The Koren equations are the only thing I've found. "Improved vacuum tube models for SPICE simulations" https://normankoren.com/Audio/Tubemodspice_article.html

The Koren equations are the only thing I've found. "Improved vacuum tube models for SPICE simulations" https://normankoren.com/Audio/Tubemodspice_article.html https://normankoren.com/Audio/Tubemodspice_article.html The intractability of the Triode is part of the reason why the Pentode exists. And, you will note, the Pentode curves in certain modes looks a lot like your bog standard MOSFET. This also discusses how the "constants" ... well, aren't. https://www.john-a-harper.com/tubes201/ https://www.john-a-harper.com/tubes201/