Comm Chptr4

CHAPTER 4INTRODUCTION

TO DIGITAL MODULATION

• The purpose of analog modulation is to impress an

• information-bearing analog waveform onto a carrier for transmission.

• The purpose of digital modulation is to convert an• information-bearing discrete-time symbol

sequence into a continuous-time waveform (perhaps impressed on a carrier).

• Key concerns : bandwidth efficiency and implementation complexity.

• Digital Modulation is defined as the transmission of digitally modulated analog signals (carriers) between 2 or more points.

• If the information signal is digital and the carrier has the following expression:

• v(t) = V sin(2ft + )

• Ac(t): amplitude modulation AM ASK• fc(t) : frequency modulation FM FSK (t) : phase modulation PM PSK

• Ac(t) and (t) QAM (Digital)

DigitalAnalog

Application of Digital Modulation : 1. Modem in personal computer 2. Digital Subscriber Lines (DSL) 3. Digital Microwave 4. Satellite Communication system 5. Cellular telephone Personal Communication Systems (PCS)

Digital Modulation involves the Digital Signal Processing because it is much simpler to store digital signals than analog signal.

There are 2 type of Digital Modulation: 1. Pulse Modulation – PAM, PWM, PPM 2. Binary Modulation – ASK, FSK, PSK, PCM

Model of Digital Comm.

The model of Digital System is shown below:

Input Signal

TRANSMITTER

Output Signal

RECEIVER

Source Encoder

Digital Demodulation

Trans. Medium or Channel

Channel Encoder

DigitalModulation

Source Decoder

ChannelDecoder

Block diagram of a digital radio system

Signal Processing

Advantages & disadv. of Digital Transmission

Advantages•Noise immunity•(Time domain) Multiplexing•Regeneration•Simple to evaluate and measure

Disadvantages•More bandwidth•Additional encoding (A/D) and decoding (D/A) circuitry

The information capacity of a communication system represents the number of independent symbols that can be carried through the system in a given unit of time.

By using Shannon limit for information capacity, the relationship between Information capacity to the signal bandwidth and SNR is defined below:

I = information capacity (bit/second)

B = system bandwidth (Hertz)

S/N =signal-to-noise power ratio (dimensionless)

2 10log 1 3.32 log 1S SI B BN N

Bandwidth and information capacity

M-ary Encoding

2logN M 2N MN = number of bits necessary

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

For binary M = 2 N = 1

1baud ss

ft

baud = fs = symbol rate (baud per second)ts = time of one signaling element (second)

symbol = one signaling element

What is the difference between baud and bits per second (bps)?

Baud and Minimum Bandwidth

Baud is rate of change of a signal on the transmission medium after encoding and modulation have occurred (symbols per seconds), rate of change at output of the Modulator.

Bit is rate of change at the input to the Modulator (bits per second, bps).

Binary signals; logic 1 => High, logic 0 => Low

Baud and Minimum Bandwidth

22 2 logb sf f N BN B M fb = bitrate (bps)fs = baud (symbols per second)B = minimum Nyquist bandwidth (hertz)M = number of discrete signals or voltage levelsN = number of bits encoded into each symbol

22log 2b bf fB

M N

EXAMPLE 1A standard voice-band communication channels have a SNR power of 1000 (30 dB) and signal Bandwidth of 2.7 kHz. Determine the information capacity.

Solution : By using Shannon’s Limit, information capacity is defined as: I = (2.7 kHz)(3.32)log10 (1 + 1000) = 26.9

kbps

Pulse ModulationPulse Modulation is a process of sampling

analog signal and then converting them into discrete pulses and transporting the pulses from a source to a destination over a transmission medium. A device to perform this is called ADC (Analog-to-Digital Converter) & DAC (Digital-to-Analog Converter).

PAM (Pulse Amplitude Modulation)It is used to describe the conversion of analog

signal to pulse-type signal in which the amplitude of the pulse denotes the analog information. In addition, it is a series of pulses in which the amplitude of each pulse represents the amplitude of the information signal at a given time.

Pulse Modulation • PWM (Pulse Width Modulation) It is a pulse duration modulation (PDM) or

pulse length modulation. The width of pulse is varied proportional to the Amplitude of the analog signal at the time signal is sampled.

• PPM (Pulse Position Modulation) It is a series of pulses in which the timing of

each pulse represents the amplitude of the information signal at a given time.

PCM (Pulse Code Modulation)• It is a series of pulse in which the amplitude of

the information signal at a given time is coded as a binary number. The pulses are of fixed length and fixed amplitude. Refer to Figure 10-1 in the textbook for PWM, PPM, PAM & PCM.

• PCM is generated by 3 processes; Sampling, Quantization & Encoding.

• An Integrated circuit that perform PCM encoding and decoding function is called CODER OR DECODER.

Pulse ModulationAnalog signal

Sample pulse

Pulse width modulationPulse position modulation

Pulse amplitude modulationPulse code modulation

8 bit

ts

PCM system Block Diagram

Signal Sampling• A process of periodically sampling the continually

changing analog input voltage and convert it to a series of constant amplitude pulses, so that it is easier to convert to binary PCM code

• 2 types of sampling:1. Natural Sampling

tops of the sample pulses retain their natural shape, making it difficult for ADC to convert to PCM codes

2. Flat-top Samplinginput voltage is sampled with narrow pulses and then held relatively constant until next sampling

Natural Sampling

Input analog signal

Sampling pulse

Sampled output

Sample-and-hold circuit

Flat-top sampling

Sample-and-hold waveforms

Sampling Rate•Sample & Hold circuit is a vital component in ADC to convert the analog signal to digital signal at certain sampling period, Ts.

•The analog signal should be sampled at the Nyquist rate Sampling Frequency,

2s af f

fs = minimum Nyquist sample rate (Hz)fa = maximum analog input frequancy (Hz)

Number of LevelThe number of level depends on the number of bits

used to express the sample value. It is defined as :

N = 2n

EXAMPLE :Calculate the number of level if the number of bit per sample is 8-bit.

Solution :1. N = 28 = 256

Output spectrum of a S&H circuitS&H circuit is non’linear which results in harmonics

Ideal

Aliasing

2s af f

2s af f

http://www.mustagh.com/alias/Alias.html

Quantization• Quantization is a process of rounding off the amplitude of

flat-top samples to a manageable number of levels

• Assigning PCM codes to absolute magnitude is called quantizing

• Total range is sub-divided into a smaller number of sub ranges.

• Magnitude difference between adjacent steps is called the quantization interval or quantum

• The magnitude of a quantum is called the resolution: equal to the voltage of the minimum step size = voltage of the least significant bit. minimum voltage other than 0 that can be decoded by ADC.

The binary codes used for PCM are n-bit codes (sign-magnitude code) where the MSB bit is the sign bit. If PCM is 3-bit codes, then the sign and magnitude are shown below:

In terms of Voltage, the maximum signal voltages are 3 V or -3 V and the minimum signal voltages are 1 V or -1 V.

Sign Magnitude Decimal value

Quantization range (V)

1 1 1 +3 +2.5 to +3.51 10 +2 +1.5 to +2.51 01 +1 +0.5 to 1.51 00 +0 0 to +0.50 00 -0 0 to -0.50 01 -1 -0.5 to -1.50 10 -2 -1.5 to -2.50 11 -3 -2.5 to -3.5

Folded binary code

Input analog signal

Sampling pulse

PCM code

Quantization

PAM signal

What is the PCM code for 2.6 V??

Quantization Error•Folded PCM code = sample voltage

resolution•For input at 2.6 V, the PCM code is therefore: 2.6/1 = 2.6 But since there is no code for +2.6, the magnitude is rounded off to the nearest valid code, which is 111 (+3V)•Thus there is difference of 0.4QUANTIZATION ERROR (Qe)•or also known as quantization noise (Qn)•Maximum magnitude Qe is equal to one-half a quantum resolution

2eQ

Linear input-output transfer curve

Linear

Quantization

Error

Input analog signal

Sampling pulse

PCM code

PAM signal

Question: What is the quantized voltage, quantization error and PCM code for 1.75 V??

Dynamic Range

max max

min

2 1resolution

nV VDRV

DR = dynamic range (unitless)Vmin = the quantum valueVmax = the maximum voltage magnitude of the DACsn = number of bits in a PCM code (excl. sign bit)

20log 2 1ndBDR

• Ratio of the largest possible magnitude to the smallest (other than 0) magnitude that can be decoded by the digital-to-analog converter (DAC) in the receiver

DR = 2n -1

Thus 2n = DR + 1

And therefore, The minimum number of bit used:n = log ( DR + 1 )

log 2

2 1 2n nDR For n > 4

20log 2 1 20 log 2 6ndBDR n n

No of Bits No of Levels DR (dB)1 2 6.022 4 123 6 18.14 16 24.15 32 30.16 62 36.17 128 42.18 256 48.29 512 54.2

10 1024 60.211 2048 66.212 4096 72.213 8192 78.314 16348 84.315 32768 90.316 65536 96.3

Dynamic Range

Coding Efficiency

minimum number of bitscoding efficiency= 100actual number of bits

Coding efficiency is a numerical indication of how efficiently a PCM code is utilized

EXAMPLEA PCM systems has the following specification:Maximum Analog Input Frequency = 4 kHzMaximum decoded voltage at the receiver = 2.55 VThe dynamic range = 46 dB Determine the following : (a) Minimum Sampling Rate (b) Minimum number of bits used in PCM code (c) Resolution (d) Quantization Error

Solution (a) The minimum sampling rate: fs = 2fa = 2(4 kHz) = 8 kHz

(b) Calculate the Dynamic range : 46 = 20log(Vmax / Vmin) Vmax / Vmin = antilog (46/20) = 199.5 Thus, the minimum number of bit used: n = log (199.5 + 1) / Log 2 = 7.63

(c) Resolution is defined as: Vmax / 2n - 1 = 0.01 V

(d) Quantization Error : Q = resolution / 2 = 0.01 V / 2 = 0.005 V

Signal-to-Quantization Noise Efficiency

min

minresolution 2

e e

VSQRQ Q

resolution2eQ

V 2e

SQRQ

max

maxe

VSQR

Q

SQR is not constant

Linear vs. Nonlinear coding

Linear Nonlinear

What is the advantage of Nonlinear coding???

Idle channel noise

Companding

Higher amplitude analog signals are compressed

Dynamic range is improved

PCM system with analog companding

-law compression

max

maxln 1

ln 1

in

out

VV VV

The 12-bit PCM can be compressed to 8-bit PCM. The 8-bit compressed code consists of a sign bit,

3 segment identifier and 10-bit magnitude code that specifies the quantization level

a) Sign Bit => 1 = + => 0 = - b) No. of leading 0s, subtract from 7:-Bit Segment

Identifier 000 111 c) 4-Bit Quantization Interval A B C D 0000 to 1111

Digital Companding

Refer to Figure 10-18(a), (b), (c) for the conversion of 12-bit PCM to 8-bit compressed code (Encoded PCM) and vise versa (Decoded PCM).

EXAMPLE : Convert the 12-bit PCM below to an 8-bit compressed

code 100110100100

Solution : 1. From Figure 10-18 (b), use segment 5, ABCD will be 1010. 2. From segment 5, the 8-bit compressed code is s101ABCD where s is a sign bit either 1 or 0. 3. Thus the 8-bit compressed code will be

Sign bit

Leading zeros

ABCD

11011010

Example(i) Determine the 12-bit code for analog signal of

+0.32V using a PCM system with 0.01V resolution. Then convert the 12 bit code to 8-bit compressed code

(ii) Repeat the question with -0.072V analog input

ANSWER:

(i) 10100000

(ii)00000111

Delta Modulation PCM Delta Modulation use a single-bit PCM code to achieve

digital transmission of analog signal.

Refer to Figure 10-20 in the textbook for Delta Modulation Transmitter and Figure 10-22 for Receiver.

When the analog signal is sampled by Sample & Hold circuit, it will create PAM (Pulse Amplitude Modulation) and compared with initial condition (zero volts => up-down converter is zeroed).

The output of Comparator is logic ‘1’. On the next clock pulse, up-down counter is incremented to a count of 1.

Each time up-down converter is incremented, logic ‘1’ is transmitted. Each time up-down converter is decremented, logic ‘0’ is transmitted.

It is a delta modulation system where the step size of the DAC is automatically varied according to previous values (refer to Figure 10-25 in the textbook)

An Adaptive Delta Modulation can transmit voice at about ½ bit rate of the PCM system.

The advantage of using Adaptive Delta Modulation:

Reduce Slope Overload The slope of the analog is greater than the delta modulator can maintain

Reduce Granular Noise The variation of the constructed signal compared to original signal.

Adaptive Delta Modulation PCM

PCM Advantages PCM systems allow the regeneration of the

signal.

PCM systems allow the analog information to be stored digitally (digital storage).

PCM systems allow the source and channel coding.

PCM systems allow successive time multiplexing of lower-rate digital streams