THEORY 
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 (R_{2}) to the input resistor (R_{1}).

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, V_{out}, with zero input voltage. Since
the differential input is zero, the full input voltage must appear across
R_{1}, making the current in R_{1}:
I_{in} = Vin / R_{1}
Also, since there is no current flow into either input terminal because
the input impedance is infinite, the current I_{in} must also flow
in R_{2}. Therefore, if the current through R_{2}
(the feedback resistor) is I_{f}:
I_{f }= I_{in
}and
I_{f} = V_{out} / R_{2 } (due to inversion)
Then: V_{out} / R_{2 } =
Vin / R_{1}
Gain = V_{out}/V_{in} = R_{2}/R_{1}
Choose R_{3} = R_{1 } R_{2}

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 R_{f
}
R_{in} 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 = (R_{in} + R_{f}) / R_{in}
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.
R_{5} = R_{1}  R_{2}  R_{3}
 R_{4}

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
R_{2}/R_{1} = R_{4}/R_{3} =
a
then V_{out} = a
(V_{2}  V_{1})

Simple
Low Pass Filter: 

This filter will have a 6 dB per octave rolloff after a closedloop
3 dB point defined by the parallel resistorcapacitor 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.



