Multi-port measurement technique

Abstract

This invention relates to an apparatus, a method and a computer program for calculating one or more scattering parameters of a linear network, the network including a number of N ports adapted to provide electric connections. The apparatus is configured to calculate, and the method includes calculating, one or more scattering parameters of the linear network, which are related to a reference impedance, on the basis of a measured electrical response at one or more ports of the linear network to an incident wave applied at a port of the linear network, measured under the condition that one or more of other ports of the linear network face a reflection coefficient with an amplitude of 0.5 or larger. The computer program is adapted to perform such a method and runs on a computer.

Claims

1. An apparatus comprising: a device operable to calculate one or more scattering parameters of a linear network comprising a number N of ports adapted to provide electric connections; wherein the device is operable to generate and apply an incident wave at a first port of the linear network; wherein the device is operable to measure electrical responses to the incident wave at the first port and/or at a second port of the linear network under a condition that one or more of other ports of the linear network face a reflection coefficient , which is defined as (ZR.sub.0)/(Z+R.sub.0), with an amplitude of 0.5 or larger, wherein Z is a port impedance; wherein the device is operable to use a result of a measurement of the electrical responses at the first port and at the second port in a calculation to calculate a scattering parameter for a 2-port network formed by the first port and the second port and that are related to a reference impedance R.sub.0 of the linear network; and wherein the device is configured to calculate one or more scattering parameters, which are related to the reference impedance R.sub.0 of the linear network, on a basis of the electrical responses, wherein the scatter parameter for the 2 port network is used in order to subsequently calculate the one or more scattering parameters of the linear network on a basis of the electrical responses.

2. The apparatus according to claim 1, wherein the device is configured to calculate the one or more scattering parameters on the basis of the electrical responses measured under the condition that the one or more of the other ports of the linear network are open-circuited so that the one or more of the other ports face the reflection coefficient with the amplitude of 0.5 or larger.

3. The apparatus according to claim 1, wherein the device is configured to keep the one or more of the other ports of the linear network open-circuited when measuring the electrical responses to the incident wave at the one or more ports of the linear network.

4. The apparatus according to claim 1, wherein the device comprises a matched receiver, and wherein the device is configured to measure the electrical responses at the one or more ports with the matched receiver connected to a port.

5. The apparatus according to claim 1, wherein the device comprises a matched generator, and wherein the device is configured to generate the incident wave with the matched generator connected to a port.

6. The apparatus according to claim 1, wherein the device is configured to use one or more of the scattering parameters of the 2-port network formed by the first port and the second port in a calculation in order to calculate one or more impedance parameters of the 2-port network formed by the first port and by the second port in order to subsequently calculate the one or more scattering parameters of the linear network.

7. The apparatus according to claim 6, wherein the device is configured to use the one or more of the impedance parameters of the 2-port network formed by the first port and the second port to calculate the one or more scattering parameters of the linear network.

8. The apparatus according to claim 7, wherein the device is configured to calculate the one or more scattering parameters of the linear network from an impedance matrix comprising the one or more of the impedance parameters of the 2-port network formed by the first port and the second port.

9. The apparatus according to claim 1, wherein the device is configured to: perform sequential measurements of electrical responses of two or more 2-port networks among the N ports of the linear network in order to calculate scattering parameters of each 2-port network under the condition of keeping the other N2 ports of the linear network open-circuited during each measurement; calculate the impedance parameters of the two or more 2-port networks from the calculated scattering parameters of each of the 2-port networks; and create a NN impedance matrix of the linear network on the basis of impedance parameters of the two or more of the 2-port networks.

10. The apparatus according to claim 1, wherein the device is configured to mathematically transform an impedance matrix created from impedance parameters of 2-port networks into an S-matrix comprising the scattering parameters of the linear network.

11. The apparatus according to claim 1, wherein the device is configured to de-embed a residual impedance at the ports of the linear network from a S-matrix calculated for the linear network.

12. The apparatus according to claim 11, wherein the device is configured to: calculate an admittance matrix of the linear network; subtract admittances of residual impedances; and calculate the S-matrix of the linear network using the inverse of the admittance matrix of the linear network.

13. The apparatus according to claim 1, wherein the number of ports of the linear network is three or more.

14. The apparatus according to claim 1, wherein the device is an S-parameter determination device.

15. The apparatus according to claim 1, wherein the device is a chip tester.

16. A method for calculating one or more scattering parameters of a linear network comprising a number N of ports adapted to provide electric connections, the method comprising: applying an incident wave at a port of the linear network; measuring an electrical response to the incident wave at one or more ports of the linear network under a condition that one or more of other ports of the linear network face a reflection coefficient , which is defined as (ZR.sub.0)/(Z+R.sub.0), with an amplitude of 0.5 or larger, wherein Z is a port impedance; calculating the one or more scattering parameters, which are related to a reference impedance R.sub.0 of the linear network, on a basis of the electrical response; calculating an admittance matrix of the linear network; subtracting admittances of residual impedances; calculating an S-matrix of the linear network using the inverse of the admittance matrix of the linear network; and de-embedding a residual impedance at the ports of the linear network from a S-matrix calculated for the linear network.

17. A non-transitory digital storage medium having a computer program stored thereon to perform a method for calculating one or more scattering parameters of a linear network comprising a number N of ports adapted to provide electric connections, the method comprising: applying an incident wave at a first port of the linear network; measuring an electrical responses to the incident wave at the first port and/or at a second port of the linear network under a condition that one or more of other ports of the linear network face a reflection coefficient , which is defined as (ZR.sub.0)/(Z+R.sub.0), with an amplitude of 0.5 or larger, wherein Z is a port impedance; using a result of a measurement of the electrical responses at the first port and at the second port in a calculation to calculate a scattering parameter for a 2-port network formed by the first port and the second port and that are related to a reference impedance R.sub.0 of the linear network; and calculating the one or more scattering parameters, which are related to a reference impedance R.sub.0 of the linear network, on a basis of the electrical response, wherein the scatter parameter for the 2 port network is used to subsequently calculate the one or more scattering parameters of the linear network on a basis of the electrical responses.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments of the present invention will be detailed subsequently referring to the appended drawings, in which:

(2) FIG. 1 shows a first N-port linear network connected to a conventional setup in order to perform a conventional calculation of S-parameters;

(3) FIG. 2A shows a schematic drawing of an exemplary apparatus according to the invention;

(4) FIG. 2B shows a measurement setup with an exemplary apparatus according to the invention connected to the first N-port linear network which may be running an exemplary computer program according to the invention, which may be thus configured to use an exemplary method according to the invention;

(5) FIG. 3 shows a Smith chart illustrating acceptable values for and according to the invention;

(6) FIG. 4 shows a second N-port linear network which may be characterized with respect to its S-parameters by an exemplary apparatus according to the invention;

(7) FIG. 5 shows a definition of a differential port with respect to the N-port linear network depicted in FIG. 4;

(8) FIG. 6 shows a diagram which compares results obtained at the second N-port linear network via the inventive method to results obtained at the second N-port linear network via the conventional method;

(9) FIG. 7 shows a flow chart comprising a method according to the invention; and

(10) FIGS. 8A and 8B show two different examples of conventional N-port networks.

DETAILED DESCRIPTION OF THE INVENTION

(11) The invention is described in detail with regards to FIG. 1 to FIG. 8B. The invention is in no way meant to be limited to the shown and described embodiment.

(12) FIG. 1 shows a first N-port linear network 1 connected to a conventional setup in order to perform a conventional calculation of S-parameters. An apparatus (not shown) is configured to calculate one or more scattering parameters of the N-port linear network 1, the N-port linear network 1 comprising a number of N ports adapted to provide electric connections. The conventional setup comprises a matched generator 2p for generating an incident wave, the matched generator 2p comprising a first matched receiver (not shown) for measuring an electrical response and a bridge (not shown). In other embodiments, the bridge may be replaced by a directional coupler. The conventional setup furthermore comprises a second matched receiver 3p being separate from the matched generator 2p that comprises the first matched receiver. The matched generator 2p is a voltage generator with an output resistance R.sub.0 and with known power. The first match receiver and the second matched receiver 3p are voltage meters with an input resistance also equal to R.sub.0. The measured voltage corresponds to the reflected wave respectively, as described in the conventional-technology section. The matched generator 2p and the first matched receiver are connected to a first port 4, port h (h=1, 2, 3, . . . N), of the first N-port linear network 1. The second matched receiver 3p is connected to a second port 5, port k (k=1, 2, 3, . . . N; kh), of the first N-port linear network 1. The N2 other ports 6a, 6b, 6c of the first N-port linear network 1 each are terminated with passive termination resistors (not shown) providing an actual impedance Z corresponding ideally to the reference resistance R.sub.0 and being connected between the other ports 6a, 6b, 6c and ground to ensure the absence of incident waves at those other ports 6a, 6b, 6c. Thus, at all of the N2 other ports 6a, 6b, 6c is smaller than as =(ZR.sub.0)/(Z+R.sub.0) equals zero because Z at each other port 6a, 6b, 6c equals R.sub.0. It is understood that the designation of the N ports 4, 5, 6a, 6b, 6c as first port 4, second port 5 and other ports 6a, 6b, 6c depends on to which two ports of the N ports 4, 5, 6a, 6b, 6c the matched generator 2p, which comprises the first matched receiver, and the second matched receiver 3p are connected to, respectively, in order to perform a measurement. These two ports 4, 5 are then designated first port 4 and second port 5, respectively, the N2 remaining ports being designated as other ports 6a, 6b, 6c.

(13) When the matched generator 2p generates an incident wave at the first port 4, port h, the incident wave, being designated as a.sub.h, the first matched receiver and the second matched receiver 3p measure the electrical response at port h, the electrical response being designated as b.sub.h, and the electrical response at the second port 5, port k, the electrical response being designated as b.sub.k, respectively. Thus, the S-parameters s.sub.kh and s.sub.hh can be calculated by the conventional apparatus via eq. 9. After that, the matched generator 2p is connected to port k and the second matched receiver 3p is connected to port h in order to obtain the s-parameters s.sub.hk and s.sub.kk. The described measurement and calculation is repeated for all possible combinations of 2-ports formed by first ports 4 and second ports 5 under the condition that the N2 other ports 6a, 6b, 6c are terminated with a resistance corresponding to R.sub.0 in order to obtain all NN S-parameters of the N-port linear network 1, therefore, being smaller than at any of the other ports 6a, 6b, 6c during each measurement. The reflection parameter of each first port 4 is re-measured each time that each first port 4 is excited. As the measurements involve reconnecting the matched generator 2p, the second matched receiver 3p and the N2 resistors to different ports 4, 5, 6a, 6b, 6c repetitively, the measurement process may take a significant amount of time. Furthermore, it may be difficult or even impossible to terminate all of the N2 other ports 6a, 6b, 6c, for example, if the first port 4, the second port 5, and the other ports 6a, 6b, 6c are situated closely to each other or if they are somehow obstructed.

(14) The invention provides an apparatus 7, a method and a computer program each being configured to calculate one or more scattering parameters of the N-port linear network 1, 8, which are related to a reference impedance R.sub.0, on the basis of a measured electrical response at a port 4, 5 of the linear network to an incident wave applied at a port 4 of the linear network, measured under the condition that one or more of other ports 6a, 6b, 6c of the N-port linear network 1 face a reflection coefficient with an amplitude of 0.5 or larger. Thus, properly terminating the N2 other ports 6a, 6b, 6c of the network 1 during a measurement at the first port 4 and/or the second port 5 in order to provide a reflection coefficient with an amplitude smaller than or at as known from conventional technology becomes unnecessary.

(15) FIG. 2A shows a schematic drawing of such an apparatus 7 according to the invention. The apparatus 7 is an S-parameter determination apparatus and comprises a matched generator 2 for generating an incident wave, the matched generator 2 comprising a first matched receiver (not shown) for measuring an electrical response. Thus, the matched generator 2 and the first matched receiver (not shown) share a connector. Additionally, the matched generator 2 comprises a bridge (not shown). The apparatus furthermore comprises a second matched receiver 3 being separate from the matched generator 2. The matched generator 2 is a voltage generator with an output resistance R.sub.0 and with known power. The first matched receiver (not shown) and the second matched receiver 3 are voltage meters with an input resistance also equal to R.sub.0. The apparatus 7, as described in view of FIG. 2A, is configured to keep one or more of the number of N other ports 6a, 6b, 6c of the linear network 1, the other ports 6a, 6b, 6c being not in use during a measurement, open-circuited under the condition of measuring an electrical response to an incident wave at a port 4, 5 of the linear network 1. The apparatus 7 comprises no additional terminations or contacts to terminate the other ports 6a, 6b, 6c of the N-port linear network 1. The apparatus 7 runs a computer program according to the invention in order to calculate S-parameters of the N-port linear network 1 by using the method according to the invention.

(16) FIG. 2B shows a technical application of the apparatus 7 according to the invention as depicted in FIG. 2A. The apparatus 7 in this embodiment is configured to operate as a chip tester. The apparatus 7 runs a computer program according to the invention in order to calculate S-parameters of a N-port linear network (N>3) of a semiconductor microchip. The apparatus 7 is configured to measure the electrical response at one or more ports 4, 5 which comprises connecting the matched receiver 3 to a port 4, 5. Furthermore the apparatus 7 is configured to generate the incident wave which comprises connecting the matched generator 2 to a port 4. For this reason, the apparatus 7 is adapted to connect the matched generator 2 comprising the first matched receiver to a first port 4, port h (h=1, 2, 3, . . . , N), of the N-port linear network 1. The apparatus 7 furthermore is adapted to connect the second matched receiver 3 to a second port 5, port k (k=1, 2, 3, . . . , N; kh), of the N-port linear network 1. While the technical features of the matched generator 2, the first matched receiver and the second matched receiver 3 are identical in comparison with the technical features described in view of FIG. 1 and while the N-port linear network 1 remains the same, the apparatus 7 according to the invention, as described in view of FIG. 2A, is configured to keep one or more of the number of N ports of the linear network 1, the other ports 6a, 6b, 6c, open-circuited under the condition of measuring an electrical response to an incident wave at a port 4, 5 of the linear network 1.

(17) In this technical application of the invention, according to FIG. 2B, all N2 other ports 6a, 6b, 6c are kept open-circuited during a measurement. Thus, the N2 other ports 6a, 6b, 6c are neither stimulated by a wave generator (I.sub.N=0), nor is an electrical response to an incident wave measured at that ports 6a, 6b, 6c, nor are they terminated with a resistor. Because of that, all of the N2 other ports 6a, 6b, 6c face a reflection coefficient of +1 in this embodiment and therefore is larger than 0.5 as equals the amplitude of . That means that the apparatus 7 is configured to calculate the one or more scattering parameters on the basis of the electrical response measured and the condition that one or more of the other ports 6a, 6b, 6c of the N-port linear network 1, 8 are open-circuited so that one or more of the other ports 6a, 6b, 6c face a reflection coefficient with an amplitude of of 0.5 or larger. In contrast to that, conventional technology allows calculating one or more S-Parameters only as long as the actual complex impedance Z at each port is close to the reference impedance R.sub.0, so that p equals or is smaller than . Thus, according to the present invention, the S-parameters of the N-port linear network 1 may be calculated despite the relatively large discrepancy between actual complex impedance Z present at one or more other ports 6a, 6b, 6c and R.sub.0.

(18) Acceptable values for and according to the invention are illustrated in FIG. 3. FIG. 3 shows a Smith chart having a first section, labelled PA1, which refers to acceptable values for according to conventional technology. According to the first section, has a value of between and +, thus leading to a value for between zero and +. A second section, labelled NMOC at an upper extreme ending, includes the acceptable reflection coefficients according to the invention, being 0.5 or larger. In a first ideal case, reflected by the upper extreme ending, is +1, which means the N2 other ports 6a, 6b, 6c are open-circuited during a measurement, as realized in the present embodiment of the invention. A third section, labelled NMSC at a lower extreme ending, includes the acceptable reflection coefficients according to the invention being 0.5 or smaller. In a second ideal case, reflected by the lower extreme ending, equals 1, which means the N2 other ports 6a, 6b, 6c of the N-port linear network 1 are short-circuited during a measurement in that case, as realized in an embodiment of the invention which is not shown. Both, the second and the third section of the Smith chart, thus refer to acceptable values of 0.5. Having the other ports 6a, 6b, 6c either open-circuited or short-circuited will lead to a maximum value of =1, =||, for each port.

(19) More in detail, according to the explanations given above, the apparatus 7 according to the embodiment as illustrated in FIG. 2A and shown in use in FIG. 2B is configured to generate the incident wave in order to stimulate a first port 4 of the N-port linear network, in this case port h, to measure the electrical response at the first port 4 and/or at a second port 5 of the N-port linear network 1, in this case port k, and to use the result of the measurement of one or more of the electrical responses at the first port 4 and/or at the second port 5 in one or more subsequent calculations in order to calculate one or more scattering parameters of the N-port linear network 1 related to the reference impedance. It is understood that, again, the designation of the N ports 4, 5, 6a, 6b, 6c as first port 4, second port 5 and other ports 6a, 6b, 6c depends on to which two ports of the N ports 4, 5, 6a, 6b, 6c the matched generator 2, which comprises the first matched receiver, and the second matched receiver 3 are connected to, respectively, in order to perform a measurement. These two ports 4, 5 are then designated first port 4 and second port 5 respectively, the N2 remaining ports being designated as other ports 6a, 6b, 6c.

(20) More specifically, the apparatus 7 according to the embodiment is configured to use the result of a measurement of electrical responses at the first port 4, port h, and at the second port 5, port k, in a calculation to calculate a scattering parameter for a 2-port network formed by the first port 4 and the second port 5 in order to subsequently calculate one or more scattering parameters of the N-port linear network 1 comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c. The embodiment is configured to use the voltage signals of the incident wave at port h, designated as a.sub.h, the electrical responses at port h, designated b.sub.h, and the electrical response at port k, designated b.sub.k, to calculate two S-parameters of the 2-port network, the S-parameters being designated as s.sub.kh and s.sub.hh, by using the formula from eq. 9. The S-parameters s.sub.hk and s.sub.kk may be obtained analogously after connecting the matched generator 2 to port k and after connecting the matched receiver 3 to port h and performing the measurement and calculation described above. Thus, for example, the S-parameters of a 2-port network formed by a seventh port and a ninth port of the linear network 1 are designated s.sub.97, s.sub.77, s.sub.79 and s.sub.99 according to the present invention. In that exemplary case, h equals 7 and k equals 9.

(21) Furthermore, the apparatus 7 according to the embodiment is configured to use one or more of the scattering parameters of the 2-port network formed by the first port 4 and the second port 5 in a calculation in order to calculate one or more impedance parameters of the 2-port network formed by the first port 4 and by the second port 5 in order to subsequently calculate one or more scattering parameters of the N-port linear network 1 comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c. It does so as it is configured to use the previously known formula from eq. 5 in order to transform the 2-port network S-parameters to 2-port network Z-parameters. To perform this calculation, the apparatus is configured to use the E-matrix adapted for N=2 (see eq. 7).

(22) In addition, the apparatus 7 according to the embodiment is configured to use one or more of the impedance parameters of the 2-port network formed by the first port 4 and the second port 5 to calculate one or more scattering parameters of the N-port linear network 1 comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c. For example, in the given embodiment according to FIG. 2B, the z.sub.kh impedance parameter of the 2-port network formed by the port h and the port k coincides by definition with the impedance parameter at row h and column k of a NN Z-Matrix of the N-port linear network 1 comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c. To exploit this correlation, the apparatus 7 as depicted in FIG. 2A is configured to perform sequential measurements of electrical responses of two or more 2-port networks among the N ports 4, 5, 6a, 6b, 6c of the N-port linear network 1 to calculate scattering parameters of each 2-port linear network under the condition of keeping the other N2 ports 6a, 6b, 6c of the N-port linear network 1 open-circuited during each measurement, to calculate the impedance parameters of the two or more 2-port networks from the calculated scattering parameters of each of the 2-port networks and to create a NN impedance matrix of the N-port linear network 1 comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c on the basis of impedance parameters of two or more of the 2-port networks. The latter may be achieved easily as the apparatus 7 is configured to mathematically transform an impedance matrix created from impedance parameters of 2-port networks into an S-matrix comprising the scattering parameters of the N-port linear network 1 comprising the first port 4, the second port 5 and the other ports 6a, 6c, 6c by using eq. 6. Thus, the apparatus 7 is readily configured to calculate one or more scattering parameters of the N-port linear network comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c from an impedance matrix comprising one or more of the impedance parameters of the 2-port network formed by the first port 4 and the second port 5. By this, it becomes possible to determine the S-matrix of a N-port linear network 1 comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c, even under the condition that one or more of the other ports 6a, 6b, 6c of the linear network 1 face a reflection coefficient with an amplitude of 0.5 or larger.

(23) Additionally, the embodiment of the apparatus 7 discussed in view of FIGS. 2A and 2B is configured to de-embed a residual interference from the S-matrix calculated for the N-port linear network 1 comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c. Given a known residual impedance at the port k (z.sub.Pk with k=1, 2, . . . , N), the N residual impedances to ground form themselves a N-port network with admittance matrix [Y.sub.RESIDUAL]. Such N-port network is parallel-parallel connected to the N-port network given by the linear network 1 (DUT) comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c. The resulting embedded Y-matrix is the sum of the admittance matrices of the DUT and of the network formed by the N impedances to ground. Therefore, via the formula [Y.sub.DUT]=[Y.sub.MEASURED][Y.sub.RESIDUAL] the Y-matrix of the linear network 1 can be easily extracted. The computation of the impedance matrix of the linear network 1, [Z.sub.DUT], reduces to the matrix inversion of [Y.sub.DUT] obtained at the previous step. Finally, the equation [S.sub.DUT]={[Z.sub.DUT][E]R.sub.0}{[Z.sub.DUT]+[Z.sub.DUT]R.sub.0}.sup.1 returns the S-matrix of the N-port linear network 1 comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c. The embodiment of the apparatus 7 is configured to perform all the calculations described above. Thus, the apparatus 7 is configured to calculate the admittance matrix of the N-port linear network 1 comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c, to subtract admittances of residual impedances and to calculate the S-matrix of the linear network 1 using the inverse of the admittance matrix of the linear network 1 (DUT).

(24) FIG. 4 shows a second N-port linear network 8 at which the embodiment of the invention is applied. The application proves the effectiveness of the invention by means of a 4-port linear network 8. More precisely, the second N-port linear network 8 (DUT) is a differential-input, differential-output filter. FIG. 5 depicts the definition of a differential port. In the considered case, a combination of 4-port S-parameters, [S.sub.D] (see eq. 16), coming from the so-called single-ended to differential transformation shall be calculated. Thus, calculating the S-parameters may be performed in this case in order to calculate their combination [S.sub.D].

(25) $\begin{array}{cc}\mathrm{Combination}\mathrm{of}S\text{-}\mathrm{parameters}\left[S_D\right]& \\ \left[S_D\right]=\frac{1}{2}\left[\begin{array}{cc}{s}_{11}+s_{22}-s_{12}-s_{21}& s_{42}+s_{31}-s_{41}-s_{32}\\ s_{13}+s_{24}-s_{13}-s_{14}& s_{33}+s_{44}-s_{34}-s_{43}\end{array}\right]& \left(\mathrm{eq}.16\right)\end{array}$

(26) The DUT used for the effectiveness check has all its four ports 4, 5, 6a, 6b accessible. Therefore, it is possible to use both the conventional apparatus and the inventive apparatus 7, computer program and method. It is understood that the designation of the ports 4, 5, 6a, 6b as first port 4, second port 5 and other ports 6a, 6b again depends on which two ports of the four ports 4, 5, 6a, 6b the matched generator 2 comprising the first matched receiver and the second matched receiver 3 are connected to in order to perform a measurement. These two ports 4, 5 are then designated first port 4 and second port 5 respectively, the two remaining ports being designated as other ports 6a, 6b. The important parameters to measure are the differential reflection and transmission coefficients of each of the 2-port networks formed by the four ports 4, 5, 6a, 6b. Both said coefficients are electrical responses in the sense of the invention as described earlier.

(27) FIG. 6 shows amplitudes in dB of the input reflection coefficient S.sub.11 of the second linear network 8 depicted in FIG. 4. The output reflection coefficient is almost identical for this DUT. Furthermore FIG. 6 shows the amplitudes in dB of the forward transmission coefficient S.sub.21 of the second linear network 8 depicted in FIG. 4. The reverse transmission coefficient is identical by definition, given the linear passive nature of the DUT. The apparatus 7 is configured to calculate the amplitude of the reflection coefficients S.sub.11 and S.sub.21 using eq. 17 and eq. 18 given below.

(28) $\begin{array}{cc}\mathrm{Amplitude}\mathrm{of}{s}_{11}& \\ \mathrm{dB}\left(S11\right)=10.Math.{\log }_{10}\left(.Math.\frac{s_{11}+s_{22}-s_{12}-s_{21}}{2}.Math.\right)& \left(\mathrm{eq}.17\right)\\ \mathrm{Amplitude}\mathrm{of}{s}_{21}& \\ \mathrm{dB}\left(S21\right)=10.Math.{\log }_{10}\left(.Math.\frac{s_{13}+s_{24}-s_{13}-s_{14}}{2}.Math.\right)& \left(\mathrm{eq}.18\right)\end{array}$

(29) The conventional apparatus and the inventive apparatus 7, computer program and method come to almost identical results. Thus, the apparatus 7 configured to calculate one or more scattering parameters of the linear network 1, 8, which may be characterized via voltages V and currents I or with respect to incident waves a and electric responses b, as illustrated in FIG. 8A and FIG. 8B, respectively, the scattering parameters being related to a reference impedance R.sub.0, on the basis of a measured electrical response at one or more ports 4, 5 of the linear network 1, 8 to an incident wave applied at a port 4 of the linear network, measured under the condition that one or more of other ports 6a, 6b of the linear network 1, 8 face a reflection coefficient with an amplitude of 0.5 or larger, comes to the same results as a conventional apparatus configured to calculate one or more scattering parameters of the linear network 1, 8, which are related to a reference impedance R.sub.0, on the basis of a measured electrical response at one or more ports 4, 5 of the linear network 1, 8 to an incident wave applied at a port 4 of the linear network 8, measured under the condition that one or more of other ports 6a, 6b of the linear network 8 face a reflection coefficient with an amplitude of or smaller.

(30) Conclusively, FIG. 7 is used to illustrate an exemplary inventive method which may advantageously be performed by an apparatus 7 according to the invention. First, 2-port S-parameters s.sub.hk of a first port 4, designated h, and a second port 5, designated k, of an N-port linear network 1, 8 are calculated (701) from electrical responses measured under the condition that the N2 other ports 6a, 6b, 6c of the N-port linear network 1, 8 are kept open-circuited during the measurement. The s.sub.hk obtained accordingly are used to calculate (702) 2-port Z-parameters z.sub.hk. One or more sequential measurements using different ports h and/or different ports k are performed (707) in order to obtain a plurality of z.sub.hk. Then, an NN Z-matrix, designated as [Z.sub.MEASURED] is created (703) from the z.sub.hk. Thus, [Z.sub.MEASURED] then comprises the element z.sub.hk at row h and column k. After that, the inverse of [Z.sub.MEASURED], an admittance matrix designated [Y.sub.MEASURED], is calculated (704). Then, an admittance matrix [Y.sub.RESIDUAL] of the linear network 1, 8, as described in a previous paragraph, is subtracted (705) from the admittance matrix [Y.sub.MEASURED]. Thus, residual impedances are de-embedded and the admittance matrix [Y.sub.DUT] of the N-port linear network 1, 8 comprising the first port 4, the second port 5 and the other ports 6a, 6b, 6c is obtained. Finally, the S-matrix [S.sub.DUT] of that N-port linear network 1, 8 is calculated (706) using [Z.sub.DUT]=[Y.sub.DUT].sup.1 in the equation [S.sub.DUT]={[Z.sub.DUT][E]R.sub.0}{[Z.sub.DUT]+[Z.sub.DUT]R.sub.0}.sup.1.

(31) Although some aspects have been described in the context of an apparatus, it is clear that these aspects also represent a description of the corresponding method, where a block or device corresponds to a method step or a feature of a method step. Analogously, aspects described in the context of a method step also represent a description of a corresponding block or item or feature of a corresponding apparatus. Some or all of the method steps may be executed by (or using) a hardware apparatus, like for example, a microprocessor, a programmable computer or an electronic circuit. In some embodiments, some one or more of the most important method steps may be executed by such an apparatus.

(32) Depending on certain implementation requirements, embodiments of the invention can be implemented in hardware or in software. The implementation can be performed using a digital storage medium, for example a floppy disk, a DVD, a Blu-Ray, a CD, a ROM, a PROM, an EPROM, an EEPROM or a FLASH memory, having electronically readable control signals stored thereon, which cooperate (or are capable of cooperating) with a programmable computer system such that the respective method is performed. Therefore, the digital storage medium may be computer readable.

(33) Some embodiments according to the invention comprise a data carrier having electronically readable control signals, which are capable of cooperating with a programmable computer system, such that one of the methods described herein is performed.

(34) Generally, embodiments of the present invention can be implemented as a computer program product with a program code, the program code being operative for performing one of the methods when the computer program product runs on a computer. The program code may for example be stored on a machine readable carrier.

(35) Other embodiments comprise the computer program for performing one of the methods described herein, stored on a machine readable carrier.

(36) In other words, an embodiment of the inventive method is, therefore, a computer program having a program code for performing one of the methods described herein, when the computer program runs on a computer.

(37) A further embodiment of the inventive methods is, therefore, a data carrier (or a digital storage medium, or a computer-readable medium) comprising, recorded thereon, the computer program for performing one of the methods described herein. The data carrier, the digital storage medium or the recorded medium are typically tangible and/or non-transitionary.

(38) A further embodiment of the inventive method is, therefore, a data stream or a sequence of signals representing the computer program for performing one of the methods described herein. The data stream or the sequence of signals may for example be configured to be transferred via a data communication connection, for example via the Internet.

(39) A further embodiment comprises a processing means, for example a computer, or a programmable logic device, configured to or adapted to perform one of the methods described herein.

(40) A further embodiment comprises a computer having installed thereon the computer program for performing one of the methods described herein.

(41) A further embodiment according to the invention comprises an apparatus or a system configured to transfer (for example, electronically or optically) a computer program for performing one of the methods described herein to a receiver. The receiver may, for example, be a computer, a mobile device, a memory device or the like. The apparatus or system may, for example, comprise a file server for transferring the computer program to the receiver.

(42) In some embodiments, a programmable logic device (for example a field programmable gate array) may be used to perform some or all of the functionalities of the methods described herein. In some embodiments, a field programmable gate array may cooperate with a microprocessor in order to perform one of the methods described herein. Generally, the methods are advantageously performed by any hardware apparatus.

(43) The apparatus described herein may be implemented using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer.

(44) The methods described herein may be performed using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer.

(45) While this invention has been described in terms of several embodiments, there are alterations, permutations, and equivalents which fall within the scope of this invention. It should also be noted that there are many alternative ways of implementing the methods and compositions of the present invention. It is therefore intended that the following appended claims be interpreted as including all such alterations, permutations and equivalents as fall within the true spirit and scope of the present invention.