Robust Position Sensor

Linear variable differential transformers are linear position sensors that are used in harsh

industrial or aerospace environments where reliability and/or performance requirements exceed

the capabilities of potentiometers. LVDTs have no sliding electrical contacts to corrode or wear.

The only moving part is a more or less inert chunk of iron. The unit can be sealed from harmful

environmental elements.

Better than Potentiometers?

We simmers get pretty good performance from potentiometers for a very reasonable price. They

turn up in joysticks, yokes, rudders pedals and throttles, just to name a few. But there are a few

applications that could use more than simply “good” performance: throttle quads that don’t track

throttle to throttle due to pot linearity issues, and military fighter style side stick controllers that

don’t move enough to actuate a pot well.

LVDTs can be very accurate with a high degree of electrical linearity. They can be designed to

have very long strokes, or to be sensitive to very small position changes. They are not inherently

expensive. They are actually quite simple devices. It’s just that when they’re sealed in stainless

steel and certified for aerospace use… Well, you get the idea.

LVDTs would seem to have a place in our hobby. The challenge is to overcome the cost.

Simple: 3 windings and a moveable core

An LVDT is a transformer with a single primary winding and two identical secondary windings.

The transformer core is moveable. If the core is centered, it provides equal coupling between the

primary winding and each of the secondary windings. As a result, each secondary produces the

same voltage. As the core is moved, the coupling with one secondary grows and its voltage

increases. The coupling with the other drops so its voltage decreases. The output windings are

generally wired together so their voltages cancel. With the core centered, the net output voltage

is nulled. The voltage increases as the core is moved from the null position.

The “Linear” in the name refers to the linear motion of the core. Turns out, an LVDT is

electrically linear too. The difference in the two output voltages varies quite linearly with the

movement of the core. Linearity better than 2% full scale comes without any particular effort in

building an LVDT. When care is taken to construct the device symmetrically, linearity in the

range of .1~.2% full scale results.

Because they are so simple, I decided to build an LVDT and measure its performance.

A prototype homemade LVDT

This one was built using (mostly) hardware store items. The bobbin is a 3½ inch length of 5/32”

diameter brass tubing from the hobby section. The core is a 2 inch piece of 1/8 inch diameter

steel rod. A piece of 1/16 inch diameter brass tubing was used as a handle to move the core. The

shield surrounding the unit is a small piece of thin gauge galvanized sheet steel sold as an

emergency roof shingle replacement. The three windings are separated by aluminum washers

cuts from a bit of scrap. They’re glued in place with 5 minute epoxy. The wire (#34 AWG) came

from an electronics store.

I wound the wire onto the core using an electric drill. I made no attempt to count turns. I just

filled up the space on the bobbin. I estimate there are 500~700 turns per winding. I did, however,

take some effort to get the same number of turns on both secondary windings. I wound them at

the same time using two spools of wire.

The wire did not go on particularly evenly. It’s tough to hold the drill with one hand and try to

guide two wires onto the bobbin at the same time with the other hand.

It actually works quite well!

Given my casual construction efforts, I am surprised the LVDT performs as well as it does.

(Linearity depends upon symmetrical construction.) Over a 1 inch core movement, I get linearity

within 2% of the full range output.

I excited the LVDT with a 1KHz, 2 volt signal. I measured the differential output voltage at tenth

inch intervals of core movement. I used Excel to fit the data to a straight line, then calculated

errors from that straight line for each measurement. At the extremes of core movement where the

core was completely out of one secondary, the error rapidly climbed, but was less than 2% of the

full scale output.

LVDT geometry determines sensing sensitivity

You can change the dimensions of the windings to customize an LVDT to a particular

application. If you have a 3 inch travel of a throttle, you could make an LVDT with the

secondary windings each spread over a 3 inch length. The linearity would be beneficial in

applications that require several throttles to track.

The primary does not need to be any longer than needed to get sufficient wire on the bobbin.

You can also make the secondary windings very small. You still need the same number of turns

or you'll loose sensitivity. You’re not drawing significant current from them so you can use very

fine wire. The length of the secondary winding bobbins can be quite short. This would make the

LVDT quite sensitive to small movements. You might find this very useful if you plan on

making a military-style side stick controller that has little movement.

Some thoughts on LVDT electronics

LVDTs are generally wired so the voltages on the secondary windings cancel each other.

(“Differential”, right?) When the core is in the center position, the output voltage nulls to very

nearly zero. The voltage increases as the core moves away in either direction from the null

position. The difference is that when the core moves one direction the voltage is in phase with

the voltage on the primary. When the core moves the other direction, the voltage is out of phase.

One can buy integrated circuits designed specifically for use with LVDTs. Chips like the Philips

NE5521 contain everything needed to generate a voltage proportional to an LVDT's core

position.

I tend not to use these specialized chips (well, at least initially) for a couple of reasons. First off,

I'm impatient. I don't want to take the time to order a specialized part. I want to do it NOW.

Often it turns out that using generic parts is less expensive, if a bit more complex, than using the

specialized part. Taking the build-it-up-from-generic-parts approach leads to a better

understanding of a circuit's functionality. Finally, generic parts tend to be more readily available

than specialized ones. I really dislike running across an intriguing circuit and not being able to

build it for lack of an esoteric part. I try not to do that to others.

A common approach taken by the specialized chips is using a synchronous demodulator to

convert the LVDT AC differential output voltage to DC. Fundamentally, this multiplies the

output voltage with the input voltage and filters the result. This is certainly doable, but offers its

own challenges.

A simple approach easily taken by the hobbyist is to individually convert the AC from each

secondary to DC, then subtract them. Converting to DC is done using a “precision rectifier”, a

circuit that uses an op-amp to remove the effects of the forward voltage drop of the diodes that

actually do the conversion. The subtraction is done with another op-amp. Since you can get a

quad op-amp for less than $0.30US and 1N4148 diodes are a few pennies apiece, this approach is

pretty reasonable.

Since I originally wrote this, I have build circuitry based on this idea. It works quite well. Even

using randomly selected components and knowing that would result in some imbalance in the

circuit operation, I saw only a small increase in non-linearity. I will admit to spending more than

expected on the op-amps. I think I paid $0.79US for each of two chips.

If you’re hacking a USB game controller of some sort, you can possibly just push a 0 to 4 volt

signal into it in place of one the existing pots. The workability of that will depend upon the

particular USB device you hack.

An Easy Circuit For Use With LVDTs

Here is a little circuitry you can use to experiment with LVDTs. Don't be put off by the number

of op-amps. They come four on a chip, and a chip costs less than a dollar.

The circuit functions by taking the absolute value of each LVDT secondary separately. This is

done by a clever op-amp and diode combination (not my design, unfortunately) that uses the op-

amp to eliminate the forward voltage drop of the diode.

The two absolute value signals are combined. Notice that the diodes are reversed between the

two circuits. One circuit takes the absolute value while the other takes the negative of the

absolute value. When combined, the two signals are effectively subtracted. The top right op-amp

performs this function plus providing a little gain.

The combined signal is passed through a passive low pass filter (the 3.3K resistors and .1 ufd

capacitors) before being further amplified and offset. The SPAN pot provides a degree of gain

adjustment while the OFFSET allows you to shift the zero point.

And How Well Does It Work?

For exact performance (whatever that means) the 10K resistors in the absolute value circuits

should all be the same value. The 20K resistors should be precisely twice the value of the 10K

resistors. It's the ratio that is important rather more so than the actual value.

So, if you happened to have a supply of super-exact 12K resistors, you could use them in place

of the 10Ks, and replace the 20Ks with two 12Ks in series.

I didn't do that.

I purposely used regular tolerance (5%) carbon film resistors to see what the effect would be. I

know by using an oscilloscope that the absolute value circuits are not balanced quite right.

Nonetheless, I'm getting quite reasonable performance. Using the roughly made LVDT described

on the LVDT page, I'm seeing a peak deviation from linearity of about 2.6% of full scale. No

parts selection, no balance adjustment and a LVDT already known to be a little short of perfect.

So, if YOU build an LVDT and take care to position the windings evenly, and use an ohm meter

to select the 10K and 20K resistors, you should expect to see linearity better (perhaps much

better) than 1% of full scale.

Signal Source

The LVDT should be excited with 2 or 3 volts at about 1 kHz. If you don't have a signal source,

here's an easy one to build. This is a buffered state variable oscillator. Once again, op-amps are

cheap...

If you are experimenting with more than one LVDT at a time, simply duplicate the buffer and

connect it to the same node as the first.

This circuit can run off the same voltage regulators as the first circuit.

Overview

The Linear Variable Differential Transformer (LVDT) is the most broadly used variable-

inductance transducer in industry. It is an electro-mechanical device designed to produce an AC

voltage output proportional to the relative displacement of the transformer and the armature, as

illustrated in the figure below.

Typical LVDT

Common Specifications

Common specifications for commercially available translational LVDT's are listed below:

Input: Power input is a 3 to 15 V (rms) sine wave with a frequency between 60 to

20,000 Hz (the two most common signals are 3 V, 2.5 kHz and 6.3 V, 60 Hz).

Stroke: Full-range stroke ranges from ±125 µm to ±75 mm (±0.005 to ±3 in).

Sensitivity: Sensitivity usually ranges from 0.6 to 30 mV per 25 µm (0.001 in) under

normal excitation of 3 to 6 V. Generally, the higher the frequency the higher

the sensitivity.

Nonlinearity: Inherent nonlinearity of standard units is on the order of 0.5% of full scale.

Pros and Cons

• Pros:

- Relative low cost due to its popularity.

- Solid and robust, capable of working in a wide variety of environments.

- No friction resistance, since the iron core does not contact the transformer coils, resulting

in an infinite (very long) service life.

- High signal to noise ratio and low output impedance.

- Negligible hysteresis.

- Infinitesimal resolution (theoretically). In reality, displacement resolution is limited by the

resolution of the amplifiers and voltage meters used to process the output signal.

- Short response time, only limited by the inertia of the iron core and the rise time of the

amplifiers.

- No permanent damage to the LVDT if measurements exceed the designed range.

• Cons:

- The core must contact directly or indirectly with the measured surface which is not always

possible or desirable. However, a non-contact thickness gage can be achieved by including

a pneumatic servo to maintain the air gap between the nozzle and the work piece.

- Dynamic measurements are limited to no more than 1/10 of the LVDT resonant frequency.

In most cases, this results in a 2 kHz frequency cap.

Applications

Although the LVDT is a displacement sensor, many other physical quantities can be sensed by

converting displacement to the desired quantity via thoughtful arrangements. Several examples

will be given.

• Displacement

- extensometers, temperature transducers, butterfly valve control, servo valve displacement

sensing

• Deflection of Beams, Strings, or Rings

- load cells, force transducers, pressure transducers

Diaphragm Pressure Gage

• Thickness Variation of Work Pieces

- dimension gages, thickness and profile measurements, product sorting by size

Profile Gage

• Fluid Level

- fluid level and fluid flow measurement, position sensing in hydraulic cylinders

Fluid Level Gage

• Velocity & Acceleration

- automotive suspension control

Typical Linear Variable Differential Transformer (LVDT)

The physical construction of a typical LVDT consists of a movable core of magnetic material

and three coils comprising the static transformer. One of the three coils is the primary coil and

the other two are secondary coils.

Transformer

The basic transformer formula, which states that the voltage is proportional to the number of coil

windings, is the backbone of the LVDT. The formula is,

where N is the number of coil windings and V is the voltage read out.

When the iron core slides through the transformer, a certain number of coil windings are affected

by the proximity of the sliding core and thus generate a unique voltage output.

Open Wiring LVDT

Most LVDT's are wired as shown in the schematic above. This wiring arrangement is known as

open wiring. Since the number of coil windings is uniformly distributed along the transformer,

the voltage output is proportional to the iron core displacement when the core slides through the

transformer. This equation is,

where D is displacement of the iron core with respect to the transformer, and M is the sensitivity

of the transformer (slope of the displacement-voltage curve).

Ratiometric Wiring LVDT

Another commonly used LVDT wiring is known as ratiometric wiring, as shown schematically

below.

Ratiometric Wiring

The displacement for ratiometric LVDT's is given by the relation,