ECE 4710: Lecture #25 1

Frequency Shift Keying

Frequency Shift Keying = FSK Two Major FSK Categories

Continuous Phase» Phase between bit transitions is continuous no abrupt change

Discontinuous Phase» Phase between bit transitions is discontinuous abrupt change

1 0 1 0 1 0

Hf Lf Hf Lf Hf Lf

)(ts

)(ts

Hf Lf Hf Lf Hf Lf

1 0 1 0 1 0

ECE 4710: Lecture #25 2

Discontinuous Phase FSK

Discontinuous Phase FSK = DP FSK Generated by switching Tx output between two different oscillators

with different frequencies (1/0) and phases (not synchronized)

"0"]2cos[

"1"]2cos[)](2cos[)(

22

11

tfA

tfAttfAts

c

ccc

ECE 4710: Lecture #25 3

Discontinuous Phase FSK

Instantaneous phase + frequency change at bit transitions cause high-frequency amplitude variations in output signal No longer constant envelope as depicted here

High-frequency variations increase BW of signal BW is made worse if non-linear Class C amplifiers are used Linear amplifiers needed for reasonable BWs

» Class A or B amplifiers

» Poor DC to RF efficiencies typically 40-65%

DP FSK is normally not used b/c of these issues

Hf Lf Hf Lf Hf Lf

1 0 1 0 1 0

ECE 4710: Lecture #25 4

Continuous Phase FSK

Continuous Phase FSK = CP FSK Generated by feeding binary signal into frequency

modulator

Bandpass Signal

Complex Envelope Representation

t

fcc dmDtfAts )(2cos)(

t

ftj

ctfj dmDteAtgetgts c )()( and)( where)(Re)( )(2

ECE 4710: Lecture #25 5

Polar NRZ line code Baseband m(t) is discontinuous between bits (t) is continuous b/c integration of m(t) is continuous Polar signal produces binary FSK (BFSK)

Constant envelope is preserved» Signal BW is much better than DP FSK» Non-linear PAs used» Class C amplifiers with 80-90% DC to RF efficiencies» Important for wireless applications that rely on battery power (cell

phone, PDA, etc.)

Continuous Phase FSK

ECE 4710: Lecture #25 6

BFSK

Polar NRZ line code BFSK signal Multi-level line code M-FSK signal BFSK widely used for early computer modems

300-1200 bps Still used for low speed data and signals in landline telephony

» Caller ID, call forwarding, etc.

Dial-up computer modems (not DSL or cable) 28.8 kbps V.34 Modem QAM (studied next!) 56 kbps V.90 Modem PCM (Section 3-3 for more

details)

ECE 4710: Lecture #25 7

Communication Channels

Full Duplex (FDX) Transmission Tx and Rx for simultaneous two-way communication Cell phone, computer modem, etc.

Half-Duplex (HDX) Transmission Two-way communication but Tx and Rx not

simultaneous Listen before talk Walkie Talkie or CB Radio

Simplex (SX) Transmission One way communication only Text pager

ECE 4710: Lecture #25 8

BFSK Modems

Modem = Mod + Demod FDX Transmission Tx + Rx in one device

BFSK for low data rates» 300 bps Bell 103 standard» 1200 bps Bell 202 standard (caller ID)

ECE 4710: Lecture #25 9

BFSK Modems

Bell 103 Modem (300 bps) Telephone line has VF range from 300 – 3,300 Hz Most line codes (unipolar, polar) have significant energy at

frequencies < 300 Hz» Must use line code to modulate carrier for transmission

over phone line Two separate frequency bands used

» One for Tx + One for Rx = FDX» Carrier #1 & #2 centered around 1.2 kHz & 2.1 kHz» Peak-to-peak f deviation about each carrier 2f =

200 Hz

ECE 4710: Lecture #25 10

PSD of BFSK signal? Difficult to evaluate just like analog FM spectrum Non-linear relationship between g(t) and m(t)

Bell 103 BFSK Modem

2f = 200 Hz

tfj

t

ftj

c

cetg

dmDteAtg

2

)(

)(Re s(t) and

)()( where)(

ECE 4710: Lecture #25 11

Bell 103 BFSK Modem

Evaluate BFSK PSD for worst-case widest BW signal Deterministic square wave corresponding to alternating

1010101 pattern Frequent data transitions high signal BW since line

code pulse width is small)(tm )(t

ECE 4710: Lecture #25 12

Bell 103 BFSK Modem

Digital Modulation Index

PSD is line spectrum since m(t) is periodic Complex mathematical solution (see Eqs. 5-85 and 5-86) Calculate numerically (computer code) for different R and

F As h then BFSK approaches wideband FM spectrum

spectrum concentrated @ fc ± F

Worst case deterministic waveform worst-case PSD

BPSK) as (same 2h

bTR

RF

h1

where22

ECE 4710: Lecture #25 13

Bell 103 BFSK PSD

12 Hz 200 2 ffhRF

Bell 103 Modem Parameters

Originate Mode

ECE 4710: Lecture #25 14

Other BFSK PSD’s

ECE 4710: Lecture #25 15

Other BFSK PSD’s

PSD’s for Tx & Rx would overlap

and interfere for Bell 103 Standard

Since fTx 1 kHz

and fRx 2 kHz

ECE 4710: Lecture #25 16

Use Carson’s Rule (just like analog FM)

F = peak frequency deviation B is bandwidth of baseband digital signal m(t) If B = FNBW of rectangular m(t) then B = R

»

If RC filter is used to shape rectangular m(t) then»

Narrowband BFSK Wideband BFSK

ΔF/BBFBBT since 22)1(2

BFSK Signal BW

)(2 RFBT

RrFBT )1(2 2 BBT

FBT 2

ECE 4710: Lecture #25 17

What about PSD for random data m(t)? Difficult to evaluate Statistical techniques

and numerical computation

Note that h = 0.7 0.67

for Bell 103 Modem Standard

Note that h = 1 we have

delta function at fc + 0.5 R

BFSK PSD

ECE 4710: Lecture #25 18

BFSK Detection

Non-coherent detection Measure frequency of incoming signal

» fc + F “1” fc - F “0”

» Zero crossing detector + digital counter + logical comparator

ECE 4710: Lecture #25 19

BFSK Detection

Coherent detection

tfftmA

tftmAtm

)(2cos)(

2cos)()(~

1221

21

2

Let f1 = “1” [m(t) +1]

Let f2 = “0” [m(t) -1]

For “1” then cos(2 f1 t ) path yields

1)()(~21

1 tmAtmand cos(2 f2 t ) path yields

which is rejected by LPFso

)(~1 tm

)(~2 tm

"1"1)(~)(~ and 0)(~212 tmtmtm