Difference amplifier

                           RF
                               
                     .---|     |----.                       
                     |      VCC     |         
                     |       |      |         
               Ri    |   |\  |      |          
                     |   |  \|      |            
      V1 ----|     |-+---|-   \     |              
                         |      >---+--- VO
      V2 ----|     |-+---|+   /                    
               Ri    |   |  /|                   
                    | |  |/  |                 
                 RF | |      |
                    | |    -VCC
                     |
                     |  
0 V -----------------+-----------------------o

As the name implies, this amplifier amplifies the difference between two signals. The output from the amplifier is proportional to the difference between its two inputs, multiplied by the gain, until saturation occurs. Note that there are two resistors marked R_F, and two marked R_i. The ratio of these two resistor pairs must be equal for the amplifier to work properly. It's usually easiest just to make both R_Fs the same value, and the same for the R_is.

The equations for this one are:

        VO        RF
AV = --------- = ----
     (V2 - V1)    Ri

      RF
VO = ---- * (V2 - V1) = AV * (V2 - V1)
      Ri

For example, let's say that V₁ and V₂ are 4 and 4.5 volts respectively. Make R_F a 100 KΩ (100 * 10³ ohms) resistor and R_i a 25 KΩ. The voltage gain (A_V) of the amplifier is therefore 100 / 25 = 4. The output voltage is 4 * (4.5 - 4) = 4 * 0.5 = 2 V.

A special case of this is the comparator, which is essentially a difference amplifier with a gain such that any difference between the two signals immediately results in either positive or negative saturation, depending on which signal is greater.

This amplifier is used in proportional control systems. One example might be a satellite aerial rotator using a potentiometer mounted on the aerial's base as one input, and a second potentiometer as the other input. In this sytem, it would be useful to be able to both rotate the aerial quickly, and also to rotate it with reasonable accuracy. With a difference amplifier, the greater the difference between the inputs the higher the output voltage.

If both pots started in the middle of their travel, and the controlling pot was turned to its maximum, the motor rotating the aerial would start turning at high speed, growing slower as the positions of the two pots became closer. If the controlling pot was now turned slowly, the motor would turn in such a way that the aerial smoothly tracked the controllor's movements.

Compare this to a digital system where the motor was either on or off, perhaps using a comparator. On turning the controlling pot, the motor would immediately start turning at max speed until the pot on the aerial base had the same value as the controller. The motor would immediately stop, but momentum would probably carry the aerial slightly further, causing the motor to turn back on in the opposite direction to compensate. Accurate smooth tracking would be impossible as slow movement of the controller would result in jerky pulses of the motor. (This is also known as a bang-bang control system.)

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