Analytical expressions for the static characteristic of the tunnel diode

The problem of obtaining an analytical expression for the tunnel-diode static characteristic is best approached using essentially a curve-matching technique. Two types of expressions are possible: (a) a simple expression (one or two terms only) which can be used in analytical studies (b) a complex expression suitable for computer manipulation. The error can be held to ±10% of the peak current using the type (a) approach, and details are given. Greater accuracy is possible with the type (b) approach, and examples are given in which a ±2% error is obtained using a ninth-order polynomial for a gallium arsenide diode; an error of ±5% is obtained using a seventh-order polynomial for a germanium diode. Using a reduction method and the type (b) expression, it is shown that representation of the static characteristics up to the valley voltage is possible using a quartic expression, the error being ±10%. This result is important in view of the number of attempts which have been made to achieve a match with a low-order polynomial. The quartic expression can be derived directly using Lagrange´s interpolation formula. The error from the type (a) approach is small, and it is expected that this approach will be entirely adequate for the solution of engineering problems.