# Linear Variable Differential Transformer (LVDT) Output Voltage Calculator

Understanding the output voltage of a Linear Variable Differential Transformer (LVDT) is crucial for accurate measurements in instrumentation and control systems. In this post, we will delve into the calculation of LVDT output voltage and address specific scenarios such as maximum output voltage, voltage at different core displacements, determining core position based on voltage, and analyzing voltage changes with core displacement.

## What is the voltage output of a LVDT?

The functionality of the LVDT hinges on the principles of electromagnetic induction. When the core deviates from the null point, the primary signal differentially couples with the two secondary windings (S1 and S2).

The output voltage manifests as the disparity between the voltages induced in S1 and S2. As the core traverses S1, the output voltage of S1(VS1) rises; conversely, as it traverses S2, the output voltage of S2(VS2) experiences an increase.

## Definition of LVDT Sensitivity:

LVDT sensitivity is a vital metric that quantifies the responsiveness of a Linear Variable Differential Transformer (LVDT) to changes in core displacement. It is typically expressed as milliVolts output per thousandths of an inch core displacement per Volt of excitation (mV/mil/Volt).

In simpler terms, sensitivity indicates how much the LVDT’s output voltage changes in response to a given unit of core displacement concerning the excitation voltage.

It is crucial to note that LVDT sensitivity is not a constant value but varies with excitation frequency.

Engineers must specify the excitation frequency when expressing sensitivity to ensure accurate and consistent measurements. The choice of excitation frequency directly influences the performance of the LVDT.

## How do you calculate LVDT sensitivity?

LVDT sensitivity is calculated by determining the change in output voltage for a given change in core displacement. The formula for LVDT sensitivity is:

Sensitivity=Change in Output Voltage/Change in Core Displacement

Typically, sensitivity is expressed in terms of millivolts output per unit of core displacement per volt of excitation (mV/unit of displacement/V). The units for core displacement could be millimeters (mm), inches (in), or any other unit depending on the system.

For example, if the output voltage changes by 20 millivolts when the core is displaced by 0.5 mm from its null position and the excitation voltage is 1 volt, the sensitivity would be:

Sensitivity=0.5mm/20mVâ€‹

Sensitivity==40mV/mm/V

It’s important to note that LVDT sensitivity may vary with excitation frequency, so the excitation frequency should be specified when expressing sensitivity for accurate measurements.

## What is the Range of LVDT Output?

The range of LVDT (Linear Variable Differential Transformer) output refers to the span of values that the output voltage can take based on the displacement of the LVDT’s core. The output voltage of an LVDT is directly proportional to the displacement of the core from its null position. Typically, the LVDT output is specified in terms of a voltage range that corresponds to the full range of motion or stroke of the LVDT.

The range of LVDT output is determined by factors such as the physical dimensions of the LVDT, the number of turns in the primary and secondary windings, and the excitation voltage applied. The full-scale output voltage (maximum voltage) occurs when the core is at one extreme of its range, and the minimum output voltage occurs when the core is at the opposite extreme.

For example, if an LVDT has a stroke length of Â±10 mm and a sensitivity of 2 mV/mm/Volt, the range of LVDT output can be calculated as follows:

Range of LVDT Output=Stroke LengthÃ—Sensitivity

Range of LVDT Output=10mmÃ—2mV/mm/Volt=20mV/Volt

This means that for every Volt of excitation, the LVDT will produce an output voltage ranging from -20 mV to +20 mV, depending on the direction of the core displacement within its specified stroke length.

It’s important to consult the manufacturer’s specifications for the specific LVDT in use, as the range of output can vary between different models and applications.

## LVDT Output Voltage Calculation – Example

A linear variable differential transformer can be moved to generate a resolution(sensitivity)  of 40mV/mm and has a stroke length of Â±150mm. Find out:

1. The maximum output voltage of the LVDT.
2. The voltage produced by moving the core 120 mm out of its null location.
3. The core’s distance from the center corresponds to a 3.75 volt output.
4. The output voltage change that occurs when the core moves from a displacement of +80 mm to -80 mm.

### Maximum Output Voltage of LVDT (VMax)

The relationship between core displacement and output voltage is established as 40mV/mm.

For a stroke length of Â±150mm, the maximum output voltage (VOUT) can be calculated as follows:

Maximum Output Voltage (Vmax) = (Sensitivity) Ã— (Â± Stroke Length)

Vmax = 40mV Ã— 150mm

Vmax = 0.04 Ã— 150

Vmax =  Â±6 Volts

### Output Voltage at Core Displacement of LVDT (Vout)

To find the output voltage when the core is moved 120mm from its null position, we use the formula:

Vout = (Core Displacement Ã— V max) / Length

Substituting the values:

Vout=(120mmÃ—6V) / 150mm

Vout = 4.8Volts

### LVDT Core Position at output voltage (D)

Determining the core position when the output voltage is 3.75 volts involves rearranging the formula to solve for core displacement:

CoreDisplacement (D) = (VoutÃ—Length) / Vmax

Substituting the values:

CoreDisplacement (D) = (3.75VÃ—150mm) / 6V

Core Displacement (D) = 93.75mm

### Voltage Change from +mm to -mm Core Displacement (Vchange)

Calculate the voltage change as the core moves from +80mm to -80mm displacement, we use the formula:

Vchange = {(Core Displacement 1âˆ’Core Displacement 2)Ã—Vmax}/Length

Substituting the values:

Vchange =(80mmâˆ’(âˆ’80mm))Ã—6V/150mm

Vchange = 6.4Volts(Span value)

This implies that the output voltage changes from +3.2 volts to -3.2 volts as the displacement of the core moves from +80mm to -80mm,

## LVDT Calculator

Our LVDT Output Calculator is easy to use and will give you exact readings. Designed by professionals to make sure your control systems work precisely

The following calculations are performed using the calculator provided below: Maximum Output Voltage of LVDT (VMax), Output Voltage at Core Displacement of LVDT (Vout), LVDT Core Position at output voltage (D) and Voltage Change from +mm to -mm Core Displacement (Vchange).