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CIRFCircuit Intégré Radio Fréquence

Lecture I

•Introduction•Baseband Pulse Transmission•Digital Passband Transmission•Circuit Non-idealities Effect

Hassan AboushadyUniversité Paris VI

CIRFCircuit Intégré Radio Fréquence

Lecture I

•Introduction•Baseband Pulse Transmission•Digital Passband Transmission•Circuit Non-idealities Effect

Hassan AboushadyUniversité Paris VI

M.H. Perrott MIT OCW M.H. Perrott MIT OCW

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M.H. Perrott MIT OCW M.H. Perrott MIT OCW

M.H. Perrott MIT OCW

Multidisciplinarity of radio design

H. Aboushady University of Paris VI

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• S. Haykin, “Communication Systems”, Wiley 1994.

• B. Razavi, “RF Microelectronics”, Prentice Hall, 1997.

• M. Perrott, “High Speed Communication Circuits and

Systems”, M.I.T.OpenCourseWare, http://ocw.mit.edu/,

Massachusetts Institute of Technology, 2003.

• D. Yee, “ A Design methodology for highly-integrated

low-power receivers for wireless communications”,

http://bwrc.eecs.berkeley.edu/, Ph.D. University of

California at berkeley, 2001.

References

H. Aboushady University of Paris VI

CIRFCircuit Intégré Radio Fréquence

Lecture I

•Introduction•Baseband Pulse Transmission•Digital Passband Transmission•Circuit Non-idealities Effect

Hassan AboushadyUniversity of Paris VI

H. Aboushady University of Paris VI

Digital Baseband Transmission

ISI : InterSymbol Interference

Channel Noise

Detecting a pulse transmitted over a channel that is corrupted by additive noise.

The result of data transmission over a non-ideal channel is that each received pulse is affected by adjacent pulses.

Major sources of errors in the detection of transmitted digital data:

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Matched Filter

Linear Receiver Model

• Filter Requirements, h(t) :• Make the instantaneous power in the output signal g0(t) , measured at time t=T, as large as possible compared with the average power of the output noise, n(t).

)()()( 0 tntgty +=Tttwtgtx ≤≤+= 0,)()()( )(th

• g(t) : transmitted pulse signal, binary symbol ‘1’ or ‘0’.• w(t) : channel noise, sample function of a white noise process of zero mean and power spectral density N0/2.

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Matched Filter for Rectangular Pulse

)()( tTgkthopt −=

g(t)

T

g(t)

tT

h(t) = g(T-t)

tT

g(-t)

t

h(t) for a rectangular Pulse:

Filter Output g(t)*h(t):

Implementation:

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Error Rate due to Noise

In the interval , the received signal:bTt ≤≤0

+−++

=sent was'0' symbol,)(

sent was'1' symbol,)()(

twA

twAtx

Tb is the bit duration, A is the transmitted pulse amplitude

• The receiver has prior knowledge of the pulse shape but not its polarity.

• There are two possible kinds of error to be considered:(1) Symbol ‘1’ is chosen when a ‘0’ was transmitted.(2) Symbol ‘0’ is chosen when a ‘1’ was transmitted.

x(t)

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PDF: Probability Density Function

Normalized PDF µµµµY= 0 and σσσσY=1

−−=2

2

2

)(exp

2

1)(

Y

Y

Y

Y

yyf

σµ

πσ

• Gaussian Distribution:

• Symbol ‘0’ was sent:

dyyf

yPP

Y

e

∫∞

=

>=

λ

λ

)0(

sent) was'0' symbol(0

b

YY T

NA

2, 02 =−= σµ

• Symbol ‘1’ was sent:

dyyf

yPP

Y

e

∫∞−

=

<=λ

λ

)1(

sent) was'1' symbol(0

b

YY T

NA

2, 02 =+= σµ

H. Aboushady University of Paris VI

BER in a PCM receiver

1100 eee PpPpP +=

10 ee PP =

2

110 == pp

10 eee PPP ==

=

02

1

N

EerfcP b

e

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CIRFCircuit Intégré Radio Fréquence

Lecture I

•Introduction•Baseband Pulse Transmission•Digital Bandpass Transmission•Circuit Non-idealities Effect

Hassan AboushadyUniversité Paris VI

• In wired systems, coaxial lines exhibit superior shielding

at higher frequencies

• In wireless systems, the antenna size should be a

significant fraction of the wavelength to achieve a

reasonable gain.

• Communication must occur in a certain part of the

spectrum because of FCC regulations.

• Modulation allows simpler detection at the receive end in

the presence of non-idealities in the communication

channel.

Why Modulation?

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• mi : one symbol every T seconds

• Symbols belong to an alphabet of M symbols: m1, m2, …, mM

MmPp

mPmPmP

ii

M

1)(

)(...)()( 21

==

===• Message output probability:

• Example: Quaternary PCM, 4 symbols: 00, 01, 10, 11

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Message Source

MidttsET

ii ...,,2,1,)(0

2 == ∫• Energy of si(t) :

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Transmitter

• Signal Transmission Encoder: produces a vector si made up of Nreal elements, where N M .• Modulator: constructs a distinct signal si(t) representing mi of duration T .

≤

• si(t) is real valued and transmitted every T seconds.

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Examples of Transmitted signals: si(t)

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• The modulator performs a step change in the amplitude, phase or frequency of the sinusoidal carrier

• ASK: Amplitude Shift Keying

• PSK: Phase Shift Keying

• FSK: Frequency Shift Keying

Special case: Symbol Duration T = Bit Duration, Tb

=≤≤

+=Mi

Tttwtstx i ,...,2,1

0),()()(

• Received signal x(t) :

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Communication Channel

• Two Assumptions:•The channel is linear (no distortion).• si(t) is perturbed by an Additive, zero-mean, stationnary, White, Gaussian Noise process (AWGN).

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Receiver

m̂

•TASK: observe received signal, x(t), for a duration T and make a best estimate of transmitted symbol, mi .

•Detector: produces observation vector x . •Signal Transmission Decoder: estimates using x, the modulation format and P(mi) .

• The requirement is to design a receiver so as to minimize the average probability of symbol error:

∑=

≠=M

iiie mPmmPP

1

)()ˆ(

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Coherent and Non-Coherent Detection

• Coherent Detection: - The receiver is time synchronized with the transmitter.- The receiver knows the instants of time when the modulator changes state.- The receiver is phase-locked to the transmitter.

• Non-Coherent Detection:- No phase synchronism between transmitter and receiver.

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H. Aboushady University of Paris VI

Coherent Binary PSK:

b

T

Edtttssb

== ∫ )()( 1

0

111 φ

• M=2, N=1

• One basis function:

• Signal constellation consists of two message points:

)2cos(2

)(1 tfT

Ets c

b

b π= )2cos(2

)(2 ππ += tfT

Ets c

b

b

bTt ≤≤0

• To ensure that each transmitted bit contains an integral number of cycles of the carrier wave, fc =nc/Tb, for some fixed integer nc.

bc

b

TttfT

t ≤≤= 0,)2cos(2

)(1 πφ

b

T

Edtttssb

−== ∫ )()( 1

0

221 φ

H. Aboushady University of Paris VI

Generation and Detection of Coherent Binary PSK

• Assuming white Gaussian Noise with PSD = N0/2 ,

The Bit Error Rate for coherent binary PSK is:

=

02

1

N

EerfcP b

e

Binary PSK Transmitter

Coherent Binary PSK Receiver

H. Aboushady University of Paris VI

Coherent QPSK:

• M=4, N=2:

• Two basis function:

≤≤

−+=elsewhere , 0

0,4

)12(2cos2

)( TtitfT

Ets c

i

ππ

)4

2cos(2

)(1

ππ += tfT

Ets c

TttfT

t c ≤≤= 0,)2cos(2

)(1 πφ

TttfT

t c ≤≤= 0,)2sin(2

)(2 πφ

)4

32cos(2

)(2

ππ += tfT

Ets c

)4

52cos(2

)(3

ππ += tfT

Ets c

)4

72cos(2

)(4

ππ += tfT

Ets c

H. Aboushady University of Paris VI

Constellation Diagram of Coherent QPSK System

=

0

2/

2

1

N

EerfcPe

=

02

1

N

EerfcP b

e

• Assuming AWGN with PSD = N0/2 ,The Bit Error Rate for coherent QPSK is:

with E = 2 Eb

Identical to BPSK

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QPSK waveform: 01101000

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Generation and Detection of Coherent QPSK Signals

QPSK Transmitter

Coherent QPSK Receiver

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Power Spectra of BPSK ,QPSK and M-ary PSK

QPSK

BPSK

8-PSK

• Symbol Duration: MTT b 2log=

• Power Spectral Density of an M-ary PSK signal: )log(sinclog2

)(sinc2)(

22

2

2

MfTME

TfEfS

bb

B

=

=

)(sinc2)( 2 fTEfS bbB =

)2(sinc4)( 2 fTEfS bbB =

)3(sinc6)( 2 fTEfS bbB =

CIRFCircuit Intégré Radio Fréquence

Lecture I

•Introduction•Baseband Pulse Transmission•Digital Passband Transmission•Circuit Non-idealities Effect

Hassan AboushadyUniversité Paris VI

9

Binary Dataantenna

011011Multiplexer

Decision Device

Threshold = 0

Threshold = 0

Decision Device

T

T

path I

path Q

∫T

dt0

∫T

dt0

)2cos(2

)(1 tfT

t cπφ =

)2sin(2

)(1 tfT

t cπφ =

I

Q

QPSK Constellation Diagram

00 10

1101

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QPSK Receiver

Circuit Noise (Thermal, 1/f)

Gain Mismatch

Phase Mismatch

DC Offset

Frequency Offset

Local Oscillator phase noise

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Receiver Circuit Non-Idealities

Circuit Noise:

• Thermal Noise• Resistors• Transistors

• Flicker (1/f) Noise• MOS transistors

I

Q

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Circuit Noise

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Q

I

A(1-α/2)

A(1+α/2)

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Gain Mismatch

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-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Q

I

H. Aboushady University of Paris VI

Phase Mismatch

offset

offset

I

Q

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Q

I

H. Aboushady University of Paris VI

DC Offset

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Q

I

H. Aboushady University of Paris VI

Frequency Offset

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Local Oscillator Phase Noise

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H. Aboushady University of Paris VI

Reciprocal Mixing

CIRFCircuit Intégré Radio Fréquence

Lecture II

•Introduction•Negative Resistance Oscillators•Integrated Passive Components•Phase Noise in Local Oscillators

Hassan AboushadyUniversity of Paris VI

CIRFCircuit Intégré Radio Fréquence

Lecture II

•Introduction•Negative Resistance Oscillators•Integrated Passive Components•Phase Noise in Local Oscillators

Hassan AboushadyUniversity of Paris VI

• M. Perrott, “High Speed Communication Circuits and

Systems”, M.I.T. OpenCourseWare, http://ocw.mit.edu/,

Massachusetts Institute of Technology, 2003.

• T. Lee, “The Design of CMOS Radio-Frequency Integrated

Circuits”, Cambridge University Press, 2004.

• B. Razavi, “Design of Analog CMOS Integrated Circuits”,

Mc Graw-Hill, 2001.

References

H. Aboushady University of Paris VI

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Binary Dataantenna

011011Multiplexer

Decision Device

Threshold = 0

Threshold = 0

Decision Device

T

T

path I

path Q

∫T

dt0

∫T

dt0

)2cos(2

)(1 tfT

t cπφ =

)2sin(2

)(2 tfT

t cπφ =

I

Q

QPSK Constellation Diagram

00 10

1101

H. Aboushady University of Paris VI

QPSK Receiver

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CIRFCircuit Intégré Radio Fréquence

Lecture II

•Introduction•Negative Resistance Oscillators•Integrated Passive Components•Phase Noise in Local Oscillators

Hassan AboushadyUniversity of Paris VI

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CIRFCircuit Intégré Radio Fréquence

Lecture II

•Introduction•Negative Resistance Oscillators•Integrated Passive Components•Phase Noise in Local Oscillators

Hassan AboushadyUniversity of Paris VI

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Vertical Metal Capacitors

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Lateral Metal Capacitors

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Vertical Mesh Metal Capacitors

K.T. Christensen,”Low Power RF Filtering for CMOS Transceivers”, Ph.D. Denmark Technical

University, 2001, http://phd.dtv.dk/2001/oersted/k_t_christensen.pdf

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22

s

CIRFCircuit Intégré Radio Fréquence

Lecture II

•Introduction•Negative Resistance Oscillators•Integrated Passive Components•Phase Noise in Local Oscillators

Hassan AboushadyUniversity of Paris VI

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Binary Dataantenna

011011Multiplexer

Decision Device

Threshold = 0

Threshold = 0

Decision Device

T

T

path I

path Q

∫T

dt0

∫T

dt0

)2cos(2

)(1 tfT

t cπφ =

)2sin(2

)(2 tfT

t cπφ =

I

Q

QPSK Constellation Diagram

00 10

1101

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QPSK Receiver

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Local Oscillator Phase Noise

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Reciprocal Mixing Phase Noise in Oscillators

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