Equivalent Circuit of an Op-Amp

Figure 1 shows an equivalent circuit of an op-amp. This circuit includes important values from the data sheets: A, R_in, and R_out. Note that AV_id is an equivalent Thevenin voltage source, and R_o is the Thevenin equivalent resistance looking back into the output terminal of an op-amp.

The equivalent circuit is useful in analyzing the basic operating principles of op-amps and in observing the effects of feedback arrangements. For the circuit shown in Figure 1, the output voltage is

V_o = AV_id = A(V₁ - V₂)    _________________  (1)

where A = large signal voltage gain

         V_id = difference input voltage

         V₁ = voltage at the non-inverting input terminal with respect to ground

         V₂ = voltage at the inverting terminal with respect to ground

Equation (1) indicates that the output voltage V_o is directly proportional to the algebraic difference between the two input voltages. In other words, the op-amp amplifies the difference between the two input voltages. In other words, it does not amplify the input voltages themselves. For this reason the polarity of the output voltage depends on the polarity of the difference voltage.

Ideal Voltage Transfer Curve

Equation (1) is the basic op-amp equation, in which the output offset voltage is assumed to be zero. This equation is useful in studying the op-amp's characteristics and in analyzing different circuit configurations that employ feedback. The graphic representation of this equation is shown in Figure 2, where the output voltage V_o is plotted against input difference V_id, keeping gain A constant.

Note, however, that the output voltage cannot exceed the positive and negative saturation voltages. These saturation voltages are specified by an output voltage swing rating of the op-amp for given values of supply voltages. This means that the output voltage is directly proportional to the input difference voltage only until it reaches the saturation voltages and that thereafter output voltage remains constant, as shown in Figure 2.

The curve shown in Figure 2 is called as an ideal voltage transfer curve, ideal because output offset voltage is assumed to be zero. In normal op-amp use (with negative feedback), this voltage is near zero and is ignored for simplicity of calculation. Notice that the curve is not drawn to scale. If drawn to scale, the curve would be almost vertical because of the very large values of A.