Special Topics in Electronics Engineering Emad Hegazi Professor, ECE Communication Circuits Research...

Special Topics in Electronics Engineering

Emad HegaziProfessor, ECE

Communication Circuits Research Grouphttp://www.iclasu.edu.eg/ehgroup

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http://www.iclasu.edu.eg/ehgroup

17!

Es/No or Eb/No=?

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Noise Figure Calculation

receiver

BasebandRF input

nfP

minSNR

NFinSNR

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

BW

RdB

NE

dBSNRBW

R

NE

SNR symbolssymbols log10)()(0

min0

min

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IP3 Calculation

10

23

3)(2

31

min3

min3

IIPdB

nfsfIIP

nfIIPsf

PP

PSNRDRP

SNRPP

DR

Standard DR SFDR IIP3 Pmax Bandwidth 10log(BW) Sensitivity(dBm)Bluetooth 50.00 36.57 -10.00 -20.00 1.00E+06 60.00 -70.00GSM 87.00 61.67 -5.00 -15.00 2.00E+05 53.01 -102.00WLAN 76.00 52.30 6.00 -4.00 2.00E+06 63.01 -80.00

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Simplified Transceiver Architecture

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Role of a Receiver

090

AD

AD

HPMX-2007

The lkhefw wlkhq wilehrwejklh wajkhrqwilu wae.esjlkh qwh wlh

lihewrw wklhjr qlih qilh q q3wih qwejklh wajkhrqwilu wae.esjlkh qwh wlh



lihewrw wklhjr qlih qilh q q3wih qwklhjr qlih qilh q q3wih qwejklh wajkhrqwilu wae.esjlkh qwh wlh


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The lkhefw wlkhq wilehrwejklh wajkhrqwilu wae.esjlkh qwh wlh lihewrw

wklhjr qlih qilh q q3wih qwejklh wajkhrqwilu wae.esjlkh qwh wlh lihewrw



wklhjr qlih qilh q q3wih qwklhjr qlih qilh q q3wih qwejklh wajkhrqwilu wae.esjlkh qwh wlh lihewrw









lihewrw wklhjr qlih qilh q q3wih qwejklh wajkhrqwilu wae.

Power Supply

uP/DSP

Low Noise Amplifier

Mixer

Oscillator

Baseband Processor

De-Modulator

bias

I Data

Q Data

1 .amplify received signal with min. added

noise

2 .shift to lower frequency (cost and/or

performance)

3 .LO for down conversion

4 .discard carrier and recover data

Information

bias bias

Antenna

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7

Can we use a BPF for channel selection?

• The adjacent channels are always considered as interferers. These interferes could affect the reception of the signal.

• It is important to filter the unnecessary channels • Example:

It is desired to filter the alternate channel by 35 dB using an LC-BPF. Determine the quality factor of the tank.

Solution:

M. El-Nozahi

B. Razavi: RF Microelectronics, 2nd Edition

Too large cannot be achieved

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Band Selection

• The BPF before the LNA is used as a band select filter– Specification is relaxed compared to the case where it is used as a

channel select filter– It has a constant frequency response and does not need to be

tunable

• The BPF is implemented using:– SAW technology for frequencies below 10 GHZ– MEMS technology for mm-wave frequencies

M. El-Nozahi

B. Razavi: RF Microelectronics, 2nd EditionDesired Band

f

Band Select filter

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9

Band Selection

• TX-RX feedthrough can limit the performance of the receiver• Typically the received signal is in the order of -70 dBm• Feedthrough may saturate the BB blocks because of the high gain• Is an issue in full duplex transceivers• Design Targets:

– LNA must tolerate this high input level– A BPF is usually included at the output of LNA provide additional filtering

M. El-Nozahi


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Band Selection

• Band select filters are usually implemented in a duplexer• Single antenna transceivers use a duplexer to isolate

between TX and RX• Duplexers are two BPF, one for RX and the other for TX

M. El-Nozahi


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Channel Selection Remarks

• Channel selection cannot be done before the LNA because:– It is hard to find a BPF with large quality factor, and achieving a very small

loss– Having a tunable BPF with high quality factor is hard to obtained

• Usually, there are two steps to select a channel:

– Band selection: In which the entire band is selected. This step usually comes before the LNA.

– Channel selection: In which the desired channel is selected. This step is usually done after the first mixer.

M. El-Nozahi

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Superheterodyne Receiver

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Example: AM Radio

• AM radio band: 530 to 1610 KHz• BW/2 = (1610-530)/2=1080/2=540, in band• IF has to be lower. Commonly: 455kHz• Image can be in AM band• If LO is on low side, LO tuning range is:

– (530 to 1610) – 455 = (75 to 1155)– LO lowest to highest is a factor of 15.4

• If LO is on high side, LO tuning range is:– (530 to 1610) + 455 = (985 to 2065)– LO lowest to highest is a factor of 2.01

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14

Typical Superheterodyne Digital Receiver

Prof. E Sanchez-Sinencio RF course slides

Advantage Disadvantages

Good selectivity High complexity

Good sensitivity High power consumption

Image problem

External components

Not suitable for multi-standard

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15

The Image Problem

• The image could be another user or standard• The image must be filtered out before going the mixer• Frequency planning is key


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Image Rejection Calculation

SNRmin

fIF

IRrequired

fRFfLO

Pdesired

PImage

minSNRPPIR desiredimagerequired

)all in dB’s(

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Mixer = Multiplying up/down conversion

• Frequency translation device• Ideal mixer:

• Doesn’t “mix”; it multiplies

A

B

AB

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Super-heterodyne Receiver

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Selection of IF

• If IF is large, – better separation between RF and image– better image rejection– easier image rejection filter design– More stages of down conversion

• Other IF selection criteria– Select IF so that image freq is outside of RF

band– IF >= (RF BW)/2

• Sometime may not be possible, if (RF BW)/2 is within RF Band

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• For each channel assignment, there are two choices of LO freq that meets the requirement |RF–LO|=IF.

• Q: should LO > RF, or LO < RF??

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Image problem converting to IF

A1cos(wRFt)

A has desired signal at wIF

plus an interference at wIM

A2cos(wIMt)

B is at wLO

And:

wRF - wLO = wLO - wIM = wIF

Both converted to IF,Can’t be cleaned once corrupted

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Image Problem

)()(cos2

)()(cos2

)cos())(cos()()()(

)cos()(

message is )();)(cos()(

tmtAB

tmtAB

ttmtABtBtAtC

tBtB

tmtmtAtA

LOx

LOx

LOx

LO

x

?

IFLOimagex

IFLORFx

if

OKif

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Problem of Image Signal

IF

RFimage LO

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• Solution: Image Rejection Filter

RFimage LO

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25

The Image Problem

• Image Reject filter versus channel selection:

• Larger IF frequencies requires channel select filter with higher Q

M. El-Nozahi


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26

Dual-IF Heterodyne Receiver

• Channel selection is done in two stages, hence relaxing the specification for each stage

• Secondary image problem– To avoid the problem, the second IF frequency is set to zero

• Is it possible to have a zero IF?

M. El-Nozahi

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27

Down Conversion to IF

M. El-Nozahi

AM modulation:

FM/ Digital ..etc . modulations:

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High Q Alternatives

• What is really needed is not really a filter.• A cancellation scheme to reject noise is

good enough

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Cosine wave

High Q Alternatives

• What if we use a sine wave instead

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j

-j

j

-j

Complex Signal Representation

Niknejad and Shana’a

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Orthogonality of I and Q


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Orthogonality

Spring2014

Des

ign

of R

F C

ircui

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Sys

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s

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33

Image Reject Receivers-I

– What is a shift by 90o?

– The 90o phase shift is also called Hilbert transform

M. El-Nozahi

ffc-fc

𝐴2

𝐴2

Re

Im

f

fc

-fc

Re

Im

− 𝑗𝐴2

𝑗𝐴2

𝑋 90(𝜔)=𝑋 (𝜔) [− 𝑗 𝑠𝑔𝑛(𝜔) ]

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Hilbert transform:

• A 90o phase shift results in:– Rotating positive frequency components CW by 90o

– Rotating negative frequency components CCW by 90o

• Multiplication by +j rotates all frequency components CCW by 90o.

• Multiplication by -j rotates all frequency components CW by 90o.

• Note that for DC frequencies these transformations do not have any meaning

M. El-Nozahi

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Hilbert transform

• Assume I(t) is shifted by 90o to produce Q(t). Find I(t)+jQ(t).

M. El-Nozahi

ffc-fc

Re{I}

Im{I}

f

fc

-fc

Re{Q}

Im{Q}

f

fc

-fc

Re{jQ}

Im{jQ} Im{I+jQ}

ffc-fc

Re{I+jQ}Spring2014

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36

Image Reject Receivers

• Idea: From the previous example it seems that one could remove the image with the help of quadrature components.

M. El-Nozahi

ffs-fs

Re{I}

Im{I}

-fi fi

f

Re{I}Im{I}{

-fIF fIF

fLO

f

Re{Q}Im{Q}

-fIF fIF

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Hartley Image Reject Architecture

• A Hilbert transform is used to cancel the image• I&Q (quadrature) signals are generated for image rejection.• The generation of the 90o could be achieved using RC phase shifter each providing 45o phase shift (narrow band solution)

M. El-Nozahi


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• Still in the BB we must generate another I&Q for digital demodulation

• Drawbacks:– Mismatch between the two path will result in finite image rejection– The RC solution can be used for narrow-band architectures. Wideband

architecture will result in degraded performance for the image rejection (IRR)– Typical values for IRR is lower than 35 dB.

M. El-Nozahi


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Implementing the Phase ShiftHartley Architecture with simple 90 deg phase shiftor

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IRRt

AAt

AAtx imLO

imLORFLO

RFLOA )sin(

2)sin(

2)(

)(cos2

)()(cos2

)()( tA

AtA

Atx imLOim

LORFLORF

LOB

)cos(2

)cos(2

)(

t

At

AAtx imLO

imRFLO

RFLOC

cos2

cos2

)()( t

AAt

AAtx RFLO

RFLORFLO

RFLOsig

cos2

cos2

)()( t

AAt

AAtx imLO

imLOimLO

imLOim

cos)(2)(

cos)(2)(.

22

22

2

2

LOLOLOLO

LOLOLOLO

RF

im

outsig

im

AAAA

AAAA

A

A

P

P

Input image power ratio

44

4

4

)cos1)((2

cos)(2)(

cos)(2)(

22

22

2

222

2

2

22

22

AA

AIRR

A

A

A

AA

AAAA

AAAAIRR

LO

LO

LO

LOLO

LOLOLOLO

LOLOLOLO

1

1

1

1222222

CRCCRR

CCRR

A

A

2

1

2

C

C

R

RC

CR

RC

CR

R

A

A

Gain Mismatch due to R, C errors

At w = 1/RC:

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Weaver Image Reject Architecture

• Hilbert transform is obtained using another quadrature (complex) mixing stage

• Advantages compared to Hartley:– Better accuracy in generating the additional 90o phase shift– IRR is limited to 40 dB, which is higher than Hartley architecture

• Disadvantages:– Secondary image problem

M. El-Nozahi


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Direct Conversion Receiver

• A single step down conversion is used. The output frequency is at DC

M. El-Nozahi

B. Razavi: RF Microelectronics, 2nd EditionAdvantages Disadvantages

No image problem LO leakage

Less complex / low power consumption

DC offset

Channel selection is done with a LPF Even order distortion

Effect of mixer spurs are reduced Flicker noise

IQ mismatch

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LO Leakage

– The LO signal can be leaked to the antenna by the capacitive coupling or substrate

– For singled ended Los, the LO leakage can reach -60 dBm– Differential LO architectures have lower LO leakage (better than -

100 dBm)

M. El-Nozahi


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• DC Offset:– The leaked LO signal can go through the antenna, LNA and down

converted – Because of the LO signal and its feedthrough signal carry the same

frequency, a DC offset is produced (this phenomena is called LO self mixing).

– BB blocks usually have high again, hence the LO self mixing may saturate the receiver– HPF are not common because they require a very low cut-off frequency

(large components, slow settling)

M. El-Nozahi


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Even Order Distortion

M. El-Nozahi


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• Flicker Noise:

• For 802.11g the channel bandwidth is 10MHz. With a noise corner frequency of 200kHz• For GSM, the channel bandwidth is 100 kHz and therefore a

large portion of noise appears due to flicker noiseM. El-Nozahi


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• IQ mismatch:– mismatch in I and Q path affects SNR of received signals– Mismatch effects are more dominate at high frequencies. Reducing the

frequency at which the I and Q signal are generated enhances the SNR– Digital calibration is used to correct these mismatches

M. El-Nozahi

Amplitude mismatch:

Phase mismatch:

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Low-IF Receiver

• Has all the advantages of direct conversion receivers• More difficult image rejection requirements• Minimum IF frequency is channel bandwidth• DC offset is outside the signal bandwidth

Complex Filter

LargeRequires matchingPower hungry

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ADC

ADC

PGA

PGA

LNA

RFPLL

DIG

ITA

LF

ILT

ER

100 kHz

I

Q

sin cos

RFSAW

sin cos

270 kS/s

925-960MHz

925.1 - 960.1MHz

Low IF receiver

-Quadrature RF down conversion required

-Require higher performance ADC-Additional mixer

-Slower RF PLL settling-Even order distortion still

problem-Low freq IF filters require large

chip area

+Eliminate IF SAW, IF PLL and image filtering

+Integration

+Relaxes image rejection requirements

+Avoids DC problems, relaxes 1/f noise problem

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Low-IF Down Conversion

LOω

Complex BPF

Mirror signal, needs removal

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Mirror Signal Suppression

ComplexBandpass

Filter

I Q I Q

LO1 LO2

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Complex Mixing- Real LO

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Complex Mixing-Complex LO

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Complex Mixing

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Bluetooth Receiver


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Little image problemNo IQ filter@ IF

PGA

PGA

LNA

RFSAW ADC

ADC

DIG

ITA

LF

ILT

ER

I

Q

RFPLL

sin cos

270 kS/s

925-960MHz

925 - 960MHz

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LO is at same frequency as RF1/f noise here can end up in channel

Self mixing cause DC problem

+Eliminate IF SAW, IF PLL and image filtering+ Integration+ easier image problem


-DC problem -Typically requires offset or

2x LO to avoid coupling

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DC Offset (Self-mixing)

AD w c

aLO(t)=ALOcos( w c+q)

0

w c

)(, tx LOoffset

capacitive couplingsubstrate couplingbondwire coupling

Saturates the following stages

AD w c 0

w c

)(, tx RFoffset

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θωω

θωθωω

ω

tAA

tAtAA

tataAtx

cLOcrosstalk

cLOcLOcrosstalk

LOLOcrosstalkLOoffset

2cos1)(

coscos)(

)()()()(

221

,

φ)(ω2cos1)ω(

φ)(ωcos)ω(

)()()ω()(

2interferer2

1

22interferer

interfererinterfererinterferer,

tmtAA

tmtAA

tataAtx

ccrosstalk

ccrosstalk

crosstalkoffset

level

DC Offset

+

-

t

φ)(ω2cos1)ω(

φ)(ωcos)ω(

)()()ω()(

2interferer2

1

22interferer


tmtAA

tmtAA

tataAtx

ccrosstalk

ccrosstalk

crosstalkoffset Spring2014

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DC Offset Cancellation

• Capacitive Coupling– Requires a large capacitor

• Negative Feedback– Nonlinear -A

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1/f noise effect

• CMOS transistors has significant 1/f noise at low to DC frequency

• Significantly noise performance of direct conversion receivers

Receive signal1/f noise

f

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Even-Order Distortion

c

0c

0

Direct feed through

Direct feed through

Interferers

y(t) = a1 x(t) + a2 x2(t)

Dw

Dw

a2 A1A2 cos(Dw)

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Mirror Signal

• Upper sideband and lower sideband are identical

RF

LO

0

0

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Mirror Signal • Upper sideband and lower sideband are not

identical

RF

LO

0

0

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• Quadrature Down Conversion

AD

090

AD

a(t)

ui(t)

uq(t)

vi(t)

vq(t)

I

Q Spring2014

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Quadrature Conversion

)(

)(tan)(

))(tan()(

)(

))(sin()(

))(cos()(

)sin()()(

)cos()()(

))(cos()(

1

21

21

tv

tvtm

tmtv

tv

tmtv

tmtv

ttatu

ttatu

tmtta

i

q

i

q

q

i

LOq

LOi

RF

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Quadrature Down Conversion

RF

LO

0

0

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I/Q Mismatch

090

I

Q

Phase & Gain Error

Phase & Gain Error

Phase & Gain Error

)(, tx ILO

)(, tx QLO

)(, tx IBB

)(, tx QBB

a(t)

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I/Q Mismatch due to LO errors

2)(sin

21

2)(

2)(cos

21

2)(

2sin

21)(

2cos

21)(

)(cos)(

,

,

,

,

tmA

tx

tmA

tx

ttx

ttx

tmtAta

QBB

IBB

cQLO

cILO

c

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2

2ˆ

ˆ

2222

1

)(

)()(ˆ Find :Exercise

unbiased. is )(ˆ Hence,

)())(ˆ( Clearly,

0)(,))((,))(( and

0)( ,0)( Suppose

)2/)(cos()2/1(

)2/)(sin()2/1(tan)(ˆ

tm

tmtmEσ

tm

tmtmE

EσEσE

EE

tm

tmtm

def

m

m

ε

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Use of I/Q down conversion recovers the nonsymmetrical receive signal spectrumBut port isolation becomes more challengingSelfmixing and even order distortion may affect both channels and affect each other, causing additional I/Q mismatch

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090

a(t)

A/D

A/D

Base Band

DSP

Phase and gain mismatchcompensation

DC and 1/fcancellation

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Summary of Direct Conversion Receiver

• No need for imager reject filter• Suitable for monolithic integration with baseband • DC offsets due to crosstalk of input ports of mixer• Even order IM direct feed through to baseband• Quadrature down conversion suppresses mirror• I/Q mismatch due to mismatches in parasitics• Low power consumption attributes to less hardware

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Balun

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Texas Instruments 2006

Phase Noise

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Texas Instruments 2006

Trsnmitter Paradigms

• Signal is strong.• We need to make sure efficient delivery

of power to the antenna.• Spectral content should be contained to

its specified limits.• Linearity matters if modulation is linear. Spring

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Transmit Specifications• Transmit spectrum mask

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Transmitter Specifications

20 20

4040

Adjacent channel

alternate adjacent channel

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Transmitter Architectures

• Direct Conversion Transmitter• Two-step Conversion Transmitter• Offset PLL Transmitter

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Direct-conversion transmitter

090

I

QwLO

Pros: less spurious synthesizedCons: more LO pulling

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Direct-conversion transmitter with offset LO

090

I

Q

wLOw1

w2

Pros: less LO pullingCons: more spurious synthesized

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090

I

Q

cosw1tcosw2t

w1+w2

Pros: less LO pulling superior IQ matching

Cons: required high-Q bandpass filter

Two-step transmitter

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Offset PLL Transmitter

090

I

Q

cosw1tPD/LPF VCO

1/NSpring2014

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Simplified Transceiver Architecture

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90

Role of a Receiver

090

AD

AD

HPMX-2007







lihewrw wklhjr qlih qilh q q3wih q

The lkhefw wlkhq wilehrwejklh wajkhrqwilu wae.esjlkh qwh wlh lihewrw













lihewrw wklhjr qlih qilh q q3wih qwejklh wajkhrqwilu wae.

Power Supply

uP/DSP

Low Noise Amplifier

Mixer

Oscillator

Baseband Processor

De-Modulator

bias

I Data

Q Data

1 .amplify received signal with min. added

noise

2 .shift to lower frequency (cost and/or

performance)

3 .LO for down conversion

4 .discard carrier and recover data

Information

bias bias

Antenna

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91

92

Can we use a BPF for channel selection?

• The adjacent channels are always considered as interferers. These interferes could affect the reception of the signal.

• It is important to filter the unnecessary channels • Example:

It is desired to filter the alternate channel by 35 dB using an LC-BPF. Determine the quality factor of the tank.

Solution:


Too large cannot be achieved

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93

Band Selection

• The BPF before the LNA is used as a band select filter– Specification is relaxed compared to the case where it is used as a

channel select filter– It has a constant frequency response and does not need to be

tunable

• The BPF is implemented using:– SAW technology for frequencies below 10 GHZ– MEMS technology for mm-wave frequencies

B. Razavi: RF Microelectronics, 2nd EditionDesired Band

f

Band Select filter

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94

Band Selection

• TX-RX feedthrough can limit the performance of the receiver• Typically the received signal is in the order of -70 dBm• Feedthrough may saturate the BB blocks because of the high gain• Is an issue in full duplex transceivers• Design Targets:

– LNA must tolerate this high input level– A BPF is usually included at the output of LNA provide additional filtering


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95

Band Selection

• Band select filters are usually implemented in a duplexer• Single antenna transceivers use a duplexer to isolate

between TX and RX• Duplexers are two BPF, one for RX and the other for TX


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96

Channel Selection Remarks

• Channel selection cannot be done before the LNA because:– It is hard to find a BPF with large quality factor, and achieving a very small

loss– Having a tunable BPF with high quality factor is hard to obtained

• Usually, there are two steps to select a channel:

– Band selection: In which the entire band is selected. This step usually comes before the LNA.

– Channel selection: In which the desired channel is selected. This step is usually done after the first mixer.

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Superheterodyne Receiver

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97

Example: AM Radio

• AM radio band: 530 to 1610 KHz• BW/2 = (1610-530)/2=1080/2=540, in band• IF has to be lower. Commonly: 455kHz• Image can be in AM band• If LO is on low side, LO tuning range is:

– (530 to 1610) – 455 = (75 to 1155)– LO lowest to highest is a factor of 15.4

• If LO is on high side, LO tuning range is:– (530 to 1610) + 455 = (985 to 2065)– LO lowest to highest is a factor of 2.01

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98

99

Typical Superheterodyne Digital Receiver


Advantage Disadvantages

Good selectivity High complexity

Good sensitivity High power consumption

Image problem

External components

Not suitable for multi-standard

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100

The Image Problem

• The image could be another user or standard• The image must be filtered out before going the mixer• Frequency planning is key


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Image Rejection Calculation

SNRmin

fIF

IRrequired

fRFfLO

Pdesired

PImage

minSNRPPIR desiredimagerequired

)all in dB’s(

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101

Mixer = Multiplying up/down conversion

• Frequency translation device• Ideal mixer:

• Doesn’t “mix”; it multiplies

A

B

AB

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102

Super-heterodyne Receiver

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103

Selection of IF

• If IF is large, – better separation between RF and image– better image rejection– easier image rejection filter design– More stages of down conversion

• Other IF selection criteria– Select IF so that image freq is outside of RF

band– IF >= (RF BW)/2

• Sometime may not be possible, if (RF BW)/2 is within RF Band

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• For each channel assignment, there are two choices of LO freq that meets the requirement |RF–LO|=IF.

• Q: should LO > RF, or LO < RF??

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105

Image problem converting to IF

A1cos(wRFt)

A has desired signal at wIF

plus an interference at wIM

A2cos(wIMt)

B is at wLO

And:

wRF - wLO = wLO - wIM = wIF

Both converted to IF,Can’t be cleaned once corrupted

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106

Image Problem

)()(cos2

)()(cos2

)cos())(cos()()()(

)cos()(

message is )();)(cos()(

tmtAB

tmtAB

ttmtABtBtAtC

tBtB

tmtmtAtA

LOx

LOx

LOx

LO

x

?

IFLOimagex

IFLORFx

if

OKif

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107


IF

RFimage LO

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108


• Solution: Image Rejection Filter

RFimage LO

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109

110

The Image Problem

• Image Reject filter versus channel selection:

• Larger IF frequencies requires channel select filter with higher Q


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111

Dual-IF Heterodyne Receiver

• Channel selection is done in two stages, hence relaxing the specification for each stage

• Secondary image problem– To avoid the problem, the second IF frequency is set to zero

• Is it possible to have a zero IF?Spring2014

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112

Down Conversion to IF

AM modulation:

FM/ Digital ..etc . modulations:

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High Q Alternatives

• What is really needed is not really a filter.• A cancellation scheme to reject noise is

good enough

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Cosine wave

113

High Q Alternatives

• What if we use a sine wave instead

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114

Complex Signal Representation


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115

Orthognality of I and Q


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116

Orthogonality

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Des

ign

of R

F C

ircui

ts &

Sys

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s

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117

118

Image Reject Receivers-I

– What is a shift by 90o?

– The 90o phase shift is also called Hilbert transform

ffc-fc

𝐴2

𝐴2

Re

Im

f

fc

-fc

Re

Im

− 𝑗𝐴2

𝑗𝐴2

𝑋 90(𝜔)=𝑋 (𝜔) [− 𝑗 𝑠𝑔𝑛(𝜔) ]

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Hilbert transform:

• A 90o phase shift results in:– Rotating positive frequency components CW by 90o

– Rotating negative frequency components CCW by 90o

• Multiplication by +j rotates all frequency components CCW by 90o.

• Multiplication by -j rotates all frequency components CW by 90o.

• Note that for DC frequencies these transformations do not have any meaning

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Hilbert transform

• Assume I(t) is shifted by 90o to produce Q(t). Find I(t)+jQ(t).

ffc-fc

Re{I}

Im{I}

f

fc

-fc

Re{Q}

Im{Q}

f

fc

-fc

Re{jQ}

Im{jQ} Im{I+jQ}

ffc-fc

Re{I+jQ}Spring2014

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Image Reject Receivers

• Idea: From the previous example it seems that one could remove the image with the help of quadrature components.

ffs-fs

Re{I}

Im{I}

-fi fi

f

Re{I}Im{I}{

-fIF fIF

fLO

f

Re{Q}Im{Q}

-fIF fIF

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• A Hilbert transform is used to cancel the image• I&Q (quadrature) signals are generated for image rejection.• The generation of the 90o could be achieved using RC phase shifter each providing 45o phase shift (narrow band solution)


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• Still in the BB we must generate another I&Q for digital demodulation

• Drawbacks:– Mismatch between the two path will result in finite image rejection– The RC solution can be used for narrow-band architectures. Wideband

architecture will result in degraded performance for the image rejection (IRR)– Typical values for IRR is lower than 35 dB.


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Implementing the Phase ShiftHartley Architecture with simple 90 deg phase shiftor

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124

Weaver

125

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128

IRRt

AAt

AAtx imLO

imLORFLO

RFLOA )sin(

2)sin(

2)(

)(cos2

)()(cos2

)()( tA

AtA

Atx imLOim

LORFLORF

LOB

)cos(2

)cos(2

)(

t

At

AAtx imLO

imRFLO

RFLOC

cos2

cos2

)()( t

AAt

AAtx RFLO

RFLORFLO

RFLOsig

cos2

cos2

)()( t

AAt

AAtx imLO

imLOimLO

imLOim

129

cos)(2)(

cos)(2)(.

22

22

2

2

LOLOLOLO

LOLOLOLO

RF

im

outsig

im

AAAA

AAAA

A

A

P

P

Input image power ratio

44

4

4

)cos1)((2

cos)(2)(

cos)(2)(

22

22

2

222

2

2

22

22

AA

AIRR

A

A

A

AA

AAAA

AAAAIRR

LO

LO

LO

LOLO

LOLOLOLO

LOLOLOLO

130

1

1

1

1222222

CRCCRR

CCRR

A

A

2

1

2

C

C

R

RC

CR

RC

CR

R

A

A

Gain Mismatch due to R, C errors

At w = 1/RC:

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131

132

Weaver or Hartley?

• Hilbert transform is obtained using another quadrature (complex) mixing stage

• Advantages compared to Hartley:– Better accuracy in generating the additional 90o phase shift– IRR is limited to 40 dB, which is higher than Hartley architecture

• Disadvantages:– Secondary image problem


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• A single step down conversion is used. The output frequency is at DC

B. Razavi: RF Microelectronics, 2nd EditionAdvantages Disadvantages

No image problem LO leakage

Less complex / low power consumption

DC offset

Channel selection is done with a LPF Even order distortion

Effect of mixer spurs are reduced Flicker noise

IQ mismatch

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134

LO Leakage

– The LO signal can be leaked to the antenna by the capacitive coupling or substrate

– For singled ended Los, the LO leakage can reach -60 dBm– Differential LO architectures have lower LO leakage (better than -

100 dBm)


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• DC Offset:– The leaked LO signal can go through the antenna, LNA and down

converted – Because of the LO signal and its feedthrough signal carry the same

frequency, a DC offset is produced (this phenomena is called LO self mixing).

– BB blocks usually have high again, hence the LO self mixing may saturate the receiver– HPF are not common because they require a very low cut-off frequency

(large components, slow settling)


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Even Order Distortion


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137


• Flicker Noise:

• For 802.11g the channel bandwidth is 10MHz. With a noise corner frequency of 200kHz• For GSM, the channel bandwidth is 100 kHz and therefore a

large portion of noise appears due to flicker noise


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• IQ mismatch:– mismatch in I and Q path affects SNR of received signals– Mismatch effects are more dominate at high frequencies. Reducing the

frequency at which the I and Q signal are generated enhances the SNR– Digital calibration is used to correct these mismatches

Amplitude mismatch:

Phase mismatch:

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Low-IF Receiver


Complex Filter

LargeRequires matchingPower hungry

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ADC

ADC

PGA

PGA

LNA

RFPLL

DIG

ITA

LF

ILT

ER

100 kHz

I

Q

sin cos

RFSAW

sin cos

270 kS/s

925-960MHz

925.1 - 960.1MHz

Low IF receiver


-Require higher performance ADC-Additional mixer

-Slower RF PLL settling-Even order distortion still

problem-Low freq IF filters require large

chip area

+Eliminate IF SAW, IF PLL and image filtering

+Integration

+Relaxes image rejection requirements

+Avoids DC problems, relaxes 1/f noise problem

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Low-IF Down Conversion

LOω

Complex BPF

Mirror signal, needs removal

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141


ComplexBandpass

Filter

I Q I Q

LO1 LO2

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142

Complex Mixing- Real LO

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143

Complex Mixing-Complex LO

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Complex Mixing

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146

Bluetooth Receiver


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Little image problemNo IQ filter@ IF

PGA

PGA

LNA

RFSAW ADC

ADC

DIG

ITA

LF

ILT

ER

I

Q

RFPLL

sin cos

270 kS/s

925-960MHz

925 - 960MHz

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LO is at same frequency as RF1/f noise here can end up in channel

Self mixing cause DC problem

+Eliminate IF SAW, IF PLL and image filtering+ Integration+ easier image problem


-DC problem -Typically requires offset or

2x LO to avoid coupling

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AD w c

aLO(t)=ALOcos( w c+q)

0

w c

)(, tx LOoffset

capacitive couplingsubstrate couplingbondwire coupling

Saturates the following stages

AD w c 0

w c

)(, tx RFoffset

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θωω

θωθωω

ω

tAA

tAtAA

tataAtx

cLOcrosstalk

cLOcLOcrosstalk

LOLOcrosstalkLOoffset

2cos1)(

coscos)(

)()()()(

221

,

φ)(ω2cos1)ω(

φ)(ωcos)ω(

)()()ω()(

2interferer2

1

22interferer


tmtAA

tmtAA

tataAtx

ccrosstalk

ccrosstalk

crosstalkoffset

level

DC Offset

+

-

t

φ)(ω2cos1)ω(

φ)(ωcos)ω(

)()()ω()(

2interferer2

1

22interferer


tmtAA

tmtAA

tataAtx

ccrosstalk

ccrosstalk

crosstalkoffset Spring2014

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150

DC Offset Cancellation

• Capacitive Coupling– Requires a large capacitor

• Negative Feedback– Nonlinear -A

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151

1/f noise effect

• CMOS transistors has significant 1/f noise at low to DC frequency

• Significantly noise performance of direct conversion receivers

Receive signal1/f noise

f

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Even-Order Distortion

c

0c

0

Direct feed through

Direct feed through

Interferers

y(t) = a1 x(t) + a2 x2(t)

Dw

Dw

a2 A1A2 cos(Dw)

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Mirror Signal

• Upper sideband and lower sideband are identical

RF

LO

0

0

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154

Mirror Signal • Upper sideband and lower sideband are not

identical

RF

LO

0

0

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• Quadrature Down Conversion

AD

090

AD

a(t)

ui(t)

uq(t)

vi(t)

vq(t)

I

Q Spring2014

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156

Quadrature Conversion

)(

)(tan)(

))(tan()(

)(

))(sin()(

))(cos()(

)sin()()(

)cos()()(

))(cos()(

1

21

21

tv

tvtm

tmtv

tv

tmtv

tmtv

ttatu

ttatu

tmtta

i

q

i

q

q

i

LOq

LOi

RF

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157

Quadrature Down Conversion

RF

LO

0

0

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158

I/Q Mismatch

090

I

Q

Phase & Gain Error

Phase & Gain Error

Phase & Gain Error

)(, tx ILO

)(, tx QLO

)(, tx IBB

)(, tx QBB

a(t)

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159

I/Q Mismatch due to LO errors

2)(sin

21

2)(

2)(cos

21

2)(

2sin

21)(

2cos

21)(

)(cos)(

,

,

,

,

tmA

tx

tmA

tx

ttx

ttx

tmtAta

QBB

IBB

cQLO

cILO

c

Spring2014

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160

2

2ˆ

ˆ

2222

1

)(

)()(ˆ Find :Exercise

unbiased. is )(ˆ Hence,

)())(ˆ( Clearly,

0)(,))((,))(( and

0)( ,0)( Suppose

)2/)(cos()2/1(

)2/)(sin()2/1(tan)(ˆ

tm

tmtmEσ

tm

tmtmE

EσEσE

EE

tm

tmtm

def

m

m

ε

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161

Use of I/Q down conversion recovers the nonsymmetrical receive signal spectrumBut port isolation becomes more challengingSelfmixing and even order distortion may affect both channels and affect each other, causing additional I/Q mismatch

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090

a(t)

A/D

A/D

Base Band

DSP

Phase and gain mismatchcompensation

DC and 1/fcancellation

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Summary of Direct Conversion Receiver

• No need for imager reject filter• Suitable for monolithic integration with baseband • DC offsets due to crosstalk of input ports of mixer• Even order IM direct feed through to baseband• Quadrature down conversion suppresses mirror• I/Q mismatch due to mismatches in parasitics• Low power consumption attributes to less hardware

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Outline

• Friis Formula• Merits of LNAs• Common Gate LNA• Common Source LNA• Highly Linear LNA• Wideband LNAs• Mixers

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Cascaded Noise Figure

• In a line-up of receiver stages, use Friis equation

• Gi is the power gain• Says that the noise factor ‘F’ is more

influenced by earlier stages Spring2014

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LNA Merits

• Gain• Low Noise (NF)• High Linearity (IIP3)• Low Reflection (S11)• High reverse isolation (S12)• High Stability (K)

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Common Gate LNA

• Input impedance is resistive (except for parasitics)

• Offers good impedance match even at low frequencies

R

vout

Cgs

Cgd

Vin

ZinRs

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Common Gate LNA

• Inductor @input tunes out transistor and board parasitics.

• Channel resistance offers good reverse isolation

R

vout

Cgs

Cgd

Vin

RsCpad

+ Csb L

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Common Gate LNA

• At matching condition, Zin = 1/gm

R

vout

Cgs

Cgd

Vin

RsCpad

+ Csb L

sms

m

RgkTR

gkTF

1

4

/41

1FSpring2014

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Common Gate LNA: Lowering Power II

• Narrowband impedance transformer (L Section) allows the LNA to have Zin>50W.

• Transformer amplifies input signal by:

R

vout

Cgs

Cgd

Vin

RsCpad

+ Csb L

50 >501

o

in

Z

ZSpring2014

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Common Gate LNA: Lowering Power II

• For same IIP3, Veff has to increase by

• Current is reduced by the

same factor • Bias current is given by:

R

vout

Cgs

Cgd

Vin

RsCpad

+ Csb L

50 >50

o

in

Z

Z

oin

effD

ZZ

VI

2

1

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Common Source Amplifier

Input impedance is purely capacitive

Resistive part appears at high frequency

No input matching is possible

R

vin

vout

Cgs

Zin= 1/jCgs

Spring2014

RF

Sys

tem

s an

d C

ircui

ts


• Rg is set to 50 W => Input Matching

• Miller Effect due to Cgd

=> Limited Bandwidth

R

vin

vout

Cgs

Rg

Cgd

p

sin j

RZ

1

)(

1

gdMgssp CACR

Spring2014

RF

Sys

tem

s an

d C

ircui

ts


• Cascode reduces Miller Effect

• Resistive Load limits linearity

R

vin

vout

Cgs

Cgd

RgSpring2014

RF

Sys

tem

s an

d C

ircui

ts


• Parallel Resonance at output boasts narrow band gain without impacting linearity

• Rg produces a lot of Noise NF>3 dB

vin

Cgs

Rg

QoL

vout

Spring2014

RF

Sys

tem

s an

d C

ircui

ts


Series resonance at input creates a resistive term

Iin= jw CgsVgs

Vin=Vgs+jwLs(Iin+gmVgs)

ssgs

in LLjCj

Z

1

QoL

vin

vout

Cgs

L

LsSeries Resonance

gmVgs

Iin

Spring2014

RF

Sys

tem

s an

d C

ircui

ts


• Series resonance at input creates a resistive term

• @ RF, input is still capacitive because Ls is very small to give 50W with high wT

QoL

vin

vout

Cgs

L

LsSeries Resonance

sgs

ms

gsin L

C

gLj

CjZ

1

gs

mT C

g

Spring2014

RF

Sys

tem

s an

d C

ircui

ts


Gate inductance offers one more degree of freedom to allow matching and series resonance at the same time

Valid for

QoL

vin

vout

Cgs

L

LsSeries Resonance

Lg s

gs

mgs

gsin L

C

gLLj

CjZ

1

gss

oCL

1 Spring

2014

RF

Sys

tem

s an

d C

ircui

ts

Parasitics

Ali Niknejad ECE142

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Design Procedure for Common Source LNAs

Spring2014

RF

Sys

tem

s an

d C

ircui

ts


Assume an equivalent resistive load Rd

@ resonance vin

vout

Cgs

Rd = QoL

LsSeries Resonance

Lg

sgs

mgs

gsin L

C

gLLj

CjZ

1

OhmLC

gZ s

gs

min 50 Spring

2014

RF

Sys

tem

s an

d C

ircui

ts


Noise Figure (F) is given by

vin

vout

Cgs

Rd = QoL

LsSeries Resonance

Lg

OhmLC

gZ s

gs

min 50

Decreases with wT

Use samll Ls

Source Coils TransistorSpring2014

RF

Sys

tem

s an

d C

ircui

ts

Optimization of CS LNA

Assume

@ Input matching condition

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Optimization of CS LNA

wT Increases

Lg Noise dominates

Higher power

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Another Way to Look at It

• If Q is input quality factor

vinCgs

Ls

Lg

vinCgs

Ls

TLs

+

-Vgs

QV

V

in

gs

sTsmo

T

LRgQ

1

smRgQF

4

11

2

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Another Way to Look at It

• The input is amplified by Q before it reaches the transistor

• This reduces linearity vinCgs

Ls

Lg

vinCgs

Ls

TLs

+

-Vgs

22

333

Q

IIP

in

gs

IIPIIP FETFET

LNA

V

V

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Other Losses: Inductor Losses

• Typically Lg losses dominate• Adds in series to source noise • Independent of FET gain

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Other Losses: Gate Resistance

• Gate Resistance creates additional noise (uncorrelated with channel noise)

• Use inter-digitated layout to reduce gate electrode resistance

rg

g

mFETn

rg

kTv

42

,

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Other Losses: Gate Induced Noise

• Due to inversion layer resistance

• Partly correlated with conventional thermal noise

• Modeled as a resistance in series with gate

GateSource Drain

oxeffinv CWV

Lr

5

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Other Losses: Gate Induced Noise

• The effective Q is lowered by losses

• Higher Q is achieved through lower Cgs

• Smaller Cgs raises rinv and also gate resistance

• There is an optimum W at each current

vin

Cgs

Ls

Lg

+

-Vgs

rinv

W

FQ increases

Fopt

Other losses dominate

FETDominates

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Other Losses: Substrate Coupling

• BSIM3V3 models do NOT capture Cgb• Gate to bulk capacitance is an additional path for

noise Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Other Losses: Substrate Coupling

• Hole distribution in the depletion layer are modulated by gate voltage

• Same effect on electrons in the inversion layer which reflects back on depletion region Spring

2014

RF

Sys

tem

s an

d C

ircui

ts

Wideband CS LNA

• Uses an LC ladder filter to widen BW

• Uses a large number of inductors

• Excellent noise performance

`

M1

M2

+r

Rs

Vs

Vo

Vbias

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Resistive Feedback

• Feedback widens BW and lowers Zin

• Power consumption is very high

• Noise Cancellation can be employed

+r

Rs

Vs

+r

M1 M2

M3

X

Y

VsRs

Vout Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Capacitive Cross Coupling Technique

,1

2

12

11 mmin gg

R

+ IN

M1 M2C1 C2

1

21

2

4

4

mn

sns

g

KTv

KTRv

+ r

vn1

vns

in_diffout

Rs Rs

M1 M2

+r

•Differential input impedance:

•Two voltage noise sources: vns & vn1 in each

half circuit

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

• The output differential noise current square due to each noise source is given by:

• Then:

• Using the input power matchingcondition:

+ r

vn1

vns

in_diffout

Rs Rs

M1 M2

+r

2

22

4

1

s

nsns_diffout R

vi

2

212

1 16

1

s

n_diffoutn R

vi

smns_diffout

_diffoutn

Rgi

iF

12

21

4

111

2

11F

Capacitive Cross-Coupling Technique

Spring2014

RF

Sys

tem

s an

d C

ircui

ts

Special Topics in Electronics Engineering Emad Hegazi Professor, ECE Communication Circuits Research...

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Transcript of Special Topics in Electronics Engineering Emad Hegazi Professor, ECE Communication Circuits Research...