DE102007057393A1 - Vectorial multi-port network analyzer calibrating method, involves mathematically determining reflection values of one-port, which is realized by unknown reflective termination to be same as short-circuit and open loop - Google Patents

Abstract

The method involves implementing a calibration measurement at a twin-port, which is realized by a direct connection of measuring ports (T1-T4) or a short adapted line. The twin-port is connected between each measuring port combination. Another calibration measurement is implemented at a one-port, which is realized by an unknown reflective termination, whose electrical characteristics are same as an open loop. Reflection values of the one-port, which is realized by the unknown reflective termination to be same as a short-circuit and the open loop, are mathematically determined.

Description

The The invention relates to a method for calibrating a measuring gate and m measuring points (n> 1) having vectorial network analyzer through each other following measurement of the reflection and transmission parameters at different, two-port calibration standards connected in any order between the test ports, all of which must have a transmission path and three different ones between the test ports in any order connected n-port calibration standards, which must have no transmission.

vectorial Network analyzers (VNA) are used for precise measurement of electronic Components and components as well as active and passive high-frequency circuits and high frequency assemblies to antennas.

The in the high-frequency technology usual Description of the electrical behavior of electronic Components and components take place via their scattering parameters (also S-parameters). They do not link streams and tensions with each other, but wave sizes. This illustration is specially adapted to the physical conditions. It will detects the so-called scattering parameters of n-gates (n = 1, 2, ...), possibly in 2n pole parameters (e.g., Z or Y parameters).

wobei [S] die Streumatrix ist, welche die elektronischen Eigenschaften des Zweitors kennzeichnet.For example, for the waves a ₁ and a ₂ , which converge, for example, on a two-port, and the waves b ₁ and b ₂ propagate correspondingly in the opposite direction, the relationship applies:

where [S] is the scattering matrix characterizing the electronic properties of the two-port.

A so-called system error correction ensures that precise measurements of the scattering parameters of components and components with vectorial network analyzers at all feasible are. This system error correction sets the precise measurement of standards advance, whose electronic behavior is known or under the System error correction can be determined.

Be known within the so-called calibration method, the reflection and / or Transmission behavior of unknown or partial or total known calibration standards at several, in terms of location and Measure the number of measuring points to be optimized.

Out The measured values of the calibration standards are obtained via special calculation methods Correction data, so-called error quantities or coefficients. With this correction data and a corresponding correction calculation you get for any measured object measured by system errors of the vectorial network analyzer and the feeder lines, for example of couplings (crosstalk) or mismatches (reflections), are exempt.

One known calibration method for a two-standard model with 10 or 12 error quantities is the so-called 10-term or 12-term procedure. In American literature it is also called SOLI (S: Short, O: Open, L: Load = Match, T: Thru) and referred to in Europe as TMSO. It is the only system calibration method for two-port network analyzers with only three measuring points, one measuring point on for both Gates common measuring channel in front of the switch, which one each the gates for the measurement switches, and in each case another measuring point at the measuring channel of each gate. With this arrangement of measuring points however, the switch is integrated into the measurement of calibration standards.

at this in practice most often used TMSO calibration procedure have to To determine the correction data, the two test ports are first connected which corresponds to the calibration standard T (T = Thru). After that At each gate, three known gates, e.g. the calibration standards Wellsock (M = match), short circuit (S = short) and idle (O = Open) and measure.

The multi-port measurement problem consists of the fact that all the test ports are coupled together via the test object. It is thus no longer possible to obtain a measure for the traversing at one measuring point, a measure for the reflected one at the next, and finally a measure for the transmitted wave which is independent of the terminations of the multi-port at another at take into account their measuring gates in the model.

Several solutions have been published and patented in recent years for this multi-port measurement problem. The solution of Ferrero's multi-port measurement problem, described in Ferrero, Pisani, Kerwin "A New Implementation of a Multiport Automatic Network Analyzer", IEEE Trans. Microwave Theory Techn., Vol. 40, Nov. 1992, pp. 2078-2085 requires a network analyzer with 2n measuring points with the same amount of calibration standards as the TMSO method. Consequently, the hardware requirements of the calibration standards are very expensive. Also, in the Ferrero method, all calibration standards must be completely known, which is a particular disadvantage since fully known standards are not perfectly feasible. Furthermore, the Ferrero method is based exclusively on the 7-term principle, which due to the inadequate feasibility of completely known standards and because of the sensitivity of the 7-term principle on such model error has significant measurement errors result, as in Heuermann "Safe Method for Calibration of Network Analyzers for Coaxial and Planar Line Systems", Dissertation, Institute for High Frequency Technology, Ruhr-University Bochum, 1995, ISBN 3-8265-1495-5 explained.

In DE 199 18 697 A1 a 10-term method is described which, like the TMSO method, requires only n + 1 measuring points but exclusively known calibration standards.

The multiport 7-term method, which is in DE 199 18 960 A1 and based on an adaptation of the known two-port methods to a multiport method, the methods thus include TAN, TNA, LAN, TRL, TLR, LLR, LRL, TAR, TMR, TRM, TMS, LMS, TMO, LMO, UMSO, TMN, LNN, TZU, TZY, TYU, LZY, ZZU, YYU, QSOLT and typically require n - 1 + 2 calibration measurements.

Another procedure of the company ATN is in the American patent specification US 5578932 described. This patent specification describes in detail a so-called test set, with which a 2-port network analyzer can be extended to n ports. Furthermore, a special calibration device is described, which is needed for the automatic calibration of this test set.

The Includes calibration in addition to the standards Open, Short and Match (also Termination) an arrangement different transmission lines, the semiconductor switch between the connections the calibration device can be switched. So everyone has to Standards as in the TMSO process to be completely known. In contrast however, the statement in the abstract does not find complete multi-well calibration and error correction instead.

Instead only two-port paths will be calibrated, the remaining goals will be not considered (Col. 18, line 57). In the later Measuring operation successively two-port measurements are performed. there The measuring gates not included in the calibration are successively by different reflection standards built in within the test set completed. For every value of the reflection standard becomes exactly a 2-port measurement carried out (Col. 21, line 1). After measurements have been taken at all test gates, can be calculated from the obtained measured values and the known values of Reflection standards corrected for the systematic errors Result can be calculated. For the measurement of a 3-door test object are according to patent document 2 two-port measurements from port 1 to port 2 and from port 1 to port 3 (column 21, line 1 and line 45), whereby the complete Characterization of all parameters not included third Gate of the test object when measuring from gate 1 to gate 2 by at least 3 different ones Reflection standards must be completed (column 21, line 28). This means that to fully characterize a 3-gates 3 + 1 = 4 two-port measurements are required.

In the DE 10 2004 020 037 A1 a so-called RRMT calibration method is described in which, unlike the aforementioned methods, not all calibration standards need to be known. From the measurement of the transmission and reflection behavior of transmission standards known in terms of length and attenuation, the reflection behavior of n known impedances realized on the inlets but different in comparison to each other, and of the n unknown, strongly reflecting standards Open and Short, first the scattering parameters of the unknown calibration standards Open and Short are computationally determined in order to determine the error coefficients of the network analyzer with the thus known terms.

Problematic However, in any case, that is the measurement of electronic components in the wafer dressing (on-wafer measurements) special boundary conditions subject, in particular, with regard to the feasibility of the calibration standards.

in the Semiconductor sector, it is not uncommon that users on the Wafern even realize the calibration standards. The geometric Reproducibility and equality of such self-made Calibration standards is very high. It is also advantageous that the calibration standards are on the same substrate carrier (semiconductor) are as well as the measurement objects. Besides the advantages of the low Travels can Furthermore parasitic Elements as well as transition effects However, it will be "calibrated out" from the tip to the wafer the electronic properties realized only to a good approximation. Especially the standard of reflection idle does not match the necessary Produce goodness.

The Reflection standards (R) can be described very precisely on semiconductors, however, they usually vary very much in terms of DC resistance values. It is the described prior art method necessary that R standards with as identical as possible reflection behavior be connected to each test port. Can not guarantee this As is the case with multi-port on wafer measurements, there are standards regularly at 90 ° to each other are arranged, so it comes to so-called tension, the regularly the Source for very big Measuring errors are.

One Another problem is the number of measuring points, in particular to optimize for automatic measurements to aparativen effort and save costs and yet reproducible measurement results to achieve. Here are the particular on wafer level lacking feasibility of calibration standards known characteristics and the need to minimize the measuring points across from. On the one hand, the use of unknown standards requires the Application of the 7-term method, to determine the scattering parameters of these standards. on the other hand is the 7-term method because of the above error rate for the Use of only n + 1 measuring points, where at each supply line to a gate one and in front of the switch to the circuit of the respective one Tores another measuring point is arranged.

Consequently the invention is the task, a method to calibrate network analyzers, which n Have test ports and serve multi-port measurement on semiconductor wafers, with the also using user-implemented and not complete known calibration standards an optimization of the number of measuring points with largely reproducible calibration with improved measurement accuracy possible is.

According to the invention Task solved by methods, which by the features according to claim 1 or alternatively claim 2 are characterized. Advantageous embodiments are entitled to the dependent claims remove.

• 1.: Die Phase des Reflexionsstandards (R) muss nur auf ±90° bekannt sein. Mehr Informationen werden nicht benötigt. In der Praxis setzt man einen realen Kurzschluss und einen Leerlauf ein. Die Abweichungen zu einem idealen Kurzschluss oder Leerlauf haben keinen Einfluss auf die Messgenauigkeit.
• 2.: Die Impedanzstandards (M) müssen vollständig bekannt sein. Diese können beim RRMT-Verfahren jedoch unterschiedlich sein. Derartige Standards werden oft auch als Transfer-Match bezeichnet.
• 3.: Der Leitungsstandard (T) bei den RRMT-Verfahren nach Anspruch 1 und 2 und ebenso (L) bei den LRRM-Verfahren nach Anspruch 3 und 4 muss vollständig bekannt sein, kann aber eine endliche Dämpfung und ggf. ein bekanntes Reflexionsverhalten aufweisen. Es können zwischen verschiedenen Messtoren auch unterschiedliche Leitungsstandards eingesetzt werden.

The methods according to the invention are characterized in that, depending on the known and unknown calibration standards and the quality of measurement requirements, the number of measuring points may be less than 2n, eg by setting only one measuring point instead of two on selected measuring lines or the switch for individual calibration measurements, as it is known from network analyzers with n + 1 measuring points. At the same time, in addition to the n impedance standards measured at the n-fold gate (n gate), two reflectance standards (R), short circuits and open circuits are measured in the usual way. Thus, the notified procedure offers the same advantages when reducing the measuring points, as the RRMT method, namely that the calibration standards need not be known exactly. Consequently, these methods and custom calibration standards allow multi-port measurements to be performed with very high precision and very low cost for the calibration standards. All methods according to the invention are characterized by the following uniqueness criteria of the calibration standards:

• 1 .: The phase of the reflection standard (R) need only be known to ± 90 °. More information is not needed. In practice, a real short circuit and an open circuit is used. The deviations from an ideal short circuit or open circuit have no influence on the measuring accuracy.
• 2 .: The impedance standards (M) must be completely known. However, these may be different in the RRMT procedure. Such standards are often referred to as a transfer match.
• 3: The line standard (T) in the RRMT method according to claim 1 and 2 and also (L) in the LRRM method according to claim 3 and 4 must be completely known, but may have a finite attenuation and possibly a known reflection behavior , Different line standards can be used between different test ports.

In particular, the use of the 10-term method for determining the error coefficients of the measured two-port calibration standards and the scattering matrix proves to be advantageous in conjunction with the further features of the method since the 10-term method is less sensitive to model errors acts.

Due to the calibration measurements of the n impedance standards on an n-port, a particular advantage of the method is that the measurement accuracy is significantly increased compared to the prior art. Deviations from the measured reference gate at the so-called adaptation point (S ₁₁ = 0), at which the properties of the M standard are only "extrapolated" to the other test ports, are avoided in this way n-1 measurements are not detrimental to on-wafer measurements as they are fully automated and therefore cost only a fraction of the cost of the overall system and provide additional information to increase the quality of the calibration process.

Furthermore The RRMT method, as well as the methods according to the claims 2 to 4 characterized in that they always lines for the connections of the test gates use. This corresponds to the special conditions of on-wafer measurements, where, in contrast to coaxial measurements, the measuring ports (on-wafer probes or Probes) and therefore never a genuine Thru standard can be used.

Usual and unavoidable fluctuations in known DC resistance values The impedance standards present on semiconductors affect the On the other hand, methods of this invention do not.

The inventive method work opposite the known methods, in particular which network analyzers use with n + 1 measuring point, much more precise and long-term stable, because in these methods drift effects of the electronic switch have no influence on the measurement quality.

The The object underlying the invention is also by the method according to the features of claim 2 solved. This procedure allows also the use of reflection standards which are not exact must be known. There about it In addition, the impedance standards are measured at the n-gate, this allows Method also calibration measurements with high accuracy.

There However, this calibration method, the 7-term method for the computational Determining the error coefficients and the litter matrix used, which reduces the computational effort, and the Thru standard instead of between all test tube combinations between a reference gate and the rest n - 1 Gates is measured, this method finds especially in Mehrtormessungen with n> 2 application. in the Hereafter referred to as multi-gate RRMT method or GRRMT method be. The higher one Sensitivity of the 7-term method to model errors has little Influence, since the impedance measurement takes place at the n-gate and no conversion is necessary and there is an optimization of the computational effort for this Represents multiple goals. The described circuit and metrological Advantages of the RRMT procedure also feature the multi-gate RRMT method.

For multi-gate measurements with n> 2 it is alternative to the RRMT and the GRRMT method also possible that the further calibration measurement instead of an n-gate, realized by means of n known impedances, performed at a one-port which is detected by means of a known impedance (e.g. wave statements with 50 Ω, M = match) and the properties of this impedance at the rest n - 1 goals calculated from this calibration measurement. These Embodiments of the invention are hereinafter referred to as LRRM and GLRRM- or Multi-port LRRM method. In these two methods finds again an optimization between the computational and the switching and metrological effort for Mehrtore with respect to the required measurement accuracy instead.

The four methods used in this invention among claims 1-4 are logged in, differ in the implementation order individual characteristics, which however have a significant effect in practice can. The biggest difference There is between the RRMT method according to claims 1 and 2 and the multi-port LRRM method among the claims 3 and 4. In the multi-port LRRM process only one impedance standard is contacted and measured at a gate, this gate serves as a reference gate. On the other hand, with the two RRMT method at each gate an impedance standard that matches with none different impedance standard, contacted and measured.

The difference between the two RRMT and multiport LRRM methods lies in the number of T or L measurements. The methods according to claims 1 and 3 require k measurements and thus more than in the methods according to claims 2 and 4, where only n-1 measurements are required. The method of claim 1 and 3 are characterized in turn by a greater robustness. So you can show eg that the transmission measurement dynamics in methods 1 and 3 correspond to those of the device and they are applied where the dynamic range of the network analyzer is to be achieved. By contrast, in the methods according to claims 2 and 4 there is a significantly greater sensitivity with respect to small contacting errors and imperfections in the calibration standards. Consequently, the methods according to FIGS. 2 and 4 will not be used until the number n of the measuring gates is disproportionately large.

With such low demands The multi-calibration calibration methods according to the invention can be applied to the calibration standards also excellent for automated calibrations of vector network analyzers in coaxial environments. For two-port calibrations Algorithms and associated switching networks already distributed by several manufacturers. For multiport calibrations the number of contacts of the calibration standards is noticeable bigger, what Time and money costs and greater error risks in harbors.

The Reflection standards Open and Short, are particularly suitable to to realize physically the same calibration standards for the individual gates, so that those required by the unknown interconnections Terms for determining the scattering parameters also from this boundary condition to win the process. This makes it possible to measure by measuring the reflection standards on the electronic properties of the to physically same standards at the other gate to sleep.

Comparable advantages are achieved when transmission standards behave symmetrically to one another. Regarding the 1a For example, the standards S ₅ and S ₆ and in 1b the standards S ₄ and S _{5 are} symmetrical to each other. With the help of the information to be obtained in this way it is possible, for example, to produce a smaller number of transmission standards, the n-1 standards between a reference gate and the other gates, which is advantageous in the aforementioned cases at the wafer level.

The Invention will be explained in more detail with reference to an embodiment. The associated Drawing shows in

1a and 1b the schematic representations of six differently realized transmission standards per one four-port on a wafer,

2 the schematic definition of a scattering matrix, the incoming and the outgoing wave at the two-port and

3 a block diagram of a vectorial 4-port network analyzer and

4 a block diagram of a vector 3-port network analyzer with 5 measuring points.

2 shows a two-port indicated by its scattering matrix [S]. The waves a ₁ and a ₂ are the waves converging to the two-port, b ₁ and b ₂ corresponding to the waves propagating in the reverse direction. It applies the relationship

In the same way, an n-port with the waves a ₁ to a _n , b ₁ to b _n and the characteristic scattering matrix [S] is to be represented.

With the block diagram of the 4 becomes the calibration method of a vectorial network analyzer on the embodiment of a measurement object 10 (DUT) with n = 3 gates T ₁ , T ₂ and T ₃ shown, which is connected to the three ports via the switch positions described below with the network analyzer. A signal from a source 17 is via a first switch 12 either directly on a branch 20 or indirectly via a second, cascaded switch 12 on one of two further two branches 18 . 19 directed.

For a traveling wave passing through said cascaded switches 12 alternatively to one of two branches 18 . 19 can be routed between the two switches 12 a first measuring point 11 arranged. Another measuring point 11 for a trailing wave is in the branch 20 arranged by only one switch 12 is to switch directly. For the returning waves is in each of the one to the gates T ₁ , T ₂ or T ₃ extending branches 18 . 19 or 20 another measuring point 11 arranged. These measuring points are located between the DUT 10 and the nearest switch 12 ,

In each of the two switches 12 possible switch position, ie in each branch 18 . 19 and 20 comes with one of these five measuring points 11 a measured value m ₁ , m ₄ for the outgoing and a measured value m ₂ , m ₃ and m _{5 recorded} for the returning wave of each realized calibration standard. For the method according to claim 1, the three transmission standard of known length and attenuation between each possible Meßstorkombination, ie between the gates T ₁ and T ₂ , T ₁ and T ₃ and T ₂ and T ₃ . In addition, transmission and reflection behavior are measured by n-fold gate, which is realized by means of n known impedances. However, the impedances may differ at any one of the gates of at least one of the others. Further, according to claim 1, reflection standards similar to short circuits and open circuits and unknown are measured. If one of the other methods is used, the measured values m _n are measured according to the characteristics described for this.

As a block diagram is the case of a 4-port network analysis system, ie n = 4, in 3 illustrated. It can be seen that n + 2 = 6 measuring points 11 necessary. 3 shows how such a structure is to be realized and serves as a basis for the following description of the Mehrtorverfahren.

in the 3 is represented as the signal of one of two sources 17 via a first switch 12 on the branches 18 and 19 and the signal of a second source 17 via a second switch 12 on the branches 20 and 21 is directed. Both switches 12 are in front of the measuring points 11 for the returning waves in the respective branches 18 . 19 . 20 and 21 , here referred to as m ₂ and m ₃ and m ₅ and m ₆ , arranged. Between one source each 17 and a switch are two more measuring points 11 arranged, referred to as m ₁ and m ₄ , which receive the measure of the running waves. The measuring points assumed to be ideal 11 are thus, in the propagation direction of the wave to be measured, always in front of a switch 12 arranged and each take a measure of the incoming and transmitted wave on. The characteristics of the switches 12 such as reproducibility, reflectance, and long-term stability are considered in the following calculation using the 10-term model. All deterministic non-idealities and imperfections in the form of mismatches and crosstalk are found in the error matrices 13 . 14a . 14b and 14c summarized and taken into account. At the gates T ₁ , T ₂ , T ₃ and T ₄ is the target 10 (DUT) connected via the appropriate switch position with the vectorial network analyzer.

In each switch position, the measured values m _n for the reflection or the transmission behavior of the realized calibration standards are recorded at the two measuring points. For the method according to claim 1, the six transmission standards of known length and attenuation between the gates T ₁ and T ₂ , T ₃ and T ₁ , T ₄ and T ₁ , T ₃ and T ₂ , T ₂ and T ₄ and T ₃ and T _{4 are} connected. In addition, these are the n-fold match standards as well as reflection standards, short circuits and open-runs similar, at each one-port, referred to as n-gate. If one of the other methods is used, the measured values m _n are measured according to the features described therefor, wherein in the method according to claim 2, any of the gates is defined as a reference gate and the two ports are formed by this reference gate and each of the other gates. From these measured values, as described below, the scattering matrix is determined.

• 1. die sog. Selbstkalibrierung der unbekannten Reflexionsstandards,
• 2. die sog. direkte Kalibrierung und
• 3. die Systemfehlerkorrektur.

The methods according to the invention can be subdivided from the mathematical side into three steps:

• 1. the so-called self-calibration of the unknown reflection standards,
• 2. the so-called direct calibration and
• 3. the system error correction.

In the first step, the unknown parameters are calculated in the calibration standards. Here, track and determinant properties of imaging matrices are exploited as in Heuermann "Safe Method for Calibration of Network Analyzers for Coaxial and Planar Line Systems", Dissertation, Institute for High Frequency Technology, Ruhr-University Bochum, 1995, ISBN 3-8265-1495-5 described. The match calibration standards are not considered with ideal properties (S11 = 0) in mathematics. As a result, the resulting equations for calculating the reflectance values of the two R standards are significantly longer. However, these equations with respect to the above-mentioned uniqueness criteria for the line, impedance and reflection standards do not differ from the usual solutions of self-calibration calculations.

The second step of direct calibration calculates the error coefficients. This ge for the RRMT method according to claim 1 and for the LRRM method according to claim 3 on classical ways of the 10-term method, as in Schick "Messsysteme der Hochfrequenztechnik", Hüthig-Verlag, Heidelberg, 1984 and in Heuermann, "Safe method for the calibration of network analyzers for coaxial and planar line systems", dissertation, Institute for High Frequency Technology, Ruhr University Bochum, 1995, ISBN 3-8265-1495-5 have been described. One carries out a two-calibration for each connection and knows the error coefficients for this connection. The way to handle the multiport method is then described as the third step.

For the methods according to claims 2 and 4, ways of the 7-term methods for calculating the error coefficients are also described in FIG Heuermann "Safe Method for Calibration of Network Analyzers for Coaxial and Planar Line Systems", Dissertation, Institute for High Frequency Technology, Ruhr-University Bochum, 1995, ISBN 3-8265-1495-5 for similar two-port processes described. The merger of these results of the two-port method into a multiport method will also be presented in the next step.

At the third step to carry out A system error correction will be the measurement data of an unknown Measured object from the errors of the vector network analyzer and the supply lines corrected.

For the procedures according to claim 1, which are based on the 10-term principle forms the Starting point for the mathematical description of the 10-term Mehrtorverfahren (often also called multiport method) the error model described above. For the sake of simplicity, here is the mathematical derivation only in the case the measurement of three-tone, be performed. By an appropriate Switch position I, II and III will be a source signal to the branch switched the respective gate. The generalization of this procedure to n-gates is possible in a simple manner.

To determine the classical error matrices of the 10-term model, a two-phase calibration is performed between each of the three possible probe stack combinations with the respective error matrices [A], [F] and [G]. The following applies: [F] = [B _I ] ^-1 and [G] = [B _II ] ^-1 .

For a first switch position I, the error matrix [A] is the reference gate containing three error sizes, for II it is [F] and for III [G], which for each switch position contains two other test gates only the two error sizes (eg; F _T , F _L ) of the transmission error network. Depending on the position of the switch, the associated variables are to be deleted once, twice and three times. For the three-port case, this results in 3 × 3 + 3 × 2 × 2 = 21 error quantities.

Nach Umstellung erhält man 6 Gleichungen für die 6 Wellengrößen a'₁, a'₂, a'₃, b'₁, b'₂, b'₃.The correction calculation of the measured values of the measurement object (mi) using the 21 error quantities can be set as follows:

After conversion _'1, a' is obtained 6 equations for the 6 wave parameters A _2, A _'3, b' _1, b _'2, b'. ₃

einsetzen. Hierbei bekommt man für jede Schalterstellung die Werte einer Matrixspalte, was letztlich zu einem linearen Gleichungssystem bestehend aus zwei n·n Messwertmatrizen und der n·n Streumatrix führt. Löst man dieses Gleichungssystem nach der [S_x]-Matrix auf, so stehen die fehlerkorrigierten Streuparameter eines n-Tores zur Verfügung.The same procedure is followed for the other switch positions. These 3 · 6 equations can be found in the equation

deploy. In this case, one obtains the values of a matrix column for each switch position, which ultimately leads to a linear equation system consisting of two n × n measured value matrices and the n × n scattering matrix. Solving this system of equations according to the [S _x ] matrix, the error-corrected scattering parameters of an n-gate are available.

For the methods according to claim 2 and 4, which are based on the 7-term principle, the starting point for the mathematical description of the 7-term Mehrtorverfahren (often called multiport method) forms also the same error model. For the sake of simplicity, the mathematical derivation should also be carried out here only for the case of the measurement of three-ports. The generalization of this procedure to n-gates can in turn be carried out in a simple manner by providing a switch with n output ports and taken into account for each additional gate of the measurement object additional measuring points.

To determine the classical error matrices of the 7-term model, a second calibration is performed between the reference gate with the error matrix [A] and the error matrices [B _i ] (i = 1, 2,..., N). The term 7-term model derives from the fact that the associated 2 × 2 error matrices [A] and [B _i ] contain a total of 7 error terms, since one of the 8 variables contained can always be set to 1.

gilt. Diese Gleichungen lassen sich nach den a_i und b_i Wellen

größen auflösen und in der Gleichung einsetzen. Hierbei bekommt man für jede Schalterstellung die Werte einer Matrixspalte, was letztlich zu einem linearen Gleichungssystem bestehend aus zwei n·n Messwertmatrizen und der n·n Streumatrix führt. Löst man dieses Gleichungssystem nach der [S_x]-Matrix auf, so stehen die fehlerkorrigierten Streuparameter eines n-Tores zur Verfügung.Furthermore, it is advantageous to set the mathematical formulation of the two-model in the inverse form of the specified transmission transmission parameters: [G] = [A] -1 , [H i ] = [B i ] -1 , i = 1, 2 (2 ) where for the inputs and outputs on the error networks

applies. These equations can be according to a _i and b _i shafts

Resolve sizes and insert in the equation. In this case, one obtains the values of a matrix column for each switch position, which ultimately leads to a linear equation system consisting of two n × n measured value matrices and the n × n scattering matrix. Solving this system of equations according to the [S _x ] matrix, the error-corrected scattering parameters of an n-gate are available.

T ₁ to T ₄

test ports 1 to 4

S ₁ to S ₆

transmission standard 1 to 6

10

measurement object

11

measuring point

12

switch

13

Fehlermatrize

14a

Fehlermatrize

14b

Fehlermatrize

17

source

18

branch

19

branch

20

branch

21

measurement object

Claims (7)

Method for calibrating a vectorial network analyzer having n measurement points and m measuring points (n> 1) by consecutively measuring the reflection and transmission parameters on k = sum (n-i) for (i = 1, 2,..., N-1 ) different, between the test ports in any order connected two-port calibration standards, all of which must have a transmission path, and three different other between the test ports in any order connected n-gate calibration standards, which must have no transmission, by computationally determining the error coefficients of the Network analyzer using 10-term method in k-fold application using the measured two-port calibration standards and by computational determination of the error-corrected scattering matrices [S _x ] of the n-port calibration standards from the error coefficients of each two-port calibration standard taking into account the transmission error magnitudes of the remaining n-2 test ports by means of 10-term multi-port methods, by (a) performing the first k calibration measurements on each of a two-port direct connection of the test ports ( Through connection, T = Thru) or a short adapted line (L = line) of known length and attenuation is realized and which is connected between each k possible Messtor combination, are performed, (b) one of the further calibration measurement at an n-fold gate ( n-gate), which is realized by means of n known impedances (eg so-called wave terminations with 50 Ω, M = match), wherein the n known impedances may be different compared to each other, (c) one of the further calibration measurements on one n-gate, which by means of n unknown highly reflective terminations (R = Reflect) whose electrical properties are similar to those of Kurzs (d) one of the further calibration measurements on an n-gate, which uses n unknown highly reflective terminations (R = Reflect), whose electrical properties correspond to those of open runs (O = Open ) and that (e) the reflection values of the n-gates, which are realized by unknown reflective, short-circuiting or open circuit-like terminations, are computationally determined, characterized in that for m: n + i <m <2n , Method for calibrating a vectorial network analyzer having n measurement points (n> 1) by sequentially measuring the reflection and transmission parameters at n-1 different, two-port calibration standards connected between the measurement ports in arbitrary order, all of which must have a transmission path, and three different further n-port calibration standards connected between the measurement ports in arbitrary order, which must not have transmission, by computation of the error coefficients of the network analyzer by means of 7-term-method in n-1-fold application and measured two-port calibration standards and by arithmetic determination of the error-corrected scattering matrices [S _x ] of the n-port calibration standards by means of 7-term multi-port methods, by (a) the first n-1 calibration measurements at a two-port, which by means of direct connection of the test ports (through-connection, T = Thru) or a short one matched line (L = line) of known length and attenuation is realized, and that is connected between a reference gate set as a reference port and the n - 1 remaining ports. (b) one of the further calibration measurements is performed on an n-gate realized by means of n known impedances (eg so-called wave terminations with 50 Ω, M = match), wherein the n known impedances may differ in comparison to each other, c) one of the further calibration measurements on an n-gate, which is realized by means of n unknown highly reflective terminations (R = Reflect) whose electrical properties are similar to those of short circuits (S = Short), (d) one of the further Calibration measurement on an n-gate, which is realized by n unknown highly reflective terminations (R = Reflect), whose electrical properties are similar to those of open runs (O = Open) is performed, (e) the reflection values of the n-gates, which are realized by unknown reflective, short-circuits or open circuits, are computationally determined, characterized in that for m: n + 1 <m <2n. Method for calibrating a network analyzer according to claim 1, characterized in that (a) n> 2, (b) the further calibration measurement instead of an n-gate realized by means of known impedances, carried out at a gate, which is detected by means of a known impedance (for example so-called wave termination) 50 Ω, M = Match) is realized and (c) the properties of the known Impedance to the rest n - 1 Eintoren from the calibration measurement of the known impedance at Eintor be determined by calculation. Method for calibrating a network analyzer according to claim 2, characterized in that (a) n> 2, (b) the further calibration measurement is carried out instead of at an n-gate, realized by means of n known impedances, at a gate which is known by means of a known Impedance (eg so - called wave termination with 50 Ω, M = match) is realized and (c) the characteristics of the known impedance at the other n - 1 inlets from the calibration measurement of known impedance at Eintor be calculated. Method for calibrating a network analyzer according to one of the claims 1 or 2, characterized in that for n> 2, the further calibration measurement instead at an n-entry, realized by means of n known impedances, at an (n - i) -intor, where i <n, is performed which by means of a known impedance or more known Impedances (for example, so-called wave terminations with 50 Ω, M = match) is realized and the properties of the known impedances on the remaining i Eintoren from the calibration measurement of the known impedances to the (n - i) Eintoren be calculated. Method for calibrating a network analyzer according to one of the claims 1 to 5, characterized in that the electrical properties one of the highly reflective terminations are known. Method for calibrating a network analyzer according to one of the preceding claims, characterized that for n> 3 at least two the unknown, reciprocal through-connections symmetrical to each other are.