ELECTRONIC FILTER DESIGN HANDBOOK PDF
6x9 Handbook / Electronic Filter Design / Williams & Taylor / / Front .. This is the fourth edition of the Electronic Filter Design Handbook, which was. Analog electronic filters are present in just about every piece of electronic equip- ment. There are the obvious Stephenson, E W. RC Active Filter Design Handbook. New York: John net site, wildlifeprotection.info as file sbfapdf). FILTER Long-established as “The Bible" of practical electronic filter design, McGraw-Hill's classic Electronic Filter Design Handbook has now been completely revised.
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and practical digital filter design techniques are provided in the later chapters. Electronic signals are complicated phenomena, and their exact behavior is. ELECTRONIC. FILTER DESIGN. HANDBOOK. Arthur B. Williams. Fred wildlifeprotection.info Fourth Edition. McGRAW-HILL. New York Chicago San Francisco Lisbon. The circuits and filters handbook / editor-in-chief, Wai Kai Chen. analog VLSI circuits, computer-aided design and optimization techniques, and design automation. In . A fellow of the Institute of Electrical and Electronics Engineers and the.
It is sometimes desirable to compute two geometrically related frequencies that correspondto a given bandwidth. For the wider cases, the arithmetic center of f 1and f 2 would be slightly above the actual geometric center frequency f 0.
Another and moremeaningful way of stating the converse is that for a given pair of frequencies, the geometricmean is below the arithmetic mean. Bandpass filter requirements are not always specified in an arithmetically symmetricalmanner as in the previous examples. Multiple stopband attenuation requirements may alsoexist. The design engineer is still faced with the basic problem of converting the given parametersinto geometrically symmetrical characteristics so that a steepness factor or factors can be determined.
The following example demonstrates the conversion of a specificationsomewhat more complicated than the previous example. Figure illustrates the comparison between the given requirement and the correspondinggeometrically symmetrical equivalent response.
A filter is required that has over20, 30, and 40 dB of rejection at, respectively, 11, 19, and Normalizing a band-reject filter requirementproceeds along the same lines as for a bandpass filter. If the ratio of the upper cutofffrequency to the lower cutoff frequency is an octave or more, a band-reject filter requirementcan be classified as wideband and separated into individual low-pass and high-passspecifications.
The resulting filters are paralleled at the input and combined at the output. The following example demonstrates normalization of a wideband band-reject filterrequirement. Example Normalizing a Wideband Band-Reject FilterRequired:A band-reject filter3 dB at and HzdB minimum at and HzResult: a Determine the ratio of upper cutoff to lower cutoff, using Hz Hz 4wideband type b Separate requirements into individual low-pass and high-pass specifications.
The basic assumption of the previous example is that when the filter outputs are combined,the resulting response is the superimposed individual response of both filters. Thisis a valid assumption if each filter has sufficient rejection in the band of the other filter sothat there is no interaction when the outputs are combined.
Figure shows the casewhere inadequate separation exists. The requirement for a minimum separation between cutoffs of an octave or more is byno means rigid.
Sharper filters can have their cutoffs placed closer together with minimalinteraction. Narrowband Band-Reject Filters. FIGURE Limitations of the wideband band-reject design approach: a combined low-pass andhigh-pass filters; b composite response; and c combined response by the summation of outputs.
The design method for narrowband band-reject filters can be defined as follows Convert the band-reject requirement directly into a normalized low-pass specification. Select a low-pass filter from the normalized curves that meets the normalizedrequirements.
Transform the normalized low-pass parameters into the required band-reject filter. Thismay involve designing the intermediate high-pass filter, or the transformation may bedirect. The band-reject response has geometric symmetry just as bandpass filters have. Figure defines this response shape. The parameters shown have the same relationship to eachother as they do for bandpass filters.
The attenuation at the center frequency is theoreticallyinfinite since the response of a high-pass filter at DC has been transformed to the centerfrequency.
For Qs of 10 or more, the response near the center frequencyapproaches the arithmetically symmetrical condition, so we can then statef 0 f L f u2 To use the normalized curves for the design of a band-reject filter, the response requirementmust be converted to a normalized low-pass filter specification.
In order to accomplishthis, the band-reject specification should first be made geometrically symmetrical—that is,each pair of frequencies having equal attenuation should satisfy which is an alternate form of Equation When two frequencies are specified at a particularattenuation level, two frequency pairs will result from calculating the correspondingopposite geometric frequency for each frequency specified.
Retain the pair having thewider separation since it represents the more severe requirement. In the bandpass case, thepair having the lesser separation represented the more difficult requirement. The band-reject filter steepness factor is defined byA s f 1f 2 f 2 0passband bandwidthstopband bandwidth A normalized low-pass filter can now be selected that makes the transition from thepassband attenuation limit to the minimum required stopband attenuation within a frequencyratio A s.
The following example demonstrates the normalization procedure for a band-reject filter. The given response requirement and the geometrically symmetricalequivalent are compared in Figure c Calculate A s.
A s passband bandwidth Hzstopband bandwidth Hz 1.
Sincethese curves are all normalized to 3 dB, a filter is required with over 40 dB of rejectionat 1. The input forcing function was a sine wave. In realworldapplications of filters, input signals consist of a variety of complex waveforms. Theresponse of filters to these nonsinusoidal inputs is called transient response.
The frequency- and time-domain parameters of a filter are directly related through theFourier or Laplace transforms. The Effect of Nonuniform Time DelayEvaluating a transfer function as a function of frequency results in both a magnitude andphase characteristic. Figure shows the amplitude and phase response of a normalizedn 3 Butterworth low-pass filter.
Butterworth low-pass filters have a phase shift ofexactly n times 45 at the 3-dB frequency. The phase shift continuously increases as thetransition is made into the stopband and eventually approaches n times 90 at frequenciesfar removed from the passband.
Since the filter described by Figure has a complexityof n 3, the phase shift is at the 3-dB cutoff and approaches in the stopband. Frequency scaling will transpose the phase characteristics to a new frequency rangeas determined by the FSF. It is well known that a square wave can be represented by a Fourier series of odd harmoniccomponents, as indicated in Figure Since the amplitude of each harmonic isreduced as the harmonic order increases, only the first few harmonics are of significance.
In addition, these components must not be displaced in time withrespect to each other. If we assume that a low-pass filter has a linear phase shift between 0 at DC and n times 45at the cutoff, we can express the phase shift in the passband asf 45nf xf c where f x is any frequency in the passband, and f c is the 3-dB cutoff frequency.
A phase-shifted sine wave appears displaced in time from the input waveform. This displacementis called phase delay and can be computed by determining the time interval representedby the phase shift, using the fact that a full period contains Example Effect of Nonlinear Phase on a Square WaveRequired:Compute the phase delay of the fundamental and the third, fifth, seventh, and ninthharmonics of a 1 kHz square wave applied to an n 3 Butterworth low-pass filterhaving a 3-dB cutoff of 10 kHz.
Assume a linear phase shift with frequency in thepassband. The output waveformwould then appear nearly equivalent tothe input except for a delay of This displacement in time of the spectralcomponents, with respect to each other,introduces a distortion of the output waveform.
Figure shows some typical effectsof a nonlinear phase shift upon a squarewave.
Most filters have nonlinear phase versusfrequency characteristics, so some waveformdistortion will usually occur forcomplex input signals. Not all complex waveforms have harmonically related spectral components.
An amplitudemodulatedsignal, for example, consists of a carrier and two sidebands, each sideband separatedfrom the carrier by a modulating frequency.
If these conditions are not satisfied, the carrier andboth sidebands will be delayed by different amounts. The carrier delay will be in accordancewith the equation for phase delay:T pd b v The terms carrier delay and phase delay are used interchangeably. A new definition is required for the delay of the sidebands. This delay is commonlycalled group delay and is defined as the derivative of phase versus frequency, which can beexpressed as T gd dbLinear phase shift results in constant group delay since the derivative of a linear functionis a constant.
Figure illustrates a low-pass filter phase shift which is non-linear inthe vicinity of a carrier v cand the two sidebands: v cv mand v cv m. The phase delayat v c is the negative slope of a line drawn from the origin to the phase shift correspondingto v c, which is in agreement with Equation The group delay at v c is shown as thenegative slope of a line which is tangent to the phase response at v c.
This can be mathematicallyexpressed asT gd dbdv 2 vv cIf the two sidebands are restricted to a region surrounding v cand having a constantgroup delay, the envelope of the modulated signal will be delayed by T gd. Figure comparesthe input and output waveforms of an amplitude-modulated signal applied to the filterdepicted by Figure Note that the carrier is delayed by the phase delay, while theenvelope is delayed by the group delay.
For this reason, group delay is sometimes calledenvelope delay. If the group delay is not constant over the bandwidth of the modulated signal, waveformdistortion will occur. Narrow-bandwidth signals are more likely to encounter constantgroup delay than signals having a wider spectrum. It is common practice to use a groupdelayvariation as a criterion to evaluate phase nonlinearity and subsequent waveform distortion. The absolute magnitude of the nominal delay is usually of little consequence.
Step Response of Networks. If we were to define a hypothetical ideal low-pass filter, itwould have the response shown in Figure The phase shift is a linearly increasingfunction in the passband, where n is the order of the ideal filter. The group delay is constantin the passband and zero in the stopband.
If a unity amplitude step were applied to thisideal filter at t 0, the output would be in accordance with Figure Since rise time is inversely proportional to v c, awider filter results in reduced rise time.
A 9-percent overshoot exists on the leading edge. This oscillation is called ringing. Overshoot and ringing occur in an ideal low-pass filter,even though we have linear phase.
This is because of the abrupt amplitude roll-off at cutoff. Therefore, both linear phase and a prescribed roll-off are required for minimum transientdistortion. Overshoot and prolonged ringing are both very undesirable if the filter is required topass pulses with minimum waveform distortion. The step-response curves provided for thedifferent families of normalized low-pass filters can be very useful for evaluating the transientproperties of these filters.
A unit impulse is defined as a pulse which is infinitely high and infinitesimallynarrow, and has an area of unity. The response of the ideal filter of Figure to aunit impulse is shown in Figure An input signal having the form of a unit impulse is physically impossible. Estimating Transient Characteristics.
Group-delay, step-response, and impulse-responsecurves are given for the normalized low-pass filters discussed in the latter section of this chapter. These curves are useful for estimating filter responses to nonsinusoidal signals. If theinput waveforms are steps or pulses, the curves may be used directly. For more complexinputs, we can use the method of superposition, which permits the representation of a complexsignal as the sum of individual components. Group Delay of Low-Pass Filters.
When a normalized low-pass filter is frequencyscaled,the delay characteristics are frequency-scaled as well. The following rules can beapplied to derive the resulting delay curve from the normalized response Multiply all points on the frequency axis by f c. The following example demonstrates the denormalization of a low-pass curve. Example Frequency Scaling the Delay of a Low-Pass FilterRequired:Using the normalized delay curve of an n 3 Butterworth low-pass filter given inFigure a, compute the delay at DC and the delay variation in the passband if thefilter is frequency-scaled to a 3-dB cutoff of Hz.
Result:To denormalize the curve, divide the delay axis by 2pf c and multiply the frequency axisby f c, where f c is Hz. The resulting curve is shown in Figure b. The delay atDC is 3. Equation is an approximation which usually is accurate to within 25 percent.
Group Delay of Bandpass Filters. When a low-pass filter is transformed to a narrowbandbandpass filter, the delay is transformed to a nearly symmetrical curve mirrored aboutthe center frequency.
For the narrowband condition, the bandpass delay curve can be approximated by implementingthe following rules A delay characteristic symmetrical around the center frequency can now be formed bygenerating the mirror image of the curve obtained by implementing steps 1 and 2. Thetotal 3-dB bandwidth thus becomes BW. Example Estimate the Delay of a Bandpass FilterRequired:Estimate the group delay at the center frequency and the delay variation over the passbandof a bandpass filter having a center frequency of Hz and a 3-dB bandwidthof Hz.
The bandpass filter is derived from a normalized n 3 Butterworth lowpassfilter.
Result:The delay of the normalized filter is shown in Figure a. We can now reflect this delay curve on both sides of thecenter frequency of Hz to obtain Figure b. The delay at the center frequencyis 6. As the fractional bandwidth increases, thedelay becomes less symmetrical and peaks toward the low side of the center frequency, asshown in Figure Start a New Search: Record 1 of 1.
Deboo, G. Center Abstract: The design of filters is described. Emphasis is placed on simplified procedures that can be used by the reader who has minimum knowledge about circuit design and little acquaintance with filter theory.
The handbook has three main parts. The first part is a review of some information that is essential for work with filters.
The second part includes design information for specific types of filter circuitry and describes simple procedures for obtaining the component values for a filter that will have a desired set of characteristics.
Multipole LC filters provide greater control of response form, bandwidth and transition bands. The first of these filters was the constant k filter , invented by George Campbell in Campbell's filter was a ladder network based on transmission line theory. Together with improved filters by Otto Zobel and others, these filters are known as image parameter filters. A major step forward was taken by Wilhelm Cauer who founded the field of network synthesis around the time of World War II. Cauer's theory allowed filters to be constructed that precisely followed some prescribed frequency function.
Classification by technology[ edit ] Passive filters[ edit ] Passive implementations of linear filters are based on combinations of resistors R , inductors L and capacitors C.
Filter Handbook: A Practical Design Guide
Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do the reverse. A filter in which the signal passes through an inductor , or in which a capacitor provides a path to ground, presents less attenuation to low-frequency signals than high-frequency signals and is therefore a low-pass filter.
If the signal passes through a capacitor, or has a path to ground through an inductor, then the filter presents less attenuation to high-frequency signals than low-frequency signals and therefore is a high-pass filter.New York: John Wiley and Sons. If we impedance-scale the filter, we obtain the circuit of Figure b. Assume a linear phase shift with frequency in thepassband. Step Response of Networks. After D s is substituted into Equation , Z 11 is expanded using the continued fractionexpansion.