The term operational amplifier, abbreviated op amp, was coined in the 1940s to refer to a special kind of amplifier that, by proper selection of external components, can be configured to perform a variety of mathematical operations. Early op amps were made from vacuum tubes consuming lots of space and energy. Later op amps were made smaller by implementing them with discrete transistors. Today, op amps are monolithic integrated circuits, highly efficient and cost effective.
Before jumping into op amps, lets take a minute to review some amplifier fundamentals. An amplifier has an input port and an output port. In a linear amplifier, output signal = A × input signal, where A is the amplification factor or gain.
Depending on the nature of input and output signals, we can have four types of amplifier gain:
Since most op amps are voltage amplifiers, we will limit our discussion to voltage amplifiers.
Thevenin’s theorem can be used to derive a model of an amplifier, reducing it to the appropriate voltage sources and series resistances. The input port plays a passive role, producing no voltage of its own, and its Thevenin equivalent is a resistive element, Ri. The output port can be modeled by a dependent voltage source, AVi, with output resistance, Ro. To complete a simple amplifier circuit, we will include an input source and impedance, Vs and Rs, and output load, RL. Figure 1-1 shows the Thevenin equivalent of a simple amplifier circuit.
It can be seen that we have voltage divider circuits at both the input port and the output port of the amplifier. This requires us to re-calculate whenever a different source and/or load is used and complicates circuit calculations.
The Thevenin amplifier model shown in Figure 1-1 is redrawn in Figure 1-2 showing standard op amp notation. An op amp is a differential to single-ended amplifier. It amplifies the voltage difference, Vd = Vp - Vn, on the input port and produces a voltage, Vo, on the output port that is referenced to ground.
We still have the loading effects at the input and output ports as noted above. The ideal op amp model was derived to simplify circuit calculations and is commonly used by engineers in first-order approximation calculations. The ideal model makes three simplifying assumptions:
Applying these assumptions to Figure 1-2 results in the ideal op amp model shown in Figure 1-3.
Other simplifications can be derived using the ideal op amp model:
Because Ri = ∞, we assume In = Ip = 0. There is no loading effect at the input.
Because Ro = 0 there is no loading effect at the output.
If the op amp is in linear operation, V0 must be a finite voltage. By definition Vo = Vd × a. Rearranging, Vd = Vo / a . Since a = ∞, Vd = Vo / ∞ = 0. This is the basis of the virtual short concept.
The ideal voltage source driving the output port depends only on the voltage difference across its input port. It rejects any voltage common to Vn and Vp.
No frequency dependencies are assumed.
There are no changes in performance over time, temperature, humidity, power supply variations, etc.