Inverting and Noninverting OpAmp Voltage Amplifier Circuits

Some texts describe the voltage gain of an inverting voltage amplifier as being a negative quantity. I tend not to look at things that way, treating all gains as positive quantities and relying on my knowledge of circuit behavior to tell whether the signal is inverted or not. In my teaching experience, I have found that students have a tendency to blindly follow equations rather than think about what it is they are calculating, and that strict adherence to the mathematical signs of gain values only encourages this undesirable behavior (Ïf the sign of the gain tells me whether the circuit is inverting or not, I can just multiply input voltage by gain and the answer will always be right!”).

This strategy is analogous to problem-solving in electromagnetics, where a common approach is to use math to solve for the absolute values of quantities (potential, induced voltage, magnetic flux), and then to use knowledge of physical principles (Lenz’ Law, right-hand rule) to solve for polarities and directions. The alternative - to try to maintain proper sign convention throughout all calculations - not only complicates the math but it also encourages students to over-focus on calculations and neglect fundamental principles.

Whether inverting amplifier gains are expressed as negative or positive quantities seems to be a matter of taste, from surveying introductory textbooks on the subject. I prefer to stick with absolute (positive) gain values and consider signal inversion separately.

Operational amplifier circuits provide a great opportunity to review basic concepts of DC circuits: voltage drops, polarity, current directions, Ohm’s Law, Kirchhoff’s Voltage Law, Kirchhoff’s Current Law, etc. This circuit is no exception. Emphasize the fact that a great many opamp circuits may be comprehensively analyzed merely with knowledge of these fundamental principles and the characteristics of an ideal opamp (zero input current, infinite open-loop gain, unlimited output voltage swing, zero voltage between input terminals when negative feedback is in effect).

Some students may arrive at the wrong gain figure because they blindly followed a formula with R₁ and R₂ shown as variables, plugging in this circuit’s values for R₁ and R₂ without considering which resistor is which (is R₁ the feedback resistor or is R₂?). This is by design, as I want students to learn to think about what they are doing rather than thoughtlessly follow instructions.