Elektrotehniški vestnik 73(4): 179-182, 2006 Electrotechnical Review: Ljubljana, Slovenija
Self-calibration on a three-sampler network analyzer with nonstandard connectors
Drago Kostevc, Jože Mlakar
Fakulteta za elektrotehniko, Univerza v Ljubljani, Tržaška 25, 1000 Ljubljana, Slovenija E-pošta: drago. kostevc@fe. uni-lj. si
Abstract. The authors show a simple method enabling a self-calibration technique with a three-sampler automatic vector network analyzer. The main purpose is to determine internal reflections of the analyzer with standard connectors by using any calibration method for the three-sampler analyzer. The rest of the error model of the analyzer with non-standard connectors, and thus the complete model, is determined by calibrating the analyzer using one of the self-calibration techniques.
Keywords: automatic vector network analyzer, three-sampler, calibration method, self-calibrating procedure
Samokalibracijske metode za tridetektorske vektorske analizatorje vezij z nestandardnimi priključki
Povzetek. Pri visokih frekvencah se za merjenje parametrov S uporabljajo izključno vektorski analizatorji vezij, bodisi tri-, bodisi štiridetektorski. Bistven del postopka pri merjenju z vektorskim analizatorjem vezij je umerjanje analizatorja pred vsako meritvijo in ne meritev sama, ki je trivialna. Analizator je mogoče umeriti z različnimi kombinacijami normal, zato je poznanih tudi veliko kalibracijskih metod. Analizatorji s tremi detektorji pri kalibraciji potrebujejo večje število normal kot analizatorji s štirimi detektorji. Za kalibracijo se pogosto uporabljajo tako imenovane samokalibracijske metode, saj je pri njih število potrebnih kalibracijskih normal najmanjše, obenem pa veljajo za najbolj natančne. Prav posebej so samokalibracijske metode uporabne za kalibriranje vektorskih analizatorjev vezij z nestandardnimi priključki, saj je treba za te priključke vsako normalo izdelati posebej. Žal pa je neposredna uporaba samokalibracijskih metod omejena na štiridetektorske analizatorje, za kalibriranje tridetektorskih je število uporabljenih normal pri teh metodah premajhno. Vendar pa bi bila uporaba samokalibracijskih normal tudi na tridetektorskih analizatorjih zelo dobrodošla, avtomatski analizatorji vezij so namreč zelo drage naprave in tridetektorski so občutno cenejši od štiridetektorskih. V članku bova pokazala, da je na razmeroma preprost posreden način mogoče uporabljati samokalibracijske metode tudi na tridetektorskih analizatorjih. Kalibriranje poteka v dveh korakih. V prvem na analizator
Prejet 13. januar, 2006 Odobren 9. maj, 2006
priključimo kable s preciznimi standardnimi priključki, za katere je na voljo zadostno število normal, in ga kalibriramo po katerikoli standardni metodi za tridetektorske analizatorje. V tem koraku določimo tiste notranje parametre analizatorja, ki se s časom ne spreminjajo in niso odvisni od priključnih kablov in konektorjev. V drugem koraku nato pri vsaki poznejši kalibraciji merilnika z morebitnimi nestandardnimi priključki določimo ostanek parametrov s poljubno samokalibracijsko metodo z zmanjšanim številom normal.
Ključne besede: tridetektorski avtomatski vektorski analizator vezij, kalibracijske metode, samokalibracijske metode
1 Introduction
The two-sampler automatic vector network analyzer was modelled using the standard 12-parameter error model (Fig. 1 - the crosstalks, of which determination is trivial, are omitted for the purpose of clarity) and calibrated with the 'short-open-load-thru' (SOLT) [1] calibration. The so-called self-calibration method emerged later, together with six-port analyzers [2] and four-sampler analyzers ([3], [4]). The most popular self-calibration method is the 'thru-reflect-line' (TRL) calibration [2], commonly accepted as more accurate than the SOLT calibration method. As the self-calibration method needs fewer calibration standards than the SOLT calibration method, it is suitable for measurements with non-standard connectors. Self-
calibrations is, however, limited to the calibration of network analyzers that can be modelled using the two-box error model (Fig. 2), i.e. a six-port analyzer and a four-sampler analyzer.
The four- and three-sampler analyzer can also be modelled using an alternative model [5],[6], [7] (Fig. 3). Within this model the influence of switches and the internal termination are modelled by reflections eR and eF, which depend only on the analyzer itself. For a four-sampler analyzer, they are determined using the fourth detector, while the rest of the two-box error model is determined by self-calibration. For a three-sampler analyzer, however, they cannot be measured directly. It is thus accepted that self-calibration cannot be used to calibrate the three-sampler analyzer.
In this paper the authors show an effective method wich enables self-calibration with the three-sampler analyzer. The method initially determines reflections eR and eF of the analyzer with standard connectors, using any calibration method for the three-sampler analyzer. When later calibrating the analyzer with non-standard connectors using one of the self-calibration methods, the rest of the alternative model, and thus the complete model, is determined.
2 Calibration
For calibration of the four-sampler analyzer the two-box error model (Fig. 1), and for three-sampler analyzer the standard model (Fig. 2) or an equivalent alternative model (Fig. 3), needs to be determined.
Fig. 1. Signal flow graph of the two-box error model with a DUT
1	> -> P > O M21
1 \ S. / Etf
M12 o-
Fig. 2. Signal flow graph of the standard error model with a DUT

IVL
y > 1 Ê21 ven e2 &12	m 1 ^ \	1 > e43 1 re33 ei44A ei4 1
	v v	
' i ve 11 e22* i ©12 < i	\ 4 / 'K s„i' / sf \	e43 ^3 644A e34 <-
M21
reF FWD
M 22
REV
Fig. 3. Alternative error model of the three- and four-sampler network analyzer
Comparing Figs. 1 and 3, it is apparent that the alternative model is in fact the two-box error model, extended by parameters eR and eF. If these parameters for the three-sampler analyzer are determined beforehand, the rest of the two-box error model can be determined, as with the four-sampler analyzer, using a self-calibration method. From the standard model, eR and eF are determined in the following way:
From the equivalence of the flow graphs of the standard model (Fig. 1) and of the alternative model (Fig. 3), the following relations can be derived [5]:
edf = e11
erf = e21e12
ESF = e22
EXF = e41
E = e21e43 TF ~ ,
1 - e44eF
7, e43e34eF ELF = e33 + 43 34 F
1 " e44eF
EDR — e44
err — e43e34
ESR — e33
EXR — e14
E — e34e12 TR ~ 1
1 _ e11eR
E — e + e21e12eR LR ~ 22 ^
1 e11eR
The following equations result from these:
eF —
elf esr
Err + edr (elf esr ) Elr ~ Esf
2)
Erf + Edf (Elr - Esf ) The relation between the alternative model (Fig. 3) and the two-box error model (Fig. 2) is shown in a signal
Self-calibration on a three-sampler network analyzer with non-standard connectors 181
flow graph (Fig. 4). M' stands for the set of the equivalent two-box error model measurements (compare Fig. 2) and M stands for the set of three-sampler measurements (compare Figs. 1 and 3). From the flow graph the following relations between M' and M result: [6]
M, = M11 - M12M21eF 11 1 - M12M21eFeR
M '12 =
M12 - M11M12^R
1 - M12 M21eFeR
M\A = M 21
-M22 m2
M 22 =
1 - M12 M21eF M22 - M21M1
1 - M12 M2
								
								
								
								
eF e
dB
-70
If


0
Frequency
18 GHz
Fig. 5. Absolute value of S„ for the APC3.5 Maury 8021C2 male to-female adapter
FWD	REV
Fig. 4. Signal flow graph of the relation between the two-box error model and the alternative error model
Thus, from the set of three-sampler measurements M, using the known eR and eF, one can determine the set of equivalent two-box error model measurements M' (Eq. 3). From this set the two-box error model can be determined, using any self-calibration method. The two-error box model constitutes, together with parameters eR and eF, the complete alternative model (Fig. 3), from which the standard model can also be calculated (Eq. 1). In short, when eR and eF parameters of a three-sampler analyzer are known, the analyzer is calibrated in the same way as a four-sampler analyzer. The determined standard model is then used directly for error correction of raw measurements [1].
3 Verification
All measurements were performed on an HP8720C three-sampler analyzer. When measuring with APC7 connectors, a Maury 2650F calibration kit was used; when measuring with APC3.5 connectors, a Maury 8050F calibration kit was used.
Internal reflections eR and eF were determined using the SOLT calibration method on an analyzer with APC7 connectors. To verify the proposed method, we used the TMR self-calibration method [3] on an analyzer with APC3.5 connectors to measure an APC3.5 Maury 8021C2 male-to-female adapter. The S11 and S21 parameters of the measured adapter are shown in Figs. 5 to 8 (solid line). For reference, the same adapter was also measured by SOLT calibration on APC3.5 connectors (Figs. 5. to 8, dotted line).
Fig 6. Phase of S11 for the APC3.5 Maury 8021C2 male to-female adapter
Fig 7. Absolute value of the S21 for APC3.5 Maury 8021C2 male to-female adapter
-1801___K. _____
0	Frequency	18 GHz
Fig 8. Phase of the S21 for APC3.5 Maury 8021C2 male to-female adapter
The reference measurement is much simpler and more accurate with precise connectors than with non-standard connectors. On the other hand, verification must prove only that parameters eR and eF are independent of the connectors of the analyzer. That is why parameters eR and eF were determined on an analyzer with precise APC7 connectors, and then used for verification in self-calibration on precise APC3.5 connectors.
4	Conclusions
We demonstrate an effective method enabling self-calibration of the three-sampler analyzer. To determine eR and eF internal reflection, one of the three-sampler analyzer calibrations is still required. But they can be determined in advance when the analyzer is equipped with precise standard connectors, for which all calibration standards are available. Later, for the measurement of devices with non-standard connectors, for which usually only a reduced number of calibration standards is available, the known internal reflections together with any of the self-calibration methods can be used for calibration.
As the internal termination of the analyzer does not change with time, it does not need to be measured before every calibration but, has to be only occasionally verified. So the proposed method is also suitable for calibrating the analyzer with standard connectors.
5	Acknowledgements
The authors wish to thank the Dielectric Laboratory of the Jožef Stefan Institute in Ljubljana for providing measuring equipment.
6 References
1)	J. Fitzpatrick, Error Models for System Measurement, Microwave Journal, May 1978, pp. 63-66
2)	G. F. Engen, C. A. Hoer, "Thru-Reflect-Line": An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer, IEEE Trans. MTT, Vol. MTT-27, No. 12, Dec. 1979, pp. 987993
3)	H. J. Eul, B. Schiek, Thru-Match-Reflect: One Result of a Rigorous Theory for De-embedding and Network Analyzer Calibration, 18th European Microwave Conference Proceedings, Sept. 1988, pp.909-914
4)	J. Silvonen, A General Approach to Network Analyzer Calibration, IEEE Trans. MTT, Vol. MTT-40, No. 4, Apr. 1992, pp. 754-759
5)	D. Kostevc, Samokalibracijske metode za tridetektorske vektorske analizatorje vezij, ERK 2002, Portorož, pp. 155-158
6)	D. Kostevc, The Measurements of S-Parameters by Vector Analyzers, Electrotechnical Review, Ljubljana, Vol. 61, (1-2), 1994, pp. 29-36 (in Slovene)
7)	J. A. Jargon, R. B. Marks, D. K. Rytting, Robust SOLT and Alternative Calibrations For Four-Sampler Vector Network Analyzers, IEEE Trans. MTT, Vol. MTT-47, No. 10, Oct. 1999, pp. 20082013
Drago Kostevc
Drago Kostevc received his dipl. ing., MS and DSc degrees from the Faculty of Electrical Engineering, University of Ljubljana, Slovenia in 1974, 1981, and 1985, respectively. Upon graduation, he stayed with the University of Ljubljana. The research fields he has worked in include design and modeling of microwave circuits and microwave measurements. Currently, he is an Associate Professor of Microwave Engineering.
Joze Mlakar
Joze Mlakar was born in Ljubljana, Slovenia, in 1941. He received his PhD in 1975 from the University of Ljubljana, Faculty of Electrical Engineering. Currently, he is a Professor of Electric Circuits and Electromagnetic Waves at the Faculty of Electrical Engineering, University of Ljubljana. His research interests include microwave circuits and measurements and numerical TLM technique for modelling electromagnetic fields.