Operational Amplifiers 1 Operational amplifiers are highly useful circuit building blocks. This is so because their behavior is nearly ideal over a wide range of operating conditions, and they can be used without worrying too much about the internal circuitry of the device. The symbol for an op amp is [op amp symbol diagram as described below] All the voltages above are defined with respect to a common or ground connection not shown in the figure. Op amps are an active device in the sense that the output voltage is created by using the power supplies +V and -V to drive the output v₀ to some desired level. Meanwhile, the inverting and noninverting input terminals draw almost no input. Diagram Description: The diagram in the center of the page depicts the standard symbol for an operational amplifier: A triangle pointing to the right, with two input terminals on the left and one output terminal on the right. The top input terminal is labeled with a "-" sign (inverting input) and is connected to a voltage source labeled "V-". The bottom input terminal is labeled with a "+" sign (noninverting input) and is connected to a voltage source labeled "V+". The output terminal on the right is connected to a voltage source labeled "v₀" (output voltage). The triangle also has two additional terminals, one at the top labeled "+V" (positive power supply) and one at the bottom labeled "-V" (negative power supply). Current (on the order of nA or less) 2 and thus require almost no input power. A circuit equivalent for the op amp is [circuit diagram as described below] Here the output voltage is modeled as generated by a dependent voltage source. That is, v₀ = a(v₊ - v₋) (1) That is, the output voltage is given by the differential input voltage v₊ - v₋ multiplied by a scale factor a. The internal circuitry which accomplishes this is fascinating, but we will not go into that in these notes. Now, we switch to a finite-gain model (i.e) for the noninverting amplifier [Circuit diagram as described below] The voltage divider result is the same as before: v₋ = v₀ R₁/(R₁ + R₂). Also, v₊ = vᵢ; and v₀ = a(v₊ - v₋). The block diagram which goes with this is [Block diagram as described below] Via Black's formula, we have v₀/vᵢ = a / (1 + a R₁/(R₁ + R₂)) = a / (R₁ + R₂)/(R₁(R₁ + R₂ + a)) = (R₁ + R₂)/R₁ * (a/(R₁ + R₂ + a)) = (R₁ + R₂)/R₁ * (a/(R₁ + R₂ + a)) (2) = (R₁ + R₂)/R₁ * (a/(R₁ + R₂ + a)) Ideal C.L. gain nonideal gain term < 1 (approaches 1 as a→∞)

Op-Amp Notes

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