The purpose of this paper is to estimate the manufacturing-related variation factor from the difference in variance and correlation of the high-precision physical model parameters for a miniature triode vacuum tube 5751 with an amplification factor of 70. The vacuum tube operating model used here is based on physical equations adapted to the large signal input behavior of vacuum tubes used in guitar amplifiers and incorporates the effect of modulation of the amplification factor. This improves the accuracy of the soft clipping and hard clipping characteristics that affect the spectrum of the distortion sound. In order to improve the accuracy of the extraction of such multivariate model parameters, we devised a new analytical formula. In addition, we devised an algorithm for sequential regression analysis of the simulated and measured values against the analytical equation, and all parameter extraction was performed automatically by a computer program. As a result, correlations between the parameters, which had not been found before, were confirmed, and it became clear that the manufacturing and assembly accuracy of the grid electrode strongly affected most of the physical parameters.

The sound of the tube amp due to the harmonic distortion has been thought to depend not only on the vacuum tube type but also on the vacuum tube manufacturer and individual differences. However, quantitative differences in tube characteristics of the manufacturer have yet to be revealed. In this study, the characteristics of the triode 12 AX 7 of the five major manufacturers were analyzed based on statistical analysis of advanced physical model parameter sets. Tube characteristics were divided into three groups by cosine similarity and group clustering method. As a result, we succeeded for the first time quantitatively combining tube distortion characteristics and tube characteristics.

We propose a unified high precision SPICE model miniature triode tube series. The model formula was devised by high precision measurement data of 12AX7, 12AU7, 12AY7, 12AT7. In the conventional model, the perveance value and the amplification factor, which are the basic parameters expressing the I-V characteristic, have been given respectively as a constant for each vacuum tube. We have found that these values are the modulation coefficient by operation conditions depending on the electrode shape. We proposed a new physical model incorporating the physical phenomena of space charge modulation including the threshold vicinity and positive grid bias. As a result, we succeeded for the first time to express the modulation of amplification factor with small signal characteristics parameters which enables to simulate the complicated non-linear behavior such as distortion property of amplifier.