Name ………………………………………………………
Advancing Physics AS
Chapter 3.2b Signalling
Student Notes
August 2008
John Mascall
The King’s School, Ely
Bandwidth, noise and rate of transmission
Finally, we bring together the ideas to consider the relation between rate of transmission of
bits and signal bandwidth and the limit imposed by the presence of noise.
Display Material 110O
OHT 'Multiple calls on the same line'
Sending many telephone calls down the same pipe: time-division multiplexing
One caller
Speech sampled 8000 times per second: approximately at 100 s intervals
8 bit sample
8 bit sample
8 bit sample
100 s
100 s
100 s
8 bit sample
8 bit sample
8 bit sample
100 s
100 s
Microwave link sending digital pulses at 10 GHz
Time to send 8-bit sample approximately 1 ns. Number of bits able to be sent in 100 s = 1 million
Many callers
Slot 8-bit samples from other callers into the 100 s gap between samples from one caller
one sample
next sample
caller 1
one sample
next sample
caller 2
other callers
caller 1 caller 2
caller 3
100 s
Advantage of digital signalling: digits can easily be switched
Exercise
(a) Show that samples are sent at roughly 100 μs intervals if the speech is sampled 8000
times every second.
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(b) Show that the time to send one 8-bit sample is approximately 1 ns if a microwave link
sends pulses at 10 GHz.
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(c) Estimate the maximum number of simultaneous calls that can be transmitted via the
microwave link described in the example above.
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We now look at Activity 240S Software Based 'Spectra of pulses’.
Digital systems transmit information in on / off pulses. But the brief time for which a pulse
exists spreads the spectrum, making digital communication demanding on bandwidth.
Here you can see these effects qualitatively.
In Activity 250S Software Based 'Pulse length and bandwidth' you should see that the
more rapidly you want to communicate, the more bandwidth you use up.
In Activity 260S Software Based 'Bits per second and bandwidth' you will see that a
channel carrying a bit stream must at least pass signals up to a frequency approximately
equal to the rate of transmission of bits if the bit stream is to be recoverable.
These ideas are summarised below.
bandwidth B needed = b bits per second
2
The noise level in the channel must also be small compared with the signal strength so
that the bits are not lost in the noise. If it possible to distinguish a ‘’1’’ from a ‘’0’’ the digital
signal can then be reconstituted and the effect of noise removed.
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Communications engineers are always looking for ways to reduce noise added to signals.
Telephone calls can be almost inaudible because of noise introduced in transmission. The
flickering white spots on a TV screen when not tuned to a TV channel are noise. Shortwave radio is often very noisy, but FM radio, digital radio and CDs are much less subject
to noise. Activity 270S: Software Based ‘Looking at and listening to noise in signals’ gives
you a chance to look at the effects of having various types of noise combined with a signal.
Display Material 120O
OHT 'Signal, noise and bandwidth'
Signal, noise and bandwidth
signal + noise
1
1
b
2 s lic es
signal
noise
voltage
variation
0
0
noise
time
Maximum signal
frequency W
2 W samples per second
needed
time
Vtotal
2b 
V noise
= 2b slices
b = number of bits
Smallest voltage
variation worth detecting
= noise voltage variation
b log2
Vtotal
( )
V noise
Divide total voltage
variation into slices equal
to noise voltage variation
Rate of transmission of information
bits per second = samples per second × bits per sample
bits per second = 2 Wb
Bandwidth B needed to transmit n bits per second
B = n/ 2
Bandwidth to transmit 2 Wb bits per second
B = Wb
Rate of transmis sion of inform ation increases with bandwidth
Noise decreases the possible rate of transmission of information
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Digital television requires about 8 MHz of bandwidth per channel.
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Questions and activities
Section
Essential
3.1
Optional
Qu 1-6 AS text p 64
Read AS text pp 57-63
Question 10E Estimate ‘Making
estimates about information’
Question 50S Short Answer 'Simple
sampling'
Question 60S Short Answer 'Sampling
repetitive motion'
Question 70S
and hearing'
Question 10C Comprehension 'Teleworking:
Working from home using telecommunications'
Question 20C Comprehension 'History of
telegraphy'
Question 30C Comprehension 'History of
telephony'
Question 40C Comprehension 'Computing and
communications come together'
Activity 10S
Software based 'Data on the
telecommunications explosion'
Short Answer 'Sampling
Activity 60D Demonstration ‘Mains interference as
noise’
Activity 70D Demonstration ‘Electrical noise
pickup’
Activity 100D Demonstration ‘The CD with a hole’
Reading 10T Text to read 'Semaphore unites
the new republic'
Reading 20T Text to read 'A poem about
messages'
Reading 30T Text to read 'Digital recording
error correction'
Reading 40T Text to read 'Optics of a CD
player'
3.2
Qu 1-6 AS text p 72
Read AS text pp 65-71
Question 100S Short Answer 'Hearing better,
phoning sooner'
Question 90S Short Answer 'Using the
wave equation'
Question 120S Short Answer
'Longitudinal and transverse waves'
Question 130S Short Answer
'Polarisation in satellite communication'
Question 140S Short Answer
'Polarisation in practice'
Question 150S Short Answer ‘Rate of
transmission of information limited by
noise’
Question 160D Data Handling
'Oscilloscope displays of waveforms'
Question 80X Explanation-Exposition
'Charting the electromagnetic spectrum'
Question 150X Explanation-Exposition
'Waveforms and frequency spectra'
Question 170X Explanation-Exposition
'Music on an answer-phone'
John Mascall
August 2008
Question 110C Comprehension 'Maritime
communications'
Activity 100D
hole'
Demonstration 'The CD with the
Activity 200E Experiment 'Hearing impairment:
Using an electronic filter'
Activity 230E Experiment 'Making an electronic
sounds generator'
Activity 110H Home Experiments 'Home
experiments with radio and television signals'
Activity 150H
Home Experiment ‘Telling
frequencies apart’
Reading 30T Text to read 'Digital recording
error correction'
Reading 40T Text to read 'Optics of a CD
player'
Reading 50T Text to Read 'Getting started with
Audacity'
Reading 60T Text to Read 'Getting started with
Multimedia Sound'
The King’s School, Ely, Cambs.
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