# The 9 reference contexts in paper V. Petrushak S., В. Петрушак С. (2018) “ИЗМЕРЕНИЕ АМПЛИТУДЫ ПЕРИОДИЧЕСКИХ СИГНАЛОВ С ИСПОЛЬЗОВАНИЕМ МЕТОДА ФИБОНАЧЧИ // MEASUREMENT OF THE AMPLITUDE OF PERIODIC SIGNALS USING THE FIBONACCI METHOD” / spz:neicon:pimi:y:2018:i:2:p:167-172

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DOI: 10.21122/2220-9506-2018-9-2-167-172 168 Приборы и методы измерений 2018. – Т. 9, No 2. – С. 167–172 Петрушак В.С. Introduction The  theoretical basis for  problems of  industrial  tomography
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requires a process of measuring the amplitude of high frequency periodic signals, but not its mean root mean square or mediandirected value. Since the  amplitude of  the  reflected  signal depends on the current image of the spatial distribution of  physical quantities.
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In  the  radio  geodesy, the area of the object of observation depends on the amplitude of  the  reflected signal to estimate  the volume of minerals. At  the  same time, the  analysis of  scientific and  technical literature and  patent search showed
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that today these problems are solved by converting the alternating voltage into an equivalent constant voltage or  thermal energy parameter. The  use  of converters  based on  the  amplitude detector [2]  results in  a  reduction in sensitivity, the occurrence of a conversion error, which respectively results in distortion of  measurement results.
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At  the  same time, the  analysis of  scientific and  technical literature and  patent search showed [2–6]  that today these problems are solved by converting the alternating voltage into an equivalent constant voltage or  thermal energy parameter. The  use  of converters  based on  the  amplitude detector
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results in  a  reduction in sensitivity, the occurrence of a conversion error, which respectively results in distortion of  measurement results. In  this  case, the  measuring  channel needs to stabilize the characteristics of the transformation into the targeted efforts of scientists.
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of converters  based on  the  amplitude detector [2]  results in  a  reduction in sensitivity, the occurrence of a conversion error, which respectively results in distortion of  measurement results. In  this  case, the  measuring  channel needs to stabilize the characteristics of the transformation into the targeted efforts of scientists. Existing means
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,  which directly measure  the amplitude of periodic signals, convert it into binary code and operate only at low frequencies (sigma-delta analog-to-digital converter) or have a low bit (parallel ADC) and not synchronized with  the  input signal.
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According to  the  scheme  presented in Figure 1, the measurement begins with the process of comparing the amplitude value of the voltage of the input periodic signal U with the value of the comparative voltage Uc, and can be determined by the equation
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: Uk1 = U  –  Uc . (1) Figure 1 – Scheme of  the  process of  measuring  the amplitude of the periodic signal by Fibonacci method Simultaneously with the  comparison process,  the allocation of a positive half-wave of a periodic signal occurs, that is, the formation of measuring periods
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1) Figure 1 – Scheme of  the  process of  measuring  the amplitude of the periodic signal by Fibonacci method Simultaneously with the  comparison process,  the allocation of a positive half-wave of a periodic signal occurs, that is, the formation of measuring periods. The  mathematical model of  such  a  process  can be described by the expression
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: Uk2 = (U  – |U–|)k,     (2)  where U_  –  amplitude of  the  negative half-wave  of the periodic signal; k – gain.  A mathematical model describing the process of phase detection can  be  set  by  a  system of  equations [9]:  where φ  –  phase shift, whose value can  be  obtained  from the  expression φ = 2πτx/T (τx  –  time shift  between the signal of the process
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The  mathematical model of  such  a  process  can be described by the expression [8]: Uk2 = (U  – |U–|)k,     (2)  where U_  –  amplitude of  the  negative half-wave  of the periodic signal; k – gain.  A mathematical model describing the process of phase detection can  be  set  by  a  system of  equations
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:  where φ  –  phase shift, whose value can  be  obtained  from the  expression φ = 2πτx/T (τx  –  time shift  between the signal of the process of forming the measuring periods (Uk2) and the signal of the comparison process (Uk1), T – input signal period).
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, whose value can  be  obtained  from the  expression φ = 2πτx/T (τx  –  time shift  between the signal of the process of forming the measuring periods (Uk2) and the signal of the comparison process (Uk1), T – input signal period). The  process of  the  number of  periods of  the  investigated signal can be conventionally described by the equation
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: C = 2k , where k  –  number of  digits required to  count  the number of periods.
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10]: C = 2k , where k  –  number of  digits required to  count  the number of periods.  The  Fibonacci sequence is  defined as  a  series  of numbers, in which each subsequent number is equal to the sum of the two previous
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: 169 (3) 0; 0. c c = , i f UU > , i f U > U φ≤  φ 170 1,  1,  2,  3,  5,  8,  13,  21,  34,  55,  89,  144,  233,  377,  610...  The  Fibonacci sequence can  be  conventionally  described by a recurrence relation: an+1 = an + an-1, where a1 = 1, a2 = 1.
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