Thermionic Vacuum Tube Current Estimation via Polynomial Voltage Modeling
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Solution Overview
Problem
Existing models for estimating total cathode space current in thermionic vacuum tubes are limited by constant assumptions for perveance and amplification factors, which vary with electrode voltages, and struggle to accurately distribute current between grid and plate currents, especially for triode, tetrode, and pentode configurations.
Innovation Solution
A method using a polynomial-based approach to determine amplification factors associated with grid voltages, where the polynomial is heuristically determined to represent multiple voltages, allowing for more accurate estimation of total cathode space current and current distribution between grids and the plate, incorporating correction constants for initial velocity effects and contact potential.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If the Child-Langmuir three-halves-power law with constant perveance and amplification factors is used, then the model is simple and easy to implement, but the accuracy of total cathode space current estimation deteriorates because perveance and amplification factors vary with electrode voltages
Solution Approach 1:
The patent transforms the static constant parameters (perveance G and amplification factor μ) into dynamic variables that change with electrode voltages. The amplification factor is expressed as a polynomial function μ(x) of a composite voltage variable x, which itself is a function of all electrode voltages (e1, e2, ..., en, eb). This dynamic approach allows the model to adapt to varying operating conditions while maintaining mathematical tractability.
Solution Approach 2:
The patent changes the parameter representation from constant values to voltage-dependent functions. Specifically, the amplification factor μ is replaced with a polynomial expression μ(x) where x combines multiple electrode voltages with weighting factors. This parameter transformation enables the model to capture the non-linear behavior of vacuum tubes across different operating regions without requiring complex multi-dimensional lookup tables.
2Measurement precision
If multivariate polynomials are used to account for voltage dependencies of perveance and amplification factors, then the accuracy of current estimation improves, but the device complexity and computational burden increase significantly
Solution Approach 1:
The patent merges multiple electrode voltage effects into a single composite variable x(e1, e2, ..., en, eb) = (e1+ε + μ2(e2-e1) + μ3(e3-e1) + ... + μn(en-e1) + μ(eb-e1))/(eb-e1). This consolidation reduces the problem from handling multiple independent voltage variables to working with one aggregated voltage parameter, allowing the use of simple univariate polynomials instead of complex multivariate expansions.
Solution Approach 2:
The composite voltage variable x acts as an intermediary that mediates between the multiple electrode voltages and the amplification factor. Rather than directly relating each voltage to the current, the patent introduces x as an intermediate representation that captures the combined effect of all voltages, simplifying the mathematical relationship and reducing computational complexity.
3Device complexity
If simplifying assumptions are made about which electrode voltage is most important, then the model complexity is reduced, but the accuracy deteriorates because such assumptions must be tested for every tube configuration
Solution Approach 1:
The patent creates a universal model formulation that works for all vacuum tube configurations (triodes, tetrodes, pentodes, and future tube types) without requiring configuration-specific assumptions. The composite voltage variable x and polynomial approach provide a general framework that automatically adapts to different tube architectures, eliminating the need to test and validate simplifying assumptions for each new tube type.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enhances the accuracy of total cathode space current estimation and current distribution, reducing discontinuities in calculations and improving the modeling of thermionic vacuum tubes, particularly for triode, tetrode, and pentode configurations, by accounting for variable electrode voltages and their interactions.
Implementation Method 1
a cathode 102 configured to be heated by a heater 104 and to emit electrons in response to heating
Implementation Method 2
anode or plate 106 configured to attract electrons from the cathode 102
Data Source
AI summary
A method includes performing by a processor: estimating a total cathode space current for a thermionic vacuum tube having at least one grid and a plate, such that at least one amplification factor associated with the at least one grid is determined by a polynomial based on a variable that represents at plurality of voltages associated with the at least one grid and the plate, the variable being heuristically determine. Transitions between positive and negative grid operation may experience a step change in estimated current value caused by the inclusion or elimination of grid current. A part of the grid current may be added back into the plate current during transition. This small contribution to plate current may gradually diminish as tube operation moves farther away from the transition boundary.