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Studying the Forward-Reverse Method Through Simulations: II Raul Monsalve SESE, Arizona State University July 13, 2014
Studying the Forward-Reverse MethodThrough Simulations: II
Raul Monsalve
SESE, Arizona State University
July 13, 2014
DescriptionThis report studies a scenario not considered in earlier reports covering theForward-Reverse Method (FRM)12. For the basics of the method and thenomenclature, please read those reports.
In practice, if the measurement port (the connector right at the VNA) is female, then thereversible test network needs to have male connectors. Therefore the standardsmeasured at the VNA need to be male, while those measured at the end of the testnetwork need to be female. Of course, if the VNA port is male, the opposite applies.
Using a gender adapter in some of the measurements seems like a viable way torequire only one set of standards, but it does not solve the problem because theadapter would need to be characterized using accurately modeled standards.Following this path only makes the problem grow, requiring more measurements tosolve for more variables.
The approach taken here is the cleanest possible. A set of standards of gender X ismeasured at the VNA, and another set of gender Y is measured at the end of the testnetwork. Then, the FRM solves for the delay of both LOAD standards. It is assumedthat the other parameters of the sets are known with enough accuracy.
The following plots show how well the delays can be recovered in realistic scenarios.The concern was how much covariance there could be between the two delays. As theplots show, and the conclusion stresses, in general the covariance is low and theprecision is good.
1http://loco.lab.asu.edu/memos/edges_reports/report_20140630.pdf
2http://loco.lab.asu.edu/memos/edges_reports/report_20140707.pdf
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Description
The settings of the nominal case are:
Simulation Parameter Value Comments
Number of repetitions 500 Sufficient repetitions for sampling parameter spaceFrequency 1 GHz The figure of merit is more sensitive as frequency increasesDelay of LOAD 1 (at VNA) 20 psDelay of LOAD 2 (at test network) 30 psOther parameters of standards nominal Nominal from AgilentSe11 0, 0 Perfect VNA calibrationSe12Se21 1, 0 Perfect VNA calibrationSe22 0, 0 Perfect VNA calibrationSt11 0.1, 45 Close to optimal test networkSt12St21 0.8, 180 Close to optimal test networkSt22 0.9, 45 Close to optimal test networkMeasurement noise 1e-5 Approximate 1σ noise level for all loads in real and imaginary domains
The following figures present the results of simulations with nominal settings,compared to cases with other realistic settings.
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Different Delay Values
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12
14
16
18
20
22
24
26
28
30
delay LOAD 2 [ps]
dela
y L
OA
D 1
[ps]
nominal: delay 1 = 20 ps, delay 2 = 30 ps
Figure : (1): The distribution of samples is very symmetrical, and the precision isbetter than ± 2 ps for both delays.
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−5 −3 −1 1 3 5 7 9 11 13 1520
22
24
26
28
30
32
34
36
38
40
delay LOAD 2 [ps]
dela
y L
OA
D 1
[ps]
delay 1 = 30 ps, delay 2 = 5 ps
Figure : (2): Different values for the delays. Their distribution and precision aresimilar as those for the nominal case.
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−10 −8 −6 −4 −2 0 2 4 6 8 10−10
−8
−6
−4
−2
0
2
4
6
8
10
delay LOAD 2 [ps]
de
lay L
OA
D 1
[p
s]
delay 1 = 0 ps, delay 2 = 0 ps
Figure : (3): Different values for the delays. Their distribution and precision aresimilar as those for the nominal case.
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Effect of Load Resistance
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12
14
16
18
20
22
24
26
28
30
delay LOAD 2 [ps]
dela
y L
OA
D 1
[ps]
R
1=50.05 Ω
R2=50.05 Ω
nominal
Figure : (4): The precision of the delays is not sensitive to the actual value ofresistance of either LOAD.
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Exploration of Se
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12
14
16
18
20
22
24
26
28
30
delay LOAD 2 [ps]
dela
y L
OA
D 1
[ps]
|Se
11|=0.3
Phase(Se11
)=45o
nominal
Figure : (5): The precision of the delays is not sensitive to reasonably imperfectvalues of Se11.
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12
14
16
18
20
22
24
26
28
30
delay LOAD 2 [ps]
dela
y L
OA
D 1
[ps]
|Se
22|=0.3
Phase(Se22
)=45o
nominal
Figure : (6): The precision of the delays is not sensitive to reasonably imperfectvalues of Se22.
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20 22 24 26 28 30 32 34 36 38 4010
12
14
16
18
20
22
24
26
28
30
delay LOAD 2 [ps]
dela
y L
OA
D 1
[ps]
|Se
12Se
21|=0.5
Phase(Se12
Se21
)=90o
nominal
Figure : (7): The precision of the delays is sensitive to the magnitude of Se11, butnot to its phase. It is better to keep Se as close to perfect as possible by calibrating theVNA before the measurements.
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Exploration of St
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12
14
16
18
20
22
24
26
28
30
delay LOAD 2 [ps]
dela
y L
OA
D 1
[ps]
|St
11|=|St
22|=0.1
|St11
|=|St22
|=0.5
|St11
|=0.9, |St22
|=0.1
nominal
Figure : (8): The best precision and most symmetrical distribution is obtained when|St11| and |St22| are the furthest apart.
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12
14
16
18
20
22
24
26
28
30
delay LOAD 2 [ps]
dela
y L
OA
D 1
[ps]
Phase(St
11)=0
Phase(St22
)=0
nominal
Figure : (9): The phases of St11 and St22 are not critical when optimizing the testnetwork.
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20 22 24 26 28 30 32 34 36 38 4010
12
14
16
18
20
22
24
26
28
30
delay LOAD 2 [ps]
de
lay L
OA
D 1
[p
s]
|St
12St
21|=0.1
|St12
St21
|=0.5
nominal
Figure : (10): The test network is optimized when the magnitude of St12St21 is ashigh as possible. In the plot, the nominal case is the best because |St12St21|=0.8.
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20 22 24 26 28 30 32 34 36 38 4010
12
14
16
18
20
22
24
26
28
30
delay LOAD 2 [ps]
dela
y L
OA
D 1
[ps]
Phase(St
12St
21)=0
o
Phase(St12
St21
)=90o
nominal
Figure : (11): As indicated by previous analyses, the best results are obtained whenthe phase of St12St21 is 180 (nominal in the plot).
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Conclusion
I The most direct implementation of the FRM requires the use of standards of thetwo genders. I take advantage of this requirement and use this method toestimate the delay of both LOAD standards.
I The previous report in this series shows that there is a strong correlationbetween the loss and delay of the LOAD, even with only one set of standards.When considering two sets, the correlations and precisions are expected todegrade significantly, and for this reason only the delays have been consideredas free parameters in this report.
I The simulations show that it is possible to estimate the LOAD delays withprecision of ± 2 ps when using an appropriate test network, and assuming nosystematic effects.
I The best test network has very different |St11| and |St22| (one close to 1 and theother close to 0). The magnitude of St12St21 has to be close to 1 and its phaseclose to 180.
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