High input resistance and high gain Inverting amplifier can be needed in some applications.
In such case an even larger feedback resistor is required. Too large resistors have issues like precision, availability and excessive stray capacitance.
The here below circuit is a way to maintain both a high input resistance, a high gain and still using not too large feedback resistors.
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The inverting input of the opamp can be considered at virtual ground potential.
The R2 and Rg resistors are in parallel.
R2g= R2Rg/(R2+Rg) = 100/101.
Ro = R3 + R2g = 100 + 100/101 = 101k
Since the input is available at the junction of R2 and R3.
The gain can be evaluated as Av= Ro/R2g
2. Av = - 101/0.99 = -102
1. Rin in this case is R1 = 100k.
The inverting input of the opamp can be considered at virtual ground potential.
The R2 and Rg resistors are in parallel.
R2g= R2Rg/(R2+Rg) = 100/101.
Ro = R3 + R2g = 100 + 100/101 = 101k
Since the input is available at the junction of R2 and R3.
The gain can be evaluated as Av= Ro/R2g
2. Av = - 101/0.99 = -102
1. Rin in this case is R1 = 100k.
