JPS58219408A - Nonlinear operation circuit - Google Patents

Abstract

PURPOSE:To obtain a higher order function signal of an input signal inexpensively and simply, by selecting the time constant of a resistor and capacitor, which constitute a smoothing circuit, so that the time constant is made larger than the period of a triangular wave. CONSTITUTION:An operational amplifier 4, which obtains the difference signal between an input signal Vin that is applied to an input terminal and a triangular wave that is the output of a triangular wave generator 2, and a smoothing circuit, which obtains a DC from an output signal Vout from the operation amplifier 4, are provided in a nonlinear operation circuit. The time constant C.R7 of a resistor R7 and a capacitor C constituting the smoothing circuit is made larger than a period T of the triangular wave. In this constitution, a higher order function signal of the input signal Vin can be obtained inexpensively and simply without using an expensive IC multiplier.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a nonlinear arithmetic circuit that provides a nonlinear relationship between an input signal and an output signal suitable for correcting nonlinear errors of thermocouples and the like.

Generally, in process measurement control, it is often necessary to linearize a non-linear signal or, conversely, to non-linearize a linear signal. In such cases, non-linear calculation circuits are used.

Conventionally, multipliers using logarithmic amplifiers or differential amplifiers have been used to obtain quadratic function signals of input signals, but the circuits are complex and require transistor pairs with well-matched characteristics, making stable It was difficult to guarantee operation.

Therefore, monolithic IC multipliers are now commercially available, and most multipliers rely on these IC multipliers. However, this IC multiplier has the drawback of being expensive.

On the other hand, methods for realizing a non-linear arithmetic circuit capable of generating higher-order function signals include a method using a plurality of broken line approximations and a method using higher-order function approximation.

In order to obtain high precision with the former method, it is necessary to increase the number of broken lines and adjust the breaking point and its slope for each broken line, which is extremely troublesome. Moreover, as for the latter method, the multiplier f,
A cubic function approximation using multiple units has been proposed, but
The disadvantage is that the circuit configuration is complicated and expensive.

An object of the present invention is to provide a nonlinear arithmetic circuit that easily obtains a high-order function signal of a human input signal at low cost without using an expensive IC multiplier.

The present invention utilizes the fact that the DC component of the difference signal between the input signal and the triangular wave is a quadratic function signal of the input signal to generate signals from quadratic functions to higher order functions. .

Hereinafter, the present invention will be explained in detail based on the drawings.

FIG. 1 is a circuit connection diagram showing an embodiment of the present invention that generates a quadratic function signal, and FIG. 2 is a diagram showing a triangular wave used in the present invention and its operation. In FIG. 1, 1 is an input terminal, 2 is a triangular wave generator, 3 is an output terminal, and 4 is an operational amplifier.

R1-, R1 is a resistor, C is a capacitor, D, l D,
is a rectifier, for example a diode. Triangle wave generator 2
The triangular wave which is the output of is assumed to have a period T1 wave height of 1.20, as shown by the east line in FIG.

In such a configuration, when the input signal Vl11 is applied, if the resistance ratios ~R1 are all equal for simplicity, the output E of the ideal diode configured with the operational amplifier 4 is , which is the diagonally shaded part in FIG. icR and capacitor Ctj constitute a smoothing circuit, and the time constant c-it, is selected to be sufficiently larger than the period T of the triangular wave. Therefore, the output V @
@t ij E The DC component of H, that is, the average direct current, becomes one shift as shown below.

In this way, the output V owl is a quadratic function signal of the input signal Vsa.

Moreover, by further performing calculations on V out and manipulating the -order term and zero-order term, various quadratic function signals can be obtained. An example of this is shown in FIG.

In Fig. 3, 1 is an input terminal, 2 is a triangular wave generator, and 3 is a triangular wave generator.
is an output terminal, 4.5 is an operational amplifier, and 6 is a constant voltage source whose voltage is Vb. , R1-R3 are resistors, VR is a variable resistor, C is a capacitor, and Dl and D2 are rectifiers, such as diodes. Here, E is ■ in Figure 1. It has the same voltage as @1, and becomes . In addition, in order to balance the impedances seen from the input terminals of the operational amplifier 5 and to make the calculation one-to-one, the variable resistor VR, is selected to be sufficiently smaller than the resistor R3, and the output resistance of the signal E is here:
By applying E and Vb, the first-order term and zero-order term of the signal E2 can be manipulated, and various quadratic function signals can be obtained.

For example ■. , to t When you want to get the signal that given that You can get something like:

The feature of the circuit of this embodiment is that the accuracy is the peak value E of the triangular wave. and is determined only by the characteristics of the ideal diode. For a triangular wave, if only the wave height [Eo] is stable, if the time constant of the smoothing circuit is made large, even if the period T is out of order, there will be no problem. For the ideal diode, an operational amplifier with a faster response than the period T of the triangular wave and a diode with less reverse leakage current may be prepared.

By doing so, a highly accurate and stable quadratic function generating circuit can be obtained.

Next, the nonlinear arithmetic unit according to the present invention will be explained with reference to FIGS. 4 to 13, taking as an example the case of correcting a nonlinear difference between thermocouples. Correction of non-linear errors is performed by passing through a circuit with non-linearity opposite to the non-linear difference. This circuit is, in other words, a nonlinear arithmetic circuit.

Looking at the interpolation formula, the electromotive force with respect to the temperature of the thermocouple is:
It is a 7th to 8th order function. Here, the R thermocouple, which has the largest nonlinear error and is difficult to correct, will be explained as an example.

In FIG. 4, the nonlinear error of the thermoelectromotive force with respect to temperature in the R type thermocouple OC~600C is shown by a solid line.

This nonlinear error is approximated by a first quadratic function signal that becomes zero at 0% and 100% of the input signal, so that the nonlinear error becomes zero at 50% of the input signal (dashed line in Figure 1). Then, the remaining error becomes as shown in FIG.

Next, calculate the nonlinear error in Figure 5 at 0% of the input signal and at 5%.
The error is zero at 25% and 75% of the input signal with the second quadratic function signal which becomes zero at 0% and the third quadratic function signal which becomes zero at 50% and 100% of the input signal, respectively. If the approximation is made so that (the broken line in FIG. 2), the remaining error becomes to, 3% or less, as shown in FIG.

These quadratic function signals approximate only the nonlinear error, and by combining these quadratic function signals and the input signal and feeding it back, nonlinearity inverse to the nonlinear error can be obtained. This is a non-linear error correction circuit for R-type thermocouples OC~600C, and can correct non-linear errors to ±0.3% or less.

As described above, since good nonlinear error correction can be performed in the RW thermocouple with the largest nonlinear error, sufficient nonlinear error correction can be performed in all other thermocouples. Examples of this are shown in FIGS. 7-9.

FIG. 10 shows an example of three quadratic function signals using the nonlinear arithmetic unit of the present invention. In the present invention, the magnitude and polarity of these three quadratic function signals are not limited, but are set and selected depending on the object to be subjected to nonlinear calculation.

Further, in the above example of thermocouple nonlinear error correction, the nonlinear calculation circuit of the present invention is included in the feedback circuit, but the present invention is not limited to this, and may be used as a feedforward. However, in the case of nonlinear error correction for thermocouples, it is better to put it in a feedback circuit than to use it as a feedforward, as overall correction accuracy is higher and error calculation is easier. In general, when the input signal is small and the error is large, the feedback type provides good results, and vice versa, the feedforward type provides good results.

FIG. 8 is a circuit connection diagram showing an embodiment of the present invention for obtaining such a function signal. In FIG. 8, 7 is an input terminal, 8 is a triangular wave generation circuit with an output Dr, 9 is a constant voltage source with an output of V, 10 is an output terminal, 11-13 are switches for selecting addition or subtraction, 14- 19 is an operational amplifier, R1~
aSS is a resistance, VR, ~ VaS is a variable resistor, C, , C
, are capacitors, and D1 to D6 are rectifiers such as diodes. FIG. 12 is a diagram for explaining the operation of this embodiment, and the triangular wave VT used here has a period T1 wave peak value mark. FIG. 13 shows how to use the nonlinear arithmetic unit shown in FIG. 11 (9). The operation will be explained below.

First, when the input signal Via is applied to the input terminal 7, the output ET of the operational amplifier 14 becomes the shaded part in FIG. R, . . . C1 constitute a smoothing circuit, and the time constants C and R are selected to be sufficiently larger than the period T of the triangular wave ET. The operational amplifier 14 is a buffer for impedance conversion. Therefore, the output E0 of the operational amplifier is the DC component of Et, that is, the average direct current, and EO is E as follows. becomes a quadratic function signal of the input signal V+m. Next, by manipulating the first order and zero order terms of signal E0 by operational amplifiers 16, 17, 18,
It is difficult to obtain the required quadratic function signal. Now, it is assumed that correction of the nonlinear error of the thermocouple is performed at a signal level of θ to 4 (V). Triangular wave (10) Since the wave height EP of ET must be larger than the input signal, set Ep = 6 (V). Then it becomes. In addition, the first quadratic function signal EIN becomes zero at 0% and 100% of the input signal.0% and 50% of the input signal
The second quadratic function signal %El, which becomes zero at times, and the third quadratic function signal E3, which becomes zero at 50% and 100% of the input signal, are expressed as follows.

To obtain the signal E1, the operational amplifier 10 can be used to select Eo, that is, , , (11) Next, to obtain the signal E, the operational amplifier 11 can be used.

Also, in order to remove unnecessary parts of this quadratic function signal,
As is well known, an ideal diode is constructed by inserting diodes D, , D, and a resistor R. Similarly, to obtain signal E3, an ideal diode is constructed to remove the operational term.

Here, if the resistors R4 to R15 are chosen to be sufficiently small compared to the resistor R8, then by setting, the quadratic function signal EH* El *
(12) E3 can be obtained.

By the way, when the numerical values are set as above, the absolute unity of the extreme value of the quadratic function signal EI + E 2 + E a is 0.33 (V) and 0.083 (V), respectively.
, 0.083 (V), and since the nonlinear error of the thermocouple is at most 8%, for a 4 (V) span, it is 0.32 (V), and due to ET, E, The correction is for the remaining error once corrected by E, so it is 2% at most, and it is 0.08 (V) for a 4 (V) span.
Therefore, it can be seen that the above numerical settings are necessary and sufficient.

The quadratic function signal El*El+Eil is multiplied by a coefficient by the second variable resistor V J , V Rt −V Ra and the switch 11
．． 12. Select addition or subtraction in step 13, and input signal ■1
The non-linear arithmetic unit of the present invention is constructed by combining the above. Variable resistance VR.

VR,,VR,is chosen to be sufficiently smaller than,R,. Also, since it becomes a load on the ideal diode, it should be made small. Here, the capacitor C3 is a capacitor for preventing oscillation when this non-linear arithmetic unit is inserted into the feedback circuit (13), and may be inserted for about 10 OFF.

The fine adjustment of this non-linear calculator is to first select the polarity with the switch 11, and when the human input signal is 50%, set the variable resistor vR8 to a predetermined output, then select the polarity with the switches 12 and 13 and input the respective input signals. This is done by setting the variable resistors vR, VR, to a predetermined output when the voltage is 25% and 75%.

FIG. 13 shows a method of connecting the present nonlinear arithmetic unit and other circuits, taking as an example nonlinear error correction of a thermocouple. The symbols are the same as in FIG. 11, T is the temperature, E is the thermoelectromotive force, and k is the proportionality constant.

FIG. 13(a) shows a feedforward type. First, a thermocouple is a converter that converts temperature T into thermoelectromotive force E. This is expressed as T-+E. In this case, if you want to obtain an output signal kT proportional to temperature T, use this nonlinear calculator to
-+kT may be calculated. However, since the thermocouple interpolation formula is given in the form T-+E (E=f(T)), error calculation is very troublesome. FIG. 13(b) shows the feedback type except for the defect (14) mentioned above.

In this case, the present non-linear calculation circuit calculates kT-+B, so error calculation becomes easy.

However, this embodiment does not limit the feedback type to the feedforward type depending on the application. Furthermore, this embodiment can of course be used not only for nonlinear error correction but also for active nonlinearization, and since it uses a quadratic function signal,
A square root calculator can also be easily configured. Furthermore, since it is possible to perform pulse width modulation using a triangular wave BT, it can be easily isolated using a photocoupler, etc., and a temperature converter can be constructed by placing a low input amplifier in the first stage. can.

According to this embodiment, there are the following effects. That is, once the quadratic function signal is set, various types of non-linear calculations can be performed by adjusting the three switches and three variable resistors, so the adjustment is easy.

In addition, when nonlinear error correction of thermocouples is performed, (15) ±0.3% in all temperature ranges of all thermocouples.
The accuracy is high because the following correction accuracy can be obtained.

Furthermore, unlike a non-linear arithmetic unit approximating a cubic function that uses a plurality of multipliers, the present invention does not use any multipliers, so it is relatively inexpensive.

Next, for example, in a thermocouple of 200 tr to 1000 U, the nonlinear error can be corrected to below ±0.1% by the above method, as shown in FIGS. 14 to 16.

Note that Fig. 14 is similar to Fig. 4, Fig. 15 is similar to Fig. 5, and Fig. 1 is similar to Fig. 1.
6 corresponds to FIG. 6, respectively.

As described above, the basic principle of the nonlinear arithmetic circuit according to the present invention can be achieved by creating three quadratic function signals each having a different weight from an input signal, as shown in FIGS. 4 to 6, for example.

Next, FIG. 7 shows a configuration diagram of a nonlinear arithmetic circuit according to the present invention based on the above basic principle. In Figure 17, 20
is an input terminal, 21 is an output terminal, 22 is a reference voltage source, 23
(16) is a multiplier, and 24 to n are addition/subtraction arithmetic units which have a rectifying function as required.

In operation, first, when the human input signal 1 is applied to the input terminal 20, the output signal of the multiplier 23 is k. It becomes V-. k here
. is a proportionality constant. Between this signal koV+2, the input signal ■1, and the reference voltage V, an adder/subtractor 25 calculates
Each weight,,,,.

k, performs addition and subtraction operations with all values, and outputs the output signal of the addition/subtraction calculator 25 as V+ =kx-ko, Vt''+kyVt+, and V-''.
Create a quadratic function signal as shown in (10). If the above equation is shown as a graph, it will be as shown in FIG. 18 or FIG.
The broken line portion in FIG. 9 is removed and only the solid line portion is output. Next, in the addition/subtraction calculator 24, the addition/subtraction calculators 25 to n
Each output signal Va + L + VB +...
The non-linear calculation circuit of this embodiment can be constructed by adding and subtracting . . . V together with the input signal Vt. FIG. 20 is a specific circuit configuration diagram when the nonlinear calculation circuit according to the present invention is used for nonlinear error correction of thermocouples.

FIG. 21 (17) shows a quadratic function signal used to explain FIG. 20.

In Figure 20, the same parts as in Figure 17 have the same symbols. 31 to 34 are operational amplifiers, D, + I)
, is a rectifier, for example, a diode, and an addition/subtraction operator 26.27
The purpose of this is to provide a rectifying effect. SW, ~SW
3 is a switch for selecting addition or subtraction, resistors R1 to R1
is the resistance R1-几.

is selected to be sufficiently smaller than R3. VR, ~VR,
is a variable resistor, and the quadratic function signal V, IVt −
This is to give weight to Va, and this is also selected to be sufficiently smaller than the resistor R1.

The signals handled in process measurement control are voltage signals of 1V to 5V or current signals of 4mA to 20mA. In order to facilitate conversion into these signals, in this case, non-linear calculations are performed in the signal range of 0 to 4. There are three quadratic function signals, and the first quadratic function signal is 0% and 1% of the input signal.
A quadratic function signal that becomes zero at 00%, and a second quadratic function signal that becomes zero at 0% and 50% of the input signal (
18) Signal, the third quadratic function signal is 50% and 100% of the input signal
It is assumed to be a quadratic function signal that becomes zero at %. , and since the non-linear error of the thermocouple is at most 8%, the absolute value of the extreme value of the first quadratic function signal only needs to be 0.32V#, which in this case is 0.4V. Since the remaining nonlinear error approximated by the first quadratic function signal is at most 1.5%,
The absolute value of the extreme values of the second and third quadratic function signals is 0.06V
In this case, it is O11■. Here, the first
The quadratic function signal of Va, the second quadratic function signal ■1,
If the third quadratic function signal is ■8, then VR, v, , v.

is as shown in Figure 11. Also, if expressed as a formula, it becomes as follows.

Next, the operation of obtaining the quadratic function signal of □ from the input signal vI and performing non-linear calculation will be described.

When the input signal ■1 is applied to the input terminal 1, the output of the multiplier (19) 23 becomes koVo''.Next, the adder/subtractor 25 subtracts V from v1'', and the output is v.
6 'Ve = "oV+" VB Then, (a signal equivalent to equation 111 is obtained.

Next, the addition/subtraction calculator 26 calculates k. - Subtract V from - and insert a rectifier D1 between the output terminal of the operational amplifier 32 and the feedback resistor R8 to form an ideal diode as is well known, remove the positive part and output only the negative part. ■.

V, = koV+” V, (V, ≦0)...
...(15)(20) A signal equivalent to equation (12) is obtained. The addition/subtraction calculator 27 calculates k. - Subtract Vs from - and add ■, configure an ideal diode in the same way as the addition/subtraction calculator 26,
Va” koV+2Vs with only the negative part as output
+V-(Va≦0), and a signal equal to equation (13) is obtained. In this way, a desired quadratic function signal can be obtained.

Next, the quadratic function signals Va, V'1 . VB KV I%
l.

Add weights to V Rx and V Ra, sw,, sw!
.

Select addition or subtraction with SW, and add/subtract operator 5 (21
) is combined with input signal 7 to produce output signal V. is working to obtain.

To adjust the circuit of this example, first select the polarity with Sw, adjust so that when the input signal is 50%, use VR to obtain the specified output, and then select the polarity with 8W@, SWa. When the input signal is 25% and 75%, respectively, VB4 and V
It is only necessary to adjust R so that a predetermined output is obtained.

In the above embodiment, three quadratic function signals are used, but
The present invention is not limited to this, and varies depending on nonlinearity and accuracy. Furthermore, it is surprisingly possible not only to correct non-linear errors but also to actively make them non-linear.

According to this embodiment, a highly accurate non-linear arithmetic circuit can be configured with a single multiplier and a relatively simple circuit. A comparison between the nonlinear calculation circuit using three quadratic function signals in this embodiment and the conventional nonlinear calculation circuit using folded-edge approximation and cubic function approximation is as follows.

Once the quadratic function signal is set, adjustment is easy because various nonlinear calculations can be performed by adjusting the three (22) switches and three variable resistors.

Furthermore, when non-linear error correction is performed for R-type thermocouples OC to 600C, the non-linear arithmetic circuit of the present invention has a non-linear error of 10.3% or less, which improves accuracy.

In contrast to the non-linear arithmetic circuit approximating a cubic function that uses a plurality of multipliers, the present invention requires only one multiplier, so it is inexpensive.

As is clear from the above description, according to the present invention, it is possible to obtain a high-order function signal with easy adjustment, an inexpensive configuration, and high accuracy.

[Brief explanation of drawings]

Fig. 1 is a circuit diagram showing one embodiment of the present invention, and Fig. 2 is a circuit diagram showing an embodiment of the present invention.
FIG. 3 is a circuit diagram showing an application example of FIG. 1, and FIGS. 4 to 10 are waveform diagrams illustrating the principle of an application example of the nonlinear arithmetic circuit of the present invention. 11 is a circuit diagram showing another embodiment of the present invention, FIGS. 12-13 are diagrams for explaining FIG. 11, and FIGS. 14-16 are R-type (23) Diagram 17 showing nonlinear errors of thermocouples, K-type thermocouples, and nonlinear errors after correction by the nonlinear calculation circuit according to the present invention.
The figure is a basic circuit configuration diagram showing still another embodiment of the present invention, FIGS. 18 to 19 are diagrams explaining quadratic function signals, and FIG. Circuit diagram, 2nd
FIG. 1 is a diagram showing a quadratic function signal used in the present invention. 1... Input terminal, 2... Triangular wave generation circuit, 3...
Output terminal, 4... operational amplifier, D, #D,...
Rectifier, R11□ (24) Haya l concave scale 4 2nd concave sheep 5th eye 7th figure brown 9 figure 7011, ka \ grass 17th eye -42- Leather! 8th figure 1q

Claims (1)

[Scope of Claims] A nonlinear arithmetic circuit comprising an arithmetic unit that obtains a difference signal between a 1° input signal and a triangular wave, and a smoothing circuit that converts the output signal of the arithmetic unit into a direct current. 2. An operational amplifier that obtains a difference signal between the input signal and the triangular wave;
It has a smoothing circuit that takes out the DC component of the difference signal, and three operational amplifiers that add and subtract the output of the smoothing circuit, the input signal, and a constant voltage.
A first quadratic function signal that becomes zero at 00%, a second quadratic function signal that becomes zero at 0% and 50% of the input signal, and zero at 50% and 100% of the input signal. Generate three quadratic function signals of the third quadratic function signal,
the fourth operational amplifier; Second. By combining the third three quadratic function signals and the fifth human power signal,
A nonlinear arithmetic circuit characterized by obtaining an output signal that approximates a high-order function.