Analog transmission

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DIGITAL-TO-ANALOG CONVERSIONDIGITAL-TO-ANALOG CONVERSION
Digital-to-analogDigital-to-analog conversion is the process ofconversion is the process of
changing one of the characteristics of an analogchanging one of the characteristics of an analog
signal based on the information in digital data.signal based on the information in digital data.
 Aspects of Digital-to-Analog Conversion
 Amplitude Shift Keying
 Frequency Shift Keying
 Phase Shift Keying
 Quadrature Amplitude Modulation
Topics discussed in this section:Topics discussed in this section:

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Digital to Analog Conversion
 Digital data needs to be carried on an
analog signal.
 A carrier signal (frequency fc) performs
the function of transporting the digital
data in an analog waveform.
 The analog carrier signal is manipulated
to uniquely identify the digital data being
carried.

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Figure 5.1 Digital-to-analog conversion

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Figure 5.2 Types of digital-to-analog conversion

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Bit rate, N, is the number of bits per
second (bps). Baud rate is the number
of signal
elements per second (bauds).
In the analog transmission of digital
data, the signal or baud rate is less than
or equal to the bit rate.
S=Nx1/r bauds
Where r is the number of data bits per
signal element.
Note

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An analog signal carries 4 bits per signal element. If
1000 signal elements are sent per second, find the bit
rate.
Solution
In this case, r = 4, S = 1000, and N is unknown. We can
find the value of N from
Example 5.1

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Example 5.2
An analog signal has a bit rate of 8000 bps and a baud
rate of 1000 baud. How many data elements are
carried by each signal element? How many signal
elements do we need?
Solution
In this example, S = 1000, N = 8000, and r and L are
unknown. We find first the value of r and then the value
of L.

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Amplitude Shift Keying (ASK)
 ASK is implemented by changing the
amplitude of a carrier signal to reflect
amplitude levels in the digital signal.
 For example: a digital “1” could not affect the
signal, whereas a digital “0” would, by making
it zero.
 The line encoding will determine the values of
the analog waveform to reflect the digital data
being carried.

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Bandwidth of ASK
 The bandwidth B of ASK is proportional
to the signal rate S.
B = (1+d)S
 “d” is due to modulation and filtering,
lies between 0 and 1.

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Figure 5.3 Binary amplitude shift keying

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Figure 5.4 Implementation of binary ASK

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Example 5.3
We have an available bandwidth of 100 kHz which
spans from 200 to 300 kHz. What are the carrier
frequency and the bit rate if we modulated our data by
using ASK with d = 1?
Solution
The middle of the bandwidth is located at 250 kHz. This
means that our carrier frequency can be at fc = 250 kHz.
We can use the formula for bandwidth to find the bit rate
(with d = 1 and r = 1).

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Example 5.4
In data communications, we normally use full-duplex
links with communication in both directions. We need
to divide the bandwidth into two with two carrier
frequencies, as shown in Figure 5.5. The figure shows
the positions of two carrier frequencies and the
bandwidths. The available bandwidth for each
direction is now 50 kHz, which leaves us with a data
rate of 25 kbps in each direction.

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Figure 5.5 Bandwidth of full-duplex ASK used in Example 5.4

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Frequency Shift Keying
 The digital data stream changes the
frequency of the carrier signal, fc.
 For example, a “1” could be
represented by f1=fc +∆f, and a “0” could
be represented by f2=fc-∆f.

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Figure 5.6 Binary frequency shift keying

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Bandwidth of FSK
 If the difference between the two
frequencies (f1 and f2) is 2∆f, then the
required BW B will be:
B = (1+d)xS +2∆f

5.19
Example 5.5
We have an available bandwidth of 100 kHz which
spans from 200 to 300 kHz. What should be the carrier
frequency and the bit rate if we modulated our data by
using FSK with d = 1?
Solution
This problem is similar to Example 5.3, but we are
modulating by using FSK. The midpoint of the band is at
250 kHz. We choose 2 f to be 50 kHz; this meansΔ

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Phase Shift Keyeing
 We vary the phase shift of the carrier
signal to represent digital data.
 The bandwidth requirement, B is:
B = (1+d)xS
 PSK is much more robust than ASK as
it is not that vulnerable to noise, which
changes amplitude of the signal.

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Figure 5.9 Binary phase shift keying

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Figure 5.10 Implementation of BASK

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Quadrature PSK
 To increase the bit rate, we can code 2 or
more bits onto one signal element.
 In QPSK, we parallelize the bit stream so that
every two incoming bits are split up and PSK
a carrier frequency. One carrier frequency is
phase shifted 90o
from the other - in
quadrature.
 The two PSKed signals are then added to
produce one of 4 signal elements. L = 4 here.

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Figure 5.11 QPSK and its implementation

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Example 5.7
Find the bandwidth for a signal transmitting at 12
Mbps for QPSK. The value of d = 0.
Solution
For QPSK, 2 bits is carried by one signal element. This
means that r = 2. So the signal rate (baud rate) is S = N ×
(1/r) = 6 Mbaud. With a value of d = 0, we have B = S = 6
MHz.

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Constellation Diagrams
 A constellation diagram helps us to
define the amplitude and phase of a
signal when we are using two carriers,
one in quadrature of the other.
 The X-axis represents the in-phase
carrier and the Y-axis represents
quadrature carrier.

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Figure 5.12 Concept of a constellation diagram

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Example 5.8
Show the constellation diagrams for an ASK (OOK),
BPSK, and QPSK signals.
Solution
Figure 5.13 shows the three constellation diagrams.

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Figure 5.13 Three constellation diagrams

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Quadrature amplitude modulation is a
combination of ASK and PSK.
Note

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Figure 5.14 Constellation diagrams for some QAMs

Analog transmission

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