Non investing op amp gain derivation

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As we saw with voltage dividers, we need to take a circuit's impedance into account when using it as part of a larger system of circuits. We need each successive circuit stage to have an input impedance at least 10 times greater than the output of the one preceeding it, to prevent loading. Since the inverting amplifier's input impedance is equal to R1, there may be times we'd be forced to pick unusually large resistors for our feedback loop, which can cause other problems.

The solution to our impedance worries lie in the Non-Inverting Amplifier, also made with an op-amp and negative feedback: Here, the signal in goes directly into the non-inverting input, which has a nearly infinite input impedance -- perfect for coupling with any previous stage. Also, the output impedance of the op-amp is nearly zero, which is ideal for connecting with whatever comes next in the circuit.

In an ideal condition, the input pin of the op-amp will provide high input impedance and the output pin will be in low output impedance. The amplification is dependent on those two feedback resistors R1 and R2 connected as the voltage divider configuration.

Due to this, and as the Vout is dependent on the feedback network, we can calculate the closed loop voltage gain as below. Also, the gain will be positive and it cannot be in negative form. The gain is directly dependent on the ratio of Rf and R1. Now, Interesting thing is, if we put the value of feedback resistor or Rf as 0, the gain will be 1 or unity.

And if the R1 becomes 0, then the gain will be infinity. But it is only possible theoretically. In reality, it is widely dependent on the op-amp behavior and open-loop gain. Op-amp can also be used two add voltage input voltage as summing amplifier. Practical Example of Non-inverting Amplifier We will design a non-inverting op-amp circuit which will produce 3x voltage gain at the output comparing the input voltage.

We will make a 2V input in the op-amp. We will configure the op-amp in noninverting configuration with 3x gain capabilities. We selected the R1 resistor value as 1. R2 is the feedback resistor and the amplified output will be 3 times than the input. Voltage Follower or Unity Gain Amplifier As discussed before, if we make Rf or R2 as 0, that means there is no resistance in R2, and Resistor R1 is equal to infinity then the gain of the amplifier will be 1 or it will achieve the unity gain.

As there is no resistance in R2, the output is shorted with the negative or inverted input of the op-amp. As the gain is 1 or unity, this configuration is called as unity gain amplifier configuration or voltage follower or buffer.

As we put the input signal across the positive input of the op-amp and the output signal is in phase with the input signal with a 1x gain, we get the same signal across amplifier output. Thus the output voltage is the same as the input voltage. So, it will follow the input voltage and produce the same replica signal across its output. This is why it is called a voltage follower circuit. The input impedance of the op-amp is very high when a voltage follower or unity gain configuration is used.

Sometimes the input impedance is much higher than 1 Megohm. So, due to high input impedance, we can apply weak signals across the input and no current will flow in the input pin from the signal source to amplifier. On the other hand, the output impedance is very low, and it will produce the same signal input, in the output.