Multiple feedback topology (electronics)

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:

:$H(s)\; =\; frac\{V\_o\}\{V\_i\}\; =\; -frac\{1\}\{As^2+Bs+C\}\; =\; frac\{K\; omega^\{2\}\_\{0\{s^\{2\}+frac\{omega\_\{0\{Q\}s+omega^\{2\}\_\{0$.

In an MF filter,:$A\; =\; (R\_1R\_3C\_2C\_5),$:$B\; =\; R\_3C\_5+R\_1C\_5+R\_1R\_3C\_5/R\_4,$:$C\; =\; R\_1/R\_4,$

:$Q\; =\; frac\{\; sqrt\{R\_3\; R\_4\; C\_2\; C\_5\}\; \}\{\; (\; R\_4\; +\; R\_3\; +\; K\; R\_3\; )\; C\_5\; \}$ 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

References

* [http://www.analog.com/UploadedFiles/Application_Notes/447952852AN-649_0.pdf Using the Analog Devices Active Filter Design Tool Application]
* [http://focus.ti.com/lit/an/slyt143/slyt143.pdf "Fully differential amplifiers applications"] by Jim Karki 2001