- State variable filter
A

**state variable filter**is a type ofactive filter . It consists of one or moreintegrator s, connected in some feedback configuration. AnyLTI system can be described as a state-space model, with n state variables for an nth-order system. A state variable filter realizes the state-space model directly. The instantaneous output voltage of one of the integrators corresponds to one of the state-space model's state variables.**Kerwin-Huelsman-Newcomb (KHN) Biquad Filter Example**The example given below can produce simultaneous

lowpass ,highpass andbandpass outputs from a single input. This is a second-order (biquad) filter. Its derivation comes from rearranging a high-pass filter's transfer function, which is the ratio of two quadratic functions. The rearrangement reveals that one signal is the sum of integrated copies of another. That is, the rearrangement reveals a state variable filter structure. By using different states as outputs, different kinds of filters can be produced. In more general state variable filter examples, additional filter order is possible with more integrators (i.e., more states).The signal input is marked Vin; the LP, HP and BP outputs give the lowpass, highpass and bandpass filtered signals respectively.

For simplicity, we set:

$R\_\{f1\}\; =\; R\_\{f2\}$

$C\_1\; =\; C\_2$

$R\_1=R\_2$

Then:

$F\_0\; =\; frac\{1\}\{2pi\; R\_\{f1\}C\_1\}$

$Q\; =\; left(1\; +\; frac\{R\_4\}\{R\_q\}\; ight)left(frac\{1\}\{2+frac\{R\_1\}\{R\_g\; ight)$

The pass-band gain for the LP and HP outputs is given by:

$A\_\{HP\}\; =\; A\_\{LP\}\; =\; frac\{R\_1\}\{R\_G\}$

It can be seen that the frequency of operation and the

Q factor can be varied independently. This and the ability to switch between different filter responses make the state-variable filter widely used in analoguesynthesizers .Values for a resonance frequency of 1 kHz are Rf1=Rf2=10k, C1=C2=15nF and R1=R2=10k

**ee also***

Linear filter

*Biquad filter **References*** Texas Instruments' [

*http://focus.ti.com/lit/ds/symlink/uaf42.pdf UAF42 Universal Active Filter*] datasheet* Analog Devices [

*http://www.analog.com/Analog_Root/static/techSupport/designTools/interactiveTools/filter/filter.html Interactive Design Tools*]

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**State variable topology**— refers to filters with two pole filter topology. State variable filters are available in lowpass, highpass, bandpass, and notch versions. The notch version is not recommended, because it requires too many amplifiers. It is one of three topologies … Wikipedia**State variable**— A state variable is an element of the set of variables that describe the state of a dynamical system.In case of simple mechanical systems, position coordinates and their derivates are typical state variables. Temperature, pressure, internal… … Wikipedia**Electronic filter topology**— An elementary filter topology introduces a capacitor into the feedback path of an op amp to achieve an unbalanced active implementation of a low pass transfer function Electronic filter topology defines electronic filter circuits without taking… … Wikipedia**Biquad filter**— For the digital implementation of a biquad filter, check digital biquad filter. A biquad filter is a type of linear filter that implements a transfer function that is the ratio of two quadratic functions. The name biquad is short for biquadratic … Wikipedia**Kalman filter**— Roles of the variables in the Kalman filter. (Larger image here) In statistics, the Kalman filter is a mathematical method named after Rudolf E. Kálmán. Its purpose is to use measurements observed over time, containing noise (random variations)… … Wikipedia**Digital filter**— A general finite impulse response filter with n stages, each with an independent delay, di, and amplification gain, ai. In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a… … Wikipedia**Electronic filter**— Electronic filters are electronic circuits which perform signal processing functions, specifically intended to remove unwanted signal components and/or enhance wanted ones. Electronic filters can be:*passive or active *analog or digital *discrete … Wikipedia**Active filter**— An active filter is a type of analog electronic filter, distinguished by the use of one or more active components i.e. voltage amplifiers or buffer amplifiers. Typically this will be a vacuum tube, transistor or operational amplifier.Active… … Wikipedia**Extended Kalman filter**— In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about the current mean and covariance. The EKF is often considered the de facto standard in the theory of nonlinear state… … Wikipedia**Mu-tron**— Musitronics, often shortened to Mu tron, was a manufacturer of electronic musical effects active in the 1970s. Their product line focused on filtering and processing effects derived from synthesizer components. Among their most well known… … Wikipedia