The macro-models used in chip-level EMC analysis usually comprise equivalent circuits whose parameters are derived from the results of scattering parameter measurements. The constant increment of IC complexity along with the increment of the pin number has made this job difficult to accomplish, because of the numerous measurements to carry out and the propagation of related errors. Aiming to address this issue, this paper explores the possibility to obtain the scattering parameter matrix of an N-port system from measurements carried out with an m-port vector network analyzer, with the remaining N-m ports left open or loaded with a set of known impedances. According to the definition of scattering parameters, the measurement must be carried out with the ports loaded by their respective characteristic impedance (usually 50Ω ), which makes such measurements time-consuming, especially with devices featuring many ports. This is mostly because the N-m port not connected to the VNA must be matched during the measurement process. This paper presents a method that allows one to obtain the scattering matrix of an N-port device, using the S-par measurements carried out with the N-m ports not connected to the VNA, left open. The proposed technique requires ( ) set of measurements (Fig. 1), but there is no need to match with the reference impedances the port of DUT that are not connected to the VNA during the measurement process. To this purpose, three different methods suitable to derive the scattering parameters with the remaining N-m ports mismatched are available in literature. All these algorithms are based on two-step matrix transformation: the first step, starting from mismatched measured parameters, builds a set of partial matrices (S^p) containing the information related to the auxiliary load, while the second one reconstructs the true S parameter matrix from the partial matrices obtained in the first step. The great advantage of this approach is that the port not connected to the VNA can be left open. Unfortunately, this condition could be problematic because the parasitic elements loading the port not connected to the VNA, could affect the elements of the extracted matrix, especially at high frequency. The use of these techniques significantly reduces the number of steps needed to extract the final matrix. Aiming to check the proposed method, a three port IC was characterized using a 2-port VNA. At first, the scattering parameters resulting from the proposed procedure and those obtained using the definition of scattering parameters do not match in some frequency ranges. The mathematical analysis carried out afterwards pointed out that the observed errors deal with the conditioning number of the matrix to be inverted in the second step. Furthermore, the more the reflection coefficient magnitude of the auxiliary loads is close to one, the higher is the probability to obtain a high condition number, increasing the error of the reconstructed matrix. Therefore, in order to avoid the matrix inversion in ill conditioned point, the Newton’s method was chosen as the optimal solution and its goodness was checked by repeating such a test on the above-mentioned circuit, as shown in Fig. 2.

A New Approach to Characterize Complex ICs in Terms of Scattering Parameters / Quitadamo, Matteo Vincenzo; Fiori, Franco. - ELETTRONICO. - 1:(2017), pp. 148-149. (Intervento presentato al convegno 49TH ANNUAL MEETING OF THE ASSOCIAZIONE SOCIETÀ ITALIANA DI ELETTRONICA tenutosi a Palermo (Italy) nel 21-23 June 2017).

### A New Approach to Characterize Complex ICs in Terms of Scattering Parameters

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*Quitadamo, Matteo Vincenzo;Fiori, Franco*

##### 2017

#### Abstract

The macro-models used in chip-level EMC analysis usually comprise equivalent circuits whose parameters are derived from the results of scattering parameter measurements. The constant increment of IC complexity along with the increment of the pin number has made this job difficult to accomplish, because of the numerous measurements to carry out and the propagation of related errors. Aiming to address this issue, this paper explores the possibility to obtain the scattering parameter matrix of an N-port system from measurements carried out with an m-port vector network analyzer, with the remaining N-m ports left open or loaded with a set of known impedances. According to the definition of scattering parameters, the measurement must be carried out with the ports loaded by their respective characteristic impedance (usually 50Ω ), which makes such measurements time-consuming, especially with devices featuring many ports. This is mostly because the N-m port not connected to the VNA must be matched during the measurement process. This paper presents a method that allows one to obtain the scattering matrix of an N-port device, using the S-par measurements carried out with the N-m ports not connected to the VNA, left open. The proposed technique requires ( ) set of measurements (Fig. 1), but there is no need to match with the reference impedances the port of DUT that are not connected to the VNA during the measurement process. To this purpose, three different methods suitable to derive the scattering parameters with the remaining N-m ports mismatched are available in literature. All these algorithms are based on two-step matrix transformation: the first step, starting from mismatched measured parameters, builds a set of partial matrices (S^p) containing the information related to the auxiliary load, while the second one reconstructs the true S parameter matrix from the partial matrices obtained in the first step. The great advantage of this approach is that the port not connected to the VNA can be left open. Unfortunately, this condition could be problematic because the parasitic elements loading the port not connected to the VNA, could affect the elements of the extracted matrix, especially at high frequency. The use of these techniques significantly reduces the number of steps needed to extract the final matrix. Aiming to check the proposed method, a three port IC was characterized using a 2-port VNA. At first, the scattering parameters resulting from the proposed procedure and those obtained using the definition of scattering parameters do not match in some frequency ranges. The mathematical analysis carried out afterwards pointed out that the observed errors deal with the conditioning number of the matrix to be inverted in the second step. Furthermore, the more the reflection coefficient magnitude of the auxiliary loads is close to one, the higher is the probability to obtain a high condition number, increasing the error of the reconstructed matrix. Therefore, in order to avoid the matrix inversion in ill conditioned point, the Newton’s method was chosen as the optimal solution and its goodness was checked by repeating such a test on the above-mentioned circuit, as shown in Fig. 2.##### Pubblicazioni consigliate

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`https://hdl.handle.net/11583/2692767`

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