Linear-Range Extension for Linear Variable Differential Transformer Using Hyperbolic Sine Function

Abstract

In this paper, a circuit technique to extend the measuring range of a linear variable differential transformer (LVDT) is proposed. The transfer characteristic of the LVDT contains the odd function form of the cubic polynomial. Therefore, the measuring range of a commercial LVDT is linear in a narrow range compared to its physical dimensions. The wide measuring range of the LVDT requires a large structure of the LVDT, which increases the scale and the cost of the measurement system. The measuring range of the LVDT can be linearly extended to the maximum of the stroke range using the proposed technique. The realization of the proposed technique is based on the use of the hyperbolic sine (sinh) function of the electronic circuit building block, named the class AB bipolar amplifier. The class AB bipolar amplifier can be obtained by the current feedback operational amplifier (CFOA). The circuit of the proposed technique requires two CFOAs and an operational transconductance amplifier (OTA) as the active devices and all devices used in the proposed technique to synthesize the sinh function are commercially available. The proposed technique exhibits an ability to compensate for the nonlinear characteristic of the LVDT without digital components. The proposed technique is attractive in terms of its simple circuit configuration, small size, and low cost. The linear range extension of the LVDT used in this paper is significantly increased with a maximum error of about 18.3 μm of 6.2 mm at the full stroke range or the full-scale percentage error of about 0.295%. The results indicate that the proposed technique provides excellent performance to extend the measuring range of the LVDT without modifying the LVDT structure.

Procedure for Determining the Upper Bound on Absolute Error for LVDT Sensors

“…This allows for precise adjustment of production processes and increased machine efficiency [4]. In medicine, LVDT sensors are used in a variety of applications, for example in medical apparatus for the precise positioning of surgical instruments, measuring displacements during diagnostic tests, or motion control for prosthetics [5]. In research laboratories, these types of sensors are used in various scientific experiments where precise measurements of displacement or deformation of materials are required [6].…”

Methodology for Eddy Current Losses Calculation in Linear Variable Differential Transformers (LVDTs)

“…Limitations include limited linear range, stray capacitance effect, electromagnetic interference, and core loss. That is why various studies, techniques for improvement, as well as novel LVDT designs for specific, or broader, applications have been investigated [ 10 , 12 , 13 , 14 , 15 , 16 ]. In [ 15 ], a compact LVDT for reactor experiment application was designed using analytical expressions, without the consideration of eddy current losses.…”

Extension of Linear Operating Range for Linear Variable Differential Transformer Using Its Inverse Transfer Characteristic

“…The LVDT transfer characteristic exhibits nonlinear behavior, which can be expressed as an odd function in the form of a cubic polynomial. (2,(24)(25)(26)(27) Therefore, the operating range of the LVDT is linear only in a narrow range close to the zero crossing of the LVDT transfer characteristic curve. Practically, the linear range of the LVDT is directly proportional to the size of its structure.…”

“…There are many approaches to enhancing the linear operating range. (22)(23)(24)(25)(26)(27)(28)(29) A fractional-order LVDT for enhancing the linear operating range has been proposed. (22) This approach requires a special design for the LVDT structure, resulting in a highcost device that is inconvenient to customize for a compact measurement system and has therefore not been commercialized.…”

“…Approaches based on the use of an analog multiplier to generate a binomial series of the LVDT inverse transfer characteristic have also been proposed. (24)(25)(26)(27) These approaches enable the realization of LVDTs with high accuracy, large linear operating range, and small size. However, they require high-precision analog multipliers to obtain the inverse transfer characteristic of the LVDT, resulting in a high production cost.…”