A Practical Approach to Calculating Optimum Performance of Semiconductor Rectifiers

Applying Kirchoff's circuit laws to a conventional four-arm rectifier bridge, an expression is derived for efficiency in terms of R (effective reverse resistance of one arm), F (effective forward resistance of one arm), and L (ohmic load resistance). Knowing that R and F can be kept constant by separate adjustments of input voltage and temperature of the cells enables us to maximize efficiency, E, with respect to L. The optimum value of L turns out to be √RF, the geometrical mean of forward and reverse resistances. This value of L yields E_max = [(q - 1)/(q + 1)]², where q = √R/F. Further analysis shows that √R/F = V_R/V_F for optimum L, where V_R and V_F are corresponding values of reverse and forward voltage drops, so that E_max is expressible in terms of V_R and V_F alone. Three families of curves are given to illustrate manipulation of the simple empirical data required, resulting in a final plot of E_max versus temperature for various current densities in the cells. An important feature of the process depends on the interesting analytical result that for maximum efficiency the reverse and forward losses are equal, making it possible to correlate values of V_R and V_F. Because the empirical data involved are strictly applicable only when R and F are not appreciably affected by previous values of V_F and V_R respectively, a modified technique is suggested in which data are observed only when optimum L is in the circuit.