agilent technologies ~ advancements in noise measurement by ken wong, 08-2008

IEEE IMS SCV Chapter Mtg

May 21, 2008

Advancements in Noise Measurement

byKen Wong, Senior Member IEEER&D Principal EngineerComponent Test DivisionAgilent Technologies, Inc.

Reproduced with Permission, Courtesy of Agilent Technologies, Inc. by Bob Laughlin.


May 21, 2008

Aerospace and Defense Symposium 2007EuMw 2007 Agilent Workshop

By Ken WongAdvancements in Noise Measurement

Noise Figure Measurements• Y-Factor • Cold source • Noise Parameters• Noise Wave• Correcting for Source Impedance Mismatch • Correcting for Receiver Mismatch and Noise

VNA Noise Figure Measurements• Setup (S)• Setting Input (Fwd) and Output (Rev) Powers• Choosing Noise Bandwidth• Setting Noise Averaging Factor• Choosing the Receiver Gain Setting

Objectives


May 21, 2008



Calibration • Noise Source Calibration (S)• S-parameter Calibration (S)• Noise Tuner Calibration (S)

Verification• Mismatch Line• Amp Characteristics• Combined S11• Combined Gain• Combined Noise Figure

Objectives (cont)


May 21, 2008



The Early Days


May 21, 2008



Agilent’s Noise Figure Legacy

340A 195889701980

SA with NF2002

8560/90 with NF1995

85120 1999

NFA2000


May 21, 2008



Definition

( )( )

/(noise factor) 1

/ *= = = +

∗in out add

a in a inout

S N N NFS N G N G N

Ga

Sin

Nin Nout

Sout

00

* ; *= =

= = +out a in out a in addT T T TS G S N G N N

DEVICE

Ga ≡ Available Gain, NF (Noise Figure) ≡ 10*log10(F) dB

D. Vondran, “Noise Figure Measurement: Corrections Related to Match and Gain,” Microwave J., pp 22-38, Mar. 1999Collantes, J. M., R. D. Pollard, et al. (2002). "Effects of DUT mismatch on the noise figure characterization: a comparative analysis of two Y-factor techniques." Instrumentation and Measurement, IEEE Transactions on 51(6): 1150-1156.


May 21, 2008



Definition in Terms of Noise Temperature

0

1*

= = +out e

a in

N TFG N T

T0 Nout

0* ; * * *= ∗ =in add a eN k T B N G k T B

DEVICE

0-23

290 ; bandwidth

Boltzmann's constant = 1.380 6505×10 joule/kelvin effective input noise temperature of device

≡ ≡

≡≡e

T K B

kT

Te, Ga


May 21, 2008



Effective Temperature Versus Noise Figure

1.00

10.00

100.00

1000.00

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

NF (dB)

Te (K

)


May 21, 2008



Definition In Terms Of Noise Parameters

2si sY ne

niNoiseless two-port

( )2

2

min min 2 20

4

1 1

Γ − Γ⎛ ⎞= + − = +⎜ ⎟

+ Γ − Γ⎝ ⎠

opt sn ns opt

s opt s

R RF F Y Y FG Z

2si sY Noisy

two-port

IRE Subcommittee 7.9 On Noise: “Representation Of Noise In Linear Two-ports,” Proc. IRE, Vol. 48, Pp. 69-74, Jan. 1960


May 21, 2008



Noise parameters Definition (cont)

Γopt ≡ optimum input noise matchZ0 = reference impedanceΓs = source match

( )2

2

min min 2 20

4

1 1

Γ −Γ⎛ ⎞= + − = +⎜ ⎟

+ Γ − Γ⎝ ⎠

opt sn ns opt

s opt s

R RF F Y Y FG Z

Yopt ≡ optimum input admittanceYs = source admittanceGs = real part of Ys

Fmin ≡ minimum noise factorRn ≡ noise resistance


May 21, 2008



Noise Source ENR – Excess Noise Ratio

h c10

0

T TENR 10log

T⎛ ⎞−

≡ ⎜ ⎟⎝ ⎠

Th = Hot Noise TemperatureTc = Cold Noise TemperatureT0 = 290 K

Tc = T0 when noise sources are calibrated by reference labs.

Noise source346C 10 MHz – 26.5 GHz


May 21, 2008



Y factor Method

( )0 0

*1 1* 1 *

−= = + = +

−out e hot cold

a in

N T T Y TFG N T Y T

Thot

Pout

DEVICE

Te, GaTcold

Pout,hot=kBGa(Thot + Te) Pout,cold=kBGa(Tcold + Te)

,

,

1

out hot hot colde

out cold

P T YTY TP Y

−= =

−

Assumes ALL Reflections are the same.

“Fundamentals of RF and Microwave Noise Figure Measurements,” Hewlett-Packard Application Note 57-1, Palo Alto, CA July 1983


May 21, 2008



Actual Y factor Measurement Calibration

Ga(R)

Thot

Nout(R)

RECEIVER

Te(R)TcoldPout

Γi(rec)

Γs(cold)

Γs(hot)

Receiver Calibration

( )( ) ( )

( )( ) 0 0

*1 1* 1 *Γ

−= = + = +

−s

out R e R hot coldR

a R in

N T T Y TFG N T Y T

Assumes Γs(hot) = Γs(cold)


May 21, 2008



Actual Y factor Measurement

Ga(D)

Thot

Nout(D)

DEVICE

Te(D)Tcold Nout(all)

RECEIVER

Pout

Γs(hot)Γs(cold) Γo(device) Γi(rec)

Γi(device)

Ga(R)Te(R)

( )( )0

*11 *Γ

−= +

−s

hot coldall

T Y TFY T

( )( )

( ) ( )( )

1Γ

Γ

−= − o device

s

R

device alla D

FF F

G

Note that ( )( ) ( )Γ Γ≠o device sR RF F


May 21, 2008



Some Y factor Measurement Assumptions

( ) ( )( )

( ) ( )

−=

−hot all cold all

a devicehot R cold R

N NG

N N

( )( ) ( )Γ Γ=o device sR RF F

( ) ( )Γ = Γs hot s cold

Notes:Ga (available gain) is a function of S11, S22 and ΓsΓs ≡ source reflection of the incident signal

True only if S11 and S22 are <<1


May 21, 2008



Four Examples Of Y-Factor Measurements

What you want for good NF accuracy!

Noise source

Noise source

Automated multi-instrument

(ATE) environment

On-wafer environment

On-wafer multi-instrument

(ATE) environment

1 2

3 4

Noise source Noise source


May 21, 2008



Cold Noise Source Technique

Ga PN

nDut

0 a

PF 1

kT BG= +

Need to know gain very accuratelyGa is a function of of S11, S22 and Γs


May 21, 2008



T = T cal

PN

T ~ 10,000K

DUT

T = T meas

PN

Calibrate

Measure

Cold Noise Figure Cal and Measurement

kGB k Gain Bandwidth= ⋅ ⋅

hot cold

hot cold

P PkGB

T T−

=−

hot 0r

nhot0

ncold

T T 1FPT 1P

−= ⋅

⎛ ⎞−⎜ ⎟⎝ ⎠

nDut r

a

P1F F 1G kGB

⎛ ⎞= ⋅ − +⎜ ⎟⎝ ⎠

ΓsΓo(device)

Γi(rec)

Γi(device)


May 21, 2008



Noise Parameters

2si sY ne

niNoiseless two-port

Noise figure varies as a function of source impedance

Noise figure varies as a function of source impedance

( )2s

2

opt

2

sopt

o

nmin

Γ1Γ1

ΓΓZ

4RFF−+

−+=

Four noise parameters: Fmin, Rn, Γopt (mag), Γopt (phase)


May 21, 2008



Noise parameters Definition


( )2

2

min min 2 20

4

1 1

Γ −Γ⎛ ⎞= + − = +⎜ ⎟

+ Γ − Γ⎝ ⎠

opt sn ns opt

s opt s

R RF F Y Y FG Z


Fmin ≡ minimum noise factorRn ≡ noise resistance


May 21, 2008



Noise parameters Definition –Noise Temperature


( )

( )2 2

0 0min min 2 2

0

4

1 1

− Γ −Γ= + = +

+Γ − Γ

n s opt opt snn

s opt s

R T Y Y T RT T TG Z


Tmin ≡ minimum noise TemperatureRn ≡ noise resistanceT0 ≡ 290°K


May 21, 2008



• Plots of noise figure circles versus impedance (at one frequency)

• Fmin is lowest noise figure and occurs at Γopt

• F changes with Γ• F changes with device bias

Noise Parameters

Fmin at Γopt

Increasing noise figure

Increasing noise figure


May 21, 2008



Measuring Noise parameters

DUT

VNA

Noise source

TUNER

NFM

A. C. Davidson, B. W. Leake, et al. (1989). "Accuracy improvements in microwave noise parameter measurements." Microwave Theory and Techniques, IEEE Transactions on 37(12): 1973-1978.


May 21, 2008



Noise wave representation – S-parameters

a1

b1 a2

b2[S]bn1

bn2

11 11 12 1

22 21 22 2

n

n

bb s s abb s s a⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞

= + ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

P. Penfield, Jr "Wave Representation of Amplifier Noise." IRE Transactions On Circuit Theory: Mach (1962) pp. 84-86K. Hartmann, “Noise Characterization of Linear Circuits,” IEEE Transactions on Circuits and Systems, Vol. cAS-23, No. 10, Oct. 1976, pp. 581-590R.P. Meys, “A Wave Approach to the Noise Properties of Linar Microwave Devices,” IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-26, No. 1, Jan. 1978, pp 34-37S. W. Wedg ,and D. B. Rutledge (1992). "Wave techniques for noise modeling and measurement." Microwave Theory and Techniques, IEEE Transactions on 40(11): 2004-2012.

2 *1 1 2 11 12

2* 21 222 1 2

C⎛ ⎞ ⎛ ⎞⎜ ⎟= = ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

n n ns

n n n

b b b cs cscs csb b b


May 21, 2008



Measurement using (S) noise correlation matrix

( )( )

2 2

2 2 *11 11 11

2 *2 2 1 222 12

1 1 11 2 122 2

21

21

* *21 2121 21

2 21

1

1 1 2 Re 1

, ,

⎧ ⎫− Γ + Γ +⎛ ⎞⎪ ⎪= ⎜ ⎟⎨ ⎬⎜ ⎟−Γ ⎡ ⎤−Γ + −Γ Γ⎪ ⎪⎝ ⎠ ⎣ ⎦⎩ ⎭

= = = = = =

s s s

outs s s s

n n nn

TkP

S S S

b b bcs csX b cs X XS

XB s

X

SS

X

S

Noise output power from two-port is

J. Randa, W. Wiatr, “Conte Carlo Estimation of Noise Parameter Uncertainties,” IEE Proc. Sci. Meas. Technology, Vol. 149, No. 6, Nov. 2002, pp. 333-337

( )0= +out av eP kBG T T


May 21, 2008



Noise correlation matrix (CS) in terms of noise parameters

( )( ) ( ) ( )

( ) ( )

2

2 11 11min 11 21 min 112 2

0 0

2

21121 min 11 21 min2 2

0 0

1 4 141 1 11 1

4 1 41 1

1 1

opt n opt optn

opt opt

n opt opt n opt

opt opt

s R sRF s s F sZ Z

R s Rs F s s F

Z Z

⎛ ⎞⎛ ⎞− Γ Γ − Γ⎜ ⎟⎜ ⎟− − + − −⎜ ⎟⎜ ⎟+ Γ +Γ⎜ ⎟⎝ ⎠⎜ ⎟= ⎜ ⎟⎜ ⎟⎛ ⎞ ⎛ ⎞Γ − Γ Γ⎜ ⎟⎜ ⎟ ⎜ ⎟− − −⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟+ Γ +Γ⎝ ⎠ ⎝ ⎠⎝ ⎠

sC


May 21, 2008



New Noise Measurement System

DUT

Noise Tuner

Noise Receiver Inside

ADAPTER Noise Source


May 21, 2008



ECal as Noise Tuner

PNA-X varies source match around 50 ohms using an ECal module ECal can provide 7 impedance states

(Z1, F1), (Z2, F2), …


May 21, 2008



Noise Figure in PNA – contributions

Speed and accuracy –• Single Connection S-parameters and Noise Figure• Fast Step Frequency Sweep • Complete Mismatch Correction

Use of ECal or Compatible Impedance Tuner

Embedding and De-embedding of Probes in On-Wafer Noise Measurements

Can Accommodate Coax Noise Source for On-Wafer Noise Measurements


May 21, 2008



Calibration of the receiver

5 unknowns, linear equation

i

( )( )

2 2

2 2

1

2 21*

11 11 11

221

1

1 1 2 Re 1

⎧ ⎫− Γ + Γ +⎛ ⎞⎪ ⎪⎜ ⎟= ⎨ ⎬⎜ ⎟−Γ ⎡ ⎤−Γ + −Γ Γ⎪ ⎪⎝ ⎠ ⎣ ⎦⎩ ⎭

s s s

outs s s s

TkP

X S

X

S XS

B S

Note: The PNA-X uses a different form of the above equation.


May 21, 2008



Calibration of receiver- solution of equations

Require Minimum Of 5 Equations To Solve

Can Be Over-determined

At Least One Measurement Must Be Made With Different Source Temperature

Use Noise Source (Known ENR, Measure ΓCold, ΓHot)

ECal Module Provides 7 Terminations


May 21, 2008



Noise Figure Mode Instrument Default Settings

S-parameter Mode Source Power -30 dBm

Noise RF BW 4 MHz

Noise IF BW 2 MHz

Noise Averaging Point to Point (1 = 10K)

Noise Receiver Gain 30 dB

Factory Receiver Cal ON


May 21, 2008



Noise Figure Measurement Instrument Setup


May 21, 2008



Noise Measurement Softkeys


May 21, 2008



Noise Set Up


May 21, 2008



Noise Figure Measurement Calibration


May 21, 2008



Noise Cal


May 21, 2008



S-parameters and Noise Calibrations

Noise Tuner

ADAPTER

Ph, Pc, Γh, Γc

Noise Source

This step provides 2 of the five measurements required.


May 21, 2008




Noise Tuner

ADAPTER This step provides the rest of measurements required to calibrate the noise receiver. Pnt(i), Γnt(i)Γnr


May 21, 2008




Noise Tuner

S-parameter calibration completes the calibration sequence.


May 21, 2008



Measurement of DUT

Known from Measured S-parameters

( )( )

2 2

2 2

1

2 21*

11 11 11

221

1

1 1 2 Re 1

⎧ ⎫− Γ + Γ +⎛ ⎞⎪ ⎪⎜ ⎟= ⎨ ⎬⎜ ⎟−Γ ⎡ ⎤−Γ + −Γ Γ⎪ ⎪⎝ ⎠ ⎣ ⎦⎩ ⎭

s s s

outs s s s

TkP

X S

X

S XS

B S

4 unknowns, linear equation


May 21, 2008



DUT S-parameters and Noise Measurement

DUT

Noise Tuner

Meas S-parametersPout(i) @ each Γnt(i)


May 21, 2008



Noise Measurement System With On-Wafer Probes

Noise Tuner

4

Noise Source

FULL 2-port Cal

1-port Cal


May 21, 2008



60 µm FET

0 5 10 15 20 25

Frequency (GHz)

F (1

dB

per

div

isio

n)

corrected

cold

Y-factor

N8975Data sets offset by 1dB


May 21, 2008



Measurements Compared

0

2

4

6

8

10

1 2 3 4 5 6

Frequency (GHz)

NF

(dB

)

0

2

4

6

8

10

12

14

16

18

20

Gai

n (d

B)

NFA

PNA/NF


May 21, 2008



Noise Figure Uncertainty Example (ATE Setup)

2.000

2.500

3.000

3.500

4.000

4.500

0.5 2.5 4.5 6.5 8.5 10.5 12.5 14.5 16.5 18.5 20.5 22.5 24.5 26.5

GHz

NF (d

B)

PNA-X

Y-factor with noise source connected to DUT via switch

matrix

Amplifier:Gain = 15 dBInput/output match = 10 dBNF = 3 dBGamma opt = 0.268 ∠ 0o

Fmin = 1.87 dBRn = 12 – 33

0.2 dB

0.75 dB

0.5 dBY-factor with noise source

directly at DUT input


May 21, 2008



Noise Figure Uncertainty Example (Wafer Setup)

PNA-X

Y-factor with noise source connected to DUT input

Y-factor with noise source connected to DUT via switch matrix


Fmin = 1.87 dBRn = 12 – 33Wave model correlation = 50%

2.000

2.500

3.000

3.500

4.000

4.500

0.5 2.5 4.5 6.5 8.5 10.5 12.5 14.5 16.5 18.5 20.5 22.5 24.5 26.5

GHz

NF (d

B)

PNA-X

Y-factor with noise source connected to probe input

Y-factor with noise source connected to probe via switch matrix


Fmin = 1.87 dBRn = 12 – 33

0.3 dB

1.1 dB

0.75 dB


May 21, 2008



Verification approach

Need To Avoid Using An Active Device– Cannot Guarantee Behavior Over Time– Dependence On Temperature– Noise May Be Injected Through Bias Supply

Use Mismatched Transmission Line, Passive Device– Noise Parameters, Noise Figure Are Calculated From S-

parameters– Can Cascade With Any Amplifier And De-embed


May 21, 2008



Mismatch Transmission Line Characteristics


May 21, 2008



Noise wave representations

a1L

b1L a2L

b2L[TL]anL

bnL

a1A

b1A a2A

b2A[TA]anA

bnA

50 Ω 25 Ω 50 Ω AMP

[TL], [CL] [TA], [CA]

2 2* *

2 2* *;C C

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟= =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

nL nL nL nA nA nAtL tA

nL nL nL nA nA nA

a a b a a b

b a b b a b


May 21, 2008



Measured S-parameters of Amplifier


May 21, 2008



Calculated vs. Measured Combined |S11|


May 21, 2008



Calculated vs. Measured Combined Gain


May 21, 2008



Calculated vs. Measured Combined Noise Figure

Uncertainty Bark=2


May 21, 2008



Additional References:

[1] D. Vondran, “Noise Figure Measurement: Corrections Related to Match and Gain,” Microwave J., pp 22-38, Mar. 1999[2] Collantes, J. M., R. D. Pollard, et al. (2002). "Effects of DUT mismatch on the noise figure characterization: a comparative analysis of two Y-factor techniques." Instrumentation and Measurement, IEEE Transactions on 51(6): 1150-1156.[3] “Fundamentals of RF and Microwave Noise Figure Measurements,” Hewlett-Packard Application Note 57-1, Palo Alto, CA July 1983[4] IRE Subcommittee 7.9 On Noise: “Representation Of Noise In Linear Two-ports,” Proc. IRE, Vol. 48, Pp. 69-74, Jan. 1960[4] A. C. Davidson, B. W. Leake, et al. (1989). "Accuracy improvements in microwave noise parameter measurements." Microwave Theory and Techniques, IEEE Transactions on 37(12): 1973-1978.[5] R.Q. Lane, “The Determination of Device Noise Parameters,” Proceedings of the IEEE, Aug. 1969, pp. 1461-1462[6] P. Penfield, Jr "Wave Representation of Amplifier Noise." IRE Transactions On Circuit Theory: Mach (1962) pp. 84-86[7] K. Hartmann, “Noise Characterization of Linear Circuits,” IEEE Transactions on Circuits and Systems, Vol. cAS-23, No. 10, Oct. 1976, pp. 581-590[8] R.P. Meys, “A Wave Approach to the Noise Properties of Linar Microwave Devices,” IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-26, No. 1, Jan. 1978, pp 34-37[9] S. W. Wedg ,and D. B. Rutledge (1992). "Wave techniques for noise modeling and measurement." Microwave Theory and Techniques, IEEE Transactions on 40(11): 2004-2012.[10] J. Randa, W. Wiatr, “Conte Carlo Estimation of Noise Parameter Uncertainties,” IEE Proc. Sci. Meas. Technology, Vol. 149, No. 6, Nov. 2002, pp. 333-337[11] E.C. Valk, D. Routledge, J.F. Vaneldik, T.L. Landecker, “De-Embedding Two-Port Noise Parameters Using a Noise Wave Model,” IEEE Transactions on Instrumentation and Measurement, vol. 37, no. 2, June 1988, pp 195-200


May 21, 2008



Test port 1

R1

Source 1

OUT 1OUT 2

Source 2

OUT 1 OUT 2

Test port 2

R2

35 dB

65 dB

65 dB

Rear panel

A

35 dB

B

Source 2 Output 1

Source 2 Output 2

Noise receivers

10 MHz -3 GHz

3 - 26.5 GHz

DUT

Noise Source

24V DC

Noise Option Block Diagram

agilent technologies ~ advancements in noise measurement by ken wong, 08-2008

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