ANALYSIS OF CORRELATIONAL DEPENDENCES BETWEEN TECHNICAL PARAMETERS AND THE PRICE OF SEMICONDUCTOR ELEMENTS OF STATIC CONVERTERS

A. S. Baturin, N. I. Dyakonov, N. I. Koroleva

The creation of semiconductor devices with high performance qualities is an important task. Already in the process of designing and developing semiconductor devices, a technical-and-economic analysis of the variants being developed is necessary in order to find the optimum. The problem of optimizing various circuit solutions for semiconductor static converters is complex and little studied. Investigation of the dependences of price on the technical parameters of semiconductor elements of static converters is the first step toward solving this problem.

On the basis of a qualitative technical-and-economic analysis of the initial data (the data were taken from the current wholesale price list [5], with additions taken into account), correlational dependences were established for functionally homogeneous groups of semiconductor elements. The grouping was carried out by types (brands) of semiconductor elements (thyristors—avalanche, thyristors—silicon, thyristors—symmetrical, valves—avalanche, etc.).

Analysis of the empirical data showed that the parameters of semiconductor elements (voltage, current) are closely related to price, and that this relationship is not functional but correlational in character.

The choice of the form of the relationship is one of the most difficult questions that arose in carrying out the study. Static models of the relationship between price and technical parameters can be constructed only on the basis of analysis and generalization of the initial data material.

To establish the dependence of price on technical parameters, power and linear functions were used. The choice of function was made with regard to the possibility of mathematical processing on a computer. However, analysis of power dependences for adequacy to the initial price values by the index of the mean approximation error showed significant deviations of the calculated prices \(Z\) from their actual values according to the price list. Preliminary graphical studies of pairwise dependences between price and a technical parameter showed that they are linear in character. Proceeding from this, a linear dependence was proposed in the following form:

\[ Z = A + (b_1 + b_2 \cdot I)V, \tag{1} \]

where

\(Z\) is the calculated value of the price, determined by the correlation dependence;

\(b_1 b_2\) are constant coefficients of price variation with technical parameters;

\(I\) is the rated current in amperes;

\(A\) is a coefficient taking into account the influence of unaccounted-for factors.

In formula (1), the price is given in the form of a linear expansion of components corresponding to the influence of the main parameters (current and voltage), including those not directly taken into account by coefficient \(A\). The results of the calculation are given in the table.

Table

Correlation dependence of the price on the technical parameters of semiconductor elements of static converters

Analysis of the data in the table makes it possible to draw a number of important conclusions that may be proposed for practical use. The price of semiconductor elements of static converters depends on voltage to a greater extent (the values of the coefficient range from 0.02 to 0.96) than on power (the values of the coefficient range from 0.0002 to 0.5108). It follows from this that, when developing circuits of identical power using semiconductor elements, it is necessary to employ elements with a higher rated current value, since this will make it possible to reduce costs substantially.

When applying formula (1), it is necessary to evaluate how well it reflects the character of the actual dependence. On the basis of the values of the mean approximation error (table), it may be concluded that the selected correlation dependences correspond to the actual data with a sufficient degree of accuracy.

The linear form of the dependence also makes it possible to determine the elasticity coefficient of the price change as a function of changes in the technical parameters; moreover, unlike the constant elasticity in the power-law form of the dependence, the linear form makes it possible to obtain variable elasticity coefficients [2].

In the linear form of the dependence, the elasticity coefficients are determined by the ratio of the corresponding technical parameter to the price. Calculation of the elasticity coefficients will make it possible to establish the upper limit of the increase in costs when changing the technical parameters of the static-converter circuits being developed on semiconductor elements.

Conclusions

1. For semiconductor elements of static converters, a change in technical parameters (current, voltage) causes a change in price.

2. The linear relationships obtained correspond, with a sufficient degree of accuracy, to the actual price values.

3. The degree of dependence of price on technical parameters varies. This makes it possible to use the relationships obtained for optimizing circuit solutions for semiconductor static converters.

References

1. Ya. I. Lukomskii. The Theory of Correlation and Its Application to the Analysis of Production. Moscow, Gosstatizdat, 1961.

2. A. M. Matlin. Prices and the Economic Efficiency of Machines. Moscow, Mashinostroenie, 1968.

3. A. A. Frenkel. Mathematical Analysis of Labor Productivity. Moscow, Ekonomika, 1968.

4. A. A. Koshuta. Prices for Machine-Building Products. Moscow, Ekonomika, 1969.

5. Price List No. 15-05, Part II. Moscow, Preiskurantgiz, 1967.