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8 AMPLITUDE SHIFT KEYING (OR) DIGITAL AMPLITUDE MODULATION (OR) OOK- SYSTEM

# 8 AMPLITUDE SHIFT KEYING (OR) DIGITAL AMPLITUDE MODULATION (OR) OOK- SYSTEM

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ANALOG AND DIGITAL COMMUNICATION

2.8.1 Mathematical representation

ASK is the simplest type of digital CW-modulation. Here carrier is a sine

wave of frequency ‘fc’.

We

can

represent

the

carrier

signal

mathematically

as follows,

Vc(t) = Ac cos ωc t ...(1)

ASK can be mathematically expressed as,

A

VASK (t)= [1+ Vm(t)]  c cos ωc t 

 2

...(2)

Where,

Vm(t) = Digital modulating signal (volts)

Ac

= Unmodulated carrier amplitude (volts)

ωc

Case 1

For a bit 1 (logic 1) input, Vm(t) = +1 volt

Equation (2) becomes,

Ac

2

cos ωct

...(3)

Case 2

For a bit 0 (logic 0) input,Vm(t) = -1 volt

Equation (2) becomes,

2

Digital Communication

V

(t) = 0 ...(4)

Thus, the VASK(t) is either Ac cos ωct (or) 0. Hence the carrier is ei-

ther ‘ON or ‘OFF’. Therefore ASK is also called ON-OFF keying.

2.8.2 Graphical representation

The Figure 2.5 shows the ASK- Modulation in graphical manner.

The Figure 2.6 shows the Ask- generation circuit

Figure 2.6 Block Diagram of ASK-generator

• The

digital

signal

from

the

computer

is

a

ANALOG AND DIGITAL COMMUNICATION

modulating signal, applied as a one input of product modulator.

• ASK – modulator is nothing but a multiplier followed by a

band-pass filter. The carrier signal is applied as a another input of

product modulator.

• Due to multiplication of the two signal, the ASK output will be

present only when a binary ‘1’ is to be transmitted.

• The ASK output corresponding to a binary ‘0’ is zero.

• We conclude that a carrier is transmitted when a binary ‘1’ is to

be sent and no carrier is transmitted. When binary ‘0’ is to be

sent is as shown in Figure 2.5

The Figure 2.7 below shows the ASK-demodulation circuit.

Signal

(or)

signal

0

Tb

Decision

making

device

Original

data

Threshold

(Carrier)

Ac cos wct

Figure 2.7 ASK - Demodulator Circuit

• The ASK –signal is applied as one input of multiplier and integrator.

• The locally generated coherent carrier is applied as another input of

multiplier

Case 1

Received signal is consider Ac cos wct then, the output of

multiplier is given by,

= Ac2 cos2 ωct

...(1)

Digital Communication

The output of multiplier given as a input to integrator, integrator

act as a LPF. Therefore LPF produce low frequency component only at

the output.

1 + cos 2ωc t 

= Ac 2 

2

=

Ac 2 Ac 2

+

cos 2 ωc t ...(2)

2

2

In equation (2), first term represents DC-term and second term

represents second order harmonic. Therefore LPF filtered out the second

term, First term only obtained at the output

Ac 2

=

...(3)

2

The output of integrator is given to Decision making device,

which is compared with threshold value and produce the output logic 1

(i.e binary ‘1’)

Case 2

Received signal consider as a zero, then the output of multiplier,

integrator and decision making device is equal to zero. Therefore the

output is logic ‘0’ (i.e) binary ‘0’.

Bit time (interval ) Tb

The bit interval is the time required to send one single bit. It is the

reciprocal of the bit rate.

Bit rate

Bit rate is the number of bits transmitted (or) sent in one second.

It is expressed in bits per second (bps).

Relation between bit rate & bit interval,

1

1

=

Bit rate =

= fb

Bit interval

Tb

ANALOG AND DIGITAL COMMUNICATION

Baud rate

Baud rate

fb

= N

...(1)

For ASK, we use one bit (0 (or) 1) to represent one symbol.

Therefore , the rate of change of the ASK wave form (baud) is the same

as the rate of change of binary input (bps), thus bit rate equals the baud

rate.

fb

Baud =

N

fb

=

= fb

1

Where N= number of bits =1

The Bandwidth of ASK in terms of bit rate is given by,

BW

= (fc + fa) - ( fc -fa)...(1)

fb

Where, fa = fundamental frequency of binary input =

2

fb  

fb 

− fc − 

BW

=  fc +

2  

2

= fc +

fb

f

− fc + b

2

2

BW

= fb

For ASK , Bandwidth is also equal to bit rate.

(1)

Simple techniques

(2)

Easy to generate and detect.

(1)

It is very sensitive to noise.

(2)

It is used at very low bit rates upto 100 bits/sec.

Digital Communication

2.9 FREQUENCY SHIFT KEYING

Definition

The frequency of a sinusoidal carrier is shifted between two

discrete values according to the binary symbol (0 (or) 1).

2.9.1 Mathematical representation

FSK is sometimes called binary FSK (BFSK).The general

expression for FSK is,

V (t)

FSK

=VC cos {2(fc + Vm(t)∆f)t}

...(1)

Where,

Vc

=Peak analog carrier amplitude.

fc

=Analog carrier centre frequency.

Vm(t) =binary input (i.e logic 1 (or) logic 0)

∆f

=Peak shift in the analog carrier frequency.

From equation (1) it can be seen that the peak shift in carrier

frequency (fc) is proportional to the amplitude of binary input signal Vm(t).

Case 1

For a logic ‘1’ input Vm(t)=+1V. the equation (1) becomes,

VFSK(t)= Vc cos{2(fc + 1 ∆f)t}

V

FSK

(t) = Vc cos{2(fc+∆f)t}

...(2)

Case 2

For logic ‘0’ input, Vm (t) = -1 V, the equation (1) becomes,

VFSK(t)= Vc cos { 2p(fc - 1. Df)t}

VFSK(t)=Vc cos {2(fc -∆f )t} ...(3)

ANALOG AND DIGITAL COMMUNICATION

In BFSK , the centre frequency fc is shifted up and down in the

frequency domain by the binary input signal, is as shown in Figure 2.8.

-∆f

+∆f

fc

fs

Logic 1

fm

Logic 0

Figure 2.8 FSK in frequency domain

When the binary input signal changes from a logic 0 to a logic 1

and vice versa, the output frequency shifts between two frequencies,

(1)

Space (or) logic 0 frequency (fs)

(2)

Mark (or) logic 1 frequency (fm)

2.9.2 Frequency Deviation (∆f)

It is half the difference between mark and space frequencies,

|fm-fs|

∆f

=

... (4)

2

Where,

∆f

= frequency deviation (HZ)

|fm- fs| = absolute difference between the mark and

frequencies.

space

Digital Communication

2.9.3 Graphical representation

The Figure 2.9 shows the Graphical representation of FSKModulation.

binary input

1

0

1

0

1

t

Carrier signal

FSK- Output Free

t

fm

fs

fm

fs

fm

Figure 2.9 FSK-Output Waveform

Where,

fm- mark frequency

fs- Space frequency

2.9.4 FSK- generation

The Figure 2.10 below shows the FSK - generation circuit.

NRZ-Binary

input

FSK-Modulator

(VCO)

FSK

Output

Figure 2.10 Block diagram of FSK generator

 The VCO act as a FSK – generator , the input

as control input of VCO.

binary data is given

ANALOG AND DIGITAL COMMUNICATION

 If binary input is not applied (i.e) there is no input signal the VCO

generates the centre frequency equal to carrier frequency.

 For logic 1 input , the VCO output frequency shifted to mark

frequency fm (i.e)( fc +∆ f).

 For logic 0 input , the VCO output frequency shifted to space

frequency fs (i.e) (fc- ∆f ).

 We conclude that the VCO output frequency changes back and forth

between space and mark frequencies.

2.9.5 FSK-detection

There are three methods to demodulate the FSK-Signal.

(1)

Non – coherent FSK demodulator

(2)

Coherent FSK demodulation

(3)

PLL-FSK demodulator

2.9.5.1 Non- Coherent FSK-demodulator

The Figure 2.11 below shows the FSK - demodulator circuit

BPF

‘fS’

FSK

Output

~

Envelope

detector

dc

comparator

-

Power

splitter

+

dc

‘fm’

BPF

~

Envelope

detector

Rectified signal

Output

Data

or

(Original

data)

Figure 2.11 Block Diagram of FSK- demodulator

Digital Communication

 FSK - demodulation is quite simple with a circuit such as the one

shown in Figure 2.11.

 FSK - input signal is simultaneously applied to the inputs of both

band pass filters (BPF) through a power splitter.

 The respective filter passes only the mark (or) only the space

frequency on to its respective envelope detector.

 The envelope detectors, in turn indicate the total power in each pass

band, and the comparator responds to the largest of the two powers.

 If Non-inverting is greater when compare to inverting than it is taken

as logic 1 and vice versa for logic 0.

 This type of FSK –detection is referred to as non-coherent detection.

 There is no frequency involved in the demodulation process that is

synchronized either in phase .frequency (or) both with the incoming

FSK-signal.

 The Figure 2.12 shows the block diagram for a coherent

Multiplier

LPF

Carrier

FSK

Input

-

Power

Splitter

+

Multiplier

LPF

Output

Data

or

Original

Data

Carrier

Figure 2.12 Block Diagram of a Coherent FSK receiver

ANALOG AND DIGITAL COMMUNICATION

 The FSK –input signal is simultaneously applied to the inputs of both

multipliers through power splitter.

 Locally generated frequencies are applied as another input of

multiplier .The two frequencies are not same as transmitter

reference frequency, it is

impractical to reproduce a local

reference that is coherent with both of them. So coherent FSK –

detection is seldom used.

 The multiplier outputs are passed through low pass filters and the

filter outputs are applied to a comparator.

 Comparator responds to the largest of the two powers.

 If non-inverting is greater than the inverting input than the output is

logic 1 and vice versa for logic 0.

2.9.5.3 PLL-FSK demodulator

Figure 2.13 PLL FSK- Demodulator

 The most common circuit used for modulation of BFSK is the phase

Locked loop (PLL) which is shown in Figure 2.13.

 Generally, the natural frequency of PLL is made equal to the

center frequency of FSK –modulator (i.e) carrier frequency (fc) before

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