In previous videos, we explored the characteristics of an ideal operational amplifier, and then we introduced negative feedback as a technique that allows us to design high-performance amplifier circuits using nonideal real-life op-amps.
Op-amps are versatile and can be incorporated into a wide variety of interesting and creative circuits. However, sometimes all we need to do is increase the amplitude of a signal, and for these applications, we have the basic op-amp non-inverting amplifier configuration. This simple topology consists of one op-amp and two resistors connected as follows:
When we say that this circuit is “non-inverting,” we mean that it applies a positive gain to the input signal. If you connect a steady voltage to the input terminal, the output voltage will be equal to the input voltage multiplied by some number, with no change in polarity. If you apply a sinusoidal signal to the input terminal, the op-amp will increase the amplitude of the signal without creating a 180° phase difference.
Non-inverting operation is achieved by connecting the input signal to the op-amp’s non-inverting input terminal. The gain is determined almost completely by the two resistors, which form a feedback network connected between the op-amp’s output and its negative input terminal.
As you may recall from the video on negative feedback, the open-loop gain of the op-amp is not infinite, and therefore it does influence the closed-loop gain (G_{CL}), but in practice the effect is small enough to be negligible. Thus, we can safely express the gain of the non-inverting amplifier as follows:
When we are trying to transfer voltage from one subcircuit to another, the subcircuit that generates the signal should have low output impedance and the subcircuit that receives the signal should have high input impedance. One notable advantage of the non-inverting amplifier is that it has very high input impedance, because the input signal is connected directly to the op-amp’s input terminal. This is not the case with the inverting configuration, which is discussed in the next video tutorial.
In the video on negative feedback, we learned that the closed-loop gain of a negative-feedback amplifier is approximately equal to the inverse of the feedback factor:
If you treat R_{1} and R_{2} as a resistive-divider feedback network, you can use this relationship between G_{CL} and β to derive the expression for the gain of the non-inverting amplifier; this technique is briefly demonstrated in the tutorial on negative feedback. In this video, we’ll find the gain using typical circuit analysis.
The input voltage V_{IN} is applied to the non-inverting input terminal, and the virtual short assumption allows us to transfer this input voltage directly to the inverting input terminal.
V_{IN} at the inverting input terminal generates a current of V_{IN}/R_{1} flowing toward ground.
We assume that no current flows into or out of the op-amp’s input terminals, and consequently, the current flowing through R_{2} must be equal to the current flowing through R_{1}: I_{R2} = V_{IN}/R_{1}. This current is flowing away from the op-amp’s output terminal.
The voltage drop across R_{2} is I_{R2} × R_{2} = (V_{IN}R_{2})/R_{1}.
Since the lower-voltage terminal of R_{2} is connected to the inverting input terminal, the output voltage is equal to V_{IN} plus the voltage across R_{2}: V_{OUT} = V_{IN} + (V_{IN}R_{2})/R_{1} = V_{IN}(1 + R_{2}/R_{1}).
by Robert Keim
by Jake Hertz