What is a voltage divider?
You are going to find out but don't be in too much of a hurry. Work through the Chapter and allow the explanation to develop.
The diagram below shows a light dependent resistor, or LDR, together with its circuit symbol:
The light-sensitive part of the LDR is a wavy track of cadmium sulphide. Light energy triggers the release of extra charge carriers in this material, so that its resistance falls as the level of illumination increases.
A light sensor uses an LDR as part of a voltage divider.
The essential circuit of a voltage divider, also called a potential divider, is:
As you can see, two resistors are connected in series. with Vin , which is often the power supply voltage, connected above Rtop . The output voltage Vout is the voltage across Rbottom and is given by:
It may help you to remember that Rbottom appears on the top line of the formula because Vout is measured across Rbottom .
This is an extremely useful formula which you should learn thoroughly
What happens if one of the resistors in the voltage divider is replaced by an LDR? In the circuit below, Rtop is a 10 resistor, and an LDR is used as Rbottom :
Suppose the LDR has a resistance of 500 , 0.5 , in bright light, and 200 in the shade (these values are reasonable).
When the LDR is in the light, Vout will be:
In the shade, Vout will be:
In other words, this circuit gives a LOW voltage when the LDR is in the light, and a HIGH voltage when the LDR is in the shade. The voltage divider circuit gives an output voltage which changes with illumination.
A sensor subsystem which functions like this could be thought of as a 'dark sensor' and could be used to control lighting circuits which are switched on automatically in the evening.
Perhaps this does not seem terribly exciting, but almost every sensor circuit you can think of uses a voltage divider. There's just no other way to make sensor subsystems work.
Here is the voltage divider built with the LDR in place of Rtop :
What effect does this have on Vout ?
The action of the circuit is reversed. that is, Vout becomes HIGH when the LDR is in the light, and LOW when the LDR is in the shade. Substitute the appropriate values in the voltage divider formula to convince yourself that this is true.
A temperature-sensitive resistor is called a thermistor. There are several different types:
The resistance of most common types of thermistor decreases as the temperature rises. They are called negative temperature coefficient, or ntc, thermistors. Note the -t° next to the circuit symbol. A typical ntc thermistor is made using semiconductor metal oxide materials. (Semiconductors have resistance properties midway between those of conductors and insulators.) As the temperature rises, more charge carriers become available and the resistance falls.
Although less often used, it is possible to manufacture positive temperature coefficient, or ptc, thermistors. These are made of different materials and show an increase in resistance with temperature.
How could you make a sensor circuit for use in a fire alarm? You want a circuit which will deliver a HIGH voltage when hot conditions are detected. You need a voltage divider with the ntc thermistor in the Rtop position:
How could you make a sensor circuit to detect temperatures less than 4°C to warn motorists that there may be ice on the road? You want a circuit which will give a HIGH voltage in cold conditions. You need a voltage divider with the thermistor in place of Rbottom :
This last application raises an important question: How do you know what value of Vout you are going to get at 4°C?
To answer this question, you need to estimate the resistance of the thermistor at 4°C.
Lots of different types of thermistor are manufactured and each has its own characteristic pattern of resistance change with temperature. The diagram below shows the thermistor characteristic curve for one particular thermistor:
On the y-axis, resistance is plotted on a logarithmic scale. This is a way of compressing the graph so that it is easier to see how the resistance changes. Between 100 and 1000 , each horizontal division corresponds to 100 . On the other hand, between 1000 and 10000 , each division corresponds to 1000 . Above 10000 , each division respresents 10000 .
As you can see, this thermistor has a resistance which varies from around 70 at 0°C to about 1 at 100°C. Suppliers catalogues usually give the resistance at 25°C, which was 20 in this case. Usually, catalogues also specify a 'Beta' or 'B-value'. When these two numbers are specified, it is possible to calculate an approximate value for the resistance of the thermistor at any particular temperature from the equation:
RT is the resistance at temperature T in Kelvin (= °C +273)
RT0 is the resistance at a reference temperature T0 in Kelvin. When the reference temperature is 25°C, T0 = 25+273.
e is the natural logarithm base, raised to the power in this equation.
B is the B-value specified for this thermistor.
You don't need to think about applying this equation at the moment, but it is useful to know that the information provided in catalogues is sufficient to allow you to predict thermistor performance. Using a spreadsheet such as Excel, it is possible to to generate characteristic curves for any thermistor by calculating resistance values for a range of temperatures.
With RT0 = 20 and B =4200, resistance changes from 0 to 10°C are as follows:
From the graph, the resistance at 4°C can be estimated as just a little less than 60 . By calculation using the equation, the exact value is 58.2 .
The biggest change in Vout from a voltage divider is obtained when Rtop and Rbottom are EQUAL in value.
What this means is that selecting a value for Rtop close to 58.2 will make the voltage divider for the ice alert most sensitive at 4°C. The nearest E12/E24 value is 56 . This matters because large changes in Vout make it easier to design the other subsystems in the ice alert, so that temperatures below 4°C will be reliably detected.
Sensor devices vary considerably in resistance and you can apply this rule to make sure that the voltage dividers you build will always be as sensitive as possible at the critical point.
Thermistors turn up in more places than you might imagine. They are extensively used in cars, for example in:
electronic fuel injection, in which air-inlet, air/fuel mixture and cooling water temperatures are monitored to help determine the fuel concentration for optimum injection.
air conditioning and seat temperature controls.
warning indicators such as oil and fluid temperatures, oil level and turbo-charger switch off.
fan motor control, based on cooling water temperature
frost sensors, for outside temperature measurement
Thermistors are used to measure surface and deepwater sea temperatures in helping to monitor El Niño ocean currents. Less obviously, thermistors are used to measure air flow, for instance in monitoring breathing in premature babies.
Sir Charles Wheatstone was a talented and versatile scientist. He invented the concertina, experimented with stereoscopic photography and invented the stereoscope and played an important part in the early development of telegraph communications. He didn't claim to have invented the circuit named after him, but was among the first to exploit the circuit effectively in making resistance measurements.
So, what is a Wheatstone bridge? This is the circuit:
It is obvious that the circuit consists of two voltage dividers. Suppose RX is an unknown resistor value. RC is adjusted until Vout from the second voltage divider is equal to Vout from the voltage divider containing RX . When the Vout values are equal, the bridge is said to be balanced. The balance point can be detected by connecting either a voltmeter or an ammeter across the output terminals. Both sorts of meter give a zero reading when balance is achieved.
In a balanced circuit, the ratio RX / RA is equal to the ratio RB / RC . Rearranging:
In other words, if the values of RA , RB and RC are known, it is easy to calculate RX . In Wheatstone bridge instruments, RA and RB were fixed and RC was adjusted on a sliding scale in such a way that the value of RX could be read off directly.
Today, Wheatstone bridge circuits are not usually used to measure resistance values, but they are used in designing sensor circuits.
A variometer is an instrument used in gliders to detect changes in air pressure due to sudden changes in altitude. The variometer alerts the glider pilot to updrafts or thermals. By circling within a thermal the pilot can gain height and keep flying for longer.
One type of variometer uses thermistors to monitor pressure changes:
Altitude changes cause pressure changes which produce air flow. A heating element in the flow passage heats air which arrives at different temperatures at a thermistor sensor upstream and downstream of the heating element depending on the rate of air flow.
The thermistor sensors are part of a Wheatstone bridge:
When the instrument is first set up, the preset resistor is adjusted for zero output. The advantage of the Wheatstone bridge is that only temperature differences between the two sensors will put the bridge out of balance. Cold or warm weather conditions affect both sensors equally. Air flow into or out of the reference chamber has the opposite effect on the two sensors: one will be heated by the airstream, while the other is cooled. As a result, the output changes by more than it would if there was just a single sensor device.
By the way, Wheatstone bridge circuits are supposed to be difficult to understand. The circuit is usually drawn as a diamond:
It's less obvious that you should be thinking about two voltage dividers, but once you know, the action of the circuit is easy to follow.
Another name for a sound sensor is a microphone. The diagram shows a cermet microphone:
'Cermet' stands for 'ceramic' and 'metal'. A mixture of these materials is used in making the sound-sensitive part of the microphone. To make them work properly, cermet microphones need a voltage, usually around 1.5 V across them. A suitable circuit for use with a 9 V supply is:
The 4.7 and the 1 resistors make a voltage divider which provides 1.6 V across the microphone. Sound waves generate small changes in voltage, usually in the range 10-20 mV. To isolate these small signals from the steady 1.6 V, acapacitor is used. Capacitors are described in Chapter 5 and an investigation of the microphone circuit is included in the practical which accompanies Chapter 4.
Signals from switches
When a switch is used to provide an input to a circuit, pressing the switch usually generates a voltage signal. It is the voltage signal which triggers the circuit into action. What do you need to get the switch to generate a voltage signal? . . . You need a voltage divider. The circuit can be built in either of two ways:
The pull down resistor in the first circuit forces Vout to become LOW except when the push button switch is operated. This circuit delivers a HIGH voltage when the switch is pressed. A resistor value of 10 is often used.
In the second circuit, the pull up resistor forces Vout to become HIGH except when the switch is operated. Pressing the switch connects Vout directly to 0 V. In other words, this circuit delivers a LOW voltage when the switch is pressed.
In circuits which process logic signals, a LOW voltage is called 'logic 0' or just '0', while a HIGH voltage is called 'logic1' or '1'. These voltage divider circuits are perfect for providing input signals for logic systems.
What kinds of switches could you use. One variety of push button switch is called a miniature tactile switch. These are small switches which work well with prototype board:
As you can see, the switch has four pins which are linked in pairs by internal metal strips. Pressing the button bridges the contacts and closes the switch. The extra pins are useful in designing printed circuit boards for keyboard input and also stop the switch from being moved about or bent once soldered into position.
There are lots of other switches which you might want to use in a voltage divider configuration. These include magnetically-operated reed switches, tilt switches and pressure pads, all with burglar alarm applications.