RU2289881C1 - Method for converting residue classes system into voltage - Google Patents

Abstract

FIELD: automatics; computer engineering; digital number code in residue classes system conversion into voltage device.

SUBSTANCE: method consist of forming of base harmonic oscillation u₀(t)=Ucos(wt), forming of harmonic oscillation u₀₁(t) from base by L phase displacements by φ_j=2πβ_j/m_j angle, and harmonic oscillation u₀₂(t) by phase displacement by π/2 angle and (N-L) phase displacements by φ_k=2π/m_k(m_k-β_k)mod m_k, where j=1,2,...L; L - integer part from division of N by 2, k=(L+1),(L+2),...N. Harmonic oscillation u₀₁(t) is exposed to detection in balance phase detector, and harmonic oscillation u₀₂(t) is used as base signal of phase detector, with oscillation u₀₂(t) amplitude set two times smaller than u₀₁(t) amplitude. Output voltage of balance phase detector is in direct proportion to value of A represented in the form of digital code in residue classes system.

EFFECT: increased conversion accuracy.

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Description

The invention relates to the field of automation and computer technology and can be used in the design of devices for converting a digital code of number A in a system of residual classes (RNS) into voltage in the interface blocks of different types of elements of computing and information-measuring systems.

There is a method (analogue) of converting the code of the RNS to voltage [1, p.239-240], which consists in converting the number code in the RNS to a positional number system (MSS) and the subsequent formation of the voltage from the resulting positional code by summing currents directly proportional to the weights of the bits position code, on the total load resistance [2, p.208-211].

The disadvantage of this method is the low speed due to the need for additional conversion of the code of the RNS to MSS.

There is also a known method (analogue) based on the algorithm for converting the positional code of the number A from its code (α ₁ , α ₂ , ..., α _N ) into an RNS in accordance with the Chinese remainder theorem [1, p.31; 3, p. 35-39, p. 77-78]:

[•] - целая часть числа; m_i - совокупность взаимно простых целых положительных чисел;

μ_i - вес ортогонального базиса, получаемый из решения сравнения (μ_iM_i)modm_i≡1; r_A - ранг числа А, представляющий собой целое неотрицательное число, показывающее, во сколько раз диапазон СОК - М был превзойден при переходе от представления числа в СОК к его позиционному представлению.Where

[•] - the integer part of number; m _i - a set of mutually prime positive integers;

μ _i is the weight of the orthogonal basis obtained from the comparison solution (μ _i M _i ) modm _i ≡1; r _A is the rank of A, which is a non-negative integer that shows how many times the RNS - M range was surpassed in the transition from representing the number in RNS to its positional representation.

This method of converting the RNS code to voltage is [4, pp.23-24] in calculating, by modules m _{i, the} products of the bits α _{i of the} code of the number A in the RNS by the weights of the orthogonal bases μ _{i of} these bits - β _i = (α _i μ _i ) modm _i , where m _i are the bases of RNS; i = 1, 2, ... N, summing on the total load resistance of the currents directly proportional to the fraction β _i / m _i , and subtracting from the voltage obtained by passing the sum of these currents through the load resistance, a voltage directly proportional to the rank of the number - r _A.

The disadvantage of the analogue is its low speed, since when converting the RNS code to voltage, it is necessary to calculate the rank of the number - r _A. Known algorithms for obtaining the rank of a number [3, p. 78-82; 4, p.23-24] require additional equipment costs and is performed only in N steps, where N is the number of bases in the RNS.

, где i=1, 2, ... N, и сдвига фазы на π/2 и определение интеграла произведения этих колебаний:

, где Т_u - интервал интегрирования, причем значение u_u при U²T=M/π, Т_u>(2...3)T и 0≤A≪M, где Т - период гармонического колебания, равно величине числа А.The closest in technical essence (the prototype of the present invention) is the method [5], which includes calculating, by modules m _{i, the} products of the bits α _{i of the} code of the number A in the RNS by the weights of the orthogonal bases μ _{i of} these bits - β _i = (α _i μ _i ) modm _i , where m _i are the bases of RNS; i = 1, 2, ... N, the formation of the reference harmonic oscillation u ₀ (t) = Ucos (ω · t), where U and ω are the amplitude and frequency of the harmonic oscillation, respectively; t is the time obtained from the reference oscillation u ₀ (t) of two harmonic oscillations u ₁ (t) and u ₂ (t), respectively, by N phase shifts by

, where i = 1, 2, ... N, and the phase shift by π / 2 and the definition of the integral of the product of these oscillations:

, where T _u is the integration interval, and the value u _u at U ² T = M / π, T _u > (2 ... 3) T and 0≤A≪M, where T is the period of harmonic oscillation, is equal to the value of the number A .

относительно возможного диапазона изменения преобразуемого числа А. В связи с этим в арифметические устройства, функционирующие в СОК, для расширения диапазона разрядной сетки необходимо вводить дополнительные основания m_i, что, в свою очередь, приводит к увеличению аппаратурных затрат вычислительных устройств.The disadvantage of the prototype lies in the fact that the required conversion accuracy is achieved only with a significant (tens of times) exceeding the range of the discharge grid of the RNS -

relative to the possible range of change of the converted number A. In this regard, in order to expand the range of the discharge grid, it is necessary to introduce additional bases m _i into the arithmetic devices operating in the RNS, which, in turn, leads to an increase in the hardware costs of computing devices.

The aim of the proposed method is to increase the range of changes of the converted value A, within which an acceptable conversion accuracy is achieved.

The technical result is expressed in increasing the accuracy of converting the code of the RNS to voltage.

, и гармоническое колебание u₀₂(t) путем сдвига фазы на угол π/2 и (N-L) сдвигов фазы на угол

, где j=1, 2, ... L; L - целая часть результата деления числа N на 2; k=(L+1), (L+2), ... N, гармоническое колебание u₀₁(t) подвергают детектированию в балансном фазовом детекторе, а в качестве опорного сигнала фазового детектора используют гармоническое колебание u₀₂(t), амплитуду которого устанавливают в два раза меньше, чем амплитуду гармонического колебания u₀₁(t), причем выходное напряжение балансного фазового детектора при - М/4<А<М/4, где

- диапазон разрядной сетки СОК, с погрешностью, не превышающей 10%, прямо пропорционально величине числа A.This goal is achieved by the fact that in the known method, which includes the calculation by modules m _{i of the} products of the bits α _{i of the} code of the number A in the RNS by the weights of the orthogonal bases μ _{i of} these bits - β _i = (α _i μ _i ) modm _i , where m _i - foundations of RNS; i = 1, 2, ... N, the formation of the reference harmonic oscillation u ₀ (t) = Ucos (ω · t), where U and ω are the amplitude and frequency of the harmonic oscillation, respectively; t is the time according to the invention from the reference oscillation u ₀ (t) form a harmonic oscillation u ₀₁ (t) by L phase shifts by an angle

, and harmonic oscillation u ₀₂ (t) by phase shift by an angle π / 2 and (NL) phase shifts by an angle

where j = 1, 2, ... L; L is the integer part of the result of dividing the number N by 2; k = (L + 1), (L + 2), ... N, harmonic oscillation u ₀₁ (t) is detected in a balanced phase detector, and harmonic oscillation u ₀₂ (t), amplitude is used as the reference signal of the phase detector which is set two times less than the harmonic amplitude u ₀₁ (t), and the output voltage of the balanced phase detector at - M / 4 <A <M / 4, where

- the range of the discharge grid of the RNS, with an error not exceeding 10%, is directly proportional to the value of the number A.

The invention is based on the use of the periodicity property of a harmonic function and the statement of the Chinese remainder theorem.

It is known that

where p = 1, 2, 3, ...

Let two harmonic oscillations form u ₁ (t) = U ₁ cos (ωt) and u ₂ (t) = U ₂ sin (ωt) with amplitude U and frequency ω.

, где L - целая часть результата деления числа N на 2; j=1, 2, ... L, а начальную фазу второго гармонического колебания u₂(t) сдвинуть (N-L) раз на величину

, где k=(L+1), (L+2), ... N, то после этих сдвигов данные гармонические колебания будут описываться соответствующими выражениями:If the initial phase of harmonic oscillation u ₁ (t) is shifted L times by

where L is the integer part of the result of dividing the number N by 2; j = 1, 2, ... L, and shift the initial phase of the second harmonic oscillation u ₂ (t) (NL) times by

, where k = (L + 1), (L + 2), ... N, then after these shifts these harmonic oscillations will be described by the corresponding expressions:

As

and in turn

then on the basis of (3) and (5) we get

Similarly, taking into account expression (4), we obtain the formula

the second term in which is converted to

Accordingly, on the basis of (4) and (7) we obtain

It is difficult to show that, in accordance with the Chinese remainder theorem, the phase difference of harmonic oscillations (6) and (8) will be directly proportional to the value of the number A whose code in the RNS is (α ₁ , α ₂ , ..., α _N ):

To obtain a voltage directly proportional to the magnitude of the phase shift (9), a balanced phase detector can be used [6, p.142, Fig.7.29]. Let a harmonic oscillation (6) be received at its signal input in such a phase detector:

, j=1, 2, ... L, а в качестве опорного сигнала используется гармоническое колебание (8):formed from oscillations u ₀ (t) by L phase shifts by an angle

, j = 1, 2, ... L, and harmonic oscillation (8) is used as a reference signal:

, k=(L+1), (L+2), ... N.formed from the oscillation u ₀ (t) by phase shift by π / 2 and (NL) phase shifts by an angle

, k = (L + 1), (L + 2), ... N.

Taking into account (9), (10) and (11), the output voltage in the balanced phase detector is formed as the difference between the envelopes of the resulting oscillations on the diodes D ₁ and D _{2 of the} amplitude detectors in the composition of this phase detector [6, p.142-143, Fig. 7.29]:

where K _PhD is the transfer coefficient of the phase detector.

When U ₂ = U _1/2 we get:

The dependence of the output voltage of the balanced phase detector (12) with such a ratio of the amplitudes of the signal and reference oscillations is close to a linear dependence in the interval - M / 4 <A <M / 4 with an error not exceeding 10%. As an illustration of this, Fig. 1 shows in a continuous line a graph of the relative deviation of the output voltage (12) from the linear dependence Δ, expressed as a percentage, which is constructed according to the following formula:

от линейной зависимости, выраженный в процентах, который построен по следующей формуле:Here the dashed line shows a graph of the relative deviation of the output voltage of the prototype [5] -

on a linear relationship, expressed as a percentage, which is built according to the following formula:

From the graphs it can be seen that, in comparison with the prototype, the proposed method provides greater accuracy of converting the code of the system of residual classes into voltage in a wider range of changes of the converted value A.

, 5 - аттенюатор, 6 - балансный фазовый детектор, 7 - выход устройства.Figure 2 shows the structural diagram of a device that implements the proposed method for converting the RNS code to voltage, where 1.1-1.N are the information inputs of the device, 2 is a harmonic oscillation generator, 3.1-3.N are controlled phase shifters, 4 is a phase shifter at an angle

5 - attenuator; 6 - balanced phase detector; 7 - device output.

4 и аттенюатор 5 - с первым входом управляемого фазовращателя 3.(L+1), причем выход управляемого фазовращателя 3.j соединен с первым входом управляемого фазовращателя 3.(j+1), где j=1, 2, ... L-1, а выход управляемого фазовращателя 3.р соединен с первым входом управляемого фазовращателя 3.(р+1), где p=L+1,L+2,...N-1, при этом выход управляемого фазовращателя 3.L подключен к первому входу балансного фазового детектора 6, второй вход которого соединен с выходом управляемого фазовращателя 3.N, причем выход балансного фазового детектора 6 является выходом 7 устройства.Information inputs 1.1-1.N are connected to the second inputs of the corresponding controlled phase shifters 3.1-3.N, while the output of the harmonic oscillation generator 2 is connected directly to the first input of the controlled phase shifter 3.1 and through the phase shifter at an angle

4 and attenuator 5 - with the first input of the controlled phase shifter 3. (L + 1), and the output of the controlled phase shifter 3.j is connected to the first input of the controlled phase shifter 3. (j + 1), where j = 1, 2, ... L -1, and the output of the controlled phase shifter 3.p is connected to the first input of the controlled phase shifter 3. (p + 1), where p = L + 1, L + 2, ... N-1, while the output of the controlled phase shifter 3.L connected to the first input of the balanced phase detector 6, the second input of which is connected to the output of the controlled phase shifter 3.N, and the output of the balanced phase detector 6 is the output 7 of the device.

Consider the operation of the device.

, где β_j=(α_jμ_j)modm_j; j=1, 2, ... L; L - целая часть результата деления числа N на 2, а в управляемых фазовращателях 3.(L+1)-3.N устанавливаются сдвиги фазы на угол

, где β_p=(α_pμ_p)modm_p; p=(L+1), (L+2), ... N.Codes α _{i of the} corresponding digits of the number A are supplied to the N information inputs 1.1-1.N of the device in the RNS, where i = 1,2, ... N. In accordance with these codes, controlled phase shifters 3.1-3.L set phase shifts by an angle

where β _j = (α _j μ _j ) modm _j ; j = 1, 2, ... L; L is the integer part of the result of dividing the number N by 2, and in the controlled phase shifters 3. (L + 1) -3.N, phase shifts by an angle are established

where β _p = (α _p μ _p ) modm _p ; p = (L + 1), (L + 2), ... N.

After passing the harmonic oscillation u ₀ (t) = Ucos (ω · t) from the output of the generator 2 through the controlled phase shifters 3.1-3.L at the output of the controlled phase shifter 3.L, the total phase shift

In the phase shifter 4, the cosine oscillation u ₀ (t) of the generator 2 is converted to a sinusoidal one, and in the attenuator 5 its amplitude becomes half as much as at the output of the generator 2. After this oscillation passes through the controlled phase shifters 3. (L + 1) -3 .N at the output of the controlled phase shifter 3.N sets the total phase shift

The harmonic oscillation generated with such a phase shift from the output of the controlled phase shifter 3.N is supplied to the second input of the balanced phase detector 6 as a reference signal. In this case, harmonic oscillation from the output of the controlled phase shifter 3.L. is supplied to the first input of the phase detector 6 as a signal voltage. The detection of this oscillation in the phase detector 6 at the output 7 of the device generates a voltage that is directly proportional

.which on the interval - M / 4 <A <M / 4 is close to a linear relationship:

.

; N=5; m₁=11; m₂=7; m₃=5, m₄=3; m₅=2; A=199.Example. Let be

; N = 5; m ₁ = 11; m ₂ = 7; m ₃ = 5, m ₄ = 3; m ₅ = 2; A = 199.

; L=2; α₁=Amodm₁=1; α₂=3; α₃=4; α₄=1; α₅=1 (A=(1, 3, 4, 1, 1)); μ₁=1; μ₂=1; μ₃=3; μ₄=2; μ₅=1.We calculate the initial data:

; L = 2; α ₁ = Amodm ₁ = 1; α ₂ = 3; α ₃ = 4; α ₄ = 1; α ₅ = 1 (A = (1, 3, 4, 1, 1)); μ ₁ = 1; μ ₂ = 1; μ ₃ = 3; μ ₄ = 2; μ ₅ = 1.

;

;

;

и

.In accordance with the values of the discharges α ₁ , α ₂ , α ₃ , α _4, and α ₅ obtained in this example, the following phase shifts are established in the controlled phase shifters 3.1-3.5:

;

;

;

and

.

After the passage of harmonic oscillations from the output of the generator 2 through the corresponding phase shifters at the output of the controlled phase shifter 3.2, a phase incursion equal to

and at the output of the controlled phase shifter 3.5, a phase incursion equal to

Given the obtained values of f ₁ and f ₂ the phase difference will be equal to the following value:

As a result of detecting a cosine harmonic oscillation with a phase incursion Φ ₁ in a balanced phase detector, in which a sinusoidal oscillation with half the amplitude and a phase incidence Φ ₂ is used as a reference signal, in accordance with expression (12) and the above initial data, we get the output voltage of the device:

This result with an accuracy of 1.5% coincides with the value of the number A = 199.

For comparison, in the prototype [5] for the same initial data the following result is obtained: u _PR (A) = 189.424, which is 4.8% different from A = 199.

Since, as in the prototype, in the claimed method, the procedure for converting the RNS code to voltage is based on phase shift operations and determining the total phase incursion, then the conversion speed in this case will be no worse than the prototype speed.

Information sources

1. Chernyavsky A.F. and others. High-speed methods and systems of digital information processing. - Мn .: Belgosuniversitet, 1996 .-- 376 p.

2. Gitis E.I., Piskulov E.A. Analog-to-digital converters. - M.: Energoizdat, 1981. - 360 p.

3. Akushsky I.Ya., Yuditsky D.I. Machine arithmetic in residual classes. - M .: Owls. Radio, 1968 .-- 440 p.

4. Abramson I.T., Avrov O.M., Lapkin L.Ya. Coding of electrical quantities in a system of residual classes. // Autometry, No. 2 (62), 1975, pp. 23-29.

5. RF patent No. 2220501, IPC N 03 M 7/18, BI No. 36, 2003.

6. Radio receivers: Textbook. allowance for radio engineering. specialist. universities / Yu.T. Davydov, Yu.S. Danilich, A.P. Zhukovsky and others; Ed. A.P. Zhukovsky. - M .: Higher. school., 1989 .-- 342 p.

Claims (1)

A method for converting a code of a system of residual classes (RNS) into a voltage, including calculating, by modules m _{i, the} products of the bits α _{i of the} code of the number A in the RNS by the weights of the orthogonal bases μ _{i of} these bits - β _i = (α _i μ _i ) modm _i , where m _i - the basis of RNS; i = 1, 2, ... N, the formation of the reference harmonic oscillation u ₀ (t) = Ucos (ω · t), where U and ω are the amplitude and frequency of the harmonic oscillation, respectively; t is the time, characterized in that a harmonic oscillation u ₀₁ (t) is formed from the reference oscillation u ₀ (t) by L phase shifts by an angle

and harmonic oscillation u ₀₂ (t) by phase shift by an angle π / 2 and (NL) phase shifts by an angle

where j = 1, 2, ... L; L is the integer part of the result of dividing the number N by 2; k = (L + 1), (L + 2), ... N, harmonic oscillation u ₀₁ (t) is detected in a balanced phase detector, and harmonic oscillation u ₀₂ (t) is used as the reference signal of the phase detector, the amplitude of which is set two times less than the amplitude of harmonic oscillation U ₀₁ (t), and the output voltage of the balanced phase detector at - M / 4 <A <M / 4, where

- the range of the discharge grid of the RNS, with an error not exceeding 10%, is directly proportional to the value of the number A.

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