Notes · ElectronicsUK · A-Levels

Wireless transmission

Wireless transmission impresses an information signal onto a radio carrier by modulation. This chapter develops amplitude modulation with its carrier and sidebands and modulation depth, frequency modulation with its frequency deviation, the bandwidth each requires, and the reasoned comparison of AM and FM for noise immunity and spectral efficiency.

4 sections~14 min reading time3 competenciesLevel Standard 1 · Advanced 3

T·141414 / 16

Exam profile

AO1 · Describe amplitude and frequency modulation and the sidebands and deviation they produce.AO2 · Calculate modulation depth, sideband frequencies and the bandwidth of AM and FM signals.AO3 · Compare and choose AM or FM for a given application on grounds of noise immunity and bandwidth.

Operators:describecalculatedeterminecomparesketchevaluate

basic level

At AS the focus is the idea of modulating a carrier and the appearance of an AM waveform.

higher level

The full A-Level develops modulation depth, sidebands, frequency deviation, bandwidth calculations and the AM-versus-FM comparison.

Depth

Text

Contents · 4 sections

Wireless transmission

Why modulate, and the carrier#

StandardWJEC/Eduqas A Level Electronics — Unit 4 Digital and Communication (modulation)

Modulation and demodulation

Fig. 1The information modulates the carrier for transmission; at the receiver the demodulator recovers the information from the received signal.

Modulation is the process of impressing a low-frequency information signal onto a high-frequency carrier so that it can be transmitted efficiently over a wireless channel. The information signal — audio, for instance — cannot be radiated directly for two practical reasons: an efficient aerial must be a sizeable fraction of a wavelength long, which at audio frequencies would mean an aerial many kilometres long, and if every station radiated audio directly they would all occupy the same low band of frequencies and interfere hopelessly.

The carrier solves both problems. Because it is a high-frequency sinusoid, its wavelength is short enough for a practical aerial, and by giving each station a different carrier frequency, many transmissions can share the airwaves without overlapping — each occupies its own band around its own carrier. Tuning a receiver means selecting the band around one carrier and rejecting the others, using the band-pass filtering ideas from the AC chapter.

There are two main ways to impress the information onto the carrier, and they define the two modulation schemes of this chapter. In amplitude modulation (AM) the information varies the amplitude (height) of the carrier while its frequency stays fixed; in frequency modulation (FM) the information varies the frequency of the carrier while its amplitude stays fixed. In both cases the carrier is the vehicle and the information is the passenger; only the property being varied differs.

At the receiver the process is reversed by demodulation, which strips the information back off the carrier. For AM this can be as simple as detecting the envelope of the received waveform; for FM it means detecting the changes in frequency. Transmitter and receiver are a matched pair: the modulation scheme chosen at the transmitter dictates the demodulator needed at the receiver, and the two must agree.

Understanding that modulation is a deliberate trade — accepting the complexity of a carrier and a modulator/demodulator in exchange for a practical aerial and a shareable spectrum — frames the whole of wireless transmission. The detailed behaviour of AM and FM, the bandwidth each needs, and the reasons to prefer one over the other all follow from how each varies the carrier, which the next sections develop quantitatively.

\text{AM: amplitude varies}, \quad \text{FM: frequency varies}

Two modulation schemes

The information varies the amplitude (AM) or the frequency (FM) of the carrier.

Worked example

Why a carrier at all

A $3\,\text{kHz}$ speech signal is to be broadcast. Explain why it is modulated onto a $1\,\text{MHz}$ carrier, referring to aerial size and to sharing the spectrum.

Aerial size
An efficient aerial is a sizeable fraction of a wavelength. At $3\,\text{kHz}$ the wavelength is about $100\,\text{km}$ , needing an impractically long aerial; at $1\,\text{MHz}$ it is $300\,\text{m}$ , so a practical aerial works.
Sharing
If every station radiated audio directly they would all occupy the same low band and interfere. Giving each a different carrier lets each occupy its own band, so many stations coexist.
Recovery
The receiver tunes to the wanted carrier's band (band-pass filtering) and demodulates it to recover the speech.

Result: Modulating onto a $1\,\text{MHz}$ carrier gives a practical aerial and lets many stations share the spectrum, each in its own band.

Typical mistakes

Confusing which property varies — AM varies amplitude, FM varies frequency.
Forgetting that the receiver's demodulator must match the transmitter's modulation scheme.

Active revision

Explain, in terms of aerial size and spectrum sharing, why an audio signal is modulated onto a radio carrier rather than transmitted directly, and state which carrier property AM and FM each vary.

Active recall

Recall the key points — then reveal.

Sources: WJEC/Eduqas GCE Electronics specification (WJEC / Eduqas)

Amplitude modulation#

AdvancedWJEC/Eduqas A Level Electronics — Unit 4 Digital and Communication (AM)

Amplitude-modulated waveform

Fig. 2An AM waveform: the carrier's amplitude follows the message, so its envelope is a copy of the information signal (here depth

0.5

In amplitude modulation the amplitude of the carrier is varied in step with the information signal, while its frequency stays constant. The result is a carrier whose envelope — the shape traced by its peaks — is a copy of the information signal. When the message is loud the carrier's peaks are large; when the message is quiet the peaks are small. This envelope is exactly what a simple AM receiver detects to recover the audio.

The extent of the modulation is measured by the modulation depth (or modulation index),

m = V_m/V_c

, the ratio of the message amplitude to the carrier amplitude, usually expressed as a percentage. It can also be read from the envelope as

m = (V_{max} - V_{min})/(V_{max} + V_{min})

, using the largest and smallest peak heights. A depth near

100\%

uses the carrier efficiently; less than that under-uses it, wasting transmitter power on the carrier.

The modulation depth must not exceed

100\%

(

m > 1

). If it does — over-modulation — the envelope would try to go negative, the carrier is switched off during the troughs, and the recovered signal is badly distorted. Well-designed AM systems therefore keep the depth comfortably below

100\%

. Recognising over-modulation on a waveform, and calculating the depth from the peaks, are standard AM exam tasks.

Mathematically, modulating a carrier of frequency

f_c

with a single tone of frequency

f_m

produces three frequencies: the carrier itself, an upper sideband at

f_c + f_m

, and a lower sideband at

f_c - f_m

. The information is carried entirely in the sidebands — the carrier alone conveys nothing — which is why the spectrum of an AM signal is a central carrier line flanked by two sidebands. For a real message with a range of frequencies, each sideband becomes a band.

Because the two sidebands sit at

f_c \pm f_m

, an AM transmission occupies a band from

f_c - f_{m(max)}

f_c + f_{m(max)}

, so its bandwidth is

2 f_{m(max)}

— twice the highest message frequency. This simple result, that AM bandwidth is twice the top audio frequency, is the key bandwidth fact of amplitude modulation and the basis of comparing it with FM. Understanding the sideband structure explains both how AM carries information and how much spectrum it uses.

m = \dfrac{V_m}{V_c} = \dfrac{V_{max} - V_{min}}{V_{max} + V_{min}}

Modulation depth

Ratio of message to carrier amplitude; must not exceed 1 (100%).

\text{sidebands at } f_c \pm f_m, \quad \text{bandwidth} = 2 f_m

AM sidebands and bandwidth

The information is in the sidebands; AM occupies twice the top message frequency.

AM spectrum: carrier and sidebands

Fig. 3The AM spectrum for a carrier at

100\,\text{kHz}

modulated by a

5\,\text{kHz}

tone: the carrier at

100

with sidebands at

95

and

105\,\text{kHz}

; bandwidth

10\,\text{kHz}

Worked example

AM depth, sidebands and bandwidth

A $1.0\,\text{MHz}$ carrier of amplitude $10\,\text{V}$ is amplitude-modulated by a $4.5\,\text{kHz}$ tone of amplitude $6\,\text{V}$ . Find the modulation depth, the sideband frequencies and the bandwidth.

Modulation depth
$m = V_m/V_c = 6/10 = 0.6 = 60\%$ , safely below $100\%$ .
Sidebands
Upper sideband $= f_c + f_m = 1000 + 4.5 = 1004.5\,\text{kHz}$ ; lower sideband $= f_c - f_m = 1000 - 4.5 = 995.5\,\text{kHz}$ .
Bandwidth
$\text{bandwidth} = 2 f_m = 2 \times 4.5 = 9.0\,\text{kHz}$ .
$\text{bandwidth} = 2 \times 4.5\,\text{kHz} = 9.0\,\text{kHz}$

Result: Depth $60\%$ ; sidebands at $995.5$ and $1004.5\,\text{kHz}$ ; bandwidth $9.0\,\text{kHz}$ .

Typical mistakes

Allowing the modulation depth to exceed $100\%$ , causing distortion (over-modulation).
Forgetting that the AM bandwidth is $2 f_m$ (both sidebands), not $f_m$ .

Active revision

An AM signal has a carrier of $10\,\text{V}$ and a message of $6\,\text{V}$ on a $1.0\,\text{MHz}$ carrier modulated by a $4.5\,\text{kHz}$ tone. Find the modulation depth, the sideband frequencies and the bandwidth.

Active recall

Recall the key points — then reveal.

Sources: WJEC/Eduqas GCE Electronics specification (WJEC / Eduqas)

Frequency modulation#

AdvancedWJEC/Eduqas A Level Electronics — Unit 4 Digital and Communication (FM)

Frequency-modulated waveform

Fig. 4An FM waveform: the amplitude is constant but the cycles bunch up and spread out as the frequency swings with the message.

In frequency modulation the frequency of the carrier is varied in step with the information signal, while its amplitude stays constant. When the message voltage rises the carrier frequency increases; when the message falls the frequency decreases. The carrier's peaks stay the same height throughout — it is the spacing of the cycles, not their size, that carries the information. This constant amplitude is the root of FM's great advantage in noise rejection.

The amount by which the carrier frequency swings away from its resting (centre) value is the frequency deviation,

\Delta f

, and it is set by the amplitude of the message: a louder message deviates the carrier further. The rate at which the frequency swings back and forth is set by the message frequency. In broadcast FM the maximum deviation is standardised (for example

\pm 75\,\text{kHz}

), which together with the message bandwidth fixes the transmission's bandwidth.

Because FM carries information in frequency changes and its amplitude is constant, it is highly immune to noise. Most noise and interference add to the amplitude of a signal, and an FM receiver deliberately ignores amplitude variations — it can be preceded by a limiter that clips the signal to a constant height, removing amplitude noise entirely before the frequency is detected. This is why FM broadcasts sound so much cleaner than AM: the noise that would corrupt an AM signal simply does not affect the frequency information FM relies on.

The bandwidth an FM signal occupies is larger than AM's and is estimated by Carson's rule:

\text{bandwidth} \approx 2(\Delta f + f_m)

, where

\Delta f

is the peak deviation and

f_m

the highest message frequency. With a large deviation for good noise performance, broadcast FM occupies a much wider band than AM — around

200\,\text{kHz}

per station compared with a few kilohertz for AM. FM trades spectrum for quality.

This trade-off — FM's superb noise immunity bought at the cost of much greater bandwidth — is the essence of the AM-versus-FM comparison. FM is chosen where quality matters and bandwidth is available (high-fidelity broadcasting, two-way radio); AM is chosen where bandwidth is scarce and simplicity or long range matters. Understanding that FM's constant amplitude gives noise immunity, and that its deviation sets both the quality and the bandwidth, is the core of frequency modulation.

\text{bandwidth} \approx 2(\Delta f + f_m) \ \text{(Carson's rule)}

FM bandwidth

Estimated from the peak deviation and the highest message frequency.

Worked example

FM bandwidth by Carson's rule

A broadcast FM signal has a peak deviation of $75\,\text{kHz}$ and carries audio up to $15\,\text{kHz}$ . Estimate the bandwidth and compare it with the AM bandwidth for the same audio.

Carson's rule
$\text{bandwidth} \approx 2(\Delta f + f_m) = 2(75 + 15) = 2 \times 90 = 180\,\text{kHz}$ .
$\text{bandwidth} \approx 2(75 + 15) = 180\,\text{kHz}$
AM for comparison
AM of the same $15\,\text{kHz}$ audio would need only $2 f_m = 30\,\text{kHz}$ .
Trade-off
FM uses about six times the bandwidth of AM, but its constant amplitude and a limiter reject amplitude noise, giving much cleaner reception.

Result: The FM signal occupies about $180\,\text{kHz}$ against AM's $30\,\text{kHz}$ — far more spectrum, in exchange for much better noise immunity.

Typical mistakes

Thinking FM varies the amplitude — it varies the frequency and keeps the amplitude constant.
Forgetting to include both the deviation and the message frequency in Carson's rule.

Active revision

A broadcast FM signal has a peak deviation of $75\,\text{kHz}$ and a maximum audio frequency of $15\,\text{kHz}$ . Estimate its bandwidth and explain why FM is more noise-immune than AM.

Active recall

Recall the key points — then reveal.

Sources: WJEC/Eduqas GCE Electronics specification (WJEC / Eduqas)

Bandwidth and AM versus FM#

AdvancedWJEC/Eduqas A Level Electronics — Unit 4 Digital and Communication (AM vs FM)

AM versus FM

Fig. 5The trade-off: AM is simple and narrowband but noisy; FM is wideband and complex but far more noise-immune.

Choosing between AM and FM is a design decision that weighs noise immunity against bandwidth, and the specification expects a justified comparison. AM is simple and spectrally economical — a station needs only twice the top audio frequency, a few kilohertz — but its information rides in the amplitude, exactly where noise and interference land, so AM reception is noisy. Its simplicity and narrow bandwidth made it the choice for long-range and early broadcasting.

FM carries the information in the frequency and keeps the amplitude constant, so a receiver can strip off amplitude noise with a limiter before detecting the frequency. This gives FM its hallmark clean, hiss-free sound. The price is bandwidth: to achieve good noise immunity FM uses a large deviation, and by Carson's rule this makes each FM station occupy far more spectrum — around

200\,\text{kHz}

against a few kilohertz for AM.

The two schemes therefore occupy opposite corners of the trade-off. AM is narrowband and noisy; FM is wideband and quiet. Where spectrum is scarce and range or simplicity matters — long-wave broadcasting, aircraft radio, some two-way systems — AM (or a variant) is used. Where quality matters and enough spectrum is available — high-fidelity music broadcasting, professional two-way radio — FM is preferred. Neither is universally better; each wins in its domain.

The bandwidth calculations are the quantitative heart of the comparison. For AM the bandwidth is simply

2 f_m

; for FM it is Carson's

2(\Delta f + f_m)

. Working these out for the same audio signal makes the trade-off concrete — the same

15\,\text{kHz}

audio needs

30\,\text{kHz}

in AM but around

180\,\text{kHz}

in FM — and shows exactly how many more stations could fit in a given band using AM, and how much cleaner each FM station sounds.

This comparison also points forward to digital modulation, which combines the noise immunity of FM-like schemes with the efficiency and error-correction of digital signals, and is developed in the next chapter. For now, the essential understanding is that AM and FM represent a clear engineering trade between spectral economy and noise immunity, that the bandwidth of each is calculable, and that the right choice depends on the specific demands of the application — a classic evaluate-and-justify exam question.

\text{AM: } 2 f_m, \qquad \text{FM: } 2(\Delta f + f_m)

AM and FM bandwidth

AM is narrowband; FM is wideband for better noise immunity.

Worked example

Comparing AM and FM bandwidth

For a $15\,\text{kHz}$ audio signal, find the AM bandwidth and the FM bandwidth (peak deviation $75\,\text{kHz}$ ), and recommend a scheme for high-fidelity music broadcasting.

AM bandwidth
$2 f_m = 2 \times 15 = 30\,\text{kHz}$ .
FM bandwidth
$2(\Delta f + f_m) = 2(75 + 15) = 180\,\text{kHz}$ .
Recommendation
For high-fidelity music, FM: its constant amplitude and limiter give clean, low-noise reception, and the wider $180\,\text{kHz}$ band is acceptable in the VHF broadcast band where spectrum is available.

Result: AM needs $30\,\text{kHz}$ , FM $180\,\text{kHz}$ ; FM is recommended for music because its noise immunity outweighs its greater bandwidth.

Typical mistakes

Saying FM is simply better; it is quieter but uses much more bandwidth, which AM economises.
Mixing up the AM and FM bandwidth formulae.

Active revision

For an audio signal up to $15\,\text{kHz}$ , calculate the AM bandwidth and (with a $75\,\text{kHz}$ deviation) the FM bandwidth, and recommend a scheme for high-fidelity music broadcasting with reasons.

Active recall

Recall the key points — then reveal.

Sources: WJEC/Eduqas GCE Electronics specification (WJEC / Eduqas)

References & sources

Sources

WJEC / Eduqas

WJEC/Eduqas GCE Electronics specification

Wireless transmission

4 sections~14 min reading time3 competenciesLevel Standard 1 · Advanced 3

Wireless transmission

Key points

Why a carrier at all

Key points

AM depth, sidebands and bandwidth

Key points

FM bandwidth by Carson's rule

Key points

Comparing AM and FM bandwidth

Sources

Wireless transmission

Key points

Why a carrier at all

Key points

AM depth, sidebands and bandwidth

Key points

FM bandwidth by Carson's rule

Key points

Comparing AM and FM bandwidth

Sources