RU2290754C1 - Method for transforming code of system of remainder classes to voltage - Google Patents

Abstract

FIELD: automatics and computer science, possible use for engineering of devices for transforming digital code of number in a system of remainder classes to voltage.

SUBSTANCE: method includes forming supporting harmonic oscillation u₀(t)=Ucos(w·t), generation of harmonic semiconductor u₁(t) from supporting oscillation by means of making N phase shifts for angle

and harmonic oscillation u₂(t) by shifting phase for angle π/2, while harmonic oscillation u₁(t) is subjected to detection in balance phase detector, and as support signal of phase detector harmonic oscillation u₂(t) is used, amplitude of which is set to be twice less than amplitude of harmonic oscillation u₁(t), while output voltage of balance phase detector is directly proportional to value of number A, represented in form of digital code in the system of remainder classes.

EFFECT: increased precision of transformation.

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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 digital code 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 RNS code to voltage [1, p.239-240], which consists in converting the number code in RNS to a positional number system (MSS) and then generating a voltage from the obtained positional code by summing the currents directly proportional to the discharge weights 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 an 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]:

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 ) mod m _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 ) mod m _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 are performed only in N steps, where N is the number of bases in the RNS.

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 ) mod m _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 of 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, equal to the value of 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.

где i=1, 2, ... N, и сдвига фазы на π/2, согласно изобретению гармоническое колебание u₁(t) подвергают детектированию в балансном фазовом детекторе, а в качестве опорного сигнала фазового детектора используют гармоническое колебание u₂(t), амплитуду которого устанавливают в два раза меньше, чем амплитуду гармонического колебания u₁(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 А.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 ) mod m _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 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, according to the invention, harmonic oscillation u ₁ (t) is detected in a balanced phase detector, and harmonic oscillation u ₂ (t ), the amplitude of which is set two times less than the amplitude of the harmonic oscillation u ₁ (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, ...

If the initial phase of harmonic oscillation with amplitude U and frequency ω

,shift N times by

,

where i = 1, 2, ... N, then after the last (Nth) shift, harmonic oscillation (3) will be described by the expression:

.Where

.

As

а в свою очередь

and in turn

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

For β _i = (α _i μ _i ) mod m _{i, the} phase shift of the harmonic oscillation u ₁ (t) in accordance with the statement of the Chinese remainder theorem [3, p. 36, formula (1.30)] will be directly proportional to the value of the number A, code in the RNS which is equal to (α ₁ , α ₂ , ..., α _N ):

Therefore, to generate a voltage directly proportional to the value of the number A, the code in the RNS of which is equal to (α ₁ , α ₂ , ..., α _N ), it is necessary to obtain a voltage directly proportional to the phase shift of the harmonic oscillation (6) relative to the phase of the reference oscillation (3).

To obtain such a voltage, 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:

and the harmonic oscillation u ₂ (t) = U ₂ sin (ω · t), which is formed from harmonic oscillation (3) by phase shift by π / 2, is used as a reference signal.

Taking into account (8), 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 (10) with this ratio of the amplitudes of the signal and reference oscillations turns out to be 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 (10) 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 a 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, причем выход управляемого фазовращателя 3.j соединен с первым входом управляемого фазовращателя 3.(j+1), где j=1, 2, ... N-1, а выход управляемого фазовращателя 3.N подключен к первому входу балансного фазового детектора 6, второй вход которого через аттенюатор 5 соединен с выходом фазовращателя на угол

4, при этом 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 to the first input of the controlled phase shifter 3.1 and the phase shifter input at an angle

4, 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, ... N-1, and the output of the controlled phase shifter 3.N is connected to the first input of the balanced phase detector 6, the second input of which through the attenuator 5 is connected to the output of the phase shifter at an angle

4, while the output of the balanced phase detector 6 is the output 7 of the device.

Consider the operation of the device.

On N information inputs 1.1-1.N of the device, codes α _{i of the} corresponding digits of the number A are received in the RNS, where i = 1, 2, ... N. In accordance with these codes, phase shifts are established in the controlled phase shifters 3.1-3.N angle

,

,

where β _i = (α _i μ _i ) modm _i ; i = 1, 2, ... N.

After passing the harmonic oscillation from the output of the generator 2 through the controlled phase shifters 3.1-3.N at the output of the controlled phase shifter 3.N, the total phase shift

4 осуществляется сдвиг фазы опорного гармонического колебания с выхода генератора гармонического колебания 2 на угол

, а в аттенюаторе 5 устанавливается амплитуда этого колебания в два раза меньше, чем амплитуда гармонического колебания на выходе управляемого фазовращателя 3.N:U₂=U₁/2.At the same time in the phase shifter at an angle

4, the phase shift of the reference harmonic oscillation is carried out from the output of the harmonic oscillation generator 2 by an angle

and in the attenuator 5 the amplitude of this oscillation is set two times smaller than the amplitude of the harmonic oscillation at the output of the controlled phase shifter 3.N: U ₂ = U _1/2 .

The harmonic oscillation thus generated from the output of the attenuator 5 is fed 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.N 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.

; α₁=Amod m₁=1; α₂=1; α₂=3; α₃=4; α₄=1; α₅=1 (А=(1, 3, 4, 1, 1)); μ₁=1; μ₂=1; μ₃=3; μ₄=2; μ₅=1.We calculate the initial data:

; α ₁ = Amod m ₁ = 1; α ₂ = 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 passing the harmonic oscillation from the output of the generator 2 through the corresponding phase shifters, at the output of the controlled phase shifter 3.5, a phase incursion equal to

As a result of detecting a harmonic signal with such a phase shift in a balanced phase detector, in accordance with expression (10) and the above source data, we obtain 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, 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, which includes calculating, by modules m _{i, the} products of the bits α _{1 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 ) mod m _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 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 a phase shift by π / 2, characterized in that the harmonic oscillation u ₁ (t) is detected in a balanced phase detector, and harmonic oscillation u is used as the reference signal of the phase detector ₂ (t), the amplitude of which is set two times less than the amplitude of the harmonic oscillation u ₁ (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%, directly proportional to the value of the number A.

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