Chapter 3 Digital Mod Part2

Chapter 3

5

DIGITAL MODULATION TECHNIQUES

Digital Modulation

Part 2

a. Information capacity, Bits, Bit Rate, Baud, M-ary Encoding

b. Digital Modulation Techniques - ASK, FSK, PSK, QAM

• Information capacity, Bits & Bit Rate– Represents the number of independent symbols

that can be carried through a system in a given unit of time.

– Binary digit or bit  is the basic unit of information in communication. It is the amount of information stored by a digital device

– Bit rate is the number of bits that are conveyed or processed per unit of time - Express the information capacity

Hartley’s Law

tBI Where

I = information capacity (bps)

B = bandwidth (Hz)

t = transmission time (s)

From the equation, Information capacity is a linear function of bandwidth and transmission time and directly proportional to both.

Shannon’s Formula

)1(log32.3)1(log 102 NS

NS BIorBI

Where

I = information capacity (bps)

B = bandwidth (Hz)

= signal to noise power ratio (unitless)

The higher S/N the better the performance and the higher the information capacity

Shannon-Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of  noise

NS

Example

By using the Shannon’s Formula, calculate the information capacity if S/N = 30 dB and B = 2.7 kHz.

Baud & Minimum BW

• Baud refers to the rate of change of a signal on the transmission medium after encoding and modulation have occurred. "Baud" is the name for an information "symbol."

Where

baud = symbol rate (symbol per second)

ts = time of one signaling element @ symbol (seconds)

stbaud

1

Cont’d…

• Minimum Bandwidth – Using multilevel signaling, the Nyquist formulation for channel

capacity

MBfb 2log2

Where fb= channel capacity (bps)

B = minimum Nyquist bandwidth (Hz)

M = number of discrete signal or voltage levels

Cont’d…

baudN

f

M

fB bb

2log

Where N is the number of bits encoded into each signaling element.

For B necessary to pass M-ary digitally modulated carriers

M-ary Encoding

• It is often advantageous to encode at a level higher than binary where there are more then two conditions possible.

• The number of bits necessary to produce a given number of conditions is expressed mathematically as

MN 2log

Where N = number of bits necessary

M = number of conditions, level or combinations possible with N bits.

Cont’d…

• Each symbol represents n bits, and has M signal states, where M = 2N.

Example

Find the number of voltage levels which can represent an analog signal with

a. 8 bits per sample

b. 12 bits per sample

There are several digital modulation techniques used to modulate digital signal or data, depending on the applications, the rate of transmission required, allocated bandwidth and cost.

• Amplitude Shift Keying (ASK)• Frequency Shift Keying (FSK)• Phase Shift Keying (PSK)• Quadrature Amplitude Modulation (QAM)

Forms of Digital Modulation

)2sin()( ftVtv

•If the amplitude, V of the carrier is varied proportional to the information signal, a digital modulated signal is called Amplitude Shift Keying (ASK)

•If the frequency, f of the carrier is varied proportional to the information signal, a digital modulated signal is called Frequency Shift Keying (FSK)

Cont’d…

• If the phase, θ of the carrier is varied proportional to the information signal, a digital modulated signal is called Phase Shift Keying (PSK)

• If both the amplitude and the phase, θ of the carrier are varied proportional to the information signal, a digital modulated signal is called Quadrature Amplitude Modulation (QAM)

Cont’d...

Amplitude Shift Keying (ASK)

In ASK, a carrier wave is switched ON and OFF

by the input data or binary signals.

During a ‘mark’ (binary 1), a carrier wave is

transmitted and during a ‘space’ (binary 0), the

carrier is suppressed.

Also known as ON-OFF Keying (OOK)

ASK Cont’d...

ASK Waveform

ASK Cont’d...

Applications of ASK

It is used in multichannel telegraph system.

Simple ASK is no longer used in digital

communication systems due to noise problems

Frequency Shift Keying (FSK)

Two different carrier frequencies are used and they are switched ON and OFF by the binary signals.

• Binary ‘1’ or ‘mark’ switches one carrier ON while the other carrier is OFF

• Binary ‘0’ or ‘space’ switches the second carrier ON while the first carrier is OFF

• At the Tx, the pulse generated will shift the frequency to either 2 frequencies used, producing 2 tones

• This signal then transmitted through the telephone line

FSK cont’d

The Rx the detect the tone by differentiating the 2 frequencies > converts to appropriate voltage level.

Data

s1f1

f2s2

FSK signal

FSK cont’d

The Rx the detect the tone by differentiating the 2 frequencies > converts to appropriate voltage level.

Data

s1f1

f2s2

FSK signal

FSK Waveform

FSK cont’d

Applications of FSK Used mainly for low-speed digital data transmission Keyboard-type computer terminal modems that connect

the terminal to a main computer –dial up lines

Advantages FSK over ASK ASK need automatic gain control (AGC) to overcome

fading effects Relatively easy for FSK generation The constant amplitude property of the carrier does not

waste power and does produce some immunity to noise

Phase Shift Keying (PSK)

• Another form of angle-modulated, constant amplitude digital modulation.

• Binary digital signal input & limited number of output phases possible.

PSK Modulator

Data

Carrier

PSK signal

PSK – cont’d

• Binary signals are used to switch the phase of a carrier wave between 2 values which are normally 00 and 1800

• For binary ‘1’, the carrier has one phase• For binary ‘0’, the carrier is reversed by 1800

• Also known as Phase-Reversal Keying (PRK)

PSK Waveform

Example

For the digital message 1101 1100 1010, sketch the waveform for the following:

a. ASK

b. FSK

c. PSK