IT part 2

7. Digital Modulation

Transmittal of digitally modulated analog signals between two or more points in a communication system.

Applications low-speed voice band data

communications modems High speed data transmission

system Digital microwave and satellite

communications systems Cellular telephone

Digital transmission

- transmittal of digital pulses between two or more points in a communications system- require a physical facility between the transmitter and receiver such as

o       metallic wire pairo       coaxial cableo       optical fiber cable

Digital radio

- transmittal of digitally modulated analog carriers between two or more points in a communications system-  transmission medium is free space or Earth’s atmosphere

Why use digital modulation?

Ease of processing Ease of multiplexing Noise immunity

Digital Modulation Techniques

1. FREQUENCY SHIFT KEYING (FSK)FSK is a relatively simple, low-

performance type of digital modulation. Binary FSK is a form of constant –amplitude angle

modulation similar to conventional frequency modulation except that the modulating signal is a binary pulse stream that varies between two discrete voltage levels rather that a continuously changing analog waveform.

The general expression for a binary FSK signal is

Where: vfsk(t) = binary FSK waveformVc = peak analog carrier amplitude (V)fc = analog carrier center frequency (Hz)vm(t) = binary input (modulating) signal (V)Δf = peak change in analog carrier frequency (Hz)

The center or carrier frequency is shifted by the binary input data. As the binary input signal changes from a logic 0 to a logic 1, and vice versa, the FSK output shifts between two frequencies; a mark or logic 1 frequency and a space or a logic 0 frequency.

FSK Bit Rate, Baud, and Bandwidth

Output rate of change is equal to the input rate of change.

Bit rate – bits per second (bps), rate of change at the input to the modulator

Baud/baud rate – reciprocal of the time of one output signaling element, rate of change at the output of the modulator.

Bit rate = baud rate The minimum bandwidth is

B = 2(Δf + fb)

Bandwidth considerations using Bessel functions

The fastest input rate of change occurs when the binary input is a series of alternating 1’s and 0’s: namely, a square wave. If only the fundamental frequency of the input is considered, the highest modulating frequency is equal to one-half of the input bit rate.

where: MI = modulation indexΔf = frequency deviation (Hz)fa = modulating frequency (Hz)Δf = peak freq. dev. of the carrier

fa = fund. freq. of the binary input

where fb = input bit rate

Example: For a binary FSK modulator with space, rest and mark frequencies of 40, 50 and 60 MHz respectively and an input bit rate of 10 Mbps, determine the output baud and the minimum required bandwidth.

Bessel Function Chart

FSK modulator

FSK RECEIVER

2. Amplitude-Shift Keying

Similar to standard amplitude modulation except there are only two output amplitudes possible. digital amplitude modulation (DAM) On-off keying (OOK)

WhereVask(t) = amplitude-shift keying waveVm(t) = digital information signal (V)A/2 = unmodulated carrier amplitude (V)ωc = analog carrier radian frequency in

rad/sec

ASK Bit Rate, Baud, and Bandwidth

Bit rate = baud rate Bit rate = minimum Nyquist bandwidth

Ex.Determine the baud and minimum bandwidth necessary to pass a 20 Kbps binary signal using ASK.

3. PHASE SHIFT KEYING (PSK)

another form of angle-modulated, constant amplitude digital modulation similar to conventional phase modulation except that with PSK the input signal is a binary digital signal.

BINARY PHASE SHIFT KEYING (BPSK)

- two output phases are possible for a single carrier frequency. One output represents a logic 1 and the other a logic 0.- (PRK) Phase Reversal Keying- Biphase Modulation

BPSK TRANSMITTER

Balanced Ring Modulator

Logic 1 input

Logic 0 input

(a) Truth table

(b) Phasor Diagram

(c) Constellation Diagram

Output phase versus time relationship for a BPSK modulator

Bandwidth Considerations of BPSK output = (sin ωat) x (sin ωct) fundamental freq unmodulated

of the carrier modulating signal

 = ½ cos(ωc - ωa)t - ½ cos(ωc + ωa)t

 The minimum double Nyquist bandwidth (fN) is

ωc + ωa ωc + ωa

-(ωc - ωa) or -ωc + ωa

2ωa

and because fa = fb/2 

fN = 2(fb/2) = fb

Example: Determine the minimum bandwidth and baud for a BPSK modulator with a carrier frequency of 40 MHz and an input bit rate of 500 kbps. Sketch the output spectrum.

BPSK RECEIVER

QUATERNARY PHASE-SHIFT KEYING (QPSK)

four output phases are possible for a single carrier frequency. the binary input data are combined into group of two bits

THE RATE OF CHANGE AT THE OUTPUT IS EQUAL TO ONE-HALF THE INPUT BIT RATE

M-ary Encoding

N = log2MWhere: N = number of bits

M = number of output conditions possible with N bits

QPSK Transmitter

QPSK Constellation Diagram

QPSK Truth Table

QPSK Phasor Diagram

Output phase versus time relationship for a QPSK modulator

BANDWIDTH CONSIDERATIONS OF QPSK

The output of the balanced modulators can be expressed mathematically as

output = (sinwat) (sinwct) or  ½ cos (wc-wa)t - ½ cos (wc+wa)t where  wat = 2Õfb/4t and wCt = 2Õfct thus output = ½ cos 2Õ (fc - fb/4)t - ½ cos 2Õ (fc + fb/4)t

Bandwidth considerations of a QPSK modulator

The output frequency spectrum extends from fc + fb/4 to fc – fb/4 and the minimum bandwidth (fN) is

(fc + fb/4) - (fc - fb/4) = 2 fb/4 = fb/2

QPSK Receiver

QPSK Receiver The receive QPSK signal (-sin ωct + cos ωct) is one of the inputs to the I product detector. The other input is the recovered carrier (sin ωct). The output of the I product detector is  I = (-sin ωct + cos ωct) (sin ωct) QPSK Input signal carrier = (-sin ωct) (sin ωct) + (cos ωct) (sin ωct) = -sin2 ωct + (cos ωct) (sin ωct) = -½ (1 – cos 2ωct) + ½ sin (ωc + ωc)t + ½ sin (ωc - ωc)t I = -½ + ½ cos 2wct + ½ sin 2wct + ½ sin 0 = -½ V (logic 0)

The receive QPSK signal (-sin ωct + cos ωct) is one of the inputs to the Q product detector. The other input is the recovered carrier shifted 90° in phase (cos wct). The output of the Q product detector is

Q = (-sin ωct + cos ωct) (cos ωct)  QPSK Input signal carrier = cos2 ωct - (sin ωct)(cos ωct) = ½ (1 + cos 2ωct) - ½ sin (ωc + ωc)t - ½ sin (ωc - ωc)t = ½ + ½ cos 2wct - ½ sin 2wct - ½ sin 0 = ½ V (logic 0)

EIGHT-PHASE PSK (8-PSK) - a form of angle-modulated, constant amplitude digital modulation wherein we encode three bits to have eight possible output phases.

Eight PSK Transmitter

Minimum Nyquist Bandwidth (fN)

= fb/2

fc - fb/4 fc + fb/4Suppresed carrier frequency

I- and Q-channel 2-to-4-level converters: truth table and PAM levels

8 PSK Phasor Diagram

8 PSK Truth Table

8 PSK Constellation Diagram and Output Waveform with binary input

Bandwidth Considerations of 8-PSK

With an 8-PSK modulator, there is one change in phase at the output for every 3 data input bits. Consequently, the baud for 8-PSK equals fb/3, the same as the minimum bandwidth. The balance modulators are product modulators; their outputs are the product of the carrier and the PAM signal.

Mathematically, the output of the balanced modulators is q = (X sinwat)(sinwct)

sinqsinF = ½ cos(q-F) - ½ cos(q+F)

q = wct F = wat

where wat = 2π(fb/6) and wct = 2πfctmodulating signal carrier

and X = ± 1.307 or ± 0.541

thus = X(1/2 cos (wct - wat) – ½ cos (wct + wat)

wa = 2π fa fa = ½ (fb/3) = (fb/6)wc = 2π fc

= X/2 cos2π(fc – fb/6)t – X/2 cos2π(fc + fb/6)t

The output frequency spectrum extends from fc + fb/6 to fc – fb/6 and the minimum bandwidth (fN) is (fc + fb/6) - (fc - fb/6) = 2 fb/6 = fb/3

1-5 For an 8-PSK modulator with an input data rate (fb) equal to 20 Mbps and a carrier frequency of 100 Mhz, determine the minimum double-sided Nyquist bandwidth (fN) and the baud. Sketch the output spectrum. With Q = 1, C = 0, and I = 0.

Solution:The bit rate in the I, Q and C channels is equal to one-third of the input bit rate: 

fb1 = fbQ = fbC = 20 Mbps / 3 = 6.667 Mbps

The highest modulating frequency to either balanced modulator: 

fa = fb1 /2 = fbQ/2 = fbC /2 = 6.667 Mbps / 2 = 3.333 Mhz

The output wave from the balanced modulators is:

= (sin 2π fat)(sin 2π fct)= ½ cos 2π (fc- fa)t - ½ cos 2π (fc+ fa)t= ½ cos 2π (100 – 3.333)t - ½ cos 2π (100 + 3.333)t= ½ cos 2π (96.667)t – ½ cos 2π (103.333)t The minimum Nyquist bandwidth is:

fN  = (103.333 – 96.667) Mhz = 6.666 or 6.67 Mhz

The baud rate equals the bandwidth:baud = 6.67 Megabauds

Eight PSK Receiver

With Q = 1, I = 0 and C = 0, the modulated output from the linear summer may be computed:

I = (-0.541)(sinwct) = -0.541 sinwct

the output from the Q – channel product modulator is:

Q = (1.307) (cos wct) = 1.307 cos wct outputs from the I- and Q- channel product modulators are combined in the linear summer to produce a modulated output of:

summer output = -0.541sinwct + 1.307 cos wct

Note: The C bit determines the magnitude of the output signal:

logic 1 = 1.307 & logic 0 = 0.541

The I or Q bit determines the polarity of the output analog signal:

logic 1 = +V & logic 0 = -V

4. QUADRATURE AMPLITUDE MODULATION (QAM)

Amplitude and phase shift keying are combined.

Bandwidth = 6.67Mhz

6.667Mhz

(LSB)

103.333Mhz

(USB)

Suppressed Carrier Freq.

(100Mhz)

8-QAM Transmitter block diagram

Phasor Diagram

Constellation Diagram

Output phase and amplitude versus time relationship for 8-QAM

Truth Table

TRELLIS CODE MODULATION Encoding technique that allows data transmission rates in excess of 56 kbps over a standard telephone circuit. Increase transmission bit rates using QAM or PSK with fixed bandwidths. Allows highly efficient transmission of information over band-limited channels Modulation technique with hardware error detection and correction

TYPICAL MODEMS MODEM – modulator and demodulator

-interface computers, computer networks, and other digital terminal equipment to analog communications facilities.

Bell system 103 modem Bell system 212 modem

BELL SYSTEM 212A MODEM Half duplex operation Two-wire telephone line 600 bps (bit rate) Dial-up transmission facility Asynchronous mode FSK modulation

BELL SYSTEM 212B MODEM Full duplex operation Four-wire telephone line 1200 bps (bit rate) Private line transmission facility Synchronous mode QPSK modulation