A state variable filter is a type of
active filter
An active filter is a type of analog circuit implementing an electronic filter using active components, typically an amplifier. Amplifiers included in a filter design can be used to improve the cost, performance and predictability of a filter.
...
in electronic circuits. It consists of one or more
integrator
An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output.
Integration is an importan ...
s, connected in some feedback configuration. It is essentially used when precise
Q factor
In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy los ...
is required, as other multi-order filters are unable to provide. The most common implementation sums the input signal with its integral and its double integral, another is an MDAC based implementation.
Kerwin–Huelsman–Newcomb (KHN) biquad filter example
The example given below can produce simultaneous
lowpass
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter ...
,
highpass
A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency d ...
, and
bandpass
A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range.
Description
In electronics and signal processing, a filter is usually a two-po ...
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 orders are possible with more integrators (i.e., more states).
The signal input is marked V
in; the LP, HP and BP outputs give the lowpass, highpass, and bandpass filtered signals respectively.
[''Introduction to Operational Amplifier Theory and Applications'', Wiate, Huelsman & Korn, McGraw Hill,1975]
For simplicity, we set:
:
:
:
Then:
:
:
The pass-band gain for the LP and HP outputs is given by:
:
It can be seen that the frequency of operation and the
Q factor
In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy los ...
can be varied independently. This and the ability to switch between different filter responses make the state-variable filter widely used in analogue
synthesizers
A synthesizer (also spelled synthesiser) is an electronic musical instrument that generates audio signals. Synthesizers typically create sounds by generating waveforms through methods including subtractive synthesis, additive synthesis and ...
.
Values for a resonance frequency of 1 kHz are R
f1 = R
f2 = 10k, C
1 = C
2 = 15nF and R
1 = R
2 = 10k.
Applications
State variable filters are frequently used for modifying frequency response in
audio signal
An audio signal is a representation of sound, typically using either a changing level of electrical voltage for analog signals, or a series of binary numbers for digital signals. Audio signals have frequencies in the audio frequency range of r ...
processing. At low Q settings they are often used in
parametric equaliser
Equalization, or simply EQ, in sound recording and reproduction is the process of adjusting the volume of different frequency bands within an audio signal. The circuit or equipment used to achieve this is called an equalizer.
Most hi-fi eq ...
circuits, and at high or variable Q settings to create resonant filter modules in analog synthesizers. For manual control of frequency, Rf1 and Rf2 in the section above may be replaced by a dual potentiometer; and for voltage control, the devices U2 and U3 may be replaced by
voltage controlled amplifier
A variable-gain (VGA) or voltage-controlled amplifier (VCA) is an electronic amplifier that varies its gain depending on a control voltage (often abbreviated CV).
VCAs have many applications, including audio level compression, synthesizers and am ...
s or operational
transconductance Transconductance (for transfer conductance), also infrequently called mutual conductance, is the electrical characteristic relating the current through the output of a device to the voltage across the input of a device. Conductance is the reciproca ...
amplifiers.
See also
*
Linear filter
Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using ...
*
Biquad filter
References
{{Reflist
* Texas Instruments
UAF42 Universal Active Filterdatasheet
* Analog Device
Linear filters