Multiple feedback topology (electronics)

Multiple feedback topology circuit.

Multiple feedback topology is an electronic filter topology which is used to implement an electronic filter by adding two poles to the transfer function. A diagram of the circuit topology for a second order low pass filter is shown in the figure on the right.

The transfer function of the multiple feedback topology circuit, like all second-order linear filters, is:

$H(s)={\frac {V_{o}}{V_{i}}}=-{\frac {1}{As^{2}+Bs+C}}={\frac {K\omega _{0}^{2}}{s^{2}+{\frac {\omega _{0}}{Q}}s+\omega _{0}^{2}}}$.

In an MF filter,

$A=(R_{1}R_{3}C_{2}C_{5})\,$

$B=R_{3}C_{5}+R_{1}C_{5}+R_{1}R_{3}C_{5}/R_{4}\,$

$C=R_{1}/R_{4}\,$

$Q={\frac {\sqrt {R_{3}R_{4}C_{2}C_{5}}}{(R_{4}+R_{3}+|K|R_{3})C_{5}}}$ is the Q factor.

$K=-R_{4}/R_{1}\,$ is the DC voltage gain

$\omega _{0}=2\pi f_{0}=1/{\sqrt {R_{3}R_{4}C_{2}C_{5}}}$ is the corner frequency

Further reading

• Using the Analog Devices Active Filter Design Tool Application
• "Fully differential amplifiers applications" by Jim Karki 2001