Group/Presentation Title Agilent 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
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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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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)
Group/Presentation TitleAgilent Restricted
Month November, 2005
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.
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Yopt ≡ optimum input admittanceYs = source admittanceGs = real part of Ys
Tmin ≡ minimum noise Temperature
Rn ≡ noise resistance
T0 ≡ 290°K
Group/Presentation TitleAgilent Restricted
Month November, 2005
• 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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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.
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
New Noise Measurement System
DUT
Noise Tuner
Noise Receiver
Inside
ADAPTER Noise Source
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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.
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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:
Group/Presentation TitleAgilent Restricted
Month November, 2005
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)
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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
Group/Presentation TitleAgilent Restricted
Month November, 2005
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