# Buffer Opamp Amplifier

A unity gain buffer amplifier is implemented using an opamp in a negative feedback configuration. The output is connected to its inverting input, and the signal source is connected to the non-inverting input. Although its voltage gain is 1 or unity, it has high current gain, high input impedance and low output impedance. It is used to avoid loading of the signal source.

The output voltage of the op-amp is given by the equation: $$V_{out} = {A_{OL} \, (V_{\!+} - V_{\!-})}$$ where V+ is the voltage at the non-inverting terminal, V− is the voltage at the inverting terminal and AOL is the open-loop gain of the amplifier.

Re-arrange the equation $${V_{out} \over A_{OL}} = V_{\!+} - V_{\!-}$$

If we assume that AOL is ∞, then $${V_{out} \over A_{OL}} = 0$$ and substituting equation 3 into equation 2, we obtain $$V_- = V_+$$ For negative feedback opamp circuits only, we use equation 4 to simplify the analysis of the circuits.

For this buffer amplifier, using equation 4, we can by inspection obtain $$V_{out} = V_- = V_+ = V_{in}$$ and derive the gain of the buffer opamp amplifier $$V_{out} = V_{in}$$

# Non Inverting Opamp Amplifier

The non inverting opamp amplifer provides voltage gain. The buffer amplifier can be considered as special case of this amplifer with Rf = 0 and Rg = ∞.

If we let the input current to the inverting input I- = 0 and apply KVL to the Vout, Rf and Rg loop $$V_- = {V_{out}} {{R_g }\over {R_f + R_g}}$$ Applying equation 4, $$V_{in} = V_+ = V_- = {V_{out}} {{R_g }\over {R_f + R_g}}$$ Re-arrange the equation to obtain the gain of the non inverting opamp amplifer $$V_{out} = (1 + {{R_f }\over {R_g}}) {V_{in}}$$

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