Modern technology, such as SPICE circuit analysis and signal processing implementation of equations, can be applied to ancient technology such as triode vacuum tubes to gain a better understanding of their properties. In this paper the authors propose a formula that can be applied uniformly to a series of miniature tubes: 12AX7, 12AU7, 12AY7, and 12AT7. This model considers the effects of the differences in physical shape and dimension on the equivalent diode characteristics in the initial velocity region. Such effects were theoretically analyzed in the beginning of the tube development in the 1920s. However, the results were never incorporated into today’s SPICE modeling. The model consists of space charge modulation formula, which enables the expression of nonlinear behavior in wide operation range of plus and minus grid bias in a circuit. Thus, the model also successfully simulates the modulation of amplification factor obtained by the differential parameters of transconductance and output resistance. Furthermore, the dispersions of the parameter-value for the different tube types are compared in detail based on the electrode shape and the physical dimension associated with various aspects of properties. From this analysis, the manufacturing stability for 12AU7 and 12AY7 is found to be better than that for 12AX7 and 12AT7 because of the difficulty of the accurate processing of high-amplification factor and high-transconductance factor, respectively.
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