Communication Systems, 5e

Transcription

1 Communicaion Sysems, 5e Chaper 3: Signal Transmission and Filering A. Bruce Carlson aul B. Crilly 010 The McGraw-Hill Companies

2 Chaper 3: Signal Transmission and Filering Response of LTI sysems Signal disorion Transmission Loss and decibels Filers and filering Quadraure filers and Hilber ransform Correlaion and specral densiy 010 The McGraw-Hill Companies

3 Signal Disorion The RF channel (and any filering) may disor he signal beween wha you hink you ransmied and wha you receive. 1. Ampliude Disorion. Delay Disorion arg H f H 3. Nonlinear Disorion No an LTI operaion f K Hf f m d 3

4 Copyrigh The McGraw-Hill Companies, Inc. ermission required for reproducion or display. Tes Signal Example Tes signal x() = cos 0-1/3 cos /5 cos 5 0 The firs 3 erms for he Fourier Series of a square wave 4

5 Copyrigh The McGraw-Hill Companies, Inc. ermission required for reproducion or display. Tes signal wih filered, linear ampliude disorion (a) low frequency aenuaed by ½ (by a HF) (b) high frequency aenuaed by ½ (by a LF) See Malab: Fig03.m Fig03 3.m Firs erm changed Third erm changed 5

6 Square Wave Filering MATLAB Fig3 4.m 0 Buerworh Filers 1000 Hz Low ass Filer Aenuaion (db) Ampliude Time (sec) 10 Hz High ass Filer khz LF 10 Hz HF Frequency (normalized) Ampliude Time (sec) LF f cuoff =1000 Hz HF f cuoff =10 Hz 6

7 hase Delay and Delay Disorion Consan ime delay resuls in linear phase delay and is desirable for disorionless ransmissions! See he ime delay propery of he Fourier Transform exp i f A consan phase shif is no linear in phase and resuls in significan signal disorion. See he following consan phase delay of 90 deg. Use an equalizer o fix he phase problems 7

8 Copyrigh The McGraw-Hill Companies, Inc. ermission required for reproducion or display. Tes signal wih consan phase disorion shif all inpus by = -90 Noe a square wave anymore Tes signal x() = cos( 0-90)- 1/3 cos( /5 cos(5 0-90) 8

9 Equalizaion o overcome linear disorion Consider a channel wih linear disorion To overcome linear disorion equalizaion jf Ke d Heq ( f) H( f) 0 H ( f) C overall sysem funcion is H( f) H ( f) H ( f) eq C 010 The McGraw-Hill Companies

10 Time Delay Disorion The effecive ime delay due o phases arg H f f f f C C The equalized ime delay can be approximaed h H f H f H f exp j f g arg arg C f f EQ f f H C H EQ C f f g H H f f C EQ C d d g g For disorionless ransmission, 0 f arg H f H f d g 0 C EQ 10

11 hase or Delay Disorion If he phase shif is no linear, he phase delay ime is d f f For a pure ime delay, he phase change is linear and he phase delay is a consan. arg H f Noe: consan ime delay is desirable, while consan phase delay is no 11

12 Envelope or Group Delay The group delay is a consan for all frequencies, i is approximaed as g 1 f This is commonly envisioned o apply o he envelope of he signal, while he phase delay is applied o he carrier. d df 1

13 Time Delay Signal Disorion For a es signal The filered oupu would become f sin x f cos x x c c 1 c d c g c d c g 1 f f sin x A f f cos x A y Expec he carrier delay o be greaer han he signal envelope delay! 13

14 Equalizaion Apply a filer ha correcs for ampliude and delay disorion in he receiver. Compensae so ha he difference beween he phase and group delay becomes zero d f g comp f f f 1 d f df comp f 0 14

15 Transmission Loss and decibels ower gain Transmission loss and he need for repeaers Media Radio ransmission 010 The McGraw-Hill Companies

16 Logarihms and Decibels RF signal power and volage magniudes are ypically described in: Decibel-Was (dbw) Decibel-milliwas (dbm) Decibel-volage (dbv) The Raio of RF power or volage is ypically describe in: Decibels (db) The relaive anenna power (ransmiing or receiving) for a paricular direcion as compared o an isoropic anenna is describe in: Decibles-isoropic (dbi) 16

17 Alexander Graham Bell The bel is defined as he log base 10 of power raios bels log ou in The magniude was oo small, herefore he Decibel was defined decibels db 10log ou in 17

18 Derived ower/volage Measures Decibels for ower, Volage, and Curren ower decibels db 10log ou in Volage decibels V R V db 10log V ou in R R ou in V decibels db 0log V For mached impedances where Rou=Rin ou in 18

19 Derived ower/curren Measures Decibels for ower, Volage, and Curren ower decibels db 10log ou in Curren I R decibels db 10log I I ou in R R ou in For mached impedances where Rou=Rin decibels db 0log I I ou in 19

20 ower Measuremen Was ( in Was) decibels was dbw 10log Milliwas (from in Was) decibels milliwas 1W 1000mW Milliwas (m in milliwas) dbm 10log W 10 3 decibels milliwas dbm 10log mw 0

21 Common Decibel Values ower Raio ( ou in ) Decibels (db) db db db db 3.01 db 1 0 db db db db db 1

22 Common Decibel ower Values ower (Was) Decibels-Was (dbw) Decibels-MilliWas (dbm) 1 megawa 60 dbw 90 dbm 1 kilowa 30 dbw 60 dbm 10 was 10 dbw 40 dbm 1 wa 0 dbw 30 dbm 0.1 wa -10 dbw 0 dbm 1vol 50ohms dbw +13 dbm 1 milliwa -30 dbw 0 dbm 1 microwa -60 dbw -30 dbm 1 nanowa -90 dbw -60 dbm 1 picowa -10 dbw -90 dbm

23 Suggesed Malab Funcions db( value) 10log dbv( value) 0log idb( value) 10 idbv( value) 10 value value value 10 value 0 Fundamenal quesion: Are you in he power domain or a volage/curren domain? 3

24 Logarihm/Decibel Reminders log log db a b loga logb a loga logb b 1 loga c log b db b dba 1 c db b a logb logc a b dba dbb a dba dbb a dbb dbc 4

25 ower Gain Componens in a radio will provide signal gain or signal aenuaion (loss). All componens also conribue addiive noise o signal ha pass hrough hem (hermal noise). Using hese facors, we can compue he gain of he receiver and a noise figure. 5

26 ower Gain Gain is defined as he power ou divided by he power in g ou H 0 in 10log Cascaded gain is he gain of he receiver chain ou1 ou ou3 ou3 G G G 1 G G3 in1 in g in3 G db db in1 G 1dB 10 G db ou in G 3dB 6

27 7 Noise Figure (App. A p. 841) The Noise Figure Described he expeced oupu noise power refleced o he inpu of he device. Thus, i defines he addiional equivalen inpu noise conribuion. 0 device 0 device 0 N N 1 N N N F Cascaded noise figure is effeced by he gain G G 1 F G 1 F F F

28 Lossy Elemens/Aenuaion Lossy elemens gain is fracional, 0<g<1. In erms of db, he db-gain is negaive. Noise Figure of a Lossy elemen When no oherwise provided, use he negaive dbgain. (e.g. -3 db gain + 3 db Noise Figure) 8

29 Cable Cable loss db loss proporional o lengh LdB l where is loss in db/lengh, and l lengh For example, 1 cm coax, a 3 MHz, 4 db/km 100 meer cable has loss of 4 db/km 0.1 km = 0.4 db. 0.4/ L L (linear loss) gain = 1/ L 1/ db 010 The McGraw-Hill Companies

30 Alpha Wire and Cable Caalog Cable Losses 50 ohm RF RG-8 RG-58 RG ohm TV Cable RG-6 RG-11 RG-59 RG

31 Receiver Sages Gain/NF Example 1 3a 3b 4 5a 5b 6 Inhase RF T/R SW Filer LNA AM Quad. Hybrid An An LF 10 MHz LF 10 MHz ADC Quadhase ADC Xm T/R Crl LO RF Inpu RF Filer and LNA Quadraure Downconversion Digiizaion wih Ani-Aliasing Filer T/R Swich RF Filer and Amplificaion Zero-IF Quadraure Downconversion Ani-Aliasing Filers ADC Isolae Transmi and Receive (TDD comm) Reduce Inerference BW and Limi NF Gain Adjusmen Downconver ADC Inpu Signal Condiioning 31

32 Receiver Cascaded Analysis 1 3a 3b 4 5a 5b 6 Inhase RF T/R SW Filer LNA AM Quad. Hybrid An An LF 10 MHz LF 10 MHz ADC Quadhase ADC T/R Crl Xm LO RF Inpu RF Filer and LNA Quadraure Downconversion Digiizaion wih Ani-Aliasing Filer Sage 1 3a 3b 4 5a 5b Gain (db) Noise FIgure (db) Noise Figure (linear) Toal Gain (db) Toal Gain (linear) E E E+04.3E+04 Toal NF (linear) Toal NF (db)

33 Receiver Sensiiviy (Advanced) dbm Maximum Signal ower o ADC Receiver Gain 43.6 db Received Signal ower Dynamic Range DT 8 db NF 5.00 db 10 MHz db 57.4 db dbm ADC SNR 70 db dbm dbm dbm dbm Maximum Inpu Signal ower Min. Deecable Signal (MDS) Receiver Noise Floor Thermal Noise Floor Receiver Noise Floor ktb (p. 413) Cascaded NF Min. Deecable Signal Deecion Threshold ADC Consideraions Max. Signal ADC SNR Dynamic Range Insananeous Spur Free Dynamic Range kt Noise Floor -174 dbm/hz 33

34 Free-Space ah Loss f Noe c f G R Gr r As an RF signal propagaes, here is pah loss. L As shown above r 4R G G L r 4f c G R G r 4 R 34

35 1 s Order RF Range Esimae Friis Transmission Formula Direc, line-of-sigh range-power equaion No real-world effecs aken ino accoun r G G r G 4 R 4 f R G r c where: r is he received (or ransmied) G is he effecive ransmier (or receiver) anenna gain R is he disance beween he ransmier and receiver, and is he wavelengh f is he frequency 35

36 Sysem Range Concep f G Gr r R G dbm dbm G r dbm r dbm 0m R 1 m Maximum Range ( r is receiver sensiiviy) R c 4 f r G G r 36

37 Copyrigh The McGraw-Hill Companies, Inc. ermission required for reproducion or display. Saellie relay sysem Ex (1 of ) 6 GHz 4 GHz ah Losses L L d u 4f c 4f c R R 46e936e6 3e8 44e936e6 3e e dB e dB 37

38 Copyrigh The McGraw-Hill Companies, Inc. ermission required for reproducion or display. Saellie relay sysem ( of ) =18 dbw r G G L r G G 4 R r =35 dbw ower Received sa _ rcv 35dBW 55dB 199.1dB 0dB 89.1dBW ou 18dBW 16 db db 51dB dbw Error in 4 h ed. Saellie Gain g amp 18dBW 89.1dBW 107.1dB 38