抄録
Theoretical and experimental considerations are thoroughly made on one-quadrant electronic analog, dividers. There are two types known in the divider circuit working on the principle of reciprocal multi-plication. One (A) employs a multiplier and a high gain amplifier, and the other (B) a multiplier, an adder and a sign changer (Fig. 1). Study is made on the both types. Conclusion of this paper is summarized as follows:
(1) Equivalent circuit of the above two is, as a principle, the same one (Fig. 2).
(2) Static error of a divider due to defficient amplification of the equivalent amplifier can be effectively compensated by inserting a constant compensating voltage to the divisor X2 terminal (Firs. 3 & 4).
(3) Graphical analysis-method has been developed to clarify the relations between divider's static errors and multiplier's ones. The method can be applied to any given divider. As a result of the analysis, it is generally said that the smaller the divisor X2 is, the worse the multiplier's error affects the divider's (Fir. 5).
(4) A multiplier incorporated into a divider must be the one that has the least static error at smaller X2 input. A divisor X2 has to be applied to a more accurate terminal of a multiplier at smaller input.
(5) Operating level of a multiplier when incorporated into a divider can not, in principle, go over its output rating XMr. divided by R (R=X2max/X2min, X2=divisor, Fig. 6).
(6) Operating level of a multiplier incorporated into a divider can be raised over the above value, only if divisor X2 always >X2 min when dividend X1=X1max or if X1 always <X1max when X2=X2min.
(7) A straightforward design method is given as to how to allocate appropriate gain constants to each element of a divider system (Figs. 7 & 8).
(8) No abnormal instability occures in (A)-type divider and (B)-type one with δ0<0 (Fig. 10). (1+δ0 means d. c. gain of the system composed of an adder and a sign changer).
(9) Only in (B)-type divider with δ0<0, abnormal instability may take place. This instability can be explained by non-linearity which may exist between multiplier's output and input at its small output and by saturation characteristics of the system composed of an adder and a sign changer (Fig. 11). The instability, however, can easily be checked by a diode shunting the output-XD terminal to chassis earth (Fig.12).
(10) Dynamic response characteristics of a divider is mainly determined by the character of divisor X2 and the lower the level of X2 is, the worse it becomes.
(11) Qualitative character of transient response of XD (divider output) is determined only by X22 and neither by X21 nor X10 when dividend input X1 (t) =X10 const. and divisor input X2 (t) varies in step from X21 to X22. This is proved theoretically and experimentally as well (Fig. 13 & Photo. 1).
(12) Amplitude of transient response in XD in the above case is proportional to (XD2-XD1). (XD1 being stationary output of a divider when X1 (t) =X10 and X2 (t) =X21 and XD2 being alike when X2 (t) =X22).
