Operational Amplifier• The operational amplifier circuit first came

into existence as a basic building block in analog computers. I t was referred to as operational because it was used to implement the mathematical operations of integration, differentiation, addition,sign changing, and scaling.

• The operational amplifier is widely known as the op amp.

• Here we shall study the terminal behavior of the op-amp

The terminals of primary interest are• inverting input• noninverting input• output• positive power supply (V+)• negative power supply (V~)The remaining three terminals are of little or no concern.

Terminal Voltages and Currents

The voltage variables are measuredfrom a common reference node.All voltages are considered as voltage rises from the common node.This convention is the same as that used in the node-voltage method ofanalysis. A positive supply voltage (Vcc) is connected between V+ and thecommon node. A negative supply voltage (—Vcc) is connected between V- and the common node. The voltage between the inverting input terminaland the common node is denoted vn. The voltage between the noninvertinginput terminal and the common node is designated as vp. The voltagebetween the output terminal and the common node is denoted vo

Terminal current variables.• Note that all the current reference directions are into the

terminals of the operational amplifier: in is the current into the inverting input terminal; ip is the current into the noninverting input terminal; ia is the current into the output terminal; ic + is the current into the positive power supply terminal;and ic- is the current into the negative power supply terminal.

When op amp is operating linearly, the op amp's output voltage is equal to the difference in its input voltages times the multiplying constant,or gain, A

• In linear operating region the constraint on the input voltages of the op amp is vp=vn

• this is obtained by feeding a signal back from the output terminal to the inverting input terminal.

• This configuration is known as negative feedback because the signal fed back from the output subtracts from the input signal.

• If a circuit containing an op amp does not provide a negative feedback path from the op amp output to the inverting input, then the op amp will normally saturate.

Current constraint is ip = in = 0 (1)From Kirchhoff's current law we know that the sum of the currents entering the operational amplifier is zero, or (2) Substituting the constraint given by Eq. 1 into Eq. 2 gives

The Inverting-Amplifier Circuit