RF Receiver Basics

Receiver Noise Figure

Pass Loss

Tx OutputRx Noise Figure

Pass Loss

Noise Floor

Prof. C. Patrick Yue, ECE, UCSB

Power Spectrum of Global System for Mobile (GSM)

In-band Close-ini t f


interferers

Sensitivity vs. SelectivityDesired Channel MIXER

Input Output

to select IF Filter

Received Channels at RF rf

LOReceived channels after

if

frequency translation

Received channels after if

frequency translation

SensitivityThe minimum (available) signal power needed at the receiver input to provide adequate SNR at the receiver output to data demodulationadequate SNR at the receiver output to data demodulationNoiseInsertion LossInter-modulation products

SelectivityBlockers (in-band and out-of-band)Phase Noise


Image-Rejection (will be discussed with radio architecture)

Required Receiver Sensitivity – A Qualitative View

What is the required receiver NF to achieve a certain level of sensitivity?

Transmit Power To find Receiver NFTransmit Power – FCC regulated

Path Loss

R i S iti it

Path lossReceiver sensitivity – govern by standards and applicationsRequired SNR depends on BER

Required SNR

Noise FigureReceiver Sensitivity Required SNR – depends on BER

requirement and modulation schemeNoise floor – thermal noise or

Noise FloorRequired SNR circuit noise limited depending on

the modulation schemes


Receiver NF Requirement CalculationsIEEE 802 11a WLANIEEE 802.11a WLANFCC limits the PSD in 5GHzto 2.5 mW/MHzChannel bandwidth is 16 MHzT it P i 40 W 16 dB

GSM (DCS-1800 ) cellularFCC limits the PSD in 1.8 GHzto 5 mW/kHzCh l b d idth i 200 kHTransmit Power is 40 mW or 16 dBm

Thermal noise floor–174 dBm/Hz X 16 MHz = –102 dBmTotal SNR budget is16 dB ( 102 dB ) 118 dB

Channel bandwidth is 200 kHzThermal noise floor–174 dBm/Hz X 200 kHz = –121 dBmRequired SNR for GSM is 9 dB16 dBm – (–102 dBm) = 118 dBm

To cover ~300 ft. at 5 GHz results in a path loss of 86 dB

i.e. Receiver sensitivity is –70 dBm (802 11a specification is 65 dBm )

Required SNR for GSM is 9 dBto keep BER < 10–3

GSM receiver sensitivity specification is –102 dBm(802.11a specification is –65 dBm )

Required SNR for 64QAM (54Mbps) is 27 dB802.11a packet length is 8 kbWorst packet loss < 10%,(1 BER)8000 = 1 10%

is 102 dBmReceiver noise figure requirement = Receive sensitivity – Noise floor –Required SNR

(1 – BER)8000 = 1 – 10%BER = 10–5

Receiver noise figure requirement = Tx Power– Path Loss – Required SNR –Noise floor

= –102 – (–121) – 9 = 10 dB


Noise floor = 16 + 102 – 86 – 27 = 5 dB

Receiver Sensitivity for GSM


One More Receiver Sensitivity Calculation Example


Fundamental Concepts in RF Systems Receiver sensitivity

Noise FigureSignal to noise ratio (SNR)Thermal noise floor

Receiver selectivityNonlinearityy

gain compressioninter-modulationdesensitizationcross modulation

Phase noise and blockersReceiver spurious-free dynamic range (SFDR)

Lower limit set by sensitivityUpper limit set by selectivity


Key Receiver MetricsAt any input signal level, the receiver must achieve a minimum Signal-to-Noise Ratio (SNR)

Detection schemes need a minimum signal-to-noise ratio for adequate fperformanceSome analog detectors (AM detectors) improve gradually with increasing SNRDigital detectors improve rapidly past a threshold SNR

Dynamic rangeDynamic rangeThe range of input power (signal and interferer) over which the receiver performs adequately

Measured by performance of the base-band transducer (speaker/video display etc)Measured by performance of the base-band transducer (speaker/video display etc)For system analysis, Bit Error Rates or final SNR are used

Smallest signal level is the receiver sensitivityLargest signal determines the upper limit of dynamic range (What does Largest signal determines the upper limit of dynamic range (What does ‘largest signal’ mean? We will come back to this point later…)


Receiver Architecture ConsiderationsHeterodyne is a well-proven architecture

Monolithic implementation (low-cost integration) is a challenge owing to the large number of BPF’s required

Alternative architecture suitable for integration will be studied laterThe architecture as shown is a consequence of available technologies

For example, if low loss, tunable front-end BPFs could be manufactured for channel select, the receiver could be replaced by one mixer

The components shown are usually common to all architectures with possibly different requirementsFront-end circuits (e. g. LNA & Mixer) are critical design challenges and technology drivers in wireless applications


Functions of Receiver Components (1)Image Ch l IADC

LNABalunT/R

Switch RF Mixer

Image

FilterReject Select

Channel

VGAIF

I

LO2 (Tuned)

ADC

Filter

RF

Filter

O PCB

Band Select ADC

LO1 (Fixed)

90o

Q

Anti-alias IF Mixer

RF band select filter

On PCB On-Chip Anti alias LPF

IF Mixer

typically a ceramic filterUsed to filter and reduce incident power levels of distant interferers at the LNAallows the entire RF Band (all possible useful channels) into the receiver rejects out-of-band signals and attenuates image signalsrejects out of band signals and attenuates image signals

Transmit / Receive Switchconnects the antenna to the receiver or transmitter in a time-division duplexed systems

Balun


“Bal”anced to “Un”-balanceddifferential to single-ended converter


LNABalunT/R

Switch RF Mixer

Image

FilterReject Select

Channel

VGAIF

I

LO2 (Tuned)

ADC

Filter

RF

Filter

O PCB

Band Select ADC

LO1 (Fixed)

90o

Q

Anti-alias IF Mixer

Low Noise Amplifier (LNA)


IF Mixer

Front-end amplifier used to amplify the signal with minimum degradation in the SNRamplifies the signal to reduce impact of noise from latter stages

Image Reject FilterCeramic (or SAW) band-pass filter used to provide filtering of distant interferersUsed primarily to reject the ‘image frequency’ of local oscillator (LO1)Allows the entire RF Band (all possible useful channels) into the receiverattenuates image-signals before mixing

RF Mixerconverts the incoming RF signal to intermediate frequency (IF) is the difference between the RF and LO1


converts the incoming RF signal to intermediate frequency (IF) is the difference between the RF and LO1Usually have stringent linearity and noise requirement


LNABalunT/R

Switch RF Mixer

Image

FilterReject Select

Channel

VGAIF

I

LO2 (Tuned)

ADC

Filter

RF

Filter

O PCB

Band Select ADC

LO1 (Fixed)

90o

Q

Anti-alias IF Mixer

Channel select filter


IF Mixer

Select the desired the channel and rejects adjacent channelsTypically requires a SAW filter with high attenuation to suppress out of band tones

Intermediate frequency variable gain amplifier (IF VGA)adjusts the received signal level so that it maps to the dynamic range of the based-band adjusts the received signal level so that it maps to the dynamic range of the based-band circuits such as the ADC

IF mixers Down-converts the I & Q signals to base-band for signal processingI th b l th t th i f i tl tt t d b th


In the above example, we assume that the image frequency is greatly attenuated by the channel select filter and therefore image-reject mixers are not used.

Receiver RequirementsGain and stability requirements

Power gain, voltage gain, stability measuresLow-noise requirements

Noise figure or temperatureDesensitization (impact of non-linearity on noise performance)

Linearity requirementsy qIntercept points, gain compression


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Noise in ReceiverReceiver “noise level” directly limits sensitivityReceiver sensitivity = minimum input power that the receiver can detectNoise figure of cascaded stagesg g

Noise figure of RF receivers from antenna to ADC outputNoise figure of passive networksNoise figure of ADCg


Input-Referred SNR in Terms of Noise Factor


Receiver Sensitivity – Min. Pin to Achieve Required SNR (1)






Noise Figure for Cascaded Stages


Noise Factor of Passive (Lossy) Networks


Noise Figure Calculation of BPF Followed by LNA


SNR of Analog-to-Digital Converter

Typically, ADC is characterized using SNR at the output rather than NFTo determine the NF of an ADC we need to compute the degradation in


To determine the NF of an ADC, we need to compute the degradation in SNR due to quantization noise after the signal passes through the ADC

Noise Figure of Analog-to-Digital ConverterN iN iPSNR /

Since the ADC only performs digitization of the input voltage and thus does not id i i P P th t t i l b t t d th i t i l

in

out

outout

inin

out

inADC Noise

NoiseNoisePNoiseP

SNRSNRNF

//

===

provide any gain, i.e. Pin = Pout, the output signal can be treated as the input signal plus quantization noise. Expressing NF in log form, we obtain:

)()( dBmNoisedBmNoiseNF inout −=

Assume that the ADC noise is completely due to quantization error, then

ADCinout SNRPdBmNoise −=)(

A th t th i t th i t i d t th l i th Assume that the noise at the input is due to thermal noise, then

kTBSNRPNoiseSNRPdBNF

ADCin

inADCin

−−=

−−=)(

One can also express NF as the power ratio of quantization noise (at the output) One can also express NF as the power ratio of quantization noise (at the output) and thermal noise (at the input) which results in:

11224 2

22)(0 =⋅

××=

×= N

FSrms

utise at InpThermal Not Outputon Noise aQuantizati

kTBRV

BkTRANP

NF


)41(

1224

,

2,

=

×××

ADCp

sN

sADCp

A

utise at InpThermal NokTBRBkTRA

Effect of Over-Sampling on ADC NF

Increasing the sampling frequency reduce noise which has the same effect as


Increasing the sampling frequency reduce noise, which has the same effect as increase the ADC resolution

Over-sampling by a factor of 4 results in 6 dB reduction in noise, or effectively 1 more bit

Receiver RequirementsGain and stability requirements

Power gain, voltage gain, stability measuresLow-noise requirements

Noise figure or temperatureDesensitization (impact of non-linearity on noise performance)

Linearity requirementsy qIntercept points, gain compression


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Interferers in Global System for Mobile (GSM)

In-band Close-ini t f


interferers

The “Large Signal”


Interferers


Linear SystemsTh t S i li if d l ifThe system S is linear if and only if:

x ySx1

x2

y1

y2

Then:x1+ x2

αx1

y1+y2

αy1x2 y2 αx1 αy1

In other words in a linear system, the output can be expressed as a linear combination of the responses to the individual inputs. In a linear system combination of the responses to the individual inputs. In a linear system with no initial stored energy, the output time function is related to the input time function by the convolution integral:

t( ) ( )h t( )d∞

∫=y t( ) x τ( )h t τ–( ) τd∞–∫=

where h(t) is the system response to a unit impulse. In frequency domain:domain: Y jω( ) X jω( )H jω( )=

System transfer function∞


H jω( ) h t( )e jωt– td∞–

∞

∫=

Source of Non-linearityA system is time-invariant if a time shift in the input results in the same time shift in the output:

x(t) y(t) Then: x(t τ) y(t τ)

In linear time invariant systems, a single frequency input can only generate a single frequency output

x(t) y(t) Then: x(t-τ) y(t-τ)

generate a single frequency output.A linear time variant system, e.g. a mixer, can generate frequency components that do not exist in the input, which cause non-linearity.Device non linearityDevice non-linearity

ID = K(VGS - VT)2

I I E ( V /KT)


Ic = Ics. Exp (qVBE/KT)

Gain Expansion or Compression due to NonlinearityF ti i t l t For time-variant, memoryless systems, we can assume

NLx(t) y(t)

2 3

x(t) = Acos(ωct)

y(t) = a1x(t) + a2x2(t) + a3x3(t) + ...

y(t) = a1Acos(ωct) + a2A2cos2 (ωct) + a3A3cos3(ωct) + ...

a22-----A2 a1 A 3

a34-----A3+

⎝ ⎠⎛ ⎞ ωct( )

a22-----A2 2ωct( )

a34-----A3 3ωct( )cos+cos+cos+=

From this equation we see that the output signal consists of a component at the applied fundamental frequency ωc and spurious signals at dc, the second harmonic 2ωc, and the third harmonic 3ωc.

2 4⎝ ⎠ 2 4

c, cThe amplitude of the fundamental component can be greater than a1A (the gain if the two-port is linear) if a3>0 and smaller than a1A if a3 < 0. This property is called gain expansion or gain compression.


1-dB Compression Point

Aout Aout

A1 dB

A A

a3<0

Aout = output amplitude @ ωc

A1dB

Gain at fundamental frequency = 20log |a1 + 0.75a3A2|Linear Gain = 20log |a |Linear Gain = 20log |a1|

At the 1-dB compression point, the actual gain is 1dB below the linear gain

20log |a1 + 0.75a3A2| = 20log |a1| – 120log |a1 0.75a3A | 20log |a1| 1Therefore for ,

A-1dB2 = – 0.145a1/a3 (a3 < 0) or

3

11 145.0

aaA dB ×=−


P-1dB = A-1dB2 / 2R

Blocker and DesensitizationBlocker: If input signal to the receiver consists of a weak desired signal at ωc1 accompanied by a strong interferer at ωc2 (the blocker). The blocker tends to reduce the average gain experienced by the desired signal:

Meaning that the effective signal gain at ωc1 (desired signal) is reduced by

For large enough A2, the receiver is “desensitized” as the output at ωc1 is


g g 2, p c1overwhelmed by the blocker.

Inter-modulationIntermodulation products due to two input tones:

14 a× = AIP3

33 a AIP3

IIP3 = AIP32 / 2R

When A = IIP3, the 3rd order term = fundamental at the output( i i i l t d i 9/4* *A3 A)


(gain compression is neglected, i.e. 9/4*a3*A3 << a1A)

Signal Corruption due to IIP3 of Interferers

Aint, outAint, in

AIM3,out

Asig, out

Asig, in

Given Asig, in, Aint, in and IIP3, we want to find

the ratio of the signal to IM3 i e A / A at the outputthe ratio of the signal to IM3, i.e. Asig, out / AIM3,out at the output

To find the dynamic range, we refer Asig, out / AIM3,out to the input


IP3 Calculation and Graphical InterpretationTo express IIP3 in terms of the input and output signal amplitudes, take the ratio of the first and third terms

2int,

23

,3

int,

in

IP

outIM

out

AA

AA

=

from the previous expression and express in terms of IIP3 (Slope = 1)

Aint,out

(Slope = 3)

AIM3,outAint,in


= AIP3AIM3, inAint,in

Signal Corruption due to IIP3 of InterferersAint, outA int, out

AAsig, out

Aint, in

AIM3,outAsig, in

outin

IP

outIM AAA

A int,2int,

23

,3

11×=insig

in

outoutsig

in

out

insig

outsig AAA

AAA

AA

,int,

int,,

int,

int,

,

, ×=⇒=in ,int,,

insigin

IP

outIM

outsig AAA

AA

,3int,

23

,3

, ×=⇒

Given Asig, in = 1μVrms, Aint, in = 1mVrms, and IIP3 = – 10dBm (AIP3 = 70mVrms on 50 Ω)

( )A outsig 1 3μ


( )( ) dBm

mA outIM

outsig 8.139.47011 3

3,3

, ==×=μ

Relation between 1-dB Compression Point and IIP3

input) tone single (with 145.03

11 a

aA dB ×=

input)tonedual(with43 1aIIP ×= input)tonedual(with 3

33a

IIP ×=

33.03/4

145.03

1 ==dBIIPA

9.6 (dB) (dB) 3 1 += dBAIIP


IIP3 of Cascaded Stages (I)


IIP3 of Cascaded Stages (II)

The term consisted of α2 (due to 2nd order distortion)can be neglected if gain of stage 1 has a band-pass characteristic


Dynamic Range

DR = P1dB – kTB(dBm) – F – SNRmin

DR IIP3 9 6 kTB(dB ) F SNRDR = IIP3 –9.6 – kTB(dBm) – F – SNRmin


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Spurious Free Dynamic Range


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Receiver SelectivityA measure of the receiver’s ability to reject signal outside of the desired A measure of the receiver s ability to reject signal outside of the desired band.We have seen that IM3 due to two adjacent channels creating spurious tone in the designed signal bandtone in the designed signal bandBlockers and phase noise of the local oscillator (LO) signal also degrades receiver selectivity.

Ph i i f t l it f th LO i lPhase noise is a measure of spectral purity of the LO signal

Blocker


Phase Noise RequirementInput

Desired

BLInput Spectrum

Receiver

BW

Sx (f)Phase Noise

f

Signal Vout

Receiver Desired Signal

Receiver Output

BlockerMixed C/I

Δfc

fL0

-PN (Δfc )

x ( )

Local Osc.Output

LO

f

Mixed Inband

C/Im in

Δfcf

Assume that the receiver is noiseless, therefore required SNR is determined by C/Imin (Carrier / Interferer ratio)

( ))log(10)/(

)( )(/ min

BWHzdBcPNSS

dBcPNSSdBIC

fcblocksignal

fcblocksignal

−−−=

+−=

Δ

Δ


)g()(fcblocksignal Δ

)log(10)(/ )/( min BWdBICSSHzdBcPN blocksignalfc −−−=Δ

Phase Noise Requirement Calculation

PCS 1900 (North America version of GSM)Desired signal at fo can be as small as –99dBm with –43-dBm blocker at 600kHzGSM required SNR is 9 dBChannel bandwidth is 200 kHzPN (at 600kHz offset)


PN (at 600kHz offset) = – 99 – (– 43) – 9 – 10log(2e5) = – 118 dBc/Hz

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RF Receiver Basics