RU2628918C1 - Hybrid functional digital-to-analog converter with spline approximation of n-th order - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: method is implemented by applying a spline approximation of the n-th order with a partition into i-number of intervals allowing to obtain the most accurate hybrid functional DAC with an increased speed. The hybrid functional DAC contains n series-connected linear multiplying DAC for specifying the n-th order of the spline, to which the code-converter is connected to the digital inputs and parallel to them n+1 linear multiplying DAC connected along digital lines to the code-converter for specifying the variable spline coefficients taking into account the signs. Spline coefficients are calculated according to well-known mathematical methods, depending on the number of the approximation intervals.

EFFECT: optimisation of constructing a nonlinear hybrid digital-to-analog converter with improved metrological and technical characteristics.

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Description

The inventive device for non-linear digital-to-analogue signal conversion relates to the field of radio engineering, telecommunications, information-measuring equipment (in particular, phase calibrators and phase shifters), to systems with phase control and can be used for nonlinear digital-to-analogue conversion of signals of different accuracy and complexity.

Hybrid functional DACs are built on DACs using various types of approximations. The hybrid method is an alternative to the digital method and combines the positive aspects of the analog and digital method.

For non-linear digital-to-analog conversion, various resistor arrays can be used, the resistors in which are selected according to special laws [Non-linear digital-to-analog converter for servo circuit (Non-linear digital-to-analog converter for drives). U.S. Patent MKI H03K 13/04 No. 4020485, 04/26/1977. Nonlinear type digital-to-analog converter. U.S. Patent MKI N03K 13/02, No. 4062013, December 6, 1977]. However, the use of such non-linear converters is limited to the implementation of only one conversion characteristic.

A device and method for constructing functional digital-to-analog converters (DACs) is known, based on a piecewise-linear approximation of the required functional dependence [Non-linear digital-to-analog converter and display incorporating the same. Non-linear digital-to-analog converter and display containing it.) US Pat. H03K 13/02, No. 6154121, 11.28.2000. Smolov V.B., Fomichev B.C. Analog-digital and digital-analog non-linear computing devices. L .: "Energy", 1974, p. 77-177]. The digital-to-analog signal conversion device includes an N-bit digital input, a decoder, and a linear DAC. The digital code N arriving at such a device is divided into two parts, the high-order bits being used by a decoder to select the maximum and minimum voltages of a given linear section of the approximation and fed to the linear DAC, which controls the low-order bits of the digital code and forms this section.

The accuracy of devices providing piecewise linear approximation will depend on the choice of the method of dividing the approximated curve into linear sections. But even with the optimal choice, the error in the reproduction of the function may turn out to be unsatisfactory.

To increase the accuracy, it is advisable to use the approximation of the necessary functional dependence of the polynomial or quotient of two polynomials. The approximation errors are significantly reduced.

Fractional rational approximation is used in functional converters consisting of multiplying DACs, to which a digital code is supplied, operational amplifiers (OA), passive voltage dividers and resistors [Electronics: Reference book / Ed. Yu.A. Bystrov. - St. Petersburg: Energoatomizdat, 1996, p. 243-245. Smolov V.B., Fomichev B.C. Analog-digital and digital-analog non-linear computing devices. L .: "Energy", 1974, p. 77-177]. The output voltage of the device depends on the input digital code as a fractional rational function R (N)

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Using the methods of the mathematical apparatus, the required conversion function is determined in a fractionally rational form, and the coefficients of the function R (N) are found, which are set using resistors and passive dividers.

A significant drawback of such a device is the invariability of the transfer characteristic, which is set when constructing the Converter, due to the connected coefficients of the rational fraction. This greatly limits the capabilities of systems and devices built using this type of functional converters. It should be noted that these converters are not able to work with a digital code that has a signed bit.

A power function of degree n can be implemented using n multiplying DACs, connected so that the voltage of the first of them is supplied with a reference voltage, and the output voltage of the previous DAC is supplied to the analog inputs of each subsequent DAC [Smolov VB, Fomichev B.C. Analog-digital and digital-analog non-linear computing devices. L .: "Energy", 1974, p. 77-177. Gnatek Yu.R. Handbook of digital-to-analog and analog-to-digital converters: Per. from English / Ed. Yu.R. Ryuzhina. - M .: Radio and communications, 1982.P. 259-260, Fig. 4.129-4.130]. At the same time, at the output of each i-th DAC, a voltage is generated proportional to the degree i of the supplied code.

Such a device has the disadvantage of being able to carry out only a certain set of functions (power functions) and does not have the ability to reconfigure. Obviously, the multiplication of the obtained stresses by certain coefficients with subsequent addition will allow us to apply a power-law approximation [Smolov VB, Fomichev B.C. Analog-digital and digital-analog non-linear computing devices. L .: "Energy", 1974, p. 77-177].

A device for implementing a functional DAC with polynomial approximation is known [Utility Model Patent No. 74022, IPC Н03М 1/66. The device of nonlinear digital-to-analog signal conversion / Sapelnikov V.M., Kanareikin V.I. et al. - No. 74022: applicant Sapelnikov V.M .; declared 2007, publ. 2008]. The disadvantage is the approximation method itself, the accuracy of the functional DAC is determined by the degree of the polynomial and the accuracy of setting constant coefficients of the polynomial. The most accurate method of approximation, as you know [Methods of computing on a computer: Reference manual / Ivanov VV - Kiev: Naukova Dumka. - 1986. - p. 144-201], when reproducing a nonlinear dependence, this is a spline approximation (piecewise polynomial approximation).

The prototype of the claimed device is a functional DAC with spline approximation by a 3rd order polynomial [RF Patent No. 2408136, IPC Н03М 1/66. Functional DAC / Sapelnikov V.M., Kanareikin V.I., Klimenko S.S.]. The functional digital-to-analog converter contains the first, second, and third linear multiplying DACs, a reference voltage source and an adder, a code converter, fourth, fifth, sixth, seventh linear multiplying DACs that specify the spline approximation coefficients for the corresponding first, second, and third linear multiplying DACs, the input the digital bus is connected to the address digital inputs of the code converter and to the corresponding digital inputs of the first, second, and third linear multiplying DACs, digital ode kodopreobrazovatelya connected to the corresponding digital inputs of the fourth, fifth, sixth, seventh linear multiplying DAC reference voltage source output is connected to the control inputs of the first and seventh linear multiplying DAC analog output of which is connected to the first input of the adder; the analog output of the first linear multiplying DAC is connected to the control input of the second and sixth linear multiplying DAC, the analog output of which is connected to the second input of the adder; the analog output of the second linear multiplying DAC is connected to the control input of the third and fifth linear multiplying DAC, the analog output of which is connected to the third input of the adder; the analog output of the third linear multiplying DAC is connected to the control input of the fourth linear multiplying DAC, the analog output of which is connected to the fourth input of the adder; the adder output is the output of the entire device.

The disadvantage of the prototype is the lack of a description of the technical implementation of the n-th order spline with optimization in accuracy and speed.

The implementation of the n-th order spline is a synthesis of solutions from the works of [RF Patent No. 2408136, IPC Н03М 1/66. Functional DAC / Sapelnikov V.M., Kanareykin V.I., Klimenko S.S. - No. 2408136, Utility Model Patent No. 74022, IPC Н03М 1/66. The device of nonlinear digital-to-analog signal conversion / Sapelnikov V.M., Kanareikin V.I. and etc.]. From [Utility Model Patent No. 74022, IPC Н03М 1/66. The device of nonlinear digital-to-analog signal conversion / Sapelnikov V.M., Kanareikin V.I. and others.] follows the principle of the formation of the nth order - this is a cascade (sequential) inclusion of multiplying DACs. The prototype describes the principle of forming variable spline coefficients.

The objective of the invention is the optimization of the construction of a nonlinear hybrid digital-to-analog converter with improved metrological and technical characteristics due to the application of the n-th order spline approximation with the number of intervals divided by i, which makes it possible to obtain the most accurate hybrid functional DAC with increased speed.

The task is achieved by the fact that in a hybrid functional DAC containing linear multiplying DACs, the digital inputs of which are connected to a code converter, a reference voltage source and an adder, in contrast to the prototype, n linear multiplying DACs are connected in series to specify the nth order of the spline, and in parallel, they introduced n + 1 linear multiplying DACs connected via digital lines to a code converter for setting variable spline coefficients taking into account the signs, and the reference voltage source li ne to the first DAC, specify the n-th order spline and the first DAC, the given variables with zero coefficient of the spline function argument dependency, the analog outputs of DAC defining the spline coefficients are connected to the adder. In this case, the spline coefficients are calculated by well-known mathematical methods, depending on the number of approximation intervals i.

The qualitative nature of the error distribution over the selected approximation interval will depend on the chosen approximation technique.

In FIG. 1 shows a block diagram of a functional DAC with spline approximation of the n-th order, in FIG. Figure 2 shows the block diagram of a functional DAC with spline approximation of the third order.

The device operates as follows.

The device comprises a code converter 1, a reference voltage source (ION) 2, n series-connected multiplying linear DACs ₁ - DAC _n 3 (for example, digital potentiometers), for setting the degree (argument) of the polynomial each digit of the digital input of which is connected to the corresponding digital bit of the information input code converter code 1. The analog input of the first DAC _{1 is} connected to the output of the reference voltage source 2. The analog inputs of each of the n-1 subsequent series-connected multiplying DACs are connected to the analog main outputs of previous DACs. The spline coefficients are set by the code converter 1 via digital lines to the digital inputs n + 1 of the parallel-connected DACs _{1 '} - DAC _{(n + 1)'} - 4. The analogue input of the DAC _{1 'is} connected to the voltage reference 2, the analogue output of the DAC _{1' is} connected to the adder 5, an analog signal U _on a _{0 is} generated at the output.

The analog input of the DAC _{2 '} - DAC _{(n + 1)'} y is connected to the analog outputs of the DAC ₁ - DAC _n, respectively, forming a multiplication of the input voltage reference by a digital code from the 1st to nth order by the coefficients for these orders.

The summation of all thus formed spline polynomials is carried out on a summing device:

where a _ni are the spline coefficients (any number is a positive number, including an irrational one);

x = N / N _max - relative code, N - current code, N _max - maximum digital code;

ƒ _i (x (t)) is any function defined by any n-order polynomial with i-number of approximation intervals (polynomial, power function, fractional rational function, linear function, etc.).

The higher the order of spline n and the greater the number of intervals of approximation i, the higher the accuracy. The amount of memory used in the code converter 1 is determined by the number of spline coefficients and is minimal in comparison with the amount of memory in the digital method, which improves performance. Functional DACs can be implemented in a modular system using switching devices operating at any frequency range, which increases the scope of such devices as elements of complex information-measuring systems.

Studies have shown in practice most often it is enough to use a 12-bit functional DAC of the 3rd order with an approximation interval of 3 or higher to ensure the accuracy of the reproduction of most nonlinear dependencies.

Example 1, in FIG. 2 shows a block diagram of a functional DAC with spline approximation of the 3rd order. This scheme of a hybrid functional DAC with spline approximation of the third order allows one to realize cosine, logarithmic, exponential, and other types of nonlinear dependencies. The signs of the spline coefficients are taken into account in the code converter 1.

Table 1 presents the cosine spline coefficients calculated by one of the well-known mathematical methods with a uniform and uneven step of the approximation intervals (natural cubic spline, Taylor, Maclaurin, Chebyshev, and other decomposition methods). Tables 2, 3 show the spline coefficients of the logarithmic and exponential functions calculated according to one of the well-known mathematical methods (natural cubic spline).

Claims (3)

1. A hybrid functional digital-to-analog converter with an n-th order spline approximation, comprising linear multiplying DACs, to which digital inputs are connected a code converter, a reference voltage source and an adder, characterized in that it contains n series-connected linear multiplying DACs for setting the n-th order of the spline , and parallel to them, n + 1 linear multiplying DACs connected to the code converter via digital lines to specify variable spline coefficients taking into account the signs, while the reference source voltage is connected to the first DAC, which defines the nth order of the spline, and to the first DAC, which sets the variable spline coefficient at the zero argument of the functional dependence, the analog outputs of all the DACs that specify the spline coefficients are connected to the adder. 2. Hybrid functional digital-to-analog converter with n-th order spline approximation according to claim 1, characterized in that as linear multiplying DACs, there are digital potentiometers for adjusting the average accuracy of variable spline coefficients. 3. Hybrid functional digital-to-analog converter with n-th order spline approximation according to claim 1, characterized in that it contains precision multiplying DACs with a resolution of 12 and higher as linear multiplying DACs for finer and more precise adjustment of variable spline coefficients.

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