Analysis of the Zero Power Reactor Transfer Function

Algebraic expressions for the amplitude and phase of the zero power transfer funciton allow these quantities to be evaluated from measured precursor data without the use of a digital computer. The asymptotic forms of the amplitude and phase for large and small values of ω are particularly simple. The expressions show the conditions under which the gain should be frequency-independent and yield a simple formula for the angular frequency ω₀ at which the phase angle reaches a maximum. The inhour relation is shown to be intimately related to the transfer function, the reactivity in dollars for any period α⁻¹ less than one second being equal to 1 − tan ε, where ε is the phase angle at ω = α. The value of α corresponding to prompt critical is shown to be always equal to ω₀.