rf module design - [chapter 2] noises

RF Transceiver Module DesignChapter 2 Noises

李健榮助理教授

Department of Electronic EngineeringNational Taipei University of Technology

Outline

• Noise Sources in Electronic Components

• Antenna Noise

• Noise Temperature

• Noise Figure

• Non-frequency-converting Circuit Output Noise Power

• Frequency-converting Circuit Output Noise Power

• Output Noise Power of Cascaded Circuits

• Sensitivity

Department of Electronic Engineering, NTUT2/42

Noise Sources in Electronic Components

• The flow of charges(holes) in a electron tube or solid-statedevice has the thermal fluctuation in any component at atemperature above absolute zero. Such motions can be causedby any of several mechanisms, leading to various sources ofnoise, thermal noise, flicker noise, and shot noise.

• Noises can be picked up by the antenna, which come fromatmospheric noise, solar noise, galactic noise, ground noise,and man-made noise.

is the Planck’s constantis Boltzman’s constant

Thermal Noise

• Johnson Noise, Nyquist Noise

• Thermal agitation of charge carriers:

v(t) is a open-circuit voltage across theresistor terminals

Department of Electronic Engineering, NTUT

( ) ( ) ( )2

2 2 4f

n rms fv t V kT R f P f df= = ∫

( )1hf kT

hf kTP f

346.546 10 J/sech −= ×231.380 10 J/Kk −= ×

( )v t

( )v tR

( )o KT

For an electron in a conductor, the probabilitydensity function (PDF) obeys

Shot Noise

• Shot noise (Schottky noise) is first observed in vacuumtubes.

• For example, theIV curve of theSchottky Contact (metal-semiconductor contact) is .The above results areapplicable also top-n junction diodes, bipolar transistors,metal-semiconductor (Schottky-barrier) diodes, and so on,where charges are carried across potential barriers.

• In summary, shot noise has two characteristics:

1) White noise spectrum similar to that of thermal noise. This is veryuseful in measuring the noise temperature or noise figure ofanamplifier or any linear receiver component for that matter.

2) The rms value of the shot noise can be easily calculated form themeasured dc current IS.

0( 1)qV KTI I e= −

Flicker Noise

• Flicker noise is a low-frequency phenomenonwhich istypically encountered in the device with a dc current flowing.It is a poorly understood phenomenonand seems to be relatedto surface properties of materials, and is also associated withimperfect contact between conductors.

• Flicker noise has the interesting characteristic thatits spectraldensity is inversely proportional to frequency.

• Van der Ziel gives the following expression for the mean-square noise current per unit bandwidth:

Ii K df

whereK : material constant,I : dc current,a : close to 2, andn : close to 1.This expression seems hold for a variety of cases, including semiconductors,carbon microphones, photoconductors, crystal diodes, and so on.

Antenna Noise

• Generally speaking, antenna noise includes a total of thefollowing noise sources:

� Atmospheric noise

� Solar noise

� Galactic noise

� Ground noise

� Man-made noise

Atmospheric Noise

• This noise is greatest at the lowest frequencies and decreaseswith increasing frequency.

• Below 30MHz, it is the strongsource of antenna noise,generated mostly by lightningdischarge in thunder storms.The noise level depends onthe frequency, the time of day,weather, the season of theyear, and geographicallocation.

Frequency (MHz)0.1 0.3 1 3 10 30 100

Galactic noise

Atmospheric noise(Central United States)

Solar Noise (I)

• The Sun is a powerful noise source.

• If a directional antenna is pointed at the Sun, it will see a largeantenna noise temperature (also contributes to antenna noisethrough sidelobes).

• During high levels of Sun spot activity, noise temperaturesfrom 100 to 10,000 times greater than those of the quietsun may be observed for periods of seconds in what iscalled solar bursts, followed by levels about 10 times thequiet level lasting for several hours

Solar Noise (II)

• The Sun’s effective noise temperature seen by an antenna ofgainGa is:

• For example, if the frequency is 1000 MHz and there are quietsun conditions, the noise temperature is about . If weassume an antenna gain in the direction of the sun of 31 dBiand an atmospheric loss of 1dB, the antenna noise temperaturewill be

52 10 K×

6 54.75 10 1259 2 10949.3 K

1.26aT−× × × ×= =

64.75 10 a sa

−×= AL : atmospheric loss (numeric)

Galactic Noise

• Typical antenna temperaturesfor frequencies above 100 MHz.

• Galactic noise is the largestnatural noise between 100~400MHz, which is most intense inthe galactic plane and reaches amaximum in the direction ofthe galactic center.

• Above 400MHz, the othercomponent dominate.

Frequency (GHz)Cosmic noise from the galactic center

Minimum noise

0.1 0.3 1 3 10 30 100

ise Fig

ure (d

Minimum noise

Cosmic noise from the galactic pole

Ground Noise

• The Earth is a radiator of electromagnetic noise.

• The thermal temperature of the Earth is typical about 290 K.

• In radar systems and directional communication systems, theEarth will be viewed mainly through the sidelobes of theantennas. The average sidelobe antenna gain typically isabout –10 dBi. A rough estimate of antenna noise temperaturein that case is 29 K.

Man-made Noise and Interference (I)

• Man-made noise is due chiefly to electric motors, neon signs,power lines, and ignition systems located within a fewhundredyards of the receiving antenna.

• There may be radiation fromhundreds of communication andradar systems that may interfere with reception.

• Generally this type of noise is assumed to decrease withfrequency as shown in the following:

whereT100 is the man-made noise temperature at 100 MHz.

Man-made Noise and Interference (II)

• For an example of the formula, assume an operating frequencyof 400 MHz and a man-made noise temperature at 100 MHz of300,000 K (Fa = 30.2 dB abovekT0B). The calculated antennanoise temperature would be

The temperature is about 15.2 dB above kT0B.

2.5100

300,000 9375 K400aT = ⋅ =

where is Boltzman’s constant

Available Thermal Noise Power

• Thermal Noise:

231.380 10 J/Kk −= ×NAP kTB=Available noise power:

Thermal noise source

,n rmsvR

( ) KT

Noisy resistor

,n rmsv

Thevenin’s Equivalent Circuit

Noise-free resistor

2, ?n rmsv =

Matched Load

2n rms

P kTBR

,n rmsv,

2n rmsv

Available Noise Power

2, 4n rmsv kTBR=

Open-circuited noise voltage?

where is Boltzman’s constant

Thermal Noise Equivalent Circuits

• Thermal Noise:

231.380 10 J/Kk −= ×NAP kTB=Available noise power:

Thermal noise source

,n rmsv,n rmsvR

( ) KT

Thevenin’s Equivalent Circuit

Noisy resistor

Noise-free resistor

Norton’s Equivalent Circuit

Noise-free resistorR

2, 4n rmsv kTBR=

,n rmsi

44n rms

v kTBi kTBG

2, 4n rmsv kTBR=

Thermal Noise Power Spectrum Density

• Available noise power :

• Thermal Noise at 290 K (17 oC):

Ideal bandpass

filterB

,n rmsv

NAP kTB=

PSD (W/Hz, or dBm/Hz)

f (Hz)BandwidthB (Hz)

Integrate to get noise power

0 0NAP kT B=Available noise power:

( ) ( )210, 0 4 10 W Hz 174 dBm HzPSDN kT −× = −≜ ≃Power spectrum density:

Equivalent Noise Temperature (I)

• If an arbitrary source of noise (thermal or nonthermal) is“white”, it can be modeled as anequivalent thermalnoisesource, and characterized with anequivalent noise temperature.

• An arbitrary white noise source with a driving-pointimpedance ofR and delivers a noise powerNo to a loadresistor R. This noise source can be replaced by a noisyresistor of valueR, at temperatureTe (equivalent temperature):

Arbitrary white noisesource

Equivalent Noise Temperature (II)

• How to define the equivalent noise temperature for a two-portcomponent? Let’s take a noisy amplifier as an example.

• In order to knowthe amplifier inherent noiseNo, you may liketo measure the amplifier by using a noise source with 0 Ktemperature. Is that possible?

Noisy amplifier

0 KsT =This means that the output noise No isonly generated from the amplifier.

Noiseless amplifier

o a iN G N=

NN kT B

G= =i o

kB G kB= =

Gain Method

• Use a noise source with the known noise temperature Ts.

Noiseless amplifier

o a iN G N=

i s eN kT B kT B= +

Noisy amplifier

_o a i o addN G N N= +

i sN kT B=

( ) ( )o a s e a s eN G kT B kT B G kB T T= + = +

G= −

� Need to know the amplifier power gainGa.

� Due to the noise floor of the analyzer, thegain method is suitable for measuring highgain and high noise devices.

The Y-factor Method

• Use two loadsat significantly different temperatures(hot andcold ) to measure the noise temperature.

• Defined theY-factoras

1 1a a eN G kT B G kT B= +

2 2a a eN G kT B G kT B= +

−=−

+= = >+

B eT 1N2N

(cold)

� You don’t have to knowGa.

� The Y-factor method is not suitable for measuring a very high noise device, sinceit will make to cause some error. Thus, we may like a noise source with highENR for measuring high noise devices.

1Y ≈

� Sometimes, you may need a pre-amplifier to lower analyzer noise for measuring alow noise device .

Noise Figure

• The amount of noise added to a signal that is being processedis of critical importance in most RF systems. The addition ofnoise by the systemis characterized by its noise figure (NF).

• Noise Factor(or Figure) is a measure of the degradation in thesignal-to-noise ratio (SNR) between the input and output:

whereSi , Ni are the input and noise powers, andSo, No are the output signaland noise powers

1i i i

SNR S NF

SNR S N= = ≥ ( )dB 10logNF F=

Gain = 20 dB

P (dBm)

Frequency (Hz)

−100

−60SNRi = 40 dB

NF = ?

P (dBm)

Frequency (Hz)

−40SNRo= 32 dB

−72 NF = 8 dB

Noisy Amplifier

Noise Figure (NF)

• By definition, the input noise power is assumed to be thethermal noise power resulting froma matched resistor atT0

(=290 K); that is, , and the noise figure is given as

1 1ei i e

kGB T TSNR S TF

SNR kT B GS T

+= = = + ≥

0iN kT B=

( ) 01eT F T= −

NoisyNetwork

G B eT

i i iP S N= + o o oP S N= +

231.380 10 J/ Kk −= × �where is Boltzman’s constant0NAP kT B=

( ) ( )210 4 10 W Hz 174 dBm HzTN kT −× = −≜ ≃

� Use the concept of SNR

� Use the concept of noise only

1 1o add e e

N kGBT N kGBT kGBT TF

GN GkT B GkT B T

+ += = = = + ≥

Non-frequency-converting Circuit Output Noise

A. Resistive-type passive circuits

When a two-port network is a passive, lossy component (an attenuator or lossy transmission line).

B. Reflective-type passive circuits

Assume an ideal bandpass filter response with passband insertion loss of L (dB) and stopband attenuation of S (dB).

C. Active circuit

An active circuit is with noise figure NF and available gain G.

Resistive-type Passive Circuits (I)

• The circuit is with a matched source resistor, which is also attemperatureT.

• The output noise power :

• We can think of this power coming fromthe source resistor(through the lossy line), and fromthe noise generated by theline itself. Thus,

0P kTB=

0 addedP kTB GkTB GN= = +

( )11added e

GN kTB L kTB kT B

−= = − =

where is the noise generated by the line.addedN

Resistive-type Passive Circuits (II)

• The lossy line equivalent noise temperature :

• The noise figure is

whereT0 denotes room temperature,T is the actual physical temperature (K). Notethat the lossL may depend on frequency.

• Output noise power :

where input thermal noise power

( )11e

GT T L T

−= = −

= + − ( )dB 10logNF F=

( ) ( ) ( )dBm dBm dBout inN N L NF= − +

( )WattinN kTB=

( )dBminN

( )dBmoutN

inN L NF− +

Reflective-type Passive Circuits (I)

• Assume an ideal BPF response with passband insertion loss ofL (dB) and stopband attenuation ofS (dB). The filter is underan environment ofT (K)

• In the passband:

= + − ( )dB 10logNF F=

0 dB−L dB

−SdB

Reflective-type Passive Circuits (II)

• Outside the passband, the noise, the same as the signal, isreflected back such that the output noise power is reduced bythe stopband attenuationS(dB).

( )0 0

2 2dBm

BW BWN L NF f f f

N S otherwise

− + − ≤ ≤ +

( )dBmoutN

inN L NF− +

inN S−

( )dBminN

Active Circuits

• An active circuit is with noise figure NF and available gain G. (Note that NF and G are usually depend on frequency.)

( ) dBmout inS S G= +

( )174 10log dBminN B= − +

( ) dBmout inN N NF G= + +

( )dBminN

( )dBmoutN

( )dBminS

( )dBmoutS

( )dBmin inS N+

( )dBmout outS N+

( ) dBG

( ) dBNF

Multiple Stages Cascaded

• Multiple stages cascaded

whereFi is thenoise factorandGi is theavailable power gainof each stage.

−= +∑∏

1 1 2 1 2 1

e e eNeT e

T T TT T

G G G G G G −

= + + + +⋯⋯

2eT eNT

NGg T addkT G N+gkT

1ekT 2ekT eNkT

gkT ( )T g eTkG T T+

1 2T NG G G G= ⋯

1 1 1g ekT G kT G+

( )1 1 1 2 2 2g e ekT G kT G G kT G+ +

( )1 2 1 1 2 2g N e N e N eN NkT G G G kT G G kT G G kT G+ + + +⋯ ⋯ ⋯ ⋯

T N jj

G G G G G−

= = ∏⋯

( ) 01eT F T= −

Cascade System

Equivalent System

( ) 321

1 1 2 1 2 1

1 111 1 N

F FFF F

G G G G G G −

− −−= + − + + + +⋯⋯

1st stage dominate less significant

Frequency-converting Circuit Output Noise

• Image Noise :

• LO Wideband Noise :

Image noise

fLO + fIFfLO − fIFfIF

LO wideband noise

Output Noise Power of Cascaded Circuits (I)

• The total mean-square noise voltage

(Assume that the circuit is under the same physical temperature Tj=T)

• The summed open-circuit mean-square voltage ata-a' istherefore given by ,where

( ) ( ) ( )2

4 4 4 4N N N

n j j j j j TT j j j

v kT BR kB T R kBT R kBTR= = =

= = = =∑ ∑ ∑

( )2 2 2 21 2 3n

Tv v v v= + + +⋯

Noisy resistors in series

NR2nNe

a a′

( ) 22 21 1 1nv v A f= ( ) 22 2

2 2 2nv v A f= ( ) 22 23 3 3nv v A f=, , and

Example – T-network

The total voltage at a-a' is the sum of the above,

where the equivalent resistance

( )( )

22 21 22 1 2

1 2 1 2

kTBR Rv Rv

R R R R= =

( )( )

22 22 12 2 1

1 2 1 2

kTBR Rv Rv

R R R R= =

2 23 3 34nv v kTBR= =

( ) ( ) ( )2 2

2 1 2 2 1 1 23 32 2

1 21 2 1 2

4 4 4n eqT

R R R R R Rv kBT R kBT R kTBR

R RR R R R

= + + = + = ++ +

R RR R

R R= +

2 21 2

+ ( )2

2 12 2

+23 1A =, , and

Output Noise Power of Cascaded Circuits (II)

• When the noise temperature and gain of each stage are determined,the overall noise temperature and gain of the whole systemcan beobtained.

• Use the following methods to calculate the output noise ,(1) Cascade Formula

(2) Walk-Through method

(3) Summation method

1 1 dBL =

1 300 KT = �

3 4 dBL =

2 150 KeT = �

2 25 dBG =

4 700 KeT = �

4 30 dBG =

50 KsT = �

stage1 stage2 stage3 stage4

Cascade Formula Method

( ) ( )1 1 11 1.259 1 300 77.7 KeT L T= − = − = �

( ) ( )3 3 31 2.512 1 300 453.6 KeT L T= − = − = �

150 453.6 70077.7 275.42 K

0.794 0.794 316.23 0.794 316.23 0.398eTT = + + + =× × ×

( ) ( )23 211.38 10 50 275.42 =4.5 10 Watts Hz = 173.5 dBm Hzs eTk T T − −+ = × × + × −

0 173.5 1 25 4 30 dBm HzN = − − + − +

1 1 dBL =

1 300 KT = �

3 4 dBL =

2 150 KeT = �

2 25 dBG =

4 700 KeT = �

4 30 dBG =

50 KsT = �

Stage 1 Teff :

Stage 3 Teff :

System equivalent noise temperature and output noise :

Walk-Through Method – Stage 1

• Calculate the noise signal fromstage to stage. At first,calculate the noise density stage by stage:

� Antenna noise:

� Cable 1 noise:

23 191.38 10 50=6.9 10 mW Hz 181.6 dBm HzskT − −= × × × = −

( ) ( )1 1 11 1.259 1 300 77.7 KeT L T= − = − = �

23 191 1.38 10 77.7=10.72 10 mW Hz 179.7 dBm HzekT − −= × × × = −

1 1 dBL =

1 300 KT = �

3 4 dBL =

2 150 KeT = �

2 25 dBG =

4 700 KeT = �

4 30 dBG =

50 KsT = �

Stage Input A Input B Sum Output Noise Density (dBm/Hz)

1 −181.6 −179.7 −177.5 −178.5

2 −178.5

1 1 dBL =

1 300 KT = �

3 4 dBL =

2 150 KeT = �

2 25 dBG =

4 700 KeT = �

4 30 dBG =

50 KsT = �

� LNA Noise:23 19

2 1.38 10 150=2.07 10 mW Hz 176.8 dBm HzekT − −= × × × = −

1 −181.6 −179.7 −177.5 −178.5

2 −178.5 −176.8 −174.6 −149.6

3 −149.6

1 −181.6 −179.7 −177.5 −178.5

2 −178.5 −176.8 −174.6 −149.6

3 −149.6 −172.0 −149.6 −153.6

4 −153.6

1 1 dBL =

1 300 KT = �

3 4 dBL =

2 150 KeT = �

2 25 dBG =

4 700 KeT = �

4 30 dBG =

50 KsT = �

� Cable 2 Noise:

( ) ( )3 3 31 2.512 1 300 453.6 KeT L T= − = − = �

23 192 1.38 10 453.6=6.26 10 mW Hz 172 dBm HzekT − −= × × × = −

1 1 dBL =

1 300 KT = �

3 4 dBL =

2 150 KeT = �

2 25 dBG =

4 700 KeT = �

4 30 dBG =

50 KsT = �

� Gain amplifier noise:23 19

4 1.38 10 700=9.66 10 mW Hz 170.2 dBm HzekT − −= × × × = −

1 −181.6 −179.7 −177.5 −178.5

2 −178.5 −176.8 −174.6 −149.6

3 −149.6 −172.0 −149.6 −152.6

4 −153.6 −170.2 −153.5 −123.5

Summation Method

• Each noise source is individually taken through the variousgains and loses to the output, and the sumof all output noisesis just the total output noise (Superposition).

� For stage1:

� For stage2:

� For stage3:

� For stage4:

181.6 1 25 4 30 131.6 dBm Hz− − + − + = −

179.7 1 25 4 30 129.7 dBm Hz− − + − + = −

176.8 25 4 30 125.8 dBm Hz− + − + = −

172 4 30 146 dBm Hz− − + = −

170.2 30 140.2 dBm Hz− + = −

1 1 dBL =

1 300 KT = �

3 4 dBL =

2 150 KeT = �

2 25 dBG =

4 700 KeT = �

4 30 dBG =

50 KsT = �

Noise Contributor Output Noise Density (dBm/Hz)

Environment −131.6

Stage 1 −129.7

Stage 2 −125.8

Stage 3 −146.0

Stage 4 −140.2

Total −123.5

40-I/42

Noise Figure Method

1 1 dBL =

1 300 KT = �

3 4 dBL =

2 150 KeT = �

2 25 dBG =

4 700 KeT = �

4 30 dBG =

50 KsT = �

Atten1 Amp2 Atten3 Amp4

Gain (dB) -1 25 -4 30

Gain 0.79432823 316.227766 0.39810717 1000

T 300 150 300 700

F 1.26785387 1.51724138 2.56402045 3.4137931

NF (dB) 1.03069202 1.81054679 4.08921484 5.33237197

Cumumlatvie Gain 0.79432823 251.188643 100 100000

Fcas 1.26785387 1.91902219 1.92524867 1.9493866

NFcas (dB) 2.89897976

Gcas (dB) 50

Ni (Ts=50 K) (dBm) -181.611509

No=Ni+Gcas+NFcas -128.7125-128.7125-128.7125-128.7125 Wrong!Since NF is defined@290 KSince NF is defined@290 KSince NF is defined@290 KSince NF is defined@290 K

Fcas=1+(Te/T0)

Te 275.322114

No=Gcas(kTsB+kTeB) 4.4894E-16 -123.47807 Correct!

Department of Electronic Engineering, NTUT40-II/42

Sensitivity

where is the on-channel noise, including thermal, shot, flicker, antenna noise.

NIMG is the image noise, contributed from the mixing function

NLO is the LO noise, down-mixing to IF signal due to the mixing function

• The systemoverall noise figure is then obtained as

where includes noise, phase jittering and channel fading effects.

( ) ( ) ( ) ( )_dBm dBm dB dBout RF systemrequired

SSensitivity N NF

N= + +

out Channel IMG LON N N N= + +

ChannelN

Module Channel IMG LOF F F F= + +

Summary

• In this chapter, we’ve introduced the thermal noise and howtouse thermal noise to define the equivalent noise temperature.

• The measuring methods of the equivalent noise temperature(and thus the noise figure) are the practical procedurecorresponding to the noise theory. Each method has its ownpros and cons.

• The calculation of a cascade systemoutput noise was alsointroduced by using cascade formula, walk-through, andoutput summation methods.

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