Noise Figure Measurements -...

Group/Presentation TitleAgilent Restricted

Month November, 2005

Noise Figure Measurements

• Y-Factor

• Cold source

• 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



Calibration

• Noise Source Calibration (S)

• S-parameter Calibration (S)

• Noise Tuner Calibration (S)

Measurement

• Noise Figure Formats (S)

• Noise Factor

• Noise Figure

• Noise Temperature

• Noise Power Density

Objectives (cont)



Definition

( )

( )

/(noise factor) 1

/ *= = = +

∗

in out add

a in a inout

S N N NF

S N G N G N

Ga

Sin

Nin Nout

Sout

00

* ; *=

=

= = +out a in out a in addT T

T T

S 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. 1999

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.



Definition in Terms of Noise Temperature

0

1*

= = +out e

a in

N TF

G N T

T0 Nout

0* ; * * *= ∗ =in add a e

N 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

k

T

Te, Ga



Definition In Terms Of Noise Parameters

2

si sYn

e

ni

Noiseless

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 F

G Z

2

si sYNoisy

two-port

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



Noise parameters Definition (cont)

Γopt ≡ optimum input noise matchZ0 = reference impedance

Γs = 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 F

G Z

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

Fmin ≡ minimum noise factor

Rn ≡ noise resistance



Noise Source ENR – Excess Noise Ratio

h c

10

0

T TENR 10log

T

−≡

Th = Hot Noise Temperature

Tc = Cold Noise TemperatureT0 = 290 K

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

Noise sources��346C 10 MHz – 26.5 GHz



Y factor Method

( )0 0

*1 1

* 1 *

−= = + = +

−

out e hot cold

a in

N T T Y TF

G 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 T

P 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



Actual Y factor Measurement Calibration

Ga(R)

Thot

Nout(R)

RECEIVER

Te(R)Tcold

Pout

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 TF

G N T Y T

Assumes Γs(hot) = Γs(cold)



The Early Days



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

*1

1 *Γ

−= +

−s

hot coldall

T Y TF

Y T

( )( )

( ) ( )

( )

1Γ

Γ

−= −

o device

s

R

device all

a D

NFF NF

G

Note that ( )( ) ( )Γ Γ

≠o device sR R

F F



Some Y factor Measurement Assumptions

( ) ( )

( )

( ) ( )

−=

−

hot all cold all

a device

hot 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 Γs

Γs ≡ source reflection of the incident signal

True only if S11 and S22 are <<1



Using the ESA to measure Noise Figure:Requires option 219



Using the ESA to measure Noise Figure

Step 1: Setup frequencies, averaging, number of points

Step 2: Connect the Noise source, and Calibrate

Step 3: Connect the Amplifier (DUT) between the Noise Source and the ESA, and measure the Noise Figure

Data may be saved to a floppy disc

The data can be in CSV (comma separated) or as a .GIF

For more Training see document:

S800NFSA.pdf



From the Training Document: (Y-factor on ESA)



From the Training Document: Entering ENR data



From the Training Document: Correcting for Second Stage Noise



From the Training Document: How does the ESA measure gain?



Let’s look at some measurement results:

LNA: 26.5 GHz, ~1.5 dB NF, 15 dB Gain, S11~2-3 dB (bad)



You can also use an NFA (Noise Figure Analyzer) in a very similar way:

SA base optimized for NF measurements:

Includes low noise pre-amp for all frequencies

Optimized IF path amplifiers/attenuators for best response

Specialized NF digitizer for faster response.



Same Amplifier: Measurement Results

12:04:11 Oct 31, 2007

A:TST00122.GIF file saved

Load

Save

File Manager

File

DUT Amplifier Sys Downconv Off

10.00

NFIGScale/1.000

dB

0.000

20.00

GAINScale/2.000

dB

0.000

Start 250.00 MHz BW 4 MHz Points 201 Stop 26.50000 GHz

Tcold 302.43 K Avgs 2 Att 0/0 dB Loss Off Corr



Comparison: ESA to NFA (noise figure)

0

1

2

3

4

5

6

7

8

9

10

1.0 26.0 51.0 76.0 101.0 126.0 151.0 176.0 201.0

ESA-NF

NFA-NF



Comparison: ESA to NFA (Available Gain)

0

2

4

6

8

10

12

14

16

18

20

1.0 26.0 51.0 76.0 101.0 126.0 151.0 176.0 201.0

ESA-Gain

NFA-Gain



Newer techniques: Using PNA-X (VNA) to measure noise figure

Full VNA PLUS Noise Figure reciever.



Cold Noise Source Technique

Ga PN

n

Dut

0 a

PF 1

kT BG= +

Need to know gain very accurately

Ga is a function of of S11, S22 and Γs



T = Tcal

PN

T ~ 10,000K

DUT

T = Tmeas

PN

Calibrate

Measure

Cold Noise Figure Cal and Measurement

kGB k Gain Bandwidth= ⋅ ⋅

hot cold

hot cold

P PkGB

T T

−=

−

hot 0

r

nhot0

ncold

T T 1F

PT1

P

−= ⋅

−

n

Dut r

a

P1F F 1

G kGB

= ⋅ − +

ΓsΓo(device)

Γi(rec)

Γi(device)



Noise parameters Definition


Γs = 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 F

G Z


Fmin ≡ minimum noise factorRn ≡ noise resistance



Noise parameters Definition –Noise Temperature


Γs = source match

( )

( )

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 T

G Z


Tmin ≡ minimum noise Temperature

Rn ≡ noise resistance

T0 ≡ 290°K



• 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 ParametersFmin at Γopt

Increasing noise figure

Increasing noise figure



Noise wave representations

a1

b1

a2

b2[S]

bn1bn2

11 11 12 1

22 21 22 2

n

n

bb s s a

bb s s a

= +

P. Penfield, Jr "Wave Representation of Amplifier Noise." IRE Transactions On Circuit Theory: Mach (1962) pp. 84-86

K. Hartmann, “Noise Characterization of Linear Circuits,” IEEE Transactions on Circuits and Systems, Vol. cAS-23, No. 10, Oct. 1976, pp. 581-590

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

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.



Noise correlation matrix – S-parameters

2 *

1 1 2 11 12

2*21 22

2 1 2

C

= =

n n n

s

n n n

b b b cs cs

cs csb b b



Noise wave representations – T parameters

11 11 12 2

11 21 22 2

n

n

aa t t b

bb t t a

= +

a1

b1

a2

b2[Tn]

an1

bn1



Noise correlation matrix – T-parameters

2 *

1 1 1 11 12

2*21 22

1 1 1

C

= =

n n n

t

n n n

a a b ct ct

ct ctb a b



Noise Wave and Cascading Networks

a1a

b1a a2a

b2a

[Tna]

ana

bna

a1b

b1b a2b

b2b

[Tnb]

anb

bnb

[ Tnc ] = [ Tna ] [ Tnb ]

[ Ctc ] = [ Cta ] + [ Tna ] [ Ctb ] [ Tna ]T



Noise correlation matrix (S) in terms of noise parameters

( )( ) ( )( )

( )( )

2

2 11 11

min 11 21 min 112 2

0 0

2

211

21 min 11 21 min2 2

0 0

1 4 141 1 1

1 1

4 1 41 1

1 1

sC

− Γ Γ − Γ − − + − − + Γ + Γ

= Γ − Γ Γ − − − + Γ + Γ

opt n opt optn

opt opt

n opt opt n opt

opt opt

S R SRF s S F S

Z Z

R S RS F S S F

Z Z



Measurement using (S) noise matrix

( )

( )

2 22

121

2 2 *11 11 2 11 3

2 *2 2 1 222 12

1 1 11 2 32 2 * *

21 2121 21

1

1 1 2 Re 1

, ,

− Γ + Γ + = − Γ − Γ + − Γ Γ

= = = = = =

s s s

out

s s s s

n n nn

T XkB SP

S S X S X

b b bcs csX b cs X X

S SS S

Noise output power from two-port is

assumes termination is ideal

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



The Problem with Measuring Noise Figure

NFA and other analyzers measure NF in a nominal 50-ohm

environment

Noise parameter analysis shows us that NF varies with source

impedance (Γs)

Test systems don’t have perfect 50-ohm source impedances

Conventional noise figure systems introduce significant error due to

non-ideal source match



New Noise Measurement System

DUT

Noise Tuner

Noise Receiver

Inside

ADAPTER Noise Source



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

28V DC



Calibration of the receiver

5 unknowns, linear equation

i

( )

( )

2 2

2 2

1

2 21

*11 11 11

2

211

1 1 2 Re 1

− Γ + Γ + = − Γ − Γ + − Γ Γ

s s s

out

s s s s

TkP

X S

X

S XS

B S

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



S11P1

S21P1

S11S22

S21

S12

“DUT”

S12P1

S22P1

S11P2

S21P2

S12P2

S22P2S11D S22D

S21D

S12D

PROBE 1 ACTUAL DUT PROBE 2

[ TA ]

[ TAD ] [ TP2 ][ TP1 ]

Probe or Fixture De-embedding – S-Parameters

[ TA ] = [ TP1 ]∗∗∗∗[ TAD ]∗∗∗∗[ TP2 ]

[ TAD ] = [ TP1 ]-1∗∗∗∗[ TA ]∗∗∗∗[ TP2 ]-1

41

41

1 2 3 4



S11P1

S21P1

S11S22

S21

S12

S12P1

S22P1

S11P2

S21P2

S12P2

S22P2S11D S22D

S21D

S12D

[ TA ]

[ TAD ] [ TP2 ][ TP1 ]

Probe or Fixture De-embedding – Nose-Parameters

[CtA]

[CtP2][CtAD][CtP1]

T

1 1 1combined 2C C T C T= + i i

Noise Correlation Matrix Propagation:



PNA-X: “Noise Pulling”

PNA-X will vary source match around 50 ohms using an ECal module (source pull)

With resulting noise-figure circle and vector error terms, very accurate 50-ohm noise figure (NF50) can be calculated

Initial implementation will not provide full noise-parameter analysis, as the range of source impedances is too small (won’t cover enough of Smith chart)

F1, F2, …



Data Comparison: PNA vs ESA or NFA (Noise Fig.)

0

1

2

3

4

5

6

7

8

9

10

0.3 3.5 6.8 10.1 13.4 16.7 19.9 23.2 26.5

PNA-NF

ESA-NF

NFA-NF



Data Comparison: PNA vs ESA or NFA (Gain)

0

2

4

6

8

10

12

14

16

18

20

0.3 3.5 6.8 10.1 13.4 16.7 19.9 23.2 26.5

PNA-S21

ESA-Gain

NFA-Gain



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 dB

Input/output match = 10 dBNF = 3 dB

Gamma opt = 0.268 ∠ 0o

Fmin = 1.87 dB

Rn = 12 – 33

0.2 dB

0.75 dB

0.5 dBY-factor with noise source

directly at DUT input



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



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



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



Noise Figure Measurement Instrument Setup



Noise Measurement Softkeys



Noise Set Up



Noise Figure Measurement Calibration



Noise Cal

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