COMPUTING

and since v C ( 0 − ) = 0 , from (5.48)V out ( s) = – sR f CV in ( s)orSumming and Averaging Op Amp CircuitsV out ( s)------------------ = – s RV in ( s)f Cc. With s = jω , the transfer function can be expressed in magnitude and phase form asV out ( jω)--------------------- = – j ωRV in ( jω)f CV---------- out = ωR f CV inθ = – 90°V---------- outV in f = 1 KHzand the phase angle is –90°= 2π × 10 3 × 10 6 × 10 – 9 = 2π × 10 3 × 10 – 3 = 2πat all frequencies.d. As f → ∞ , the capacitor behaves as a short circuit and so with the addition of a resistor R 1 inseries with the capacitor, the closed loop voltage gain isG v = – R f ⁄ R 1and with = 1 MΩ , for a gain of 100 , R 1 = 10 KΩ .R fG v5.14 Summing and Averaging Op Amp CircuitsThe circuit of Figure 5.60 shows the basic inverting summing and averaging op amp circuit.+v in1−+v in2−R 1R 2+v inN−R Ni 1i 2i Nii−+R f+v out−Figure 5.60. Basic inverting summing and averaging op amp circuitElectronic Devices and Amplifier Circuits with MATLAB Computing, Second EditionCopyright © Orchard Publications5−37