NIST Technical Note 1337: Characterization of Clocks and Oscillators

12 FREQUENCY AND TIME MEASUREMENT 231The average beat frequency VB2(t.v; IN) cannot be known exactly, but it maybe estimated with sufficient precision if it changes slowly compared to theinterval between measurements. If the primed and unprimed variablesrepresent two independent measurements, then12.3.3.3 FREQUENCY MULTIPLICATION(12-87)A frequency multiplier produces n fulI cycles of the output signal for eachcycle of the input signal, where n is an integer determined by the design of thedevice. Such a device is also a phase multiplier, that is, the total phaseaccumulation of the output signal is n times as great as the phase accumulationof the input signal:(12·88)It follows that the spectral density of the output signal is enhanced by a factorof n 2 compared to the input signal,2SiPouJf) = n S¢'lft(f),making it easier to perform the necessary noise measurements. Similarly, it isalso easier to make Allan-variance measurements. If the oscillator under testand the reference are both multiplied by the same factor, the beat frequencywill be n times larger than with no multiplication but the heterodyne factorwill be the same. The zero crossings that must be detected by the counterhave n times higher slope and more easily overcome the voltage noise in thecounter trigger circuits. The ability to measure frequency stability is onlyenhanced if the multipliers have extremely low phase noise themselves. This isthe case for many modern multipliers that are triggered by the zero crossingsof the input signal. As a result, the use of multipliers can reduce theperformance requirements on the phase detector and the following low-noiseamplifiers.12.4 CO~CLUSIO;.'>iThe IEEE recommendations have achieved the goal of introducingsubstantial uniformity in the specification of oscillator performance. TheAllan variance and the one-sided power spectral density of phase have provedsufficient to evaluate oscillators for all common applications. In a few casesmore specialized measures are helpful in relating performance to the specificapplication. For example, the rms time-prediction error is helpful in judging aclock·s ability to keep time over long intervals (Allan and Hellwig, 1978).TN-lOl