How to determine the feedback resistor in negative feedback op-amp configuration ? How does the feedback resistor affect the signal output of op-amp ? What is the consequence of using high resistance or low resistance in feedback circuit ?
Answer
The transfer function of the inverting amplifier is
\$ V_{OUT} = -\dfrac{R_{feedback}}{R_{in}} \cdot V_{IN} \$
For the non-inverting amplifier it is
\$ V_{OUT} = \left(1 + \dfrac{R_{feedback}}{R_{g}}\right) \cdot V_{IN} \$
where \$R_g\$ is the resistor to ground.
So the gain is determined by a resistance ratio, where a higher feedback resistance gives a higher gain. About the choice for higher or lower resistance values: lower is better, because at higher resistances the input bias current may begin to play a role. But don't overdo it: if your inverting amplifier would have a 1 kΩ feedback resistor and you want a gain of 10 \$\times\$, then the input resistance should be 100 Ω, and that may be a bit too little for the signal source. So see how much current the source can supply, and calculate the feedback resistor from that.
The non-inverting amplifier doesn't have that problem: the input signal feeds directly to the high impedance of the non-inverting input. To minimize offset error you'll have to make the input impedances for both inputs equal, that means on the signal input a series resistance equal to \$R_{feedback}\$ and \$R_g\$ in parallel. Example: if the feedback resistor is 10 kΩ and \$R_g\$ 1 kΩ then place a 9.1 kΩ in series with the source.
By the way, that equal impedance rule also goes for the inverting amplifier. You'll often see the non-inverting input directly connected to ground, but again placing a resistor between the input and ground will reduce offset error. Again the resistance is the parallel of the other two resistors.
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