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Active Filters
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. An amplifier prevents the load impedance of the following stage from affecting the characteristics of the filter. An active filter can have complex poles and zeros without using a bulky or expensive inductor. The shape of the response, the Q (quality factor), and the tuned frequency can often be set with inexpensive variable resistors. In some active filter circuits, one parameter can be adjusted without affecting the others.Don Lancaster, ''Active-Filter Cookbook'', Howard W. Sams and Co., 1975 pages 8-10 Types Using active elements has some limitations. Basic filter design equations neglect the finite Bandwidth (signal processing), bandwidth of amplifiers. Available active devices have limited bandwidth, so they are often impracti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Low-pass Filter
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 design. The filter is sometimes called a high-cut filter, or treble-cut filter in audio applications. A low-pass filter is the complement of a high-pass filter. In optics, high-pass and low-pass may have different meanings, depending on whether referring to the frequency or wavelength of light, since these variables are inversely related. High-pass frequency filters would act as low-pass wavelength filters, and vice versa. For this reason, it is a good practice to refer to wavelength filters as ''short-pass'' and ''long-pass'' to avoid confusion, which would correspond to ''high-pass'' and ''low-pass'' frequencies. Low-pass filters exist in many different forms, including electronic circuits such as a '' hiss filter'' used in audio, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linkwitz–Riley Filter
A Linkwitz–Riley (L-R) filter is an infinite impulse response filter used in Linkwitz–Riley audio crossovers. It is named after its inventors Siegfried Linkwitz and Russ Riley and was originally described in ''Active Crossover Networks for Noncoincident Drivers''. It is also known as a ''Butterworth squared'' filter. A Linkwitz–Riley crossover consists of a parallel combination of a low-pass and a high-pass L-R filter. These filters are typically designed by cascading two Butterworth filters, each providing a gain at the cut-off frequency. The resulting Linkwitz–Riley filter has a gain at the cut-off frequency. This means that when summing the low-pass and high-pass outputs, the gain at the crossover frequency is . As a result, the crossover network behaves like an all-pass filter, all-pass, exhibiting a flat amplitude response with a smoothly changing phase response. This is a primary advantage of L-R crossovers compared to even-order Butterworth filter crossovers, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if it is either entirely non-decreasing, or entirely non-increasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is termed ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\right), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimum "L" Filter
The Optimum "L" filter (also known as a Legendre–Papoulis filter) was proposed by Athanasios Papoulis in 1958. It has the maximum roll off rate for a given filter order while maintaining a monotonic frequency response. It provides a compromise between the Butterworth filter which is monotonic but has a slower roll off and the Chebyshev filter which has a faster roll off but has ripple in either the passband or stopband. The filter design is based on Legendre polynomials which is the reason for its alternate name and the "L" in Optimum "L". Synthesizing the characteristic polynomials The solution to N order Optimum L filter characteristic polynomial synthesis emanates from solving for the characteristic polynomial, L_N(\omega^2), given the below constraints and definitions. : \begin &L_N(0)=0 \\ &L(1) = 1\\ & \geq \text \leq \omega \leq 1 \\ & \biggr, _ \text \\ \end The odd order case and even order case may both be solved using Legendre polynomials as follows. : \beg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Butterworth Filter
The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter. It was first described in 1930 by the British engineer and physicist Stephen Butterworth in his paper entitled "On the Theory of Filter Amplifiers". Original paper Butterworth had a reputation for solving very complex mathematical problems thought to be 'impossible'. At the time, filter design required a considerable amount of designer experience due to limitations of the theory then in use. The filter was not in common use for over 30 years after its publication. Butterworth stated that: Such an ideal filter cannot be achieved, but Butterworth showed that successively closer approximations were obtained with increasing numbers of filter elements of the right values. At the time, filters generated substantial ripple in the passband, and the choice of component values was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chebyshev Filter
Chebyshev filters are analog filter, analog or digital filter, digital filters that have a steeper roll-off than Butterworth filters, and have either passband ripple (filters), ripple (type I) or stopband ripple (type II). Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the operating frequency range of the filter, but they achieve this with ripples in the frequency response. This type of filter is named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials. Type I Chebyshev filters are usually referred to as "Chebyshev filters", while type II filters are usually called "inverse Chebyshev filters". Because of the passband ripple inherent in Chebyshev filters, filters with a smoother response in the passband but a more irregular response in the stopband are preferred for certain applications. Type I Chebyshev filters (Chebyshev filters) Type I Chebys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Wave (waveform)
A square wave is a non-sinusoidal waveform, non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same duration at minimum and maximum. In an ideal square wave, the transitions between minimum and maximum are instantaneous. The square wave is a special case of a pulse wave which allows arbitrary durations at minimum and maximum amplitudes. The ratio of the high period to the total period of a pulse wave is called the duty cycle. A true square wave has a 50% duty cycle (equal high and low periods). Square waves are often encountered in electronics and signal processing, particularly digital electronics and digital signal processing. Its stochastic counterpart is a two-state trajectory. Origin and uses Square waves are universally encountered in digital switching circuits and are naturally generated by binary (two-level) logic devices. They are used as timing references or "clock signa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Staggered-tuning
Staggered tuning is a technique used in the design of multi-stage tuned amplifiers whereby each stage is tuned to a slightly different frequency. In comparison to synchronous tuning (where each stage is tuned identically) it produces a wider Bandwidth (signal processing), bandwidth at the expense of reduced Gain (electronics), gain. It also produces a sharper transition band, transition from the passband to the stopband. Both staggered tuning and synchronous tuning circuits are easier to tune and manufacture than many other filter types. The function of stagger-tuned circuits can be expressed as a rational function and hence they can be designed to any of the major filter responses such as Butterworth filter, Butterworth and Chebyshev filter, Chebyshev. The Pole (complex analysis), poles of the circuit are easy to manipulate to achieve the desired response because of the amplifier buffering between stages. Applications include television Intermediate frequency, IF amplifiers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operational Amplifiers
An operational amplifier (often op amp or opamp) is a DC-coupled electronic voltage amplifier with a differential input, a (usually) single-ended output, and an extremely high gain. Its name comes from its original use of performing mathematical operations in analog computers. By using negative feedback, an op amp circuit's characteristics (e.g. its gain, input and output impedance, bandwidth, and functionality) can be determined by external components and have little dependence on temperature coefficients or engineering tolerance in the op amp itself. This flexibility has made the op amp a popular building block in analog circuits. Today, op amps are used widely in consumer, industrial, and scientific electronics. Many standard integrated circuit op amps cost only a few cents; however, some integrated or hybrid operational amplifiers with special performance specifications may cost over . Op amps may be packaged as components or used as elements of more complex integrat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrical Impedance
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of Electrical_resistance, resistance and Electrical_reactance, reactance in a electrical circuit, circuit. Quantitatively, the impedance of a two-terminal Electrical element, circuit element is the ratio of the phasor, complex representation of the Sine wave, sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. In general, it depends upon the frequency of the sinusoidal voltage. Impedance extends the concept of Electrical resistance, resistance to alternating current (AC) circuits, and possesses both Euclidean vector, magnitude and Phase (waves), phase, unlike resistance, which has only magnitude. Impedance can be represented as a complex number, with the same units as resistance, for which the SI unit is the ohm (). Its symbol is usually , and it may be represented by writing its magnitude and phase in the Polar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Filter
An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer, or as a Zolotarev filter, after Yegor Zolotarev) is a filter (signal processing), signal processing filter with equalized ripple (filters), ripple (equiripple) behavior in both the passband and the stopband. The amount of ripple in each band is independently adjustable, and no other filter of equal order can have a faster transition in Gain (electronics), gain between the passband and the stopband, for the given values of ripple (whether the ripple is equalized or not). Alternatively, one may give up the ability to adjust independently the passband and stopband ripple, and instead design a filter which is maximally insensitive to component variations. As the ripple in the stopband approaches zero, the filter becomes a type I Chebyshev filter. As the ripple in the passband approaches zero, the filter becomes a type II Chebyshev filter and finally, as both ripple values approach zero, the filter becomes a B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
