Module 3
Analog Transmission.
Converting digital data to a bandpass analog signal.is traditionally called digitalto-analog
conversion. Converting a low-pass analog signal to a bandpass analog signalis traditionally
called analog-to-analog conversion.
Modulation of Digital Data (Digital to Analog Conversion)
Digital-to-analog conversion is the process of changing one of the characteristics- amplitude,
frequency or phase ofan analog signal based on the information in digital data.
Data Element Versus Signal Element
A data element is the smallest piece of information to be exchanged, thebit. A signal element is
the smallest unit of a signal that is constant.
Data Rate Versus Signal Rate
Data rate (bit rate) is the number of bits per second and the signal rate (baud rate) is the number
of signal elements per second. The relationship between them is
S=Nx 1 baud
r
where N is the data rate (bps) and r is the number of data elements carried in one signal
element. The value of r in analog transmission is r =log2 L, where L is the type of signal
element, not the level.
Bandwidth
The required bandwidth for analog transmission of digital data is proportional to thesignal rate
except for FSK, in which the difference between the carrier signals needs tobe added.
Carrier Signal
In analog transmission, the sending device produces a high-frequency signal that actsas a base
for the information signal. This base signal is called the carrier signal or carrierfrequency. Digital
information then changes the carrier signal by modifyingone or more of its characteristics
(amplitude, frequency, or phase). This kind ofmodification is called modulation (shift keying).
Amplitude Shift Keying (ASK)
In amplitude shift keying, the amplitude of the carrier signal is varied to create signal elements.
Both frequency and phase remain constant while the amplitude changes.
Binary ASK (BASK)
ASK is normally implemented using signal elements with two different amplitude levels. This is
referred to asbinary amplitude shift keying or on-off keying (OOK). The peak amplitude of one
signal level is 0; the other is the same as the amplitude of the carrier frequency.
Mathematically ASK can be expressed as
Acos(2πfct)
ASK s(t)=
0
binary 1
binary 0
Where the carrier signal is Acos(2πfct)
Bandwidth of ASK
B= (1+d)S
Where d is the modulation and filtering factor (0<d<1) and S is the signal rate.
Implementation
Frequency Shift Keying
In frequency shift keying, the frequency of the carrier signal is varied to represent data.The
frequency of the modulated signal is constant for the duration of one signal element,but changes
for the next signal element if the data element changes. Both peakamplitude and phase remain
constant for all signal elements.
Binary FSK (BFSK)
In binary FSK (or BFSK)two carrier frequencies are used to represent data bits - f1 to represent
0 and f2 to represent 1. Normally the carrierfrequencies are very high, and the difference
between them is very small. Resulting FSK signal can be expressed as
FSK s(t)=
Acos(2πf1t)
binary 1
Acos(2πf1t)
binary 0
Where f1 and f2 are typically offset from the carrier frequency fc
Bandwidth
Consider FSK as two ASK signals, each with its own carrier frequency f1
and f2. If the
difference between the two frequencies is 2∆f, then the required bandwidth is
B=(l+d)S+2∆f
The minimum value of 2∆fshould be at least S, forthe proper operation of modulation and
demodulation.
Implementation
There are two implementations of BFSK: noncoherent and coherent.
In noncoherent BFSK, there may be discontinuity in the phase when one signal
element ends and the next begins. In coherent BFSK, the phase continues through theboundary
of two signal elements.
Noncoherent BFSK can be implemented by treatingBFSK as two ASK modulations and
using two carrier frequencies. Coherent BFSK canbe implemented by using one voltagecontrolled oscillator that changes its frequencyaccording to the input voltage.
The input to the oscillator is the unipolar NRZ signal. Whenthe amplitude of NRZ is zero,
the oscillator keeps its regular frequency; when theamplitude is positive, the frequency is
increased.
Multilevel FSK
Multilevel modulation (MFSK) is not uncommon with the FSK method. In MFSK we use
more than two frequencies. For example, we can use four different to send 2 bits at a time. To
send 3 bits at a time, we can use eight frequencies. The frequencies need to be 2∆ apart.For the
proper operation of the modulator and demodulator, it can be shown that theminimum value of
2∆ needs to be S.
Phase Shift Keying
In phase shift keying, the phase of the carrier is varied to represent two or more differentsignal
elements. Both peak amplitude and frequency remain constant as the phasechanges.
Binary PSK (BPSK)
The simplest PSK is binary PSK, in which we have only two signal elements, one with
a phase of 0°, and the other with a phase of 180°. BPSK is simple and less susceptible to noise
than ASK. Binary PSK can be mathematically represented as
Acos(2πfct+π)
PSK s(t)=
Acos(2πfct)
binary 1
binary 0
Where Acos(2πfct)is the carrier signal and the phase is measured relative to the previous bit interval
BPSK is implemented by polar NRZ signal is multiplied by the carrier frequency;the 1 bit
(positive voltage) is represented by a phase starting at 0°; the 0bit(negative voltage) is
represented by a phase starting at 180°.
Quadrature PSK (QPSK)
In QPSK, use 2 bits at a time in each signal element, so the baud rate is decreased and eventually
the required bandwidth. The scheme iscalled quadrature PSK or QPSK because it uses two
separate BPSK modulations; oneis in-phase, the other quadrature (out-of-phase). Mathematically
QPSK can be represented as
Acos(2πfct+π/4)
11
Acos(2πfct + 3π/4) 10
QPSK s(t)=
Acos(2πfct + 5π/4)
00
Acos(2πfct + 7π/4)
01
QPSK uses phase shifts of multiples of π/2
Constellation Diagram
A constellation diagram can help us define the amplitude and phase of a signal element. In a
constellation diagram, a signal element type is represented as a dot. Thebit or combination of bits
it can carry is often written next to it.The diagram has two axes. The horizontal X axis is related
to the in-phase carrier;
The vertical Y axis is related to the quadrature carrier. For each point on the diagram,four
pieces of information can be deduced. The projection of the point on the X axisdefines the peak
amplitude of the in-phase component; the projection of the point onthe Y axis defines the peak
amplitude of the quadrature component. The length of theline (vector) that connects the point to
the origin is the peak amplitude of the signalelement (combination of the X and Y components);
the angle the line makes with theX axis is the phase of the signal element.
a. For ASK, we are using only an in-phase carrier. Therefore, the two points should be on the
X axis. Binary 0 has amplitude of 0 V; binary 1 has amplitude of 1V (for example).The points
are located at the origin and at 1 unit.
b. BPSK also uses only an in-phase carrier. However, we use a polar NRZ signal for modulation.
It creates two types of signal elements, one with amplitude 1 and the other withamplitude -1.
This can be stated in other words: BPSK creates two different signal elements,one with
mplitude1 V and in phase and the other with amplitude 1V and 1800 out of phase.
c. QPSK uses two carriers, one in-phase and the other quadrature. The point representing 11 is
made of two combined signal elements, both with an amplitude of 1 V. One element is
representedby an in-phase carrier, the other element by a quadrature carrier. The amplitude of
the final signal element sent for this 2-bit data element is 21/2, and the phase is 45°. Theargument
is similar for the other three points. All signal elements have amplitude of 21/2,but their phases
are different (45°, 135°, -135°, and -45°). Of course, we could have chosen
the amplitude of the carrier to be (21/2) to make the final amplitudes 1 V.
Quadrature Amplitude Modulation
Quadrature amplitude modulation is a combination ofASK and PSK.QAM uses two carriers, one
in-phase and the other quadrature, with different amplitude levels for each carrier.
QAM modulation scheme:- The input is a stream of binary digits arriving at a rate of R bps. This
stream is converted into two separate bit streams of R/2 bps each, by taking alternate bits for the
two streams. In the diagram, the upper stream is ASK modulated on a carrier of frequency fc by
multiplying the bit stream by the carrier. Thus, a binary zero is represented by the absence of the
carrier wave and a binary one is represented by the presence of the carrier wave at a constant
amplitude. This same carrier wave is shifted by 90˚ and used for ASK modulation of the lower
binary stream. The two modulated signals are then added together and transmitted.
If two-level ASK is used, then each of the two streams can be in one of two states and the
combined stream can be in one of 4 = 2  2 states. This is essentially QPSK. If four-level ASK is
used (i.e., four different amplitude levels), then the combined stream can be in one of 16 = 4  4
states. The greater the number of states, the higher the data rate that is possible within a given
bandwidth. Of course, the greater the number of states, the higher the potential error rate due to
noise and attenuation.
Bandwidth for QAM
The minimum bandwidth required for QAM transmission is the same as that required
for ASK and PSK transmission.ie,
B =(1 +d) S
ANALOG-TO-ANALOG CONVERSION
Analog-to-analog conversion, or analog modulation, is the representation of analoginformation
by an analog signal.Modulation has been defined as the process of combining an input signal
m(t) and a carrier at frequency fc to produce a signal s(t) whose bandwidth is (usually) centered
on fc. Modulation is needed if the medium is bandpass in nature or if only a bandpass channel is
available to us. An example is radio. The government assignsa narrow bandwidth to each radio
station. The analog signal produced by each station isa low-pass signal, all in the same range. To
be able to listen to different stations, thelow-pass signals need to be shifted, each to a different
range.
Analog-to-analog conversion can be accomplished in three ways: amplitude
modulation (AM), frequency modulation (FM), and phase modulation (PM). Frequency and
Phase modulation are special cases of angle modulation.
Amplitude Modulation
In AM transmission, the carrier signal is modulated so that its amplitude varies with thechanging
amplitudes of the modulating signal. The frequency and phase of the carrierremain the same;
only the amplitude changes to follow variations in the information. The modulating signal is the
envelope of the carrier.
AM is normally implemented by using a simple multiplierbecause the amplitude of the
carrier signal needs to be changed according to the amplitudeof the modulating signal.
The total bandwidth required for AM can be determinedfrom the bandwidth of the audio signal:
BAM
=2B , where B is the bandwidth of the modulating signal (information signal).
Frequency Modulation
In FM transmission, the frequency of the carrier signal is modulated to follow the changing
voltage level (amplitude) of the modulating signal. The peak amplitude and phase ofthe carrier
signal remain constant, but as the amplitude of the information signalchanges, the frequency of
the carrier changes correspondingly. For frequency modulation, the derivative of the phase is
proportional to the modulating signal.
The total bandwidth required for FM can be determined fromthe bandwidth of the audio signal:
BFM =2(1 + β )B.
Where B is the bandwidth of analog signal and β is a factor depends on modulation
techniquewith a common value of 4.
Phase Modulation
In PM transmission, the phase of the carrier signal is modulated to follow the changingvoltage
level (amplitude) of the modulating signal. The peak amplitude and frequencyof the carrier
signal remain constant, but as the amplitude of the information signalchanges, the phase of the
carrier changes correspondingly. In PM the instantaneous change in the carrier frequency is
proportionalto the derivative of the amplitude of the modulating signal.
PM is normally implemented by using a voltage-controlledoscillator along with a
derivative. The frequency of the oscillator changes according tothe derivative of the input
voltage which is the amplitude of the modulating signal.
The total bandwidth required for PM can be determined from the bandwidth
andmaximum amplitude of the modulating signal:
BPM = 2(1 + β )B.