Application of LOG104 in Wheatston strain measurement bridge

Introduction
The unbalanced Wheaston strain bridge powered by a constant voltage source is widely used in stress and strain measurement. It is one of the main means to extract stress and strain parameters of the measured object in industry, construction, and metrology [1]. It is increasingly showing its great advantages in signal processing and analog/digital conversion. In industrial sites, it is not easy to obtain a high-precision constant voltage bridge source. If the constant voltage source has a slight fluctuation, it will have a direct impact on the output signal after being amplified by the amplifier circuit, which cannot be eliminated in traditional dynamic strain measurement and data acquisition systems [2]. Therefore, the problem of the influence of the Wheaston strain bridge source can be solved without adding an additional compensation circuit, which will play a positive role in reducing the volume of the strain bridge circuit, improving the bridge processing accuracy, and expanding the scope of use of the strain bridge.

In response to this requirement, this paper studies and utilizes the characteristics of logarithmic operations. It uses a high-precision logarithmic operational amplifier chip LOG104 to perform logarithmic operations on the strain bridge output signal and the bridge source signal, filters out the influence of the bridge source offset on the measured output signal, and realizes a new type of Wheatston strain bridge measurement circuit design without bridge source influence.

LOG104 precision logarithmic operational amplifier
LOG104 is the latest precision logarithmic operational amplifier produced by BURR-BROWN in the United States. It can perform logarithmic operations on the ratio of two input currents [3]. The device has a wide dynamic range of input current and can vary in the range of . Due to the use of advanced integrated circuit technology, when the input current ratio varies in the range of 100dB, the device can ensure that the total output error is less than 0.01% of the full-scale output voltage (FSO), and the deviation from the ideal logarithmic relationship does not exceed 0.01%, and the output signal is accurately adjusted to 0.5V/10dB. LOG104 has extremely low DC bias voltage and temperature drift characteristics, and can measure low-amplitude current signals in a large temperature range. Its operating temperature range can reach -40℃ to +85℃.

The excellent performance of LOG104 makes it have a wide range of application potential. In addition to logarithmic and antilogarithmic operations, it can also compress and decompress data in the fields of communication and test instrument signal analysis, measure optical density signals in the field of optical applications, or be made into portable high-precision instruments for various occasions related to logarithmic operations. Here, logarithmic operation chips with similar functions to LOG104 are compared, and their typical parameter values ​​are shown in Table 1.

It can be seen from the data in Table 1 that LOG104 has excellent performance among logarithmic operation chips.

The circuit structure model of LOG104 is shown in Figure 1.

Figure 1. Circuit structure model of LOG104

Since the base-emitter voltage of a bipolar transistor is

(1)

Where , joule/degree (Boltzmann constant), coulomb (electron charge), is the absolute temperature (Kelvin); Ic is the collector current; Is is the reverse saturation current.

From the circuit in Figure 1, we can see

Substituting equation (1) into equation (2)

If the two transistors have the same performance and the same temperature, then

In addition, since , Equation (4) can be transformed into

Thus, we can get

After the internal precision resistors of LOG104 are properly selected, the final logarithmic equation is:

Or written as

Where C is a constant determined by R ₁ and R _{2. [page]}

Error Analysis Caused by Misalignment of Bridge Source in Wheatston Strain Gauge Bridge

In the DC unbalanced Wheatston strain bridge circuit, the errors caused by the bridge source mainly include:

1. Error caused by bridge source offset
This error is related to the nature of the constant voltage source itself and has strong randomness. Different models of constant voltage source offset characteristics are also different. The error of the constant voltage source provided in general industrial measurement is between tens of millivolts. If a DC-DC module is directly used as a bridge source, the error may reach hundreds of millivolts. Such a large offset will cause serious offset errors in the output signal. Assuming a conservative offset value for the bridge source , it will generate an output voltage in the strain gauge full-bridge circuit with sensitivity K = 2, theoretical bridge voltage , strain gauge resistance , strain

This value is equivalent to the signal generated by 10 microstrains, which shows the extent of its influence. And the direct output error caused by this is

This is absolutely unacceptable for high-precision sensor design. Since the bridge source offset error is directly determined by the characteristics of the bridge source itself, it is difficult to completely offset it in traditional dynamic measurement systems. If a high-voltage bridge circuit is used for voltage supply, the volume of the measurement circuit will inevitably increase, and the restrictions on processing technology and environmental factors will increase, which will bring inconvenience in application.

2. Error caused by transmission line resistance
Since there is resistance in the wire between the bridge source and the strain bridge, when this resistance reaches a certain level, it will have a serious impact on the measurement output. For each meter of wire resistance, when the total length of the transmission line is 20m, the actual bridge voltage will drop , and the output error caused by this is

3. Errors caused by constant voltage source temperature drift and environmental factors Because in industrial sites, the working environment of the bridge circuit is full of harsh factors such as electromagnetic radiation, thermal radiation, vibration, dust, etc., which aggravate the unstable characteristics of the constant voltage source. The output error e _E
caused by this is no less than the impact caused by the bridge source imbalance.

Combining the above points, the overall error caused by the worst bridge source effect is

For industrial applications that require higher precision, general constant voltage sources obviously cannot meet the application requirements, and high-precision constant voltage sources must be used as Wheatston bridge sources. However, many applications limit the use of high-precision constant voltage sources. For example, the power supply of the resistive strain torque meter used for torque measurement on a rotating body is mostly supplied by AC-DC. The DC voltage generated is difficult to be used directly as a bridge source. A high-precision compensation adjustment circuit must be used, which not only increases the cost, but also increases the volume and design complexity of the circuit, which is contrary to the requirement of miniaturization of measuring instruments. Therefore, filtering out the influence of the bridge source and normalizing the bridge source error to the subsequent processing circuit will directly improve the accuracy of the measuring instrument, reduce the complexity of the circuit design, and improve the reliability of the instrument.

Eliminate the influence of bridge source by logarithmic method
Using the excellent logarithmic operation characteristics of LOG104 , connect one end of the Wheatston bridge source to I1 as the reference input of LOG104, and connect the strain bridge output to I2 as the measurement input of LOG104. When the input range of I1 and I2 changes from 1nA to 100uA, connect resistors in series at I1 and I2 respectively to limit the current, which can ensure the use of Wheatston bridge circuit measurement with 5V bridge source power supply, maximum strain of 1000 microstrain and sensitivity of 2. The measurement circuit design is shown in Figure 2.

Figure 2 Wheatston strain bridge measurement circuit

in

α and β are the upper and lower input current limits of I ₁ and I _{2 respectively.}

Here, the high-precision instrumentation op amp LTC2053 from Linear Technology is used as the strain bridge measurement front-end circuit processing chip ^[4] . This op amp has extremely high precision, a supply voltage range from 2.7V to 11V, an offset voltage of less than 10uV, a bias drift of less than 50nV/℃, a common mode rejection ratio (CMRR) greater than 116dB, a gain error of less than 0.01%, and a gain nonlinearity of less than 10ppm. Compared with other similar devices, it has an excellent performance-price ratio, as shown in Table 2.

[page]

Equivalent follow-up Wheatston strain bridge output changes

For a strain bridge with a bridge source offset voltage of , the current entering the logarithmic operation circuit after the above processing is

Where I1 is the ideal current value and _is the offset current coefficient.

At this time, the output of the logarithmic operation circuit LOG104 is

Among them, for a strain bridge with certain parameters and bridge pressure value , substituting into formula (16) we get

Substituting equation (12) into equation (17)

Here, since , substituting into equation (18)

From equation (19), we can see that the output function obtained after logarithmic operation of the strain bridge output signal is a single-valued function relationship with the strain value, and is independent of the values ​​of resistors R ₃ and R _4. As long as the input range of I ₁ and I ₂ is determined , the logarithmic equation can be determined. Here, since the input range of I ₁ and I ₂ is 100nA to 100μA, and the C value is adjusted to 0.5V, the output of the logarithmic operational amplifier is

The curve simulation diagram of this output relationship is shown in Figure 3.

Figure 3 Relationship between LOG104 output voltage and strain measurement value

It can be seen that when the strain range of the strain bridge is 1μm/m～1000μm/m, the output voltage range is +1.5V～0V. It can be seen that the minimum output voltage (from the 999th microstrain to the 1000th microstrain) that can be generated by a microstrain is 0.22mV, and the maximum output voltage (from the 1st microstrain to the 2nd microstrain) is 0.15V. It can be seen that the sensitivity of the circuit of this design is much higher than that of the circuit of large strain when the strain is small. The main reason for this phenomenon is that the above design directly sets the bridge source input to the upper limit reference value of LOG104, so that the measurement results gradually approach the reference current from small to large. Since the output function is a logarithmic function with a gradually decreasing attenuation rate, the above phenomenon occurs; therefore, as long as the bridge source input is set to the lower limit reference value (achieved by increasing the resistance value of R1), the measurement result is far away from this reference current, which can improve the circuit sensitivity in a large measurement range.

Through this phenomenon, the measurement circuit design with different sensitivity range requirements can be realized: when the sensitivity requirement for the small strain range is high, the upper limit setting reference is adopted; when the sensitivity requirement for the large strain range is high, the lower limit setting reference is adopted. In this way, the measurement circuit will achieve unexpected output effects. At the same time, it can be seen from formula (19) that the output function does not include the influence of the bridge source, and the additional resistors R3 _and R4 _are ultimately only used to set the input range of the logarithmic operational amplifier, and have no effect on the output, thus realizing the filtering function of the bridge source error. Moreover, after this circuit processing, a large part of the error influence of the measurement circuit can be directly eliminated from the measurement result as a constant during system calibration, thereby simplifying the circuit design. According to different needs, the subsequent results can be processed by an ADC chip with more than 14 bits; the measurement results can also be directly subjected to antilogarithmic operations to meet application requirements.

Conclusion
In summary, this paper uses the logarithmic circuit LOG104 to filter out the error caused by the offset of the Wheatston strain bridge on the measurement output, simplifies the compensation circuit, and designs a strain bridge processing circuit that can be used in harsh industrial environments. It provides a reference method for other sensor circuit designs with similar requirements.