The operational amplifier, commonly known as an op-amp, is a specially designed electronic circuit component. Its purpose is to work in conjunction with other circuit elements to execute a defined signal-processing operation. Consider an equivalent circuit model of an op-amp, as depicted in Figure 1; the output section comprises a voltage-controlled source in parallel with the output resistance R_o.

Figure 1: The equivalent circuit of the nonideal op-amp

Figure 1 shows that the input resistance R_i equates to the Thėvenin equivalent resistance observable at the input terminals. Similarly, the output resistance R_o corresponds to the Thėvenin equivalent resistance discernible at the output. The differential input voltage (v_d) is calculated as the difference between the noninverting terminal's voltage relative to the ground and the inverting terminal's voltage relative to the ground.

The op-amp discerns the difference between these two inputs and amplifies it by the gain A, thus generating a voltage that appears at the output. Here, A represents the open-loop voltage gain - named so because it signifies the gain of the op-amp in the absence of any external feedback from the output to the input.

Feedback is an integral concept to comprehend when studying op-amp circuits. Negative feedback can be achieved by feeding the output back to the op-amp's inverting terminal. When a feedback path from output to input exists, the resulting ratio of the output voltage to the input voltage is known as the closed-loop gain.

The op-amp does have its practical limitations. One such limitation is that the magnitude of its output voltage cannot surpass |V_CC|. Essentially, the power supply voltage determines and restricts the output voltage. Depending on the differential input voltage, the op-amp can function in one of three modes: positive saturation, linear region, or negative saturation. If an attempt is made to increase v_d beyond the linear range, the op-amp reaches saturation, yielding either v_o = V_CC or v_o = -V_CC.