Electricity Tutorial 6 - Transducers

Contents

Active Transducers

Passive Transducers

Light Dependent Resistor

Thermistor

Potential Divider Circuits

Bridge Circuits

Metre Bridge

Semiconductors

Resistance of LDR

Resistance of Thermistor

Insulators

Lightning

Active Transducers

Sensors, or transducers, detect a change in the environment.  Active transducers generate a voltage when there is a change in the physical conditions.  If the voltage is connected to a circuit, a current flows.

 

A pick-up cartridge on a record deck is an active transducer.  A small magnet is vibrated within coils of wire, and a tiny voltage is induced.  The voltage is amplified so that we can hear the sound recorded on the LP.  (LP records have made a comeback recently.)

 

 

 

Many mechanical transducers use the piezo-electric effect.  A typical example of this is commonly found in gas lighters.  You squeeze the trigger.  A quartz crystal is deformed and a voltage is induced.  In the case of the gas lighter, it is about 7000 V.

 

The induced voltage is shown in the animation below:

 

Animation by Tizeff, Wikimedia Commons

 

Note that the deformation is exaggerated.  Many substances, when deformed, will generate a voltage.  These include:

The displacement of charge, leading to the voltage induced, is proportional to the deformation.  When there is zero deformation, there is zero voltage.

 

Cheap pick-up cartridges use piezo-electric transducers to generate voltages.  These are rather higher than the voltages from a magnetic cartridge, but the signal is not of such high quality.  Also the cartridges can do mechanical damage to the surface of the record.

 

A simple microphone, like the ones in your physics lab, uses the piezo-electric effect.  They are often referred to as crystal mikes.

 

 

As the diaphragm moves, a voltage is induced in the crystal, and this can be amplified.  While the output voltage is quite high (about 0.5 V) the frequency response and sensitivity are not very good, and such microphones are of little use for music recording. 

 

It is possible to reverse the piezo-electric effect. A changing voltage applied to the terminals of a crystal mike will cause the diaphragm to vibrate and make a sound.  Its quality is not good.

 

 

 

Passive Transducers

Passive transducers  are often referred to as resistive transducers.  They detect a change in the environment (e.g. light level) by changing resistance (hence resistive).  They do NOT generate an electric current.  That is why they are called passive.  The table shows some passive devices.

 

Here are some passive devices:

 

Device

Action

Where used

Light Dependent Resistor

Resistance falls with increasing light level

Light operated switches

Thermistor

Resistance falls with increased temperature

Electronic thermometers

Strain gauge

Resistance changes with force

Sensor in an electronic balance

Moisture detector

Resistance falls when wet

Damp meter

 
The picture below shows examples:

 

 

 

Light dependent resistor (LDR)

The light dependent resistor consists of a length of material (cadmium sulphide) whose resistance changes according to the light level.  Bright light releases electrons so that the material conducts better.  Therefore the brighter the light, the lower the resistance. 

The characteristic graph of the LDR is shown below:

The graph shows us the variation using a linear scale.  Often the graph is shown as a logarithmic graph as below:

 

 

However, the measurement of light intensity is not an easy scale to work with. 

Here is a list of typical intensities:

Light Source
Illumination (lux)

Moonlight

0.1

60 W light bulb at 1 m

50

1 W MES bulb at 0.1 m

100

Fluorescent lighting

500

Bright sunlight

30 000

 

Typical values for the range of resistance of an LDR vary from 10 MW in the dark to about 400 W in light levels of 1000 lux.

 

Resistive components can get hot when excessive current is flowing through them, and this can impair their function, or damage them. This can be prevented by connecting a current limiting resistor in series, as shown in the picture below:


 

 

 LDRs are used for:

 

Thermistors

The word thermistor comes from the mixture of thermal and resistor.  So it changes its resistance in response to a temperature change.

The most common type that we use has a resistance that falls as the temperature rises.  It is referred to as a negative temperature coefficient device.  A positive temperature coefficient device has a resistance that increases with temperature.

 

Question 1

Explain the difference between a positive temperature coefficient thermistor and a negative temperature coefficient thermistor.

Answer

 

Below is a picture of typical thermistors and their symbols:

 

We can use apparatus like this to measure the way that the resistance of the thermistor changes with different temperatures:

 

 

The oil is heated with the 50 W heater and the temperature recorded.  The multimeter shows the resistance.  The data are plotted as a graph that looks like this:

 

 

The data that form the graph were taken from an experiment.  The graph was plotted using an Excel spreadsheet.  The purple line is a line of best fit.

 

We can also use a graph like this as a calibration curve.  If we measure the resistance at 40 oC, we will find that the resistance is about 280 W.  Even then this has quite a lot of uncertainty.  Physicists and engineers often use calibration curves.  Such curves are drawn using high quality data with professional equipment that is both accurate and precise.  Such equipment has to be used very skilfully, and the equipment is very expensive.

 

If we plot the vertical axis as log10 (resistance) and the horizontal axis as log10 (temperature), we should get a straight line, indicating that the temperature and resistance are linked by a logarithmic function:

 

You will need to know about logarithmic functions in the A-level year.

 

Question 2

A thermistor has a negative temperature coefficient.  At 10 oC it has a resistance of 170 ohms.  It is connected to a 20 V supply. 

a.       What current passes through the thermistor?

b.      What is the power dissipated by the thermistor?

c.       Explain what could happen to the thermistor if it were to be left connected to the supply.                                                                                                      

Answer

 

 

Strain Gauge

A strain gauge is a sensor whose resistance changes when a force is a applied.  This picture shows a strain gauge found in an electronic balance:

 

 

The construction of a strain gauge is simplicity itself.  It consists of a length of constantan wire mounted on a flexible piece of material like this:

 

When the strain gauge is put under load, it stretches by an extension x:

 

The way the wire is mounted on the material ensures that the wire does not just stretch by x m, but by 8x (in this case).  The arrangement ensures that the resistance increases by a larger amount that it would if there were only a single wire.  We know that the resistance is given by:

 

Therefore the length term changes from l to l + 8x.  So the resistance increases.  It does so in a linear way like this:

 

This graph is linear as long as Hooke's Law is obeyed (see Materials Tutorial 2).  You could investigate the change in the resistance of a single long constantan wire with load as a class experiment.

 

The change in resistance is not that great, so the strain gauge is set up in a bridge circuit:

 

 

The strain gauge is represented as a variable resistor in the diagram.  It has a resistance of R W.  The three other resistors have a resistance of R W as well.  The voltage v in this case is zero, and the circuit is balanced.  When a load is put on the strain gauge, the resistance results in the bridge circuit becoming unbalanced, so there is a small voltage, v.  This will be detected by a voltage amplification circuit, to be displayed on a suitably calibrated meter.

 

 
Potential Divider Circuit

Resistive transducers like LDRs or thermistors are often put into a potential divider circuit.

 

 

If the output current is zero, the current flowing through R1 also flows through R2, because the resistors are in series.  So we can use Ohm’s Law to say:

 

Now:

 

Therefore:    

 

 

This result can be thought of as the output voltage being the same fraction of the input voltage as R2 is the fraction of the total resistance.


 

 

Question 3   

What is the output voltage of this potential divider? 

Answer

 

If the light level rose, the resistance of the LDR would fall.  Therefore the voltage Vout would rise.  If the output were connected to a transistor, the transistor would switch on as Vout rose above 0.7 V.

 

Question 4

At a certain light level, an LDR has a resistance of 200 ohms.  It is connected  to a 1000 ohm resistor in a potential divider circuit, as shown:

The output voltage is 0.6 V.  What is the input voltage?

Answer

 

Voltage (potential) dividers are used to feed an input voltage into an electronic circuit.  Here is a light dependent resistor in a potential divider circuit (R1 and R2) feeding the base (input terminal, B) of a bipolar transistor.

 

When it's dark, the resistance of R2 is high.  The output voltage of the potential divider is high.  The resistor R3 is there to limit the current into the base to about 10 mA and the base voltage to about 0.7 V.  The transistor is a solid state switch which is turned on when the base voltage is about 0.7 V.  Current therefore flows between the collector (C) and the emitter (E).  The relay is turned on and the mains circuit is turned on to make the mains bulb glow.

 

As the light level increases, the resistance of R2 decreases.  The voltage across R2 decreases, and the base voltage decreases.  When the base voltage falls below about 0.6 V, the transistor turns off and no longer conducts.  The relay turns off.  (The reverse bias diode D1 is there to protect against a reverse voltage spike that could destroy the transistor.)  The mains bulb turns off as well.

 

The resistor R1 is a variable resistor to allow the light level at which the transistor turns off to be adjusted.

 

 

Bridge Circuits (Irish Higher Syllabus)

The bridge circuit is sometimes called the Wheatstone Bridge, named after the British physicist and inventor, Charles Wheatstone (1802 - 1875).  It is simply two voltage dividers in parallel like this:

 

 

We can write an expression for the circuit.  We know that the voltage divider equation is:

 

 

Similarly, for R3 and R4, we can write:

 

The key point with a bridge circuit is that the voltage between X and Y is zero.  Or we can put a microammeter or even a galvanometer between X and Y.  The current will be zero if the circuit is balanced.  So:

Vout (X) = Vout (Y)

 

We can write:

 

The Vin terms cancel and we can rearrange the equation to give:

 

Open the brackets:

And the R2R4 terms cancel:

To give:

Or:

 

Worked Example

A bridge circuit is set up like this:

 

 

(a)  What is the voltage at X, if Vin = 12.0 V?

(b)  What is the resistance of R3 if Vout = 0 V?

Answer

(a) Use the voltage divider equation:

 

 

     Vout = 12 V × (250 W ÷ (150 W + 250 W)) = 7.5 V

 

(b)  Use:

     Rearrange:

     

     R3 = (150 W × 150 W) ÷ 250 W = 90 W

 

 

 

The Metre Bridge

A metre bridge works in a similar way to the Wheatstone Bridge.  It is also known as a slide wire.   It allows us to measure a resistance with a reduced uncertainty.

 

In circuit diagram form we see:

 

Electrically, the metre bridge is a potentiometer in parallel with voltage divider consisting of a variable resistor, and an unknown resistor.  The variable resistor is usually a resistance box (or decade box) in which there are highly accurate and precise resistors.  These can be selected using rotary switches.  Older versions used brass pegs.

 

The potentiometer consists of a metre length of resistance wire of known resistance.  (If we don't know the resistance, we can measure it.)  A galvanometer is connected to point X.  This is a meter that shows a very small current.  It is connected to the potentiometer at point Y using a probe that is often called a jockey (or slider).  When the voltage at the point X is the same as the voltage at  point Y, the galvanometer reads zero.  Because it detects very tiny currents, we can say that the when the galvanometer reads zero, the current is truly zero.  The circuit is balanced.  We read the distance at point Y.  If the full voltage is at 0 mm, and the balance point is at 55 cm, we can say that:

 

VY = (100 cm - 55cm) × (Vin / 100 cm) = 0.45 Vin

 

To reduce uncertainty further, we should repeat the experiment several times and get an average of the balance point.

 

If we know what the resistance box value is, we can work out the value of the unknown resistance.  We don't need to know the input voltage though.  This we do by using the idea that the ratio of the resistances of the potentiometer is the same as the ratio of the resistances on the voltage divider.  As the potentiometer is made of a uniform wire, the ratio of the resistances is the same as the ratio of the lengths. 

 

Therefore we can use the principle of the Wheatstone Bridge:

 

 

So we can rewrite this as:

 

Rearranging gives us:

 

Worked example

The galvanometer on a metre bridge reads zero when it is set up like this:

 

 

What is the resistance of the unknown resistance?

Answer

Using the principle of the Wheatstone bridge:

 

 

Rx = 43 W × (65.7 cm ÷ 34.3 cm) = 82.4 W

 

As the resistance box gives resistance to two significant figures, we need to give our answer as 82 W.

 

The metre bridge seems to be a lot of bother to determine a resistance (you can use an ohmmeter for the same purpose), but it can give a result that has a lower uncertainty.  This is useful where a precise value of resistance is critical.

 

 

Semiconduction (Extension)

Thermistors are made of a semiconductor. We will look at how semiconductors work.  If you want to to skip the next section and go to the explanation of why the resistance falls, click HERE.

 

Semiconductors have a resistivity (or conductivity) that is intermediate between a conductor (like a metal) and a insulator (like glass). They are usually based on silicon, which is in the same group as carbon. Group IV elements have 4 valence electrons and form a lattice like this:

 

 

The valence electrons form covalent bonds. There are very few free electrons so pure silicon is a very poor conductor.

The conductivity can be increased by doping the semi-conductor.  We can do this by adding an impurity, for example, phosphorus:

 

 

We have a spare electron left over, because phosphorus is a Group V element, which has 5 valence electrons.  4 are used to make covalent bonds, while the one left over is free.  The free electron acts as a negative charge carrier.  It will be attracted to the positive terminal.  We call this kind of material a n-type semiconductor.

 

If we use aluminium, or other Group III element as a dopant, we only have 3 valence electrons. Therefore there is one of the silicon electrons that is unpaired.

 

 

This missing electron is called a hole and it acts as a positive charge carrier.  Since the silicon atoms can borrow electrons from their neighbours, the hole can move about, and move away from the original aluminium atom. 

 

Bipolar Semiconductors (Scottish Higher Syllabus)

The hole will move towards the negative terminal of the semiconductor.  The electron will move towards the positive terminal of the semiconductor.

 

 

If we place an n-type semiconductor next to a p-type, we find that some of the holes will diffuse into the n-type material at the interface, or junction, between the materials. We also find that some of the electrons will diffuse into the p-type material. The electrons and the holes combine and act as neutral. So the n-material there has been depleted of electrons, and the p-material has been depleted of holes. We call this region the depletion layer and it acts as an insulator.

 

If we apply a positive voltage to the n-type material (and a negative voltage to the p-type), the depletion layer gets wider. This is because more holes are attracted from the p-material towards the negative (and electrons to the positive). The increased combination of electrons and holes increases the width of the depletion layer.

If we swop the polarity about, so that the n-type material is negative, the holes get attracted to the negative and the electrons get attracted to the positive. The depletion layer is lost, and conduction starts.

This could be thought of merely as an interesting physics curiosity, but is actually an important concept at the heart of all solid state electronic devices.

 

 

In the early part of the Twentieth Century, quantum physics grew to allow physicists to explain a lot of observations that cannot be explained by normal (or classical) physics.  Quantum physics is not at all easy to understand, but there are two things that we can use:

The key point is that electrons are quantum beings.  If you try to catch an electron, you will never do so.  The closer you are to getting hold of the little brute, the less likely it is that you will catch it.

 

Let's try to illustrate these ideas with another model:

 

"Fingers" is a criminal.  He is in prison, but he doesn't think he should be inside.  He wants to be outside to commit more crimes.

 

 

In the real world, Fingers can jump, but not that high.  He could not jump from the Inside to the Outside.  So he remains in the nick.   But in the quantum world, Fingers is in a probability cloud.

 

Fingers' probability cloud extends to just over the prison wall.  So there is a tiny, but real, probability that he could happen to be just on top the prison wall, so he could make good his escape.  Also, in the quantum world, the closer the coppers are to nicking him, the more likely he is to get away.

 

 

Now electrons perch on different rungs of the energy ladder.  They have to be on a particular rung; they cannot perch between rungs.  Because they live in probability clouds, there is a chance that they can fly up to the next rung of the energy ladder, as long as another electron comes down from a higher perch (which it will).  For most of their time, electrons are in the valence band, perching on the normal rungs of their ladder.

 

Above the normal rungs (the valence band) there is a forbidden gap, a space where there are no rungs for them to perch.  Above forbidden gap is the conduction band in which the electrons are free to move about.  It's a bit like aeroplanes flying about an aerodrome.  They can be on the ground, but once in the air, they must not fly below 500 m in the region of the aerodrome.  They can fly at any height above 500 m, but if they fall below, the pilots could be in trouble.

 

 

The electrons can get sufficient energy to jump the forbidden gap to go into the conduction band.  This is because of the probability cloud.  If the forbidden gap is small, as in metals, the probability that the electrons will make it to the conduction band is high.  In a pure semiconductor, the forbidden gap is bigger, so the probability of electrons jumping to the gap is smaller, but not impossible.

 

If we put impurities into the crystal lattice of the semi-conductor, we put extra levels in the forbidden gap, a bit like wires for the electrons to perch on.  This allows for a greater probability of the electrons reaching the conduction band.

 

Why does the resistance of an LDR decrease with increased Light Level?

If we look at an LDR, we see a narrow channel of cadmium sulphide (CdS) or some other semiconductor.  It looks like this:

 

When light energy falls onto the track, electrons are given extra energy so that they can jump the forbidden gap from the valance band to the conduction band.  Once they have done this, they are free to act as conduction electrons. The more conduction electrons that are available, the lower the resistance. The higher the light level, the greater is the probability of an electron having sufficient energy to jump the forbidden gap. 

 

If the light gets too intense, the resistance can become very low, so a large current flows through the LDR.  The heating effect can cause the LDR to go into thermal runaway, resulting in its destruction.  This can be prevented by a current limiting resistor.

 

 

Why does a Thermistor's resistance fall with increased Temperature?

When the thermistor's temperature rises, more electrons can jump the forbidden gap into the conduction band.  So a bigger current flows, hence the resistance falls.  We can get a situation that the heating effect of the moving electrons increases the internal energy, so the temperature increases further.   Thus the current gets bigger.  Thermal runaway is a problem in all semiconductor components.  It can be prevented by having heatsinks that conduct the excess internal energy away in the form of a heat flow.  If the heatsink is inadequate, the semiconductor can overheat and will be destroyed. 

 

 

Insulators

In an insulating material the outer shells of the valence electrons are full.   The forbidden gap between the valence electrons  is much bigger than the insulator.  Therefore there is much less probability of an electron being able to jump the forbidden gap to the conduction band.  Going back to our model with Fingers in prison, it's like making the prison wall much higher.  In the quantum world, the probability of Fingers having the energy to jump the wall is much reduced.  However there is a tiny probability of the electron being able to jump, so no insulator is perfect.

 

If the voltage (energy per unit charge) is large enough, the electrons have an increased probability of having enough energy to jump the forbidden gap.  Therefore the insulation breaks down.  To prevent this, we simply increase the thickness of the insulation.

 

Insulators are described in terms of their breakdown voltage or dielectric strength.  Breakdown voltage is commonly measured given in units of V mm-1 (or kV mm-1)  In SI units, this is converted to V m-1 by multiplying by 1000. 

1 kV mm-1 = 1000 V m-1 = 1.0 × 106 V m-1

A potential difference per unit distance is an electric field, which is summed up in the formula:

[E - electric field (V m-1); V - potential difference (V); d - distance (m)]

 

All gases are insulators.  The usual break-down voltage for air is 3000 V mm-1 (3.0 × 106 V m-1).  Here are some more gases:

 

Gas

Breakdown voltage  / × 106 V m-1

Argon

0.52

Methane

2.9

Carbon dioxide

5.6

Sulphur dioxide

7.7

Sulphur hexaflouride

8.5

 

Sulphur hexafluoride (SF6) is the best insulating gas.

 

Liquids that are not ionic solutions are insulators.  Pure water is a good insulator with a breakdown voltage of 65 × 106 V m-1.  However if there are any ions in solution, the insulating properties are lost.  Here are some data for other liquids.

 

Liquid

Breakdown voltage  / × 106 V m-1

Carbon tetrachloride

5.5

Octane

17

Benzene

163

Decane

192

Toluene

199

 

Non-metallic solids are insulators, except carbon, silicon, and germanium. 

 

Solid

Breakdown voltage  / × 106 V m-1

PVC

14

Epoxy resin

20

Enamel

79

Natural rubber

100

Solid sodium chloride

150

Fused silica glass

500

 

Crystalline sodium chloride is a very good insulator.  Unfortunately it easily dissolves in water which does not help its insulating properties.

 

Lightning

In a thunderstorm, very high voltages are generated by static induction within the clouds, until the air gets sufficiently conductive for a discharge to occur.  The picture shows an earth strike.

 

 

This would suggest an electric field strength of 3 × 106 V  m-1.  Measurements in thunderclouds have revealed electric field strengths of 3000 V m-1 or less.  In theory lightning should not happen at all.  The latest thinking is that a lightning strike is started by the passage of a high energy particle from space, for example a muon, or a cosmic ray, which causes ionisation of air molecules.  An electronic avalanche is started.  This enables the discharge to propagate.