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On-Wafer S- and Noise-Parameters Measurements
Signal Integrity and Multiport Measurements
Coaxial VNA Measurements Forum
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Yahoo! MTT-11 Coaxial VNA Newsgroup addresses questions about coaxial VNA calibrations and associated measurement uncertainties.
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Moderator
The moderator for this forum is Dr. Jon Martens. Jon received a Ph.D. in Electrical Engineering from the University of Wisconsin, Madison in 1990. He joined Anritsu Company in 1995 where he develops measurement system architectures, measurement algorithms and helps implement various calibration structures. He can be contacted directly at jmartens@anritsu.com.
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Frequently Asked Questions
Q. What are the open and short models one sees associated with coaxial (and other) calibration kits? How do they work and what are their limitations?
A. In SOLT (and related families of calibrations such as offset short), the exact value of the reflection coefficients of the open and short must be provided to the calibration in order to determine the error coefficients (see e.g., W. Kruppa, “An explicit solution for the scattering parameters of a linear two-port measured with an imperfect test set,” IEEE Trans. On Micr. Theory and Tech., vol. 19, pp. 122-123, Jan. 1971 or G. J. Scalzi, A. J. Slobodnik, and G. A. Roberts,”Network analyzer calibration using offset shorts,” IEEE Trans. On Micr. Theory and Tech., vol. 36, pp. 1097-1100, June 1988.).
While the reflection coefficient versus frequency itself can be provided (and is sometimes done), historically a polynomial model has been used instead. In this case, the capacitance (for the open) or the inductance (for the short) is modeled as a polynomial in frequency (usually 3rd order). The coefficients of this polynomial are then provided in the calibration kit.
This approach works, obviously, as long as the polynomial model accurately fits the behavior of the reflection coefficient. This becomes more and more problematic in the mm-wave ranges. One could band the polynomials, go to higher order or different functional fits, or go to straight S-parameter characterization.
Q. Why do passive devices appear to have gain when I calibrate with long line standards?
A. If the line being used as the ‘thru’ is long enough that it has noticeable loss, this loss might be being neglected in the calibration. In that case, a device with less loss than the calibration line would appear to have gain. Sometimes the loss of the line can be specified as part of the cal or it can be de-embedded later.
Q. Why do I get unusual phase hops in my LRL/TRL measurements?
A. 1. The LRL/TRL family of calibrations (see e.g., H. Eul and B. Schiek, “A generalized theory and new calibration procedures for network analyzer self-calibration,” IEEE Trans. On Micr. Theory and Tech., vol. 39, pp. 724-731, Apr. 1991) has as part of the process the selection of one of two possible square roots (a sign ambiguity). A phase hop in the data is often a sign that this root choice is being made incorrectly. There are many different ways that implementations may solicit information to help determine the correct roots but they often involve line lengths (offset lengths of reflects, line length deltas,…). One should check that these lengths have been entered correctly and that they are with respect to the expected reference plane.
Q. Why do my reference planes seem to be in the wrong place when using LRL/LRM?
A. The fundamental reference plane in the entire TRL family is at the center of line 1 (usually first line measured but depends on the implementation). Many implementations, allow one to rotate the reference planes out to the ends of line 1 but some knowledge of the line length is required (it can be extracted from the algorithm as discussed in Eul and Schiek, MTT vol. 39, Apr. 1991 and many other places)
Q. What is a sliding load and how does it help or hurt my SOLT-like calibration?
A. The sliding load consists of a lossy slider attached to a coaxial airline (with some supporting structures). As the slider is moved, the ideal is that the impedance presented at its connector traces out a circle on the Smith chart centered at the origin. The lossy material is not a perfect match due to the interfaces so it will not be entirely in the center but it should not be highly reflective. If such a circle is traced out with 4-8 measurements, then the center of the circle can be fairly accurately calculated thus allowing the cal information on a synthetic, nearly perfect composite load. In general, this will lead to better residual directivities than using a single fixed load (unless that load was well-characterized in advance). The sliding load does require reasonable mechanical precision to maintain the circle generation and deviations form concentricity are particularly problematic at very high frequencies.
Q. Can I change the power level after I do my calibration and maintain accuracy?
A. It depends on the instrument and the situation. One generally does not want to try to change the power level so far that a step attenuator moves since this will change the match somewhere in the transmission path of the instrument (depending on where the step attenuator exactly is, this defect may be acceptable in some cases). One should also consider if the compression state of the receiver will be changing (i.e., going from a very high power to a very low power or vice-verse). Going from no compression to 0.1 or 0.2 dB compression can have a disproportionately large effect on a calibrated response.
Q. Aside from the classical error model terms, what other things can affect my measurement accuracy?
A. Many things can enter into this but include connector repeatability, cable drift, linearity (of the receiver usually, can be other places in a complex test system), and spurious responses.
Q. When I try to extract model parameters (e.g., inductance and resistance of a lumped inductor), I seem to have problems with noisy and/or wrong data at low frequencies. What is happening here?
A. Many model extraction problems involve a pole in frequency (very often at DC). Simple inductor and capacitor modeling problems fall into this category for the obvious reason that the impedance contribution of the element in question vanishes at DC. Thus at low frequency, the extracted value becomes extremely sensitive to small changes in the underlying S-parameter. It may reach a point where even fairly low trace noise from the instrument (<.01 dB) produces a scatter in the extracted parameter that is larger than the mean value. Increasing averaging or decreasing IF bandwidths can help but only up to a point.
Q. What is the difference between two or three line TRL/LRL and multiline TRL?
A. Classical TRL/LRL uses two lines per band and many common implementations will allow the use of 3-4 lines to cover two bands. Here a band is defined by the requirement in TRL/LRL that the line length difference be distinct from 0 or 180 degrees at every frequency being calibrated.
Multiline TRL is a more recent innovation where many lines are used in a single band to produce a more robust solution that is tolerant of single line defects and repeatability effects up to a point. The calibration is solved in a least-squares sense or with more sophisticated statistical techniques. See, for example,
R. B. Marks, “A multiline method of network analyzer calibration,” IEEE Trans. On Micr. Theory and Tech., vol. 39, pp. 1205-1215, Jul. 1991.
D. F. William, C. M. Wang, and U. Arz, “An optimal multiline TRL calibration algorithm,” 2003 IEEE MTT-S Digest, pp. 1819-1822, June 2003.
Q. How do automatic calibration devices work and what are their advantages/disadvantages?
A. Automatic calibration devices are based on the idea of electronically (or electromechanically) switching in various impedance and/or transmission states to present to the VNA. If the S-parameters of these states are known a priori the calibration can be solved either deterministically (if there are no extra states provided) or stochastically (if enough states are provided, like in multiline TRL, so that the problem is overdetermined).
Since far fewer connections are being made, there is certainly a reduction in connector repeatability issues, there are fewer chances for connection errors, and calibration time is reduced. Accuracy will depend on how the states were originally characterized since the device is acting like a transfer standard. A very accurate and careful characterization measurement can lead to quite accurate automatically calibrated measurements assuming the calibration device is time stable.
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Selected Bibliography
Disclaimer: This is not an exhaustive bibliography. If you would like to suggest a suitable paper to be listed here, please email the moderator.
Background
| A general waveguide
circuit theory R. B. Marks and D. F. Williams J. Rsrch. of the Nat. Inst. Of Stds. And Tech. Volume 97, Sep-Oct 1992 Page(s):533 - 561 |
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| Power Waves and
the Scattering Matrix Kurokawa, K.; Microwave Theory and Techniques, IEEE Transactions on Volume 13, Issue 2, Mar 1965 Page(s):194 - 202 |
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AbstractPlus | Full Text:
PDF(880 KB) IEEE JNL |
General Calibration Techniques
| An Explicit
Solution for the Scattering Parameters of a Linear Two-Port Measured
with an Imperfect Test Set (Correspondence) Kruppa, W.; Sodomsky, K.F.; Microwave Theory and Techniques, IEEE Transactions on Volume 19, Issue 1, Jan 1971 Page(s):122 - 123 |
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AbstractPlus | Full Text:
PDF(264 KB) IEEE JNL |
| Network
analyzer calibration using offset shorts Scalzi, G.J.; Slobodnik, A.J., Jr.; Roberts, G.A.; Microwave Theory and Techniques, IEEE Transactions on Volume 36, Issue 6, June 1988 Page(s):1097 - 1100 Digital Object Identifier 10.1109/22.3638 |
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AbstractPlus | Full Text:
PDF(328 KB) IEEE JNL |
| A circle fitting
procedure and its error analysis I. Kasa IEEE Trans. On Instr. And Meas. Volume 25, Mar 1976 Page(s):8 - 14 |
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Thru-Reflect-Line: An Improved Technique for Calibrating the Dual
Six-Port Automatic Network Analyzer Engen, G.F.; Hoer, C.A.; Microwave Theory and Techniques, IEEE Transactions on Volume 27, Issue 12, Dec 1979 Page(s):987 - 993 |
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AbstractPlus | Full Text:
PDF(736 KB) IEEE JNL |
| A generalized
theory and new calibration procedures for network analyzer
self-calibration Eul, H.-J.; Schiek, B.; Microwave Theory and Techniques, IEEE Transactions on Volume 39, Issue 4, April 1991 Page(s):724 - 731 Digital Object Identifier 10.1109/22.76439 |
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AbstractPlus | Full Text:
PDF(620 KB) IEEE JNL |
| Two-port
network analyzer calibration using an unknown `thru' Ferrero, A.; Pisani, U.; Microwave and Guided Wave Letters, IEEE [see also IEEE Microwave and Wireless Components Letters] Volume 2, Issue 12, Dec. 1992 Page(s):505 - 507 Digital Object Identifier 10.1109/75.173410 |
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AbstractPlus | Full Text:
PDF(156 KB) IEEE JNL |
| A multiline
method of network analyzer calibration Marks, R.B.; Microwave Theory and Techniques, IEEE Transactions on Volume 39, Issue 7, July 1991 Page(s):1205 - 1215 Digital Object Identifier 10.1109/22.85388 |
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AbstractPlus | Full Text:
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Multiport and Leaky Calibration Techniques
| Multiport
vector network analyzer calibration: a general formulation Ferrero, A.; Sampietro, F.; Pisani, U.; Microwave Theory and Techniques, IEEE Transactions on Volume 42, Issue 12, Part 1-2, Dec 1994 Page(s):2455 - 2461 Digital Object Identifier 10.1109/22.339781 |
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AbstractPlus | Full Text:
PDF(492 KB) IEEE JNL |
| LMR 16-a
self-calibration procedure for a leaky network analyzer Silvonen, K.; Microwave Theory and Techniques, IEEE Transactions on Volume 45, Issue 7, July 1997 Page(s):1041 - 1049 Digital Object Identifier 10.1109/22.598439 |
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References | Full Text:
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| A simplified
algorithm for leaky network analyzer calibration Ferrero, A.; Sanpietro, F.; Microwave and Guided Wave Letters, IEEE [see also IEEE Microwave and Wireless Components Letters] Volume 5, Issue 4, April 1995 Page(s):119 - 121 Digital Object Identifier 10.1109/75.372811 |
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AbstractPlus | Full Text:
PDF(208 KB) IEEE JNL |
| A
Generalization of the TSD Network-Analyzer Calibration Procedure,
Covering n-Port Scattering-Parameter Measurements, Affected by Leakage
Errors Speciale, R.A.; Microwave Theory and Techniques, IEEE Transactions on Volume 25, Issue 12, Dec 1977 Page(s):1100 - 1115 |
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AbstractPlus | Full Text:
PDF(1560 KB) IEEE JNL |