- All-pass filter
An all-pass filter is an
electronic filterthat passes all frequencies equally, but changes the phase relationship between various frequencies. It does this by varying its propagation delaywith frequency. Generally, the filter is described by the frequency at which the phase shift crosses 90° (i.e., when the input and output signals go into quadrature— when there is a quarter wavelengthof delay between them).
They are generally used to compensate for other undesired phase shifts that arise in the system, or for mixing with an unshifted version of the original to implement a notch
They may also be used to convert a mixed phase filter into a
minimum phasefilter with an equivalent magnitude response or an unstable filter into a stable filter with an equivalent magnitude response.
Active analog implementation
operational amplifiercircuit shown in Figure 1 implements an active all-pass filter with the transfer function:which has one pole at -1/RC and one zero at 1/RC (i.e., they are "reflections" of each other across the imaginary axis of the complex plane). The magnitude and phase of H(iω) for some angular frequencyω are:As expected, the filter has unity- gainmagnitude for all ω. The filter introduces a different delay at each frequency and reaches input-to-output " quadrature" at ω=1/RC (i.e., phase shift is 90 degrees).
This implementation uses a
high-pass filterat the non-inverting input to generate the phase shift and negative feedbackto compensate for the filter's attenuation.
* At high frequencies, the
capacitoris a short circuit, thereby creating a unity- gainvoltage buffer (i.e., no phase shift).
* At low frequencies and DC, the capacitor is an
open circuitand the circuit is an inverting amplifier (i.e., 180 degree phase shift) with unity gain.
* At the
corner frequencyω=1/RC of the high-pass filter (i.e., when input frequency is 1/(2πRC)), the circuit introduces a 90 degree shift (i.e., output is in quadrature with input; it is delayed by a quarter wavelength).In fact, the phase shift of the all-pass filter is double the phase shift of the high-pass filter at its non-inverting input.
Implementation using low-pass filter
A similar all-pass filter can be implemented by interchanging the position of the resistor and capacitor, which turns the high-pass filter into a
low-pass filter. The result is a phase shifter with the same quadrature frequency but a 180 degree shift at high frequencies and no shift at low frequencies. In other words, the transfer function is negated, and so it has the same pole at -1/RC and reflected zero at 1/RC. Again, the phase shift of the all-pass filter is double the phase shift of the first-order filter at its non-inverting input.
Voltage controlled implementation
The resistor can be replaced with a FET in its "ohmic mode" to implement a voltage-controlled phase shifter; the voltage on the gate adjusts the phase shift. In electronic music, a phaser typically consists of four or six of these phase-shifting sections connected in tandem and summed with the original. A low-frequency oscillator (LFO) ramps the control voltage to produce the characteristic swooshing sound.
These circuits are used as phase shifters and in systems of phase shaping and time delay. Filters such as the above can be cascaded with unstable or mixed-phase filters to create a stable or minimum-phase filter without changing the magnitude response of the system. For example, by proper choice of pole (and therefore zero), a pole of an unstable system that is in the right-hand plane can be canceled and reflected on the left-hand plane.
Passive analog implementation
The benefit to implementing all-pass filters with active components like
operational amplifiersis that they do not require inductors, which are bulky and costly in integrated circuitdesigns. In other applications where inductors are readily available, all-pass filters can be implemented entirely without active components. There are a number of circuit topologies that can be used for this. The following are the most commonly used circuits.
The lattice phase equaliser, or filter, is a filter composed of lattice, or X-sections. With single element branches it can produce a phase shift up to 180°, and with resonant branches it can produce phase shifts up to 360°. The filter is an example of a
constant-resistance network(i.e., its image impedanceis constant over all frequencies).
The phase equaliser based on T topology is the unbalanced equivalent of the lattice filter and has the same phase response. While the circuit diagram may look like a low pass filter it is different in that the two inductor branches are mutually coupled. This results in transformer action between the two inductors and an all-pass response even at high frequency.
Bridged T-section filter
The bridged T topology is used for delay equalisation, particularly the differential delay between two
landlines being used for stereophonic soundbroadcasts. This application requires that the filter has a linear phaseresponse with frequency (i.e., constant group delay) over a wide bandwidth and is the reason for choosing this topology.
Z-transformimplementation of an all-pass filter with a complex pole at is:which has a zero at , where denotes the complex conjugate. The pole and zero sit at the same angle but have reciprocal magnitudes (i.e., they are "reflections" of each other across the boundary of the complex unit circle). The placement of this pole-zero pair for a given can be rotated in the complex plane by any angle and retain its all-pass magnitude characteristic. Complex pole-zero pairs in all-pass filters help control the frequency where phase shifts occur.
To create an all-pass implementation with real coefficients, the complex all-pass filter can be cascaded with an all-pass that substitutes for , leading to the
Z-transformimplementation:which is equivalent to the difference equation:where is the output and is the input at discrete time step .
Filters such as the above can be cascaded with unstable or mixed-phase filters to create a stable or minimum-phase filter without changing the magnitude response of the system. For example, by proper choice of , a pole of an unstable system that is outside of the
unit circlecan be canceled and reflected inside the unit circle.
Lattice phase equaliser
* [http://ccrma.stanford.edu/~jos/pasp/Allpass_Filters.html JOS@Stanford on all-pass filters]
* [http://www.tedpavlic.com/teaching/osu/ece209/lab1_intro/lab1_intro_phase_shifter.pdf ECE 209 Phase-Shifter Circuit] — Analysis steps for a common analog phase-shifter circuit.
Wikimedia Foundation. 2010.
Look at other dictionaries:
all-pass filter — fazinis filtras statusas T sritis fizika atitikmenys: angl. all pass filter; phase filter vok. Phasenfilter, n rus. фазовый фильтр, m pranc. filtre passe tout, m … Fizikos terminų žodynas
Low-pass filter — A low pass filter is a filter that passes low frequency signals but attenuates (reduces the amplitude of) signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter … Wikipedia
Band-pass filter — A band pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. An example of an analogue electronic band pass filter is an RLC circuit (a resistor–inductor–capacitor circuit) … Wikipedia
band-pass filter — /band pas , pahs /, Elect., Electronics. a filter that attenuates all frequencies except those of a specific band, which it amplifies. [1920 25] * * * ▪ electronics arrangement of electronic components that allows only those electric waves… … Universalium
band-pass filter — ˈ ̷ ̷ˌ ̷ ̷ noun : filter 3a * * * /band pas , pahs /, Elect., Electronics. a filter that attenuates all frequencies except those of a specific band, which it amplifies. [1920 25] * * * band pass filter noun (telecommunications) A filter which… … Useful english dictionary
band-pass filter — [band′pas΄] n. Electronics a filter which will pass frequencies within a desired range but will virtually cut out all other frequencies … English World dictionary
High-Pass Filter — F/A/V An electronic filter used in various audio circuits to attenuate all frequencies below a chosen frequency … Audio and video glossary
Filter design — is the process of designing a filter (in the sense in which the term is used in signal processing, statistics, and applied mathematics), often a linear shift invariant filter, which satisfies a set of requirements, some of which are contradictory … Wikipedia
filter — i. A device to trap and hold all impurities or solids beyond a specific thickness. The thicknesses of impurities are measured in microns. See fuel filter. See also micron (i). ii. To study all information and discard what is irrelevant. iii. A… … Aviation dictionary
Filter capacitor — Filter capacitors are any capacitors used for filtering. Filter capacitors are common in electrical and electronic work, and cover a number of applications, such as: * Glitch removal on dc power rails * Radio frequency interference (RFI) removal… … Wikipedia