comparison of tuner-based noise-parameter extraction...
Post on 05-May-2018
228 Views
Preview:
TRANSCRIPT
L. BelostotskiMay 4, 2010, BUY 1
Comparison of tuner-based noise-parameter extraction methods for
measurements of room-temperature SKA LNAs
Leonid BelostotskiMay 4, 2010
L. Belostotski 2/26May 4, 2010, BUY
Outline
• Review: Two-port networks • Noise-parameter measurement• Equipment measurement accuracy• Monte Carlo analysis• Experimental results• SKA LNA example• Conclusions
L. Belostotski 3/26May 4, 2010, BUY
Review: Two-port networks
• A single-ended low noise amplifier (LNA) can be represented by a two-port network
• The electrical performance of two-port is analyzed with:– Z-parameters– Y-parameters– S-parameters– ABCD parameters– Etc.
• These electrical parameters are represented by 2x2 matrices
[ ] [ ][ ]( )IZV =
[ ] [ ][ ]( )VYI =
=
2
2
1
1
IV
DCBA
IV
[ ] [ ][ ]( ) wavereflected theis and aveincident w theis where baasb =
L. Belostotski 4/26May 4, 2010, BUY
Review: Two-port networks• Similarly to electrical parameters, noise parameters of two-
ports can be expressed with 2x2 matrices.• The noisy two port networks are represented by a noiseless
two-port network (discussed above) and two noise sources.
• The noise sources may be correlated
**
**
*222
*1
*21
*11
*222
*1
*21
*11
21
21
21
nnnn
nnnnABCDZY iiiv
ivvvf
Cvvvvvvvv
fC
iiiiiiii
fC
∆=
∆=
∆=
L. Belostotski 5/26May 4, 2010, BUY
Review: Noisy two-port networks• Why does one need the noise correlation matrices?
– Consider a two-port network driven by a signal source
– The noise figure (factor) of this two-port is:
– For a given Ys, the noise figure of a two-port network is obtained from CABCD! Nothing else is required!
2221
1211**
**
22
1cccc
kTiiivivvv
fC
nnnn
nnnnABCD =
∆=
( )( )2
******
2
*
2
22
11s
nnssnnsnnsnn
s
nsnnsn
s
nsns
ivvYYviYivYii
ivYivYi
ivYii
F ++++=
+++=
++=
{ } { }s
sssss Y
cYcYcYcFYfkTi
Re1 then Re4 since and 11
221
*12222 +++
+=∆=
L. Belostotski 6/26May 4, 2010, BUY
Review: Two-port networks
• The noise figure (factor) of this two-port was found to be:
• Can solve for Ys,opt= Gs,opt+jBs,opt that minimizes the noise figure
• The lowest (minimum) noise figure is obtained by substituting Ys,optback into F:
• If Ys ≠ Ys,opt then the noise figure (factor) is
{ } { }11
12
2
11
12
11
22,
ImImc
cjc
cccY opts +
−=
{ } { }( )11,12,
11
2
,21*,12,22
min Re21Re
1 cGcY
cYcYcYcF opts
opts
optsoptsopts ++=+++
+=
{ }2
,11
min Re optsss
YYY
cFF −+=
{ }s
sss
YcYcYcYc
FRe
1 112
21*
1222 ++++=
L. Belostotski 7/26May 4, 2010, BUY
Review: Two-port networks• Ys,opt, Fmin, and F can be found directly by using the noise
correlation matrix:
• Commonly Ys,opt, Fmin, and Rn=c11 are called the noise parameters of a two-port network.
• In terms of noise parameters, the noise correlation matrix is
{ } { }11
12
2
11
12
11
22,
ImImc
cjc
cccY opts +
−=
{ }( )11,12min Re21 cGcF opts++={ }
2
,11
min Re optsss
YYY
cFF −+=
11 12
21 22
2ABCD
c cC kT
c c=
2
,,min
*,
min
21
21
2optsnoptsn
optsnn
ABCD
YRYRF
YRFRkTC
−−
−−
=
L. Belostotski 8/26May 4, 2010, BUY
Noise-parameter measurement
• There are a few techniques: tuner based, mismatched line based, and noise wave-amplitude based, etc
• This talk focus on tuner-based extraction techniques
Noise source
L. Belostotski 9/26May 4, 2010, BUY
Noise-parameter measurement
LNA
Source tuner(Focus)
Tri-state noise source LN2 (outside
temporary)
Helium
Shielded box
PNA-X NFA
Source tuner(Maury)
Temperature monitor
L. Belostotski 10/26May 4, 2010, BUY
Noise-parameter measurement
• Tuner can generates a number of impedances (admittances) at the receiver (or the DUT) input
• Remember
• Measurement of noise figures at a few of these admittances allows the extraction of (Fmin, Rn and Yopt)
2
min sopts
n YYGRFF −+=
L. Belostotski 11/26May 4, 2010, BUY
Noise-parameter measurement
• How are the noise figures measured?• Two approaches:
– Cold methods– Hot-cold methods (aka modified Y-factor methods)
L. Belostotski 12/26May 4, 2010, BUY
Noise-parameter measurement (Cold methods)• Cold methods:
–Noise source only toggles from OFF to ON when tuner synthesizes 50Ohm impedance and the receiver measures two noise power levels
where Mc(h)Grec is the receiver transducer gain, Pc(h)in noise power at
the receiver input, Pc(h)rec,cal receiver noise power, and Tc(h)
iNet and Gc(h)
A,iNet are the noise temperature and available gain of the tuner.– With a few different impedances at the receiver input, Grec and the
receiver noise parameters are obtained–Note: noise source impedance changes when it toggles which
complicates the extraction of Grec.
L. Belostotski 13/26May 4, 2010, BUY
Noise-parameter measurement (Cold methods)
• Based on the way Grec is found, cold methods are subdivided into:– Simplified Cold method (assumes noise source impedance does
not change when it toggles and assumes Ta=Tcns)
– Iterative Cold method (uses iterative approach to finding Grec)– Direct Cold method (uses least-squares approach to find Grec and
the noise parameters simultaneously, similar to the modified Y-factor method)
• For DUT measurements the noise source is always OFF. – Noise powers measured by receiver are related to the DUT noise
powers through Grec .– Errors in Grec cause errors in noise parameters.
L. Belostotski 14/26May 4, 2010, BUY
Noise-parameter measurement (modified Y-factor)
• Modified Y-factor method (Hot-Cold method):– Noise source toggles from OFF to ON at impedance synthesized
by the tuner– The receiver measures two noise power levels for each tuner
impedance
– Grec and the noise parameters are determined using a least-squares fit
– For each impedance synthesized by the tuner, Grec is indirectly measured expect better accuracy in extracting Grec.
L. Belostotski 17/26May 4, 2010, BUY
Monte Carlo analysis
• Simple Cold method gives the worst performance• Modified Y-factor is the best for Rn extractions but not Γopt.
L. Belostotski 18/26May 4, 2010, BUY
Monte Carlo analysis
• Modified Y-factor is the best for Fmin and Grec extractions but not Rn and Γopt.
L. Belostotski 19/26May 4, 2010, BUY
Experimental results
Van den Bosch
Van den Bosch
Van den Bosch
Van den Bosch
Van den Bosch
Tuner calibration
L. Belostotski 20/26May 4, 2010, BUY
Experimental results
NFA averaging is important!!!
Tuner repeatability is themost dominant source of error
S-parameter measurementsare good enough
L. Belostotski 22/26May 4, 2010, BUY
Experimental results (150 measurements)
These numbers don’t capture systematic offsets seen in the previous slide. The simplified Coldmethod deviates the most from the other methods.
L. Belostotski 26/26May 4, 2010, BUY
Conclusions
• A combination of noise extraction methods produces the best results in terms of smallest standard deviations
• Tuner repeatability and noise power measurements are the most critical contributors to measurement errors
• S-parameter measurements are sufficiently accurate and don’t contribute significantly to noise parameter extractions
• Errors in ENRs contribute directly to systematic offsets
top related