The effect of deep frequency division and its possible applications in precision phase measurements

Abstract

Phase angle measurements are used in all leading fields of science and engineering --in space research, in ranging and navigation measurements, and automatic control, etc. Their accuracy is constantly increasing. Especially accurate phase meters must be certified against standards [i].Standards for reproduction of phase angles between two electrical voltages, e.g., in the NBS of the USA and FRG, have an error not exceeding 0.003 to 0.01 ~ only at relatively low frequencies from 10 -3 Hz to 20-50 kHz [2,3]. Besides certification of phase measuring instruments, modern science and engineering (circular particles accelerators, optoelectronic systems in microcircuit technology, etc.) demand setting of phase angles at high frequencies up to 30 MHz and more with a resolution of 10 -3 to 10 -4 deg [4]. This presents the following difficulties. Accuracy is usually increased by dividing the frequency of the standard source in two channels by a factor of, e.g., i0 to i00. Simultaneously, the phase angle, the phase angle error, and the frequency also are divided, i.e., the desired goal is not attained, since the higher the accuracy the lower the frequency and vice versa. For example, in the FI-4 instrument at frequencies below i MHz (36 MHz divided by 36), the phase step is i0 ~ with an error of 0.03 ~ and at i0 MHz (120 MHz divided by 12) 30 ~ and 0.15 ~ respectively. For a resolution of at least 0.1 ~ at 10 MHz a frequency of 36000 MHz must be divided by 3600, which is at present unrealistic to achieve directly, i.e., without heterodyning.This "vicious circle"has been broken using the effect of deep frequency division (DFD) in the decade structure of direct frequency synthesis based on the 8 + i + 1 algorithm [5,6]. where K > 1 is a coefficient that gives the desired output frequency, 0 < m < 9 is the coefficient of variation of the output frequency within one decade, and F 8 = Fs'8 and FI = F s" i.To simplify setting of phase angles and frequencies, all decades are fixed at m = 0, i.e., ~(8+L+~)K/L0=~K.Thus, the output frequencies of decades DCI through DC m are FsK , while the output frequency of decade DCm+I, 10FsK, are applied to the output circuit unit OCUI of channel I of the DFDS.The phase angle is set in mixer M2 of converter DCI by replacing the frequency F I = Fs(K + m0/10) with the frequency F I' = Fs(K + mz/10) at the instants when the frequencies corresponding to m = 0 and m z = 1 coincide: this state remains for a time t and is then replaced by the state m0 = 0 (Fig. 2). The phase angle is then given by