The Operation of Linear Variable Differential Transformer (LVDT)

 Linear variable differential transformer (LVDT) is an inductive transducer that is commonly used to translate linear motion into electrical signals.

An illustration of LVDT circuit is shown below:

Fig 1.0 LVDT connection circuit

The transformer consists of a single primary winding P and two secondary windings S₁ and S₂ wound on a cylindrical former. A sinusoidal voltage of amplitude 3 to 15 volt and frequency 50 to 20 kHz is employed to excite the primary winding. The two secondary windings have equal number of turns and are identically placed on either side of the primary winding.

The primary winding is connected to an alternating current source. A movable soft-iron core is placed inside the former. The displacement to be measured is applied to the arm attached to the soft iron core. The core is usually made of high permeability, nickel iron. This is slotted longitudinally to reduce eddy current losses. The assembly is placed in a stainless steel housing to provide electrostatic and electromagnetic shielding. The frequency of ac signal applied to primary winding can be between 50 Hz and 20 kHz.

As the primary winding is excited by an alternating current source, it produces an alternating magnetic field which in turn induces alternating voltages in the two secondary windings.

The output voltage of secondary S₁ is ES₁ and that of secondary S₂ is E_S2. In order to convert the outputs from S₁ and S₂ into a single voltage, the two secondary S₁ and S₂ are connected in series opposition. The differential output voltage is:

E₀ = ES₁ – ES₂                                                                        

Operation of LVDT

When the core is at its normal (NULL) position, the flux linking with both the secondary windings is equal and hence equal voltages are induced in them. Therefore at null position: E_S1 = E_S2. Thus, the output voltage E₀ is zero at null position.

If the core is moved to the left of the null position, more flux links with S₁ and less with winding S₂. Correspondingly, output voltages E_S1 is greater than E_S2. The magnitude of output voltage is thus,

 E₀ = E_S1 – E_S2 and we can say, it is in phase with primary voltage.

In the same way, when the core is moved to the right of the null position E_S2 will be more than E_S1. Therefore the output voltage 

E₀ = E_S1 – E_S2 and 180° out of phase with primary voltage.

The amount of voltage change in either secondary winding is proportional to the amount of movement of the core. Thus, we have an indication of amount of linear motion. By noticing whether output voltage is increased or decreased, we can determine the direction of motion.

 Related: Transducers and Sensors

Merits of LVDT

• Output is quite high. Hence, immediate amplification is not necessary.
• Output voltage is step-less and hence the resolution is very good.
• The sensitivity is high (about 40 V/mm).
• It does not load the measured mechanically.
• Linearity is good up to 5 mm of displacement.
• It consumes low power and low hysteresis loss.

The Limitations of LVDT

• It is affected by stray electromagnetic fields. Thus, proper shielding of the device is required.
• LVDT has large threshold.
• The ac inputs generate noise.

Also read: Signal Converters commonly used in Industrial Instrumentation

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The Principle of Operation of an Electromagnetic Flowmeter

Electromagnetic flowmeters are widely used in industrial process flow measurement. These meters come with several features for example: they offer non-invasive flow measurement, they can measure reverse flows and are insensitive to viscosity, density and flow disturbances. Additionally, electromagnetic flowmeters can respond swiftly to flow changes and are linear devices for a wide range of measurements.

Working Principle of the Electromagnetic Flowmeter

Electromagnetic flowmeter operation is based on Faraday’s law of electromagnetic induction. The induced voltages in an electromagnetic flow meter are linearly proportional to the mean velocity of liquids or to the volumetric flow rates. As in the case in many applications, if the pipe walls are made from non-conducting elements, then the induced voltage is independent of the properties of the fluid.

Faraday’s law of induction states that if a conductor of length l (m) is moving with a velocity v (m/s) perpendicular to a magnetic field of flux density B (Tesla) then the induced voltage (e) across the ends of a conductor can be expressed by:

   e = Blv                                      

This is demonstrated in the figure below:

Figure 1.0 The Operational principle of electromagnetic flowmeter

In the above illustration, the magnetic field, the direction of the movement of the conductor, and the induced emf are all perpendicular to each other.

Let’s consider a simplified electromagnetic flowmeter construction below:

Figure 1.1 Construction of practical electromagnetic flowmeter

The externally located electromagnets create a homogenous magnetic field (B) passing through the pipe and the liquid inside it. When a conducting flowing liquid cuts through the magnetic field, voltage is generated along the liquid path between the two electrodes positioned on the opposite sides of the pipe.

The conductor is the liquid flowing through the pipe, and the length of the conductor is the distance between the two electrodes, which is equal to the tube diameter (D). The velocity of the conductor is proportional to the mean flow velocity (v) of the liquid. Hence, the induced voltage becomes:

  e = BDv

If the magnetic field is constant and the diameter of the pipe is fixed, the magnitude of the induced voltage will be proportional to the velocity of the liquid. If the ends of the conductor, in this case the sensors that are connected to an external circuit, the induced voltage causes a current, i to flow, which can be processed appropriately as a measure of the flow rate.

Electromagnetic flowmeters are often calibrated to determine the volumetric flow of the liquid. The volume of liquid flow Q can be related to the average fluid velocity as:

Q = Av

Where A is the area of the pipe, which can be written as:

That gives the induced voltage as a function of the flow rate:

We know that fluid velocity v = Q/A

We can derive the induced voltage as:

          

Equation 1.4 indicates that in a well-designed electromagnetic flowmeter, if all other parameters are kept constant, the induced voltage is linearly proportional to the liquid flow only.

Even though the induced voltage is directly proportional to the mean value of the liquid flow, the main problem in the use of electromagnetic flowmeters is that the amplitude of the induced voltage is small relative to extraneous voltages and noise. The noise sources include:

• Capacitive coupling between signal and power circuits.
• Stray voltage in the process liquid.
• Capacitive coupling in connection leads.
• Inductive coupling of the magnets within the flowmeter.
• Electromechanical emf induced in the electrodes and the process fluid.

Key Merits of Electromagnetic Flowmeters

The electromagnetic flowmeters have the following advantages:

• The output (voltage) is linearly proportional to the input (flow).
• There is no obstacle to the flow path which may cause reduction in pressure.
• The electromagnetic flowmeter can measure flow in pipes of any size provided a powerful magnetic field can be produced.
• The output is not affected by changes in the characteristics of the liquid such as pressure, viscosity, and temperature.

You can also read: Working Principle of Ultrasonic Flowmeter

Shortcomings of Electromagnetic Flowmeters

The electromagnetic flowmeters have the following limitations:

• The conductivity of the liquid being measured should not be less than 10 μꭥ/m.  It is important to note that most water based/aqueous solutions are adequately conductive while a majority of hydrocarbons solutions are not sufficiently conductive.
• The operating cost is usually very high in an electromagnetic flowmeter specifically if heavy slurries are handled.

Related resource: Ultimate guide to Industrial flow Instruments

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