“In the information acquisition system, the sensor is usually at the front end of the system, that is, the first of the detection and control system. It provides the original information necessary for system processing and decision-making. Therefore, the accuracy of the sensor is critical to the entire system. In the measurement of displacement, velocity and acceleration, differential transformer type sensors are often used because of their high sensitivity, good linearity and supporting integrated circuits. However, traditional LVDT sensors have too high requirements for the stability and accuracy of the working power supply, and Circuit boards are mostly formed by overlapping separate components, which are prone to loosening and damp deterioration, which affects the service life and overall performance of the sensor.

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**introduction**

In the information acquisition system, the sensor is usually at the front end of the system, that is, the first of the detection and control system. It provides the original information necessary for system processing and decision-making. Therefore, the accuracy of the sensor is critical to the entire system. In the measurement of displacement, velocity and acceleration, differential transformer type sensors are often used because of their high sensitivity, good linearity and supporting integrated circuits. However, traditional LVDT sensors have too high requirements for the stability and accuracy of the working power supply, and Circuit boards are mostly formed by overlapping separate components, which are prone to loosening and damp deterioration, which affects the service life and overall performance of the sensor. This article introduces a kind of LVDT linear displacement sensor based on AD598 signal processing chip, and discusses its error and accuracy through examples.

**1 Basic principles**

The differential transformer type sensor is a device that uses the change of the self-inductance or mutual inductance of the coil to achieve measurement. Its core is variable self-inductance or variable mutual inductance. The variable air gap type differential transformer type inductance sensor used in this article uses the change of mutual inductance to work.

**1.1 Basic structure and working principle**

There are 1 excitation coil and 1 output coil on the upper and lower 2 iron cores. The upper and lower two excitation coils are connected in series and then the AC excitation power supply voltage Uin, and the two output coils are connected in series in the opposite direction according to the potential.Ignoring high-order infinitesimals, when ωR (ω is the frequency of the AC excitation power supply voltage Uin, R is the equivalent resistance of the excitation coil), it can be derived

In the formula: Uin is the excitation power supply voltage (unit V); Uout is the output voltage (unit V); N1, N2 are the number of turns of the excitation coil and the output coil respectively; △δ is the distance of the shaft offset balance position (unit mm) ; δ accounted for the size of the air gap when the shaft is in the equilibrium position (unit: mm).

When the shaft is in the middle position, δ1=δ2=δ, alternating magnetic fluxes φ1 and φ2 are generated in the excitation coil, and an AC induced electric potential is generated in the output coil. Because the air gaps on both sides are equal, the magnetic resistance is equal, so, φ1=φ2, the electric potential induced in the output coil E21=E22, because the secondary is connected in the opposite direction of the electric potential, the output voltage Uout=0. When the shaft deviates from the middle position, the air gaps on both sides are not equal (that is, δ1≠δ2), the potential induced in the output coil is no longer equal (that is, E21≠E22), and there is a voltage Uout output. The magnitude and phase of Uout depend on the magnitude and direction of the axis displacement.

**1.2 Output characteristic equation**

Suppose the primary excitation voltage of the differential transformer is Ep, the angular frequency is ω, the current is Ip, the inductance is Lp, and the equivalent resistance is Rp. The secondary voltage is E21 and E22, and the mutual inductance is M1 and M2. If we ignore the influence of hysteresis eddy current and coupling capacitance, we can get:

** 2 Sensor measurement circuit**

AD598 is a new LVDT dedicated signal processing chip introduced by Analog Device. The schematic diagram is shown in Figure 2. It can be seen from the figure that the chip mainly contains two parts: one part is a sine wave generator, whose frequency and amplitude can be determined by a few external components; the other part is the signal processing part of the LVDT secondary. Through this part, a DC voltage signal proportional to the displacement of the iron core is generated. AD598 can drive up to 24 V, a frequency range of 20Hz～20kHz LVDT primary coil, and can accept a minimum of 100 mV secondary input, so it is suitable for many different types of LVDT.

**3 Error analysis of measurement system**

The error of the measurement system can also be divided into two categories: fixed error and random error according to the source.

**3.1 Fixed error**

The fixed error refers to the error caused by the structure (processing accuracy) and material (hysteresis eddy current) of the differential transformer. This is a comprehensive consideration that must be combined with measurement accuracy requirements and economic indicators during system demonstration. Once the system is determined, these factors generally cannot be changed.** 3.2 Random error**

Random errors can be divided into errors caused by the fluctuation of the excitation source and errors caused by the phase-sensitive detection according to the error source. Because AD598 encapsulates the oscillator, LVDT and phase-sensitive demodulator together, it not only improves the integration of the product, but also greatly reduces the number of external components, which greatly improves the performance of the sensor. Therefore, it is not correct in this article. The error caused by the phase-sensitive detection is derived.

**3.2.1 Error caused by amplitude fluctuation of excitation source**

From equation (3), it can be seen that when Ep, ω, Lp, and Rp are constants, E2 is proportional to △M. The differential transformer is a non-closed magnetic circuit, and the iron core length is much shorter than the coil length, so △M is proportional to the iron core displacement, that is, E2 is proportional to the iron core displacement. When the iron core is fixed at a certain position, the output voltage E2 should also be a fixed value. But Ep or ω has changed. Although the iron core position has not changed, the output voltage E2 has changed. This is the error caused by the instability of excitation voltage and frequency. E2 is a linear function of Ep. Differentiate equation (3) to Ep to get:

Divide formula (4) by formula (3) to get:

dE2/E2=dEp/Ep That is, under other conditions unchanged, the error of the excitation source is the error of the differential output.

**3.2.2 Error caused by frequency fluctuation of excitation source**

In the formula: Qp=ωLp/Rp is the quality factor of the primary side of the differential voltage transformer, the larger the value, the smaller the error caused by the ω fluctuation.

**4 Measurement of error and precision**

Take the CWZ-23F differential transformer as an example. After calibration, the input voltage is given by an optical length gauge, and the output voltage is measured with a 4.5-digit digital voltmeter.

Accuracy=β×standard deviation=3×1.106≈3.32 (μm)

It can be considered that the system accuracy is 3.32μm. At this time, the confidence probability is 99.73%, which can fully explain the situation of the system.

**5 concluding remarks**

AD598 integrates most of the functions of a high-precision sine wave generating circuit and a differential transformer signal conditioning circuit on a chip, which reduces the volume of the circuit and simplifies the design and debugging of the circuit.

The Links: **NL10276AC30-03A** **MPI4040R3-220-R**