Theory

Let the measured response be represented by a(t). During all calculations the z=ln t logarithmic time variable is used instead of the time. This way, the processed function will be a(z).

The method for smoothing and calculating the 1^st derivative is linear regression, applied consecutively to the short regions along the logarithmic time axis. The rate of the "smoothed" points along the ln t axis is determined in the evaluation program by the parameter Resolution (point/decade) in the Evaluation window, the default value is 20. The 1^st derivative of the response is related to the logarithmic scale as well: da/dz. Transformation to the frequency domain is done by convolution, as described in [1]. The calculation of the R(z) time-constant spectrum is based on the convolution equation:

For the required deconvolution operation the Bayes iteration is used. The number of iteration steps of this calculation can be set in the Evaluation window, the default value is 512 (see Figure 4-11). For details some related papers are referred [2],[3].

The pulse thermal resistance diagram is calculated using the convolution equation as follows:

For details, see [4]. The following results will be written into files:

• the derivative and the time-constant spectrum (if exists - time constant spectrum is calculated for driving point impedances only),
• the response in the frequency domain (complex locus), the data of the pulse thermal resistance diagram.

The second processing phase

This phase involves the following steps:

• generation of the integral structure function (also called cumulative profile function),
• generation of the differential structure function (sometimes simply referrer to as the structure function).

In this phase only the "driving point" measurement is evaluated. The algorithm uses the Foster-Cauer transformation for a very detailed (100-180 stages) RC model. For details of this algorithm see [2] and [3].

In order to reduce the runtime of the calculation the user can reduce the resolution of the detailed Foster/Cauer model. At the end of the second evaluation phase the differential and the cumulative profile function (structure function) will be written into a file on the control computer. These functions are the ultimate results of the evaluation. Structure functions are optimal for pointing out small differences between devices measured in similar arrangements.

More information regarding structure functions (together with other "views" of a measurement project) is given in Section 3.3.8.