Operational Amplifiers
The name operational amplifier was originally adopted for a series of high performance DC amplifiers used in analog computers.  These amplifiers were used to perform mathematical operations applicable to analog computation such as summation, scaling, subtraction, integrating, etc. - essentially any feedback operation.  The applications of operational amplifiers has become so widely diversified that this original terminology is inappropriate since Op Amps are now used as a basic building block for phase shifting, filtering, signal conditioning, multiplexing, detecting, etc.

Since op amps are designed for use in a feedback loop, the ideal op amp would have the following characteristics. 

Equivalent Circuit for an Ideal Operational Amplifier

Two very important concepts follow from these basic characteristics:
Since the voltage gain is infinite, any output signal developed will be the result of an infinitesimally small input signal.  Therefore:
1.  The differential input voltage is zero.
Also, if the input resistance is infinite:
2.  There is no current flow into either input terminal.
These two properties are the basics for op amp circuit analysis and design.

Unfortunately the cost of production of an ideal op amp would be extremely high.  Real amplifiers, especially those made of integrated circuits, are very good engineering approximations to these standards.

      Labelling of Integrated Circuits:
ICs are distinctively labelled to ease identification and placement.  The markings on two of the operational amplifiers used in this lab are shown on the left.  They are typical ICs in their labelling.  The markings are read as follows.  The dot near a pin or a notch in the end of the package identifies Pin 1.  This ensures that ICs are correctly mounted in a circuit.  Pin numbers proceed counterclockwise from Pin 1.

Two sets of numbers also appear on each IC.  The four digit number is a manufacturer reference indicating the year and month the IC was fabricated (top right corner on diagram).  The longer alphanumeric value indicates, from left to right:  manufacturer (one or two letters), and the part number.   This latter may also include letters as well as numbers.  For example, digital IC families might be something like SN75xxx where the SN means a particular manufacturer and the 74 represents a family of TTL logic circuits.  The 'xxx' would be two or three more digits depending on the logic function.  Op amps have a slightly different and less consistent numbering system.

Common Amplifier Circuits
The operational amplifier is used in many applications.  A few common ones are shown below. 
      Inverting Amplifier:
One of the most common applications is the simple inverting amplifier.  The output is inverted, and the gain is determined by the ratio of the feedback resistor (R2) to the input resistor (R1). 
We can use the two ideal op amp properties discussed above to analyze this circuit.  Since the amplifier has infinite gain, it will develop its output voltage, Vout, with zero input voltage.  Since the differential input is zero, the full input voltage must appear across R1, making the current in R1:
Iin = Vin / R1
Also, since there is no current flow into either input terminal because the input impedance is infinite, the current Iin must also flow in R2.  Therefore, if the current through R2 (the feedback resistor) is If:
    If = Iin          and         
If = -Vout / R (due to inversion)
Then:     -Vout / R = Vin / R1
   Gain = Vout/Vin = -R2/R1

   Choose  R3 = R1 || R2

      Noninverting Amplifier:
Another common configuration is the noninverting amplifier, where the output signal is not inverted.  In this circuit, the input voltage is applied to the positive input of the op amp, and a fraction of the output signal is applied to the negative input from the Rf - Rin voltage divider.  Using the same principles that were used to derive the gain equation for the inverting amplifier, the gain of the noninverting amplifier is:
Gain = (Rin + Rf) / Rin
Note:  Is = 0, Es = 0, SP (Summing Point) is at zero potential
           SP is a virtual ground
      Summing Amplifier:
This is a special case of the inverting amplifier, as it gives an inverted output which is equal to the weighted algebraic sum of all inputs.  If the input resistors, and the feedback resistor are chosen to be equal, the output is simply the negative sum of the inputs.  Since there is no interaction between inputs, the operations of summing and weighting is very easily done.
R5 = R1 || R2 || R3 || R4
      Difference Amplifier:
The difference amplifier is the complement of the summing amplifier and allows the subtraction of two voltages or, as a special case, the cancellation of a signal common to the two inputs.  If
R2/R1 = R4/R3 = a           then     Vout = a (V2 - V1)
      Simple Low Pass Filter:
This filter will have a 6 dB per octave roll-off after a closed-loop 3 dB point defined by the parallel resistor-capacitor from output to input.  At frequencies will above the corner, this circuit may be considered as an AC integrator;  however, the time domain response is that of a single RC rather than an integral.

      Simple High Pass Filter:
The low pass filter can be easily converted to a high pass filter by putting the capacitor in series with the input resistance.  In this case:

      Basic Comparator:
A comparator is a special type of op amp that is used to compare the voltages of the two inputs.  A basic comparator circuit is operated without a feedback loop. 

When one input of the comparator is at a reference potential, the output will indicate whether the unknown voltage at the other input is higher or lower than the reference.