Data processing takes place in two subsequent evaluation phases that have been united into a single menu item in the present version of the T3Ster software.
This phase involves the following steps:
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 1st 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 Set evaluation params menu, the default value is 20. The 1st 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:
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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 2-8). For details some related papers are referred [2],[3].
The pulse thermal resistance diagram is calculated using the convolution equation as follows:
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For details, see [4]
The following results will be written into the files on the control computer:
This phase involves the following steps:
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. The reduction factor can be set in the Evaluation window (see Figure 2-8), in the Resolution tint->Foster: field. The default value is 1. Further possible values are: 2, 3 or 4.
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 and they are best to be used for the comparison of measurement results of different setups.
More information regarding structure functions is given in section 7.6.
[1] V.Székely: "Convolution calculus in network theory and identification", ECCTD, 1997
[2] V.Székely, Tran Van Bien: "Fine structure of heat-flow path in semiconductor devices: a measurement and identification method", Solid-State Electronics, Vol.31, pp.1363-1368 (1988)
[3] V.Székely: "A new evaluation method of thermal transient measurement results", Microelectronics Journal, Vol.28, pp.277-292 (1997)
[4] V.Székely and M. Rencz: "Thermal dynamics and the time constant domain", IEEE Transactions on Components and Packaging Technologies, V.23, No.3. September 2000, pp. 587-594
[5] http://www.micred.com/prodserv/products/measdev/t3ster/strfunc/index.html
Figure 2-9 presents the time-constant spectrum derived from the temperature response. It is obvious that the present MCM module has two main time constants, at 0.08 and 100 seconds.
Based on this spectrum the program calculates the structure function as well. Such a function is shown in Figure 2-10 for a BJT mounted on a small cooling fin. Many fine details can be read from this function. For example, the peak at Rth = 9.3 K/W corresponds to the heat capacity of the fin. Thus the partial thermal resistance values as junction-fin, fin-ambience can be easily determined, chip delamination can be detected, etc. Beside this, the structure function provides an easy way to generate dynamic compact thermal model for the given package mount.
The control & evaluation software of T3Ster provides an easy way to compare results of measurements made on different packages: a multitude of the functions can be displayed and investigated at a time - such as shown in Figure 2-11.
Figure 2-8: Window for setting the parameters of the evaluation procedure
Figure 2-9: Time-constant spectrum
Figure 2-10: A structure function
Figure 2-11: Different functions on the screen (thermal response and its 1st derivative, time-constant spectrum and the differential structure function)
