Slide from before: Performance Concerns •DC offset •Image rejection Communication system •Quadraturerequirements performance •Noise and noise figure •Phase noise and Jitter revisited •Distortion –Compression –Desensitization –Cross modulation –Intermodulation –IP2, IP3 –Harmonic distortion (THD, SFDR,…) •Bit error rate •Data rate (bandwidth)

1 2

System level concerns Mobility vs. Bit Rate •Data rate (voice, text, image, video,…) Where is Military? •Cost (CMOS, SiGe, …) Where is UWB? •Mobility (fixed, indoor, outdoor, ground Vehicle r o

vehicle, airborne, …) o

d Walk t u

•Battery life (power consumption) O

y WLAN t i

l Stationary W-CDMA/ i

•Weight (discrete, multi-chip, single chip, ) b EDGE (IEEE o M r Walk 802.11a/b/g) •Multi-standard support (hardware sharing) o o

d Bluetooth

n Stationary/ I Zigbee (IEEE 802.15) LAN •Security (baseband DSP) Desktop •Quality of service (protocol, transceiver) 0.1 1 10 100 Mb/s Bit Rate

3 4

Motorola 3G Smart Phone Architecture Cost vs. Bit Rate

$

High t i b

/

t Medium W-CDMA/

s W-CDMA/

o EDGE

C EDGE

r

e HIPERLAN/2 s Low WLAN U Bluetooth (IEEE Very Low Zigbee (IEEE 802.15) 802.11a/b/g) LLANAN 0,1 1 10 100 Mb/s Bit Rate

5 6

1 Transceiver performance Generic Transceiver Architecture •Transceiver Overview •Transmitter Performance Spec. •Transmitter Architecture •Receiver Performance Spec. •Receiver Architecture •Receiver Link Budget

7 8

Transceiver Role of a Receiver Role of a Transmitter Information

Information HPMX-2007

4. discard carrier and Th e kl eh fwkhqlw Th e kl eh fwkhqlw Th e kl eh fwkhqlw wehrilekj hl khjaw rqiluw wehrilekj hl khjaw rqiluw wehrilekj hl khjaw rqiluw wesaekhqjl. hw hlw heli wrwwesaekhqjl. hw hlw heli wrw wesaekhqjl. hw hlw heli wrw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw HPMX-2007 wekj hl khjaw rqiluw wekj hl khjaw rqiluw wekj hl khjaw rqiluw q q q wae. wesaekhqjl. hw hlw heli wrw wesaekhqjl. hw hlw heli wrw eskhqjl hw hlw heli wrwwkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wekj hl khjaw rqiluw wekj hl khjaw rqiluw q q qwekj hl khjaw rqiluw wesaekhqjl. hw hlw heli wrw wesaekhqjl. hw hlw heli wrw wesaekhqjl. hw hlw heli wrwwkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wekj hl khjaw rqiluw q q qwekj hl khjaw rqiluw wesaekhqjl. hw hlw heli wrw wkhl rj hliq qhqil 3q hiw wesaekhqjl. hw hlw heli wrwwkhl rj hliq qhqil 3q hiw qwekj hl khjaw rqiluw wkhl rj hliq qhqil 3q hiw eskhqjl hw hlw heli wrw q wae. Th e kl eh fwkhqlw Th e kl eh fwkhqlw Th e kl eh fwkhqlw q wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw qwekj hl khjaw rqiluw qwekj hl khjaw rqiluw wehrilekj hl khjaw rqiluw wehrilekj hl khjaw rqiluw wehrilekj hl khjaw rqiluw qwekj hl khjaw rqiluw wesaekhqjl. hw hlw heli wrw wesaekhqjl. hw hlw heli wrw wesaekhqjl. hw hlw heli wrw wesaekhqjl. hw hlw heli wrwwesaekhqjl. hw hlw heli wrw recover data 2. add data to carrier wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wesaekhqjl. hw hlw heli wrwwkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw qwekj hl khjaw rqiluw qwkhl rj hliq qhqil 3q hiw qwekj hl khjaw rqiluw qwekj hl khjaw rqiluw qwekj hl khjaw rqiluw wekj hl khjaw rqiluw eskhqjl hw hlw heli wrw wekj hl khjaw rqiluw wae. wesaekhqjl. hw hlw heli wrwwesaekhqjl. hw hlw heli wrw q wae. q eskhqjl hw hlw heli wrw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wesaekhqjl. hw hlw heli wrwwkhl rj hliq qhqil 3q hiw wesaekhqjl. hw hlw heli wrw wkhl rj hliq qhqil 3q hiw qwkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw qwekj hl khjaw rqiluw qwekj hl khjaw rqiluw wekj hl khjaw rqiluw wekj hl khjaw rqiluw qwekj hl khjaw rqiluw wesaekhqjl. hw hlw heli wrwwesaekhqjl. hw hlw heli wrw q q q eskhqjl hw hlw heli wrw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wesaekhqjl. hw hlw heli wrw wae. waekhl. rj hliq qhqil 3q hiw qwekj hl khjaw rqiluw q qwekj hl khjaw rqiluw wesaekhqjl. hw hlw heli wrwwkhl rj hliq qhqil 3q hiw wesaekhqjl. hw hlw heli wrw wkhl rj hliq qhqil 3q hiw qwekj hl khjaw rqiluw wkhl rj hliq qhqil 3q hiw q wesaekhqjl. hw hlw heli wrw q wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wekj hl khjaw rqiluw wekj hl khjaw rqiluw q q qwekj hl khjaw rqiluw wesaekhqjl. hw hlw heli wrwwesaekhqjl. hw hlw heli wrw wesaekhqjl. hw hlw heli wrw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw qwekj hl khjaw rqiluw qwkhl rj hliq qhqil 3q hiw qwekj hl khjaw rqiluw wesaekhqjl. hw hlw heli wrwqwekj hl khjaw rqiluw wesaekhqjl. hw hlw heli wrw wkhl rj hliq qhqil 3q hiw wesaekhqjl. hw hlw heli wrw 2. shift to lower frequency wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw wkhl rj hliq qhqil 3q hiw q q qwekj hl khjaw rqiluw qwekj hl khjaw rqiluw 3. shift to high wesaekhqjl. hw hlw heli wrwwae. Modulator (cost and/or performance) De-Modulator frequency A A D D Baseband Mixer Mixer Processor I Data I Data 0 0 9 uP/ 9 uP/ 0 Antenna DSP Antenna 0 DSP

Power Amplifier Baseband Low Noise Amplifier A Q Data Processor A Q Data 4. amplify to D D broadcast 1. amplify received signal with min. added noise Oscillator Oscillator bias bias bias bias bias

1. create carrier 3. LO for down conversion Power Supply Power Supply

9 10

Transmitter Performance Spec. Digital Communication System:

•Output Power •Spurious Emission Information per bit increases Bandwidth efficiency increases •Adjacent Channel Power Ratio; ACPR •Frequency Stability •Data rate noise immunity increases •Bandwidth efficiency Transmitter •Noise immunity Receiver

11 12

2 Increasing Information Increasing Noise Immunity •Information in a source –Mathematical Models of Sources Error correction –Information Measures coding •Compressing information Block coding –Huffman encoding Channel coding –Lempel-Ziv-Welch Algorithm Adaptive feedback –Optimal Compression? coding •Quantization of analog data … –Scalar Quantization Diversity –Vector Quantization Space time –Model Based Coding diversity • m-law encoding •Delta Modulation •Linear Predictor Coding (LPC)

13 14

Increasing bandwidth Efficiency

Output Power Gt•Pt •Modulation of digital data into l P analog waveforms r –Impact of d Modulation on 2 Bandwidth æ λ ö 1 LoLossss f afactcortor n noot t efficiency Pr = Pt Gt Gr ç ÷ related to propagation è 4πd ø L related to propagation 2 æ P ö æ æ λ ö 1 ö PL = -10logç r ÷ = -10logçG G ÷ ç ÷ ç t r ç ÷ ÷ è Pt ø è è 4πd ø L ø f (GHz) D (m)Prop Loss (dB)Pt (dBm)Pr (dBm)L (dB) 2.45 10 60.23 20 -70.23 30

15 16

Adjacent Channel Power Ratio Spurious Emission

•Definition depends on specification

P ACPR = adjacent Main P Channel main

Adjacent Channel Pmain

Padj

17 18

3 Adjacent channel reject Transmit Specifications •Transmit spectrum mask

19 20

Transmitter Architecture RF/BB Interface

•RF/BB Interface •Direct Conversion Transmitter •Two-step Conversion Transmitter •Offset PLL Transmitter

21 22

BPSK Transmitter QPSK transmitter

Bit 1: A S (t) Bit 0: -Ax BPSK in Pulse shaping cos(2pf t+q ) a cos(2pf t+f) c c n c s(t) bit 2 bits to Map to Local + 2 E stream 4 levels constellation Oscillator s (t ) = b cos( 2pf t + q ) (bit 1) 90o BPSK T c c b b n -sin(2pfct+f) Pulse 2 E b shaping s BPSK (t ) = - cos( 2p f c t + q c ) (bit 0 ) T b

23 24

4 •Direct-conversion transmitter •Direct-conversion transmitter with offset LO

I I 0 9 0 0 9 0

wLO Q w1 wLO Q w2 Pros: less spurious synthesized Pros: less LO pulling Cons: more LO pulling Cons: more spurious synthesized

25 26

•Two-Step Transmitters •Two-step transmitter

I 0 9 0 w +w cosw1t 1 2 t Q cosw2

Pros: less LO pulling superior IQ matching Cons: required high-Q bandpassfilter

27 28

Transmitter Performance Check •Offset PLL transmitter 1.Sensitivity and Dynamic Range 2.Unwanted Emission

I 0 9 0 PD/LPF VCO

cosw1t Q 1/N

29 30

5 Receiver Performance Spec. •Sensitivity Sensitivity •Selectivity •Adjacent Channel •Co-Channel •Spurious Response Rejection Interference Interference

•IntermodulationRejection Adjacent Adjacent 890.4 890.4 Channel Channel

•Receiver Self-quieting Desired •Dynamic Range Channel 890.4 890.4 890.4

890.4 890.4 890.2 890.4 890.6 MHz 31 32

Receiver Specifications Sensitivity alternate adjacent channel

Noise Floor = Pnf (dBm) = kTB(dBm) + Freceiver (dB) Adjacent channel Sensitvity = Pin,min (dBm) = kTB(dBm) + Freceiver (dB) + SNRmin (dB)

= Pnf (dBm) + SNRmin (dB)

Desired Signal (must be higher than sensitivity)

SNRmin Receiver Added Noise 200 200 Receiver Thermal Noise 400 400 33 34

Sensitivity Example Calculate Receiver Noise Figure Power to Antenna: +45 dBm Transmitter: TX. Antenna Gain: +10 dB ETP + 55 dBm Frequency: 10 GHz Path Losses -200 dB Bandwidth: 100MHz Rcvr. Ant. Gain 60 dB •Stage Thermal Noise Rcvr. Antenna Gain: +60 dB Power to Receiver -75 dBm •Image Noise Receiver: Noise Floor @ 290K -174 dBm/Hz Margin: 4 dB Noise in 100 MHz BW + 80 dB •LO Wideband Phase Noise ETP = +55 dBm Receiver N.F. +10 dB SNR min +5 dB Path Losses: 200 dB Receiver Sensitivity -79 dBm F1 -1 F2 -1 F3 -1 F4 -1 Ftot = 1+ + + + +L 1 G1 G1G2 G1G2G3 How to increase Margin by 3dB ?

35 36

6 Selectivity •IF filter rejection at the adjacent channel •LO spurious in IF bandwidth •Phase noise of LO

RF Filter

IF Filter

Receiver Added Noise Receiver Thermal Noise

37 38

Selectivity Spurious Response RF Filter IF Filter

Ch Ch Ch Ch Ch Ch Ch Ch 1 2 3 n 1 2 3 n f f RF n × f RF IF

fIF freq fRF freq

f LO m × f LO

f freq LO 39 40

Spurious Reponses Spurious Response Chart

IF = n × RF + m × LO IF LO = m × + n RF RF IF LO y = , x = RF RF y = m × x + n m + n = order of spurious response

41 42

7 IntermodulationRejection •Nonlinearity and Spurious respone

1 IP3 output = (mW ) å 1 i IP 3i Gi+1Gi + 2 L Gn

43 44

Receiver Self-quieting Dynamic Range

P DR1dB = P1dB ,in - Pin,min out 1dB n × f LO 2 = P1dB ,in - Pnf - SNR min f IF1 f IF 2 Psf,out DR sf = Psf ,in - Pin,min f RF 2P + P = IIP 3 IM ,in - P SNR 3 in,min f LO1 f LO 2 P 2PIIP 3 + Pnf IM,out DP DP DP = - Pin,min n × f LO 2 Pin PI 3 Pnf DR IP3 sf Psf,in 2(PIIP 3 - Pnf ) DR1dB = - SNR f RF = f LO1 + f IF1 = n × f LO 2 P min Pin,min 1dB,in 3 45 46

Receiver Architectures Super-heterodyne Receiver –easy to design •Heterodyne Receiver –problem of image •Direct Conversion Receiver –problem of half IF •Low-IF Receiver •Image Reject Receiver

47 48

8 Heterodyne Receiver Problem of Image Signal •IF receiver a(t) = cos(wxt + m(t) +f)

b(t) = a(t) ×cos(wLOt +q )

= cos(wxt + m(t) +f) ×cos(wLOt +q ) RF b(t) 1 = cos((wx + wLO )t + m(t) +f +q ) A 2 D 1 a(t) IF + cos((w -w )t + m(t) +f -q ) 2 x LO LO1 LO2 if wx = wRF = wLO +wIF Þ OK

if wx = wimage = wLO -wIF Þ ?

49 50

Problem of Image Signal Problem of Image Signal •One solution: Image Rejection Filter H (w ) 1 •Image rejection ratio: IR RF = w H IR (wimage ) image H IR ( ) wRF w w -w image LO wRF w w w -w image LO wRF w

wIF Need wRF and wLO to be far away 51 52

Problem of Half IF How to Select IF? •Second order harmonic

(win +wLO ) - 2wLO = wIF •Spurious Response w + w w -w w •Image Rejection v.s. Channel Selection in LO -w = in LO = IF 2 LO 2 2 •Filter Availability

win wLO 0 wIF

win + wLO wIF 2 2

53 54

9 Image Rejection v.s. Channel Filter Availability f Selection Q = IF f CH BW •Example 1 Q = RF Image CH Channel RF BW Reject Select – fRF=1800MHz Filter Filter

– fIF=10MHz –Is this filter available? w w 0 image LO wRF wIF f fRF 1800 RF = 180 Q = ³ = 90 BW 20 f IF

w w LO 0 image wRF wIF

1780 1800

55 56

IF Selection

•Usually fRF/fIF<10 •Example 2 (Multistage IF)

– fRF=900MHz

– fIF1=250MHz

– fIF2=50MHz

– fIF3=10MHz

57 58

Summary of Heterodyne Receiver Direct Conversion Receivers

•Down converts RF to IF thus introduces •Easy to single chip image problem; avoid image signal by image •Channel Selection reject filter •DC offsets •I/Q Mismatch •As frequency / bandwidth increases, multi- •Even-Order stage IF is necessary Distortion •Not suitable for integration due to off-chip •Flick Noise:choose filters a suitable code •LO Leakage •Sensitive to external parasitic signal •Expensive and high power consumption

59 60

10 Direct Conversion Receiver Channel Selection

•Different placement of three block •Zero-IF Receiver

A D A D A D w 0 0

A cosw0 t D A D

A D

61 62

Comparison and trade-offs A D •Assume normalized input full range of +- •BPF 1V for the ADC –Good Q(>25), excellent dynamic range –Blocks unwanted channels •Input signal (signal after mixer) amplitude •AGC amplifier can range from ~<1 mV to just under 1V –Only need to maintain in-channel linearity –Example gains: 1, 4, 16, 64, 250, 1000 •fRF=1.8GHz, fIF=100MHz, fch=200KHz –Ensures vinADC ¼to full range •Input signal is wideband but the desired •ADC signal component is narrow band (IF) –6 bit is sufficient, this gives at least: •DSP in digital domain is omnipotent –16 quantization levels for ¼full range –Can do sub-sampling, =>low speed ADC: ADC speed >400KSPS

63 64

A D A •AGC amplifier D •AGC amplifier –Need excellent dynamic range and wand band –Need excellent dynamic range and wand band linearity linearity –Example gains: 1, 4, 16, 64, 250, 1000 –Example gains: 1, 4, 16, 64, 250, 1000 –Ensures v ¼to full range inBPF –Ensures v ¼to full range •BPF inBPF •ADC –Good Q(>25), but no need for high dynamic range –Blocks unwanted channels –6 bit is sufficient, this gives at least: •ADC –16 quantization levels for ¼full range –6 bit is sufficient, this gives at least: –But need high-speed ADC: ADC speed >200MSPS –16 quantization levels for ¼full range •BPF –Can do sub-sampling, => low speed ADC: ADC –Implement in DSP domain speed >400KSPS 65 66

11 A A D D •BPF •ADC –Good Q(>25), excellent dynamic range –ADC input ranges from sub mV to 1V –Blocks unwanted channels –High resolution is required –But ADC input ranges from sub mV to 1V –At least 16 bits to ensure 16 quantization levels for ¼ •ADC mV weak signals –Full IF band requires high-speed ADC: ADC speed –High resolution is required >200MSPS –At least 16 bits to ensure 16 quantization levels for ¼ mV weak signals –Currently 12 bit 200MSPS ADCs available, which gives 4 quantization levels for 1mV signals –Narrow band allows sub-sampling, =>low speed ADC: ADC speed >400KSPS •BPF –Currently 16 bit 1-5MSPS ADCs available –Implement in DSP domain •No AGC amplifier used •No AGC amplifier used 67 68

Mirror Signal Mirror Signal

•Upper sideband and lower sideband are •Upper sideband and lower sideband are not identical identical wLO wLO

0 0 -w wRF w -w wRF w

0 0 69 70

Mirror Signal Suppression QuadratureConversion •QuadratureDown Conversion a ( t ) = cos( w RF t + m ( t ) + f )

u i ( t ) = a ( t ) × cos( w LO t + q )

ui(t) vi(t) u q ( t ) = a ( t ) × sin( w LO t + q )

A 1 D I v i ( t ) = 2 cos( m ( t ) + f - q ) -1 v q ( t ) = 2 sin( m ( t ) + f - q ) 0 9 0 v ( t ) q = tan( - m ( t ) + q - f ) a(t) A v i ( t ) D Q æ v (t ) ö v (t) -1 ç q ÷ uq(t) q m ( t ) = - tan ç ÷ + q - f è v i (t ) ø

71 72

12 QuadratureDown Conversion DC Offset (Self-mixing)

wLO xoffset,LO(t) A D w c 0 0 capacitive coupling Saturates the following stages -w wRF w substrate coupling bondwirecoupling aLO(t)=ALOcos(w c+q) w c

xoffset,RF (t)

A D w c 0

0

w c 73 74

DC Offset (Self-mixing) DC Offset Cancellation

xoffset,LO (t) = Acrosstalk (ω)× aLO (t) ×aLO (t) = A (ω)× A cos(ω t + θ)× A cos(ω t + θ) crosstalk LO c LO c •Capacitive Coupling = 1 × A (ω) × A2 (1+ cos 2(ω t + θ)) 2 crosstalk LO c –Requires a large capacitor

xoffset,interferer (t) = Acrosstalk (ω) ×ainterferer (t)× ainterferer (t) = A (ω) × A2 cos 2 ω t + m(t) + φ crosstalk interferer ( c ) •Negative Feedback = 1 × A (ω) × A2 1+ cos2 ω t + m(t)+ φ -A 2 crosstalk interferer ( ( c )) –Nonlinear + level •TDMA Offset Cancellation DC Offset –Requires a large capacitor t - 75 76

I/Q Mismatch I/Q Mismatch

a(t) = Acos w t + m(t) +f ( c ) Phase error Phase & Gain Error æ e ö æ q ö xLO,I (t) = ç1+ ÷cosçwct + ÷ è 2 ø è 2 ø I x (t) BB,I æ e ö æ q ö xLO,I (t) xLO,Q (t) = ç1- ÷sinçwct - ÷ 0 2 2

9 è ø è ø 0 Phase & Gain Error A æ e ö æ q ö xLO ,Q (t) Gain error xBB,I (t) = ç1+ ÷cosçm(t) +f - ÷ a(t) 2 è 2 ø è 2 ø Q xBB,Q (t) A æ e ö æ q ö xBB,Q (t) = - ç1- ÷sinçm(t) +f + ÷ Phase & Gain Error 2 è 2 ø è 2 ø

77 78

13 x (t) = BB,I Even-Order Distortion æ e ö q æ e ö q aç1+ ÷cos -bç1+ ÷sin è 2 ø 2 è 2 ø 2

xBB ,Q (t) = 0 w æ e ö q æ e ö q c - aç1- ÷ sin + bç1- ÷ cos è 2 ø 2 è 2 ø 2 Direct feed through

wc 0

Direct feed through

79 80

Summary of Direct Conversion Low-IF Receivers Receiver •Possible way to implant digital IF •No need for imager reject filter •Low-IF cause image reject problem •Suitable for monolithic integration with baseband •DC offsets due to crosstalk of input ports of mixer •Even order IM direct feed through to baseband •Quadraturedown conversion suppresses mirror •I/Q mismatch due to mismatches in parasitics •Low power consumption attributed to less hardware

81 82

Mirror Signal Suppression (1) Low-IF Down Conversion Image Reject Receiver

Complex -w ωLO w Bandpass Filter

Complex BPF

I Q I Q LO1 LO2

83 84

14 Image Reject Receiver r(t) = ARF coswRFt + Aim coswimt •Hartley Architecture A A x (t) = RF sin(w - w )t + im sin(w - w )t A 2 LO RF 2 LO im A A A C = - RF sin(w - w )t + im sin(w - w )t 2 RF LO 2 LO im -90° A A x (t) = + RF cos(w -w )t - im cos(w -w )t sinωLOt C RF LO LO im

0 2 2 RF r(t) IF 9

input 0 w LO output ARF Aim cosω t xB (t) = cos(wLO -wRF )t + cos(wLO - wim )t LO 2 2

B xIFoutput (t) = ARF cos(wLO - wRF )t = ARF coswIFt

85 86

Graphical interpretation in spectral domain IQ error effect •Ideal IQ: image completely rejected •If signal and image not single tone, 90o w wLO -wLO 0 shift is not exact + j /2 xcos •Local oscillator’s sine and cosine not w -90o w X A(w) 0 0 matched in magnitude and phase w w - j /2 0 •90o phase shifter may have both gain and xsin phase error X (w) w B 0 w w 0 0 •All lead to incomplete image rejection

87 88

IPR Evaluation and IRR – LO error P A2 (A +e )2 - 2A (A + e) cosq + A2 A A A A im im LO LO LO LO LO RF LO im = 2 . 2 2 xA (t) = sin(wLO -wRF )t + sin(wLO -wRF )t P A (A + e ) + 2A (A +e )cosq + A 2 2 sig out RF LO LO LO LO Input image power ratio A A x (t) = (A +e ) RF cos[(w -w )t +q ]+ (A +e ) im cos[(w -w )t +q ] B LO 2 LO RF LO 2 LO im 2 2 (ALO +e ) - 2ALO (ALO + e) cosq + ALO IRR = 2 2 (ALO + e ) + 2ALO (ALO +e )cosq + ALO é ARF Aim ù xC (t) = ALO cos(wLO -wRF )t - cos(w LO -wim )t ëê 2 2 ûú DA DA (1+ )2 - 2(1+ )cosq +1 = A A (ALO + e )ARF ALO ARF DA 2 DA xsig (t) = cos[(wLO -wRF )t +q ]+ cos(wLO -wRF )t (1+ ) + 2(1+ ) cosq +1 2 2 A A

(A + e)A A A 2 x (t) = LO im cos[(w -w )t +q ]- LO im cos(w -w )t (DA ) +q 2 im 2 LO im 2 LO im IRR » A q in radians 89 4 90

15 Image Reject Receiver 90 degree phase shift •Hartley Architecture

sin ωt -90° sin (ωt - 90°) = - cosωt A R sin ωt - cosωt

sinωLOt C

t 0 RF r(t) IF 9

0 w input LO output + j cosω t + j /2 LO C

ω ´ ω = ω 0 0 0 B R - j / 2 -1 / 2 -1/ 2 1 - j = wIF 91 RC 92

•Check IEL for “polyphasefilter”or “image Gain Mismatch Due to RC errors: reject filter” –All suffer from error due to frequency DA (R + DR)(C + DC)w -1 1 mismatch if signal is not pure single tone = ¸ o 2 2 2 2 2 2 •For 90 phase shifter for LO, there are A 1+ (R + DR)(C + DC)w 1+ R C w several alternatives DR DC –Differential ring oscillators with even # of DA + 1 » R C ¸ delay stages A 2 + DR + DC 2 –D-FF based phase delays R C DR DC –Double-integrator based oscillators » + R C –Delay-locked loops –Phase-locked loops

93 94

x(t) = A cos w t +q + A cos w t +q Image Reject Receiver RF [ RF 1 ] im [ im 2 ]

ARF Aim xA (t) = sin[(wLO1 -wRF )t -q1 ]+ sin[(wLO1 -wim )t -q 2 ] •Weaver Architecture 2 2 ARF Aim A C = - sin[(w -w )t +q ]+ sin[(w -w )t -q ] 2 RF LO1 1 2 LO1 im 2

sinω t sinω t LO1 LO2 A A 0 RF 0 IF RF im 9 9 x (t) = cos (w - w )t -q + cos[(w - w )t -q ] 0 0 B [ LO1 RF 1 ] LO1 im 2 input wLO1 wLO2 output 2 2 cosω LO1t cosω t LO2 A A = RF cos[(w -w )t + q ]+ im cos[(w - w )t -q ] 2 RF LO1 1 2 LO1 im 2 B D

95 96

16 xC (t) = xA (t)sin w LO2t A Weaver Architecture = - RF cos[(w -w -w )t +q ] 4 RF LO1 LO2 1

Aim + cos[(w LO1 -wim -wLO2 )t -q 2 ] wLO w 4 -ω LO1 0 ωLO1

xD (t) = xB (t) cos wLO2t + j /2 XC (w) w w ωLO2 ARF X A (w) 0 0 = cos[(wRF - wLO1 - w LO2 )t +q1 ] w -ω 4 LO2 0 w - j / 2 0 Aim + cos[(wLO1 - wim - wLO2 )t -q2 ] 4 1/ 2 1/ 2 X (w ) w D X B (w) w A 0 0 RF w x (t) = x (t) - x (t) = cos[(w - w -w )t +q ] w -ω LO2 0 ωLO2 output D C 2 RF LO1 LO2 1 0 0

97 98

QuadratureWeaver Architecture Weaver Architecture 2wLO1 + 2wLO2 -wRF

w -ω LO1 0 ω LO1 ωRF

+ j /2 wRF -wLO1 -wLO2 XC (w) w w ω ω ωLO2 X A (w) 0 RF - LO1 0 w -ω LO2 0 w - j / 2 0

1/ 2 1/ 2 X (w ) w D X B (w) w I Q I Q 0 0 w LO1 LO2 w -ω LO2 0 ωLO2 0 0 w + 2w - w 99 LO1 LO 2 RF 100

Noise Figure Calculation E R E æ R ö s symbol s ç symbol ÷ Receiver Link Budget Analysis SNRmin = × Þ SNRmin (dB) = (dB) +10 logç ÷ N0 BW N0 è BW ø SNR SNR •Noise Figure Calculation in min RF input NF Baseband •IP3 Calculation Input noise power : Pnf Input referred noise floor •Image Rejection Calculation receiver = -174dBm +10log BW = -174dBm +10log BW + NF •Frequency Planning +

Standard Bandwidth10log(BW) Sensitivity(dBm) Noise Floor (dBm)SNRin(dB) NF(dB) SNRmin(dB) DECT 1.70E+06 62.30 -83.00 -111.50 28.50 18.20 10.3 GSM 2.00E+05 53.01 -102.00 -120.79 18.79 9.79 9 WLAN 2.00E+06 63.01 -80.00 -110.79 30.79 15.69 15.1

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17 IP3 Calculation Image Rejection Calculation Input referred npoise In dBm 2(PIIP 3 - Pnf ) DR sf = - SNR min PImage 3 In dB 3 IRRrequired P = (DR + SNR )+ P P IIP3 2 sf min nf desired SNR P-1dB » PIIP3 -10 min

Standard DR SFDR IIP3 Pmax Bandwidth10log(BW)Sensitivity(dBm) Bluetooth 50.00 36.57 -10.00 -20.00 1.00E+06 60.00 -70.00 f fRF IF fLO GSM 87.00 61.67 -5.00 -15.00 2.00E+05 53.01 -102.00 WLAN 76.00 52.30 6.00 -4.00 2.00E+06 63.01 -80.00 IRR required = Pimage - Pdesired + SNR min

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