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I am looking for the transfer function of the filter below :

MFB Filter with Reference voltage

This is a multiple feedback second order analog filter, I was already able to calculate the transfer function of the filter without VRef in the positive pin of the op-amp, but I couldn't find it with Vref.

Can anyone give me the transfer function of this filter or maybe a tip on how to calculate it ? Also how does it affect the offset is it added directly to the output?

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A DC bias voltage Vref is applied (instead of grounding the non-inv. input node) to establish a suitable bias point at the opamp output that is NOT zero volts. This is necessary in case of single supply only.

On the other hand, the transfer function of the whole circuit concerns the ac response only - independent on the supply voltage and the chosen dc bias point.

Hence, there is no influence of Vref on the transfer function.

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  • \$\begingroup\$ How would it affect the DC voltage? is it added directly to the output? for example if i have Vin as a DC voltage will Vout be equal (DC Gain*Vin +Vref)? \$\endgroup\$
    – L. Lt.
    Commented Jan 31, 2018 at 8:33
  • \$\begingroup\$ The voltage Vref appears at the outpiut multiplied with the dc gain (referenced to the non-inv. input): Vout, ref= Vref*(1+R3/R1). This holds as long as the signal voltage has a DC path to ground. If the signal is applied through a large capacitor, this factor reduces to unity. \$\endgroup\$
    – LvW
    Commented Jan 31, 2018 at 10:07

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