Electricity Tutorial 6 - 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.

 

Active transducers generate a current.  A pick-up cartridge on a record deck is one such.

 

 

 

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:

 

 

This picture shows a strain gauge, which is found in an electronic balance:

 

 

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.  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

 

 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.

 

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

 
 
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 Ohmís 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

 

 

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.

 

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.  This enables the discharge to propagate.

 

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.