Electronic filter topology
Common types of linear filter transfer function are; high-pass, low-pass, bandpass, band-reject or notch and all-pass.
Implementations such as electronic mixers and stereo sound may require arrays of identical circuits.
The chart at the bottom of the page shows these various topologies in terms of general constant k filters.
Filters designed using network synthesis usually repeat the simplest form of L-section topology though component values may change in each section.
Ladder topology, often called Cauer topology after Wilhelm Cauer (inventor of the elliptic filter), was in fact first used by George Campbell (inventor of the constant k filter).
A ladder network consists of cascaded asymmetrical L-sections (unbalanced) or C-sections (balanced).
In low pass form the topology would consist of series inductors and shunt capacitors.
Image filter design commonly uses modifications of the basic ladder topology.
These topologies, invented by Otto Zobel,[1] have the same passbands as the ladder on which they are based but their transfer functions are modified to improve some parameter such as impedance matching, stopband rejection or passband-to-stopband transition steepness.
Usually the design applies some transform to a simple ladder topology: the resulting topology is ladder-like but no longer obeys the rule that shunt admittances are the dual network of series impedances: it invariably becomes more complex with higher component count.
It is possible to generalise the m-type topology for filters with more than one passband using parameters m1, m2, m3 etc., which are not equal to each other resulting in general mn-type[2] filters which have bandforms that can differ in different parts of the frequency spectrum.
It is, however, a rarely used design due to increased component count and complexity as well as its normally requiring basic ladder and m-type sections in the same filter for impedance matching reasons.
The higher component and section count of these designs usually limits their use to equalisation applications.
Topologies usually associated with constant resistance filters are the bridged-T and its variants, all described in the Zobel network article; The bridged-T topology is also used in sections intended to produce a signal delay but in this case no resistive components are used in the design.
The elementary feedback topology is based on the simple inverting amplifier configuration.
A diagram of the circuit topology for a second order low pass filter is shown in the figure on the right.
Hence, usually the term biquad refers to the two-integrator-loop state variable filter topology.
For example, the basic configuration in Figure 1 can be used as either a low-pass or bandpass filter depending on where the output signal is taken from.
The Sallen-Key design is a non-inverting second-order filter with the option of high Q and passband gain.
