operated, e.g. walkie talkies)

• The bandwidth is big and given by Carson’s rule:

2(mf + 1)fm

• Broadcast uses a f of 75 kHz
• If fm = 15 kHz the bandwidth is 180 kHz
• This is the reason why FM is broadcast on high

frequencies – if it were broadcast on MW only one
station would take up LW, MW and most of SW

Frequency modulation - FM

• If m<0.28 we have two side frequencies (the same as

AM)

• This is known as NarrowBand FM as opposed to

WideBand FM

• NBFM is used for personal communications
• WBFM is used for broadcast
• Check lecture notes and tutorials for method of

generating NBFM using a tuned circuit

• Also check how to use harmonic generator to

increase f and mixers to get to final frequency

Frequency modulation - FM

• A Phase Lock Loop (PLL) is used to demodulate

FM (both NBFM and WBFM)

• Basically a servo loop

Frequency modulation - FM

• When the loop is locked, the VCO frequency

and phase are the same

• If the input frequency varies, as in FM, the

VCO tries to follow it

• To do this, the voltage to the VCO must

change in sympathy with the input frequency

• Thus the “DC” signal to the VCO is the audio

that is frequency modulating the carrier in the
transmitter