Tuesday 30 August 2011

Tuesday 19 July 2011

An Introduction To Bridge Circuits - Why Do You Need Them?

An Introduction To Bridge Circuits - Why Do You Need Them?
        Making measurements with sensors is a common way in which many engineers and scientists encounter electrical devices.  There are many different ways in which physical variables like temperature, light intensity, pressure and numerous other physical variables can be measured electrically.  Devices used to measure a physical variable are called sensors.  Some different kinds of sensors include the following.
  • Sensors which change resistance as the physical variable changes.
  • Thermistors for temperature measurement
  • Photo-resistors for light measurement
  • Strain gages for measurement of mechanical strain
  • Sensors which produce a voltage change for a change in a physical variable.
  • Thermocouples for temperature
  • Solar cells for light.
Other kinds of sensors might include:
  • Sensors which produce some other sort of electrical change.  Some examples might include the following.
    • A tachometer that produces a frequency proportional to rpm.
    • Sensors which produce a set of signals in binary code proportional to pressure.
    • Sensors which produce a voltage signal with a frequency proportional to flow rate.
        First, let us consider what happens if we put a temperature sensor (a thermistor) into a voltage divider circuit.  Here's the circuit.  Actually, we examined this circuit in the lesson on voltage dividers, and you should review that material if you don't remember it.  Click here for that material.


What we found in the voltage divider lesson is the following.
  • At some nominal value of the temperature (if we have a temperature sensor) the voltage divider will have a nominal output voltage.
  • As the temperature changes the voltage output of the voltage divider changes.
    • The voltage change will probably be a nonlinear function of temperature as the temperature deviates from the nominal value of the temperature.
        There are some problems with using a voltage divider.  Consider the following.
  • You might want an output signal that is zero at the nominal conditions.
  • You could then have an output signal that was positive when the temperature deviated in one direction and a negative output signal when the temperature deviated in the other direction.
  • If the outut is something other than temperature that becomes even more clear.
    • If the sensor is a strain gage, the strain could be positive or negative, and you would want the output voltage to be similarly positive or negative, and ideally it would be proportional to strain.
    • If the sensor is a pressure sensor, you could want a positive signal for a presssure above atmospheric (or any other reference) and negative for a pressure below.
The point here is that it is common to want a zero output signal under certain, known conditions.  There are several ways you could subtract out that pesky DC voltage.  For example, you could use an operational amplifier circuit to subtract out the DC voltage.  That's more complex than another solution - using a bridge circuit. Usually a bridge circuit is what is used in this situation, and in this lesson you're going to learn about bridge circuits.  Bridge circuits are simple circuits that permit us to solve the problems noted above, and you need to learn about them.

Bridge Circuits         What is a bridge circuit?  It's easier to look at one than to try to describe it.  Here is a bridge circuit.



The bridge circuit has two arms (Ra and Rb constitute one arm here, and Rc and Rs constitute the other arm).  Each arm is composed of two resistors in series, and you may want to think of each arm as a voltage divider.  The output is the difference between the outputs of the two voltage dividers.  In the bridge circuit above we have also included some source resistance for the source which drives the bridge circuit.  This is the circuit we want to understand.
        What are you trying to do in this lesson?
  • Given a sensor that changes resistance as some physical variable changes,
    • Be able to use the sensor in a bridge circuit.
    • Be able to choose components for the bridge circuit that will produce good performance.

Analysis Of Bridge Circuits - Balancing The Bridge         We have noted that it might be possible to get a bridge output of zero volts.  That's true, but it only happens under certain conditions.  When the output of a bridge is zero, the bridge is said to be balanced.  The first thing we will do is to determine the conditions for a bridge circuit to be balanced.
        If the output voltage of a bridge circuit is zero, that will happen when the outputs of both dividers is the same.  Here's the bridge circuit again.  We'll probably have to be looking at it as we make this argument.



        The first thing that we notice is that both voltage dividers have the same voltage at the "top" of the bridge.  Call that voltage Vtop.  Then, the voltage at the left terminal (labelled "+") is given by:



Vtop. [Rb/(Ra + Rb)]
Similarly, the voltage at the right terminal (labelled "-") is given by:



Vtop. [Rs/(Rc + Rs)]
The difference between these two voltages - the output voltage - is given by:



Vtop. [Rb/(Ra + Rb)] - Vtop. [Rs/(Rc + Rs)]
Setting the output voltage to zero (the condition for a balanced bridge), we get:



Vtop. [Rb/(Ra + Rb)] - Vtop. [Rs/(Rc + Rs)] = 0
Since Vtop is a common factor it can be removed.  Then, we get:



[Rb/(Ra + Rb)] - [Rs/(Rc + Rs)] = 0
or
[Rb/(Ra + Rb)] = [Rs/(Rc + Rs)]
Now, cross-multiply the denominators.



RbRc + RbRs= RsRa + RbRs
Note that the term RsRb appears on both sides of the equation and can be taken out on both sides.  That gives us:



RbRc = RsRa
This is the condition for balance that we were looking for.  It is a very simple relationship that must be obeyed by the resistors in the bridge portion of the circuit.

Analog to Digital Converters (A/Ds)

A/D Converters
        Analog-to-Digital converters - a.k.a. A/D converters - are widely used by many engineers and scientists of all types, often without their realizing it.  Whenever they make a measurement of a voltage, and that measurement is taken into a computer, an A/D is used.
        If you're going to take measurements - and just about every engineer will do a lot of that - then you will be better off if you understand some of the basic ideas behind A/D converters.  There are two simple goals for this lesson.
  Given an A/D converter with a given range and number of bits,
  To be able to calculate the resolution of the converter.
  Given an A/D converter in the laboratory,
  To be able to determine the resolution of the converter and the number of bits used in the converter.
What Are A/D Converters?
        A/D converters are electrical circuits that have the following characteristics.
  • The input to the A/D converter is a voltage.
    • A/D converters may be designed for voltages from 0 to 10v, from -5 to +5v, etc., but they almost always take a voltage input.  (Some rare exceptions occur with current inputs!)  In any event, the input is an analog voltage signal for most cases.
  • The output of the A/D converter is a binary signal, and that binary signal encodes the analog input voltage.  So, the output is some sort of digital number.
  Comparator Simulator
Sim1  Here is the comparator simulator.  You can think of a comparator as a one-bit A/D converter.  The input is an analog signal, and the output is a one bit digital representation of the analog signal.  In the simulator, you can control a simulated voltage source that is the input the the comparator, and the digital output bit is indicated with a simulated LED.  Notice the following.
  • The input can range from zero (0) to ten (10) volts.
  • When the input voltage goes above five (5) volts, the output is a binary one (1) and the LED lights.  When the input voltage is less than five volts, the output is a binary zero (0) and the LED does not light.

Properties of A/D Converters
       The comparator simulation reveals a few important facts about A/D converters.
  • An A/D converter has a range.  The simulator has a range from 0v to 10v, or a total of ten (10) volts.  The total range of an A/D is the difference between the highest and lowest voltages the A/D can convert.
  • An A/D has a resolution that is determined by the largest count that the A/D's counter/register can hold.
  • The largest count is determined by the number of bits in the counter.
    • If there are N bits in the counter, the largest count is 2N-1.
    • In the comparator, there is only one bit, and the largest count is 1, and there are only two different outputs that are possible.
        Clearly, if you want a more accurate conversion the converter will need to have a lot more than just one bit.  Let's look at another simulation.  This simulation is a four-bit A/D converter.

Four Bit A/D Converter Simulator
Sim2  Here is a simulation of a four bit A/D converter.  Note the following:
  • As in the comparator simulation, we assume that the input voltage can range from zero (0) to ten (10) volts.
  • We have added some "fine control" with two buttons that "nudge" the voltage up or down, but not beyond the 0-10v range.
Try the simulator first, and then we will examine what happens in a little more detail.

        Now, consider the following observations about the converter above.
  • There are four bits in the simulation converter.
  • The range is from 0v to 10v, or 10v total range.
  • With four bits, there are 16 different count values (0 through 15).
  • Thus, 10v is divided into 16 different parts, each part being:
    • 10/16 = 0.625 volts wide.
        Now, let's consider an example question.

Example
E1   How many bits would you need to divide 10 v into .01 v intervals?  To get the answer to the question consider the following.
  • If you divide 10 v into .01 v intervals you need 1000 intervals.
  • If you need 1000 intervals you need to think about a power of 2 that is larger than 1000.
    • The smallest power of 2 that is larger than 1000 is 210 which is equal to 1024.
  • That means that you need 10 bits in the converter, and the the count in the counter/register will run from 0 to 1023.
  • And that leads us to observe that real converters often go to 10.23v, not 10v because that gives perfect .01v increments between resolvable voltages.
    • And another converter might run from -5.12v to +5.11v for the same reason.
      


AC Circuit Problem - Notes on an Operational Amplifier Circuit - with General Impedance Values