CN113114123B - Nonlinear curve fitting device and method - Google Patents
Nonlinear curve fitting device and method Download PDFInfo
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- CN113114123B CN113114123B CN202110316852.1A CN202110316852A CN113114123B CN 113114123 B CN113114123 B CN 113114123B CN 202110316852 A CN202110316852 A CN 202110316852A CN 113114123 B CN113114123 B CN 113114123B
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- H03F1/00—Details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements
- H03F1/32—Modifications of amplifiers to reduce non-linear distortion
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Abstract
The application discloses a fitting device and method of nonlinear curves, wherein the fitting device comprises an operational amplifier circuit A n Operational amplifier circuitB n Operational amplifier circuit C n And a maximum value taking circuit D; the operational amplifier circuit A n An input end of the operational amplifier circuit B is connected with an output end of an input analog signal n Is connected with the input end of the voltage transformer and the preset voltage V ref_n The output end of the operational amplifier circuit A is connected with n And the operational amplifier circuit B n And the operational amplifier circuit C n Is connected with the input end of the operational amplifier circuit C n The output end of the (C) is connected with the input end of the maximum value taking circuit D; and the output end of the maximum value taking circuit D outputs the fitted analog signal. The piecewise linearization fitting of a monotonically increasing or monotonically decreasing nonlinear curve is realized in a pure analog circuit mode; the circuit is simple, the cost is low, and the precision is high.
Description
Technical Field
The present disclosure relates to the field of signal processing technologies, and in particular, to a device and a method for fitting a nonlinear curve.
Background
The current nonlinear curve fitting method commonly comprises a software table look-up linear interpolation method and a software polynomial fitting method. The software look-up table linear interpolation method is simpler to realize; in order to have higher fitting precision, a higher order polynomial is needed to be adopted to realize fitting, a software algorithm is complex, and more storage resources are occupied.
The two methods are all carried out by a software mode, and AD sampling is needed first, then the AD sampling is processed by a digital processing chip with computing capability such as a singlechip, a DSP or an FPGA, and DA conversion is carried out. The realization circuit is complex, the cost is high, and the combination of software and hardware is needed. In some cases where low cost is required or where there is a limit to the size of the veneer, the above method is too complex to use.
Disclosure of Invention
In view of this, the present application aims to provide a device and a method for fitting a nonlinear curve, so as to solve the problem that the existing nonlinear curve fitting method is unsuitable for occasions requiring low cost or limiting the size of a single board.
The technical scheme adopted for solving the technical problems is as follows:
according to one aspect of the present application, there is provided a fitting device of a nonlinear curve, the fitting device including an operational amplification circuit a n Operational amplifier circuit B n Operational amplifier circuit C n And a maximum value taking circuit D;
the operational amplifier circuit A n An input end of the operational amplifier circuit B is connected with an output end of an input analog signal n Is connected with the input end of the voltage transformer and the preset voltage V ref_n The output end of the operational amplifier circuit A is connected with n And the operational amplifier circuit B n And the operational amplifier circuit C n Is connected with the input end of the operational amplifier circuit C n The output end of the (C) is connected with the input end of the maximum value taking circuit D; and the output end of the maximum value taking circuit D outputs the fitted analog signal.
According to another aspect of the present application, there is provided a method of fitting a nonlinear curve, the method comprising:
operational amplifier circuit A n Generating a piecewise fitted curve y n ＝f n (x) Slope a of (a) n ；
Operational amplifier circuit B n Generating a piecewise fitted curve y n ＝f n (x) The intercept b of (2) n ；
Operational amplifier circuit C n For amplifying the operation amplifier circuit A n Output result a of (a) n * x and the operational amplifier circuit B n Output result b of (2) n Adding;
the maximum value taking circuit D takes the maximum value or the minimum value for the multi-section fitting curve.
According to the fitting device and method for the nonlinear curve, piecewise linearization fitting of the monotonically increasing or monotonically decreasing nonlinear curve is achieved in a pure analog circuit mode; the circuit is simple, the cost is low, and the precision is high.
Drawings
Fig. 1 is a schematic diagram of a fitting device for a nonlinear curve according to an embodiment of the present application;
FIGS. 2-3 are schematic diagrams of a piecewise curve with increasing slope according to embodiments of the present application;
FIGS. 4-5 are schematic diagrams of a piecewise curve with decreasing slope according to embodiments of the present application;
fig. 6 to 11 are specific schematic diagrams of a nonlinear curve fitting apparatus according to an embodiment of the present application.
The realization, functional characteristics and advantages of the present application will be further described with reference to the embodiments, referring to the attached drawings.
Detailed Description
In order to make the technical problems, technical schemes and beneficial effects to be solved by the application clearer and more obvious, the application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the present application.
Example 1:
as shown in fig. 1, a first embodiment of the present application provides a fitting device for nonlinear curves, which includes an operational amplifier circuit a n Operational amplifier circuit B n Operational amplifier circuit C n And a maximum value taking circuit D;
the operational amplifier circuit A n An input end of the operational amplifier circuit B is connected with an output end of an input analog signal n Is connected with the input end of the voltage transformer and the preset voltage V ref_n The output end of the operational amplifier circuit A is connected with n And the operational amplifier circuit B n And the operational amplifier circuit C n Is connected with the input end of the operational amplifier circuit C n The output end of the (C) is connected with the input end of the maximum value taking circuit D; and the output end of the maximum value taking circuit D outputs the fitted analog signal.
In this example, the operational amplifier circuit A n For generating piecewise fitted curve y n ＝f n (x) Slope a of (a) n The operational amplifier circuit B n For generating piecewise fitted curve y n ＝f n (x) The intercept b of (2) n The operational amplifier circuit C n For amplifying the operation amplifier circuit A n Output result a of (a) n * x and the operational amplifier circuit B n Output result b of (2) n And adding, wherein the maximum taking circuit D is used for taking the maximum value or the minimum value of the multi-section fitting curve.
In this example, the operational amplifier circuit A n Is one of a homodromous proportional amplifying circuit, a reverse proportional amplifying circuit and a resistor voltage dividing circuit.
In the present example, the operational amplifier circuit B n Is one of a homodromous proportional amplifying circuit, a reverse proportional amplifying circuit and a resistor voltage dividing circuit.
In this example, the operational amplifier circuit C n Is one of a same-direction operation addition circuit, a reverse operation addition circuit and an operation subtraction circuit.
In this example, the maximum value taking circuit D is a maximum value taking circuit or a minimum value taking circuit.
In this example, the maximum value taking circuit D is constituted by a unidirectional conduction device, or is constituted by a chip selection logic chip and a peripheral circuit. The unidirectional conduction device includes a diode.
In the present example, the voltage V is preset ref_1 、V ref_2 、V ref_3 、.....、V ref_n The preset voltages may be different or the same.
In this example, n is an integer greater than or equal to 1.
After the piecewise fitting, the functional expression of each fitted curve is as follows:
y 1 ＝f 1 (x)＝a 1 *x+b 3 ，x＜X 1
y 2 ＝f 2 (x)＝a 2 *x+b 2 ，X 1 ≤x＜X 2
y 3 ＝f 3 (x)＝a 3 *x+b 3 ，X 2 ≤x＜X 3
……
y n ＝f n (x)＝a n *x+b n ，X n-1 ≤x＜X n
if a monotonic curve y n ＝f n (x) Piecewise linear function slope a n Monotonically increasing, i.e. a n ＞a n-1 The curves of > … … > a2 > a1 are shown in FIG. 2 and FIG. 3. Such monotonically increasing or monotonically decreasing nonlinear curves may be implemented using the specific embodiment circuits shown in fig. 6, 8, and 10 to achieve curve y n ＝f n (x) Fitting, wherein the maximum circuit D is a maximum circuit.
In fig. 6, an operational amplifier circuit a 1 The non-inverting input end of the circuit is connected with an input analog signal X, and the inverting input end is grounded through a resistor; operational amplifier circuit B 1 The non-inverting input end of the capacitor is grounded, and the inverting input end is connected with a preset voltage V through a resistor ref_1 Connecting; operational amplifier circuit A 1 And operational amplifier circuit B 1 Output terminal of (a) and operational amplifier circuit C 1 Is connected with the non-inverting input end of the operational amplifier circuit C 1 The inverting input end of the capacitor is grounded through a resistor; operational amplifier circuit C 1 The output end of the (c) is connected with the anode of the diode, and the cathode of the diode outputs the fitted analog signal f (x). In fig. 6, other operational amplifier circuits are similar to those described above, and are not described in detail herein.
In fig. 8, an operational amplifier circuit a 1 The non-inverting input end of the circuit is grounded, and the inverting input end is connected with an input analog signal X through a resistor; operational amplifier circuit B 1 Is connected to the non-inverting input terminal of (a) and the preset voltage V ref_1 The inverting input end is grounded through a resistor; operational amplifier circuit A 1 And operational amplifier circuit B 1 Output terminal of (a) and operational amplifier circuit C 1 Is connected with the inverting input terminal of the operational amplifier circuit C 1 Is grounded; operational amplifier circuit C 1 The output end of the (c) is connected with the anode of the diode, and the cathode of the diode outputs the fitted analog signal f (x). In fig. 8, other operational amplifier circuits are similar to those described above, and are not described here.
In fig. 10, an operational amplifier circuit a 1 The non-inverting input end of the circuit is grounded, and the inverting input end is connected with an input analog signal X through a resistor; operational amplifier circuit B 1 Is connected to the non-inverting input terminal of (a) and the preset voltage V ref_1 The inverting input end is grounded through a resistor; operational amplifier circuit A 1 Output terminal of (a) and operational amplifier circuit C 1 Is connected with the inverting input terminal of the operational amplifier circuit B 1 Output terminal of (a) and operational amplifier circuit C 1 Is connected with the non-inverting input end of the power supply; operational amplifier circuit C 1 The output end of the (c) is connected with the anode of the diode, and the cathode of the diode outputs the fitted analog signal f (x). In fig. 10, other operational amplifier circuits are similar to those described above, and are not described here.
If a monotonic curve y n ＝f n (x) Piecewise linear function slope a n Monotonically decreasing, i.e. a n ＜a n-1 The curves of the graph (… …) and a2 and a 1) are shown in FIG. 4 and FIG. 5. Such monotonically increasing or monotonically decreasing nonlinear curves may be implemented using the specific embodiment circuits shown in fig. 7, 9, 11 to achieve curve y n ＝f n (x) Fitting, and taking the circuit D with the highest value as the circuit with the lowest value.
In fig. 7, an operational amplifier circuit a 1 The non-inverting input end of the circuit is connected with an input analog signal X, and the inverting input end is grounded through a resistor; operational amplifier circuit B 1 Through resistor and preset voltage V ref_1 The inverting input end is connected with the output end; operational amplifier circuit A 1 And operational amplifier circuit B 1 Output terminal of (a) and operational amplifier circuit C 1 Is connected with the non-inverting input end of the operational amplifier circuit C 1 The inverting input end of the capacitor is grounded through a resistor; operational amplifier circuit C 1 The output end of the (c) is connected with the cathode of the diode, and the anode of the diode outputs the fitted analog signal f (x). In fig. 7, other operational amplifier circuits are similar to those described above, and are not described in detail herein.
In fig. 9, an operational amplifier circuit a 1 The non-inverting input end of the circuit is grounded, and the inverting input end is connected with an input analog signal X through a resistor; operational amplifier circuit B 1 Is connected to the non-inverting input terminal of (a) and the preset voltage V ref_1 Connection, inversionThe input end is grounded through a resistor; operational amplifier circuit A 1 And operational amplifier circuit B 1 Output terminal of (a) and operational amplifier circuit C 1 Is connected with the inverting input terminal of the operational amplifier circuit C 1 Is grounded; operational amplifier circuit C 1 The output end of the (c) is connected with the cathode of the diode, and the anode of the diode outputs the fitted analog signal f (x). In fig. 9, other operational amplifier circuits are similar to those described above, and are not described here.
In fig. 11, an operational amplifier circuit a 1 The non-inverting input end of the circuit is grounded, and the inverting input end is connected with an input analog signal X through a resistor; operational amplifier circuit B 1 Is connected to the non-inverting input terminal of (a) and the preset voltage V ref_1 The inverting input end is grounded through a resistor; operational amplifier circuit A 1 Output terminal of (a) and operational amplifier circuit C 1 Is connected with the inverting input terminal of the operational amplifier circuit B 1 Output terminal of (a) and operational amplifier circuit C 1 Is connected with the non-inverting input end of the power supply; operational amplifier circuit C 1 The output end of the (c) is connected with the cathode of the diode, and the anode of the diode outputs the fitted analog signal f (x). In fig. 11, other operational amplifier circuits are similar to those described above, and are not described here.
Example 2:
the second embodiment of the present application provides a fitting method for a nonlinear curve, and the fitting device can be described in the first embodiment.
The method comprises the steps of:
s1, operational amplifier circuit A n Generating a piecewise fitted curve y n ＝f n (x) Slope a of (a) n ；
S2, operational amplifier circuit B n Generating a piecewise fitted curve y n ＝f n (x) The intercept b of (2) n ；
S3, operational amplifier circuit C n For amplifying the operation amplifier circuit A n Output result a of (a) n * x and the operational amplifier circuit B n Output result b of (2) n Adding;
s4, the maximum value taking circuit D takes the maximum value or the minimum value for the multi-section fitting curve.
In this embodiment, the piecewise fitting curve y n ＝f n (x) Slope a of (a) n Monotonically increasing or monotonically decreasing.
In the present embodiment, the voltage V is preset ref_1 、V ref_2 、V ref_3 、.....、V ref_n The preset voltages may be different or the same.
The preferred embodiments of the present application have been described above with reference to the accompanying drawings, and are not thereby limiting the scope of the claims of the present application. Any modifications, equivalent substitutions and improvements made by those skilled in the art without departing from the scope and spirit of the present application shall fall within the scope of the claims of the present application.
Claims (9)
1. A nonlinear curve fitting device is characterized by comprising an operational amplifier circuit A n Operational amplifier circuit B n Operational amplifier circuit C n And a maximum value taking circuit D;
the operational amplifier circuit A n An input end of the operational amplifier circuit B is connected with an output end of an input analog signal n Is connected with the input end of the voltage transformer and the preset voltage V ref_n The output end of the operational amplifier circuit A is connected with n And the operational amplifier circuit B n And the operational amplifier circuit C n Is connected with the input end of the operational amplifier circuit C n The output end of the (C) is connected with the input end of the maximum value taking circuit D; the output end of the maximum value taking circuit D outputs a fitted analog signal;
the operational amplifier circuit A n For generating piecewise fitted curve y n ＝f n (x) Slope a of (a) n The operational amplifier circuit B n For generating piecewise fitted curve y n ＝f n (x) The intercept b of (2) n The operational amplifier circuit C n For amplifying the operation amplifier circuit A n Output result a of (a) n * x and the operational amplifier circuit B n Output result b of (2) n Adding, wherein the maximum value taking circuit D is used for fitting the curve y to the segments n ＝f n (x) Take the maximum valueOr a minimum value;
wherein n is an integer greater than or equal to 1, and x is an input analog signal.
2. Fitting device according to claim 1, wherein the piecewise fitting curve y n ＝f n (x) Slope a of (a) n Monotonically increasing or monotonically decreasing.
3. Fitting device according to claim 1, characterized in that the operational amplifier circuit a n Is one of a homodromous proportional amplifying circuit, a reverse proportional amplifying circuit and a resistor voltage dividing circuit;
the operational amplifier circuit B n Is one of a homodromous proportional amplifying circuit, a reverse proportional amplifying circuit and a resistor voltage dividing circuit;
the operational amplifier circuit C n Is one of a same-direction operation addition circuit, a reverse operation addition circuit and an operation subtraction circuit.
4. Fitting device according to claim 1, wherein the maximizing circuit D is a maximizing circuit or a minimizing circuit.
5. The fitting device according to claim 4, wherein said maximizing circuit D is composed of a unidirectional conductive device or a chip selection logic chip and a peripheral circuit.
6. Fitting device according to claim 1, characterized in that the preset voltage V ref_1 、V ref_2 、V ref_3 、.....、V ref_n The preset voltages may be different or the same.
7. A method of fitting a device based on the nonlinear curve of claim 1, the method comprising:
operational amplifier circuit A n Generating a piecewise fitting curveLine y n ＝f n (x) Slope a of (a) n ；
Operational amplifier circuit B n Generating a piecewise fitted curve y n ＝f n (x) The intercept b of (2) n ；
Operational amplifier circuit C n For amplifying the operation amplifier circuit A n Output result a of (a) n * x and the operational amplifier circuit B n Output result b of (2) n Adding;
the maximum value taking circuit D takes the maximum value or the minimum value for the multi-section fitting curve.
8. The method of claim 7, wherein the piecewise fitting curve y n ＝f n (x) Slope a of (a) n Monotonically increasing or monotonically decreasing.
9. The method according to claim 7, wherein the preset voltage V ref_1 、V ref_2 、V ref_3 、.....、V ref_n The preset voltages may be different or the same.
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| CN202110316852.1A CN113114123B (en) | 2021-03-22 | 2021-03-22 | Nonlinear curve fitting device and method |
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| CN202110316852.1A CN113114123B (en) | 2021-03-22 | 2021-03-22 | Nonlinear curve fitting device and method |
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| CN113114123B true CN113114123B (en) | 2023-04-21 |
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| CN107255439A (en) * | 2017-06-12 | 2017-10-17 | 中国航空工业集团公司西安飞行自动控制研究所 | A kind of linear movement pick-up is excitatory and signal demodulating method |
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| JP2006025039A (en) * | 2004-07-06 | 2006-01-26 | Sony Corp | Operational amplifier circuit and headphone amplifier |
| CN102545793A (en) * | 2010-12-17 | 2012-07-04 | 南京航空航天大学 | Weak current amplifier with pA (picoamperes)-mu A(microamperes) range |
| US9979350B2 (en) * | 2014-11-17 | 2018-05-22 | Mediatek Inc. | Operational amplifier based circuit with compensation circuit block used for stability compensation |
| CN209543098U (en) * | 2019-04-23 | 2019-10-25 | 帝森克罗德集团有限公司 | The maximum value Acquisition Circuit of multi-analog |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107255439A (en) * | 2017-06-12 | 2017-10-17 | 中国航空工业集团公司西安飞行自动控制研究所 | A kind of linear movement pick-up is excitatory and signal demodulating method |
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