An Audio Satori

   The research that produced the Pritchard amplifiers are the result of an audio satori, an engineering epiphany. This enlightenment came from the inability to meet musicians' demands upon amplifiers with standard engineering theories and practices. Unfortunately, the communications between musicians and engineers are hampered by two problems: First, although musicians and engineers nominally speak the same language, their words often have at least dual meanings that are misunderstood by the other. Engineers think in terms of comparatively abstract concepts of amplitudes and frequencies while musicians sense the essence of the music and readily translate their experiences to other senses. Second, engineers have learned their craft from respected professors who teach the findings of other respected professors and engineers, therefore tradition says their narrow view must be correct. Therefore to the engineer a musicians' objections are mere imagination, nostalgia, or worse. Consequently, artistic audio (audio that really appeals to artists) is an engineering enigma cloaked by a linguistic mystery.

   After years of design efforts following traditional engineering concepts and not achieving my goal of creating the greatest guitar amplifier ever, I had to seriously reexamine my engineering training and experience in the light my undergraduate studies in mathematics. College mathematics is quite theoretical and positively logical. The world of mathematics has been created by assuming the least and moving from there in layers upon layers of thorough proof. Theorems contain statements of the result and all of the assumptions. I did not appreciate this discipline until I started taking engineering where the results are often stated with an incomplete statement of assumptions. On the other hand, engineers have had to create their world in less than a century while mathematics has been in development for more than two millennia. Engineers are usually under pressure to produce a product, while most mathematicians have the time to consider a problem completely. Further and prior to computers and their numerical analysis capabilities, engineers had to choose between mathematical models that were precise and models that were useful and useable.

   An excellent example of the incomplete statement of concepts is Child's Law for diodes and its extension to triode behavior. Child's Law relates the plate current to the plate-to-cathode voltage. The proof assumes a variety of conditions that are not realistic, such as infinite length cylindrical structure and zero electron velocity at the cathode. The result of this proof is that Ip= Io * Vpk ^ 3/2.

The triode extension is Ip=Io*(Vpk+Mu*Vgk)^3/2 where

Ip = plate current

Io = plate current constant

Vpk = voltage from plate to cathode

Mu = voltage gain constant

Vgk = voltage from grid to cathode

When real data for the very popular 12AX7 is put into this equation, the plate currents do not match by a large margin. Nonetheless, technical papers on computer models of vacuum tubes (one was even peer reviewed) have been published based on the Child's Law. This casts doubt on engineering statements. If the authors of those papers had checked the derivation of Child's Law, they would have known that the 12AX7 did not fit the Child's Law assumptions and such errors would have not been made.