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An analytic expression for the current-voltage characteristics of resonant tunneling diodes is derived from basic principles. The form is ideal for insertion into circuit simulation models. It is demonstrated for a conventional InGaAs-AlAs RTD and for an InAs-AlSb-GaSb RIT diode. The expression is based on the quantum tunneling formalism and contains parameters that originate from physical quantities, but which can also be treated as empirical. Empirical fitting is straightforward and results in an excellent match to the data. Additional levels of physical realism can be incorporated in a natural way.