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{{About|roll-off in electrical network analysis|the dumpster|Roll-off (dumpster)}}
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'''Roll-off''' is a term commonly used to describe the steepness of a [[Transfer function|transmission function]] with [[frequency]], particularly in [[network analysis (electrical circuits)|electrical network analysis]], and most especially in connection with [[filter (signal processing)|filter circuits]] in the transition between a [[passband]] and a [[stopband]].  It is most typically applied to the [[insertion loss]] of the network, but can in principle be applied to any relevant function of frequency, and any technology, not just electronics.  It is usual to measure roll-off as a function of [[logarithmic scale|logarithmic]] frequency, consequently, the units of roll-off are either [[decibel]]s per [[decade (log scale)|decade]] (dB/decade), where a decade is a 10-times increase in frequency, or decibels per [[octave (electronics)|octave]] (dB/8ve), where an octave is 2-times increase in frequency.
 
The concept of roll-off stems from the fact that in many networks roll-off tends towards a constant gradient at frequencies well away from the [[cut-off frequency|cut-off]] point of the frequency curve. Roll-off enables the cut-off performance of such a filter network to be reduced to a single number. Note that roll-off can occur with decreasing frequency as well as increasing frequency, depending on the [[:File:Bandform template.svg|bandform]] of the filter being considered: for instance a [[low-pass filter]] will roll-off with increasing frequency, but a [[high-pass filter]] or the lower [[stopband]] of a [[band-pass filter]] will roll-off with decreasing frequency.  For brevity, this article describes only low-pass filters. This is to be taken in the spirit of [[prototype filter]]s; the same principles may be applied to high-pass filters by interchanging phrases such as "above cut-off frequency" and "below cut-off frequency".
 
==First order roll-off==
[[File:First order RC circuit.svg|thumb|250px|First order RC filter [[low-pass filter]] circuit.]]
[[File:Roll-off graph 6dB.svg|thumb|250px|Roll-off of a first order low-pass filter at 6&nbsp;dB/8ve (20&nbsp;dB/decade)]]
A simple [[First order linear differential equation|first order]] network such as a [[RC circuit]] will have a roll-off of 20&nbsp;dB/decade.  This is approximately equal (to within normal engineering required accuracy) to 6&nbsp;dB/8ve and is the more usual description given for this roll-off. This can be shown to be so by considering the voltage [[transfer function]], ''A'', of the RC network:<ref name=Jacob>J. Michael Jacob, ''Advanced AC circuits and electronics: principles & applications'', pages 150-152, Cengage Learning 2003 ISBN 0-7668-2330-X.</ref>
 
:<math>A=\frac{V_o}{V_i}=\frac{1}{1+i\omega RC}</math>
 
[[Prototype filter#Frequency scaling|Frequency scaling]] this to ''ω''<sub>c</sub>=1/''RC''=1 and forming the power ratio gives,
 
:<math>|A|^2=\frac{1}{1+\left( {\omega \over \omega_c} \right)^2} = \frac{1}{1+\omega^2}</math>
 
In decibels this becomes,
 
:<math>10\log \left({\frac{1}{1+\omega^2}}\right)</math>
 
or expressed as a loss,
 
:<math>L=10\log \left({1+\omega^2}\right) \ \mathrm{dB}</math>
 
At frequencies well above ''ω''=1, this simplifies to,
 
:<math>L \approx 10\log \left(\omega^2\right)= 20\log \omega \ \mathrm{dB}</math>
 
Roll-off is given by,
 
:<math>\Delta L = 20\log \left( {\omega_2 \over \omega_1} \right) \ \mathrm{dB/interval_{2,1}}</math>
 
For a decade this is;
 
:<math>\Delta L = 20\log 10 = 20 \ \mathrm{dB/decade}</math>
 
and for an octave,
 
:<math>\Delta L = 20\log 2 \approx 20 \times 0.3 = 6 \ \mathrm{dB/8ve}</math>
 
==Higher order networks==
[[File:High order buffered RC circuit.svg|thumb|500px|left|Multiple order RC filter buffered between stages.]]
[[File:Roll-off graph multiple.svg|thumb|250px|none|Roll-off graph of higher-order low-pass filters showing various rates of roll-off]]
A higher order network can be constructed by cascading first-order sections together.  If a [[unity gain buffer amplifier]] is placed between each section (or some other [[active filter|active topology]] is used) there is no interaction between the stages.  In that circumstance, for ''n'' identical first-order sections in cascade, the voltage transfer function of the complete network is given by;<ref name=Jacob/>
 
:<math>A_{\mathrm T}=A^n \ </math>
 
consequently, the total roll-off is given by,
 
:<math>\Delta L_{\mathrm T} = n \Delta L = 6n \ \mathrm{dB/8ve}</math>
 
A similar effect can be achieved in the [[digital filter|digital domain]] by repeatedly applying the same filtering algorithm  to the signal.<ref>Todd, pp107-108</ref>
 
[[File:LC ladder circuit.svg|thumb|500px|LC low-pass ladder circuit.  Each element (that is L or C) adds an order to the filter and a [[pole (complex analysis)|pole]] to the [[driving point impedance]].]]
The calculation of transfer function becomes somewhat more complicated when the sections are not all identical, or when the popular [[ladder topology]] construction is used to realise the filter. In a ladder filter each section of the filter has an effect on its immediate neighbours and a lesser effect on more remote sections so the response is not a simple ''A<sup>n</sup>'' even when all the sections are identical.  For some filter classes, such as the [[Butterworth filter]], the insertion loss is still [[monotonic function|monotonically]] increasing with frequency and quickly [[Asymptote|asymptotically]] converges to a roll-off of 6''n''&nbsp;dB/8ve, but in others, such as the [[Chebyshev filter|Chebyshev]] or [[elliptic filter]] the roll-off near the cut-off frequency is much faster and elsewhere the response is anything but monotonic. Nevertheless, all filter classes eventually converge to a roll-off of 6''n''&nbsp;dB/8ve theoretically at some arbitrarily high frequency, but in many applications this will occur in a frequency band of no interest to the application and [[parasitic capacitance|parasitic effects]] may well start to dominate long before this happens.<ref>Giovanni Bianchi, Roberto Sorrentino, ''Electronic filter simulation & design'', pages 129-130, McGraw-Hill Professional 2007 ISBN 0-07-149467-7.</ref>
 
==Applications==
Filters with a high roll-off were first developed to prevent crosstalk between adjacent channels on telephone [[Frequency division multiplexing|FDM]] systems.<ref>Lundheim, L, "On Shannon and "Shannon's Formula", ''Telektronikk'', '''vol. 98''', no. 1, 2002, pp. 24-25.</ref> Roll-off is also significant on audio loudspeaker [[audio crossover|crossover filters]]: here the need is not so much for a high roll-off but that the roll-offs of the high frequency and low-frequency sections are symmetrical and complementary.  An interesting need for high roll-off arises in [[EEG]] machines.  Here the filters mostly make do with a basic 6&nbsp;dB/8ve roll-off, however, some instruments provide a switchable 35 Hz filter at the high frequency end with a faster roll-off to help filter out noise generated by muscle activity.<ref>Mayer et al, pp104-105.</ref>
 
==See also==
*[[Bode plot]]
 
==Notes==
{{reflist}}
 
==References==
*J. William Helton, Orlando Merino, ''Classical control using H [infinity] methods: an introduction to design'', pages 23-25, Society for Industrial and Applied Mathematics 1998 ISBN 0-89871-424-9.
*Todd C. Handy, ''Event-related potentials: a methods handbook'', pages 89-92, 107-109, MIT Press 2004 ISBN 0-262-08333-7.
*Fay S. Tyner, John Russell Knott, W. Brem Mayer (ed.), ''Fundamentals of EEG Technology: Basic concepts and methods'', pages 101-102, Lippincott Williams & Wilkins 1983 ISBN 0-89004-385-X.
 
 
[[Category:Electronic design]]
[[Category:Tone, EQ and filter]]
[[Category:Filter frequency response]]

Latest revision as of 14:01, 29 December 2014

There are many types of link spamming. A simple one is known as link farming which involves developing areas of pages that make reference to each...

Link spamming is a kind of black cap Search Engine Optimisation that tries to exploit weaknesses in link-based ranking methods including the one used by Googles PageRank algorithm. PageRank give a higher standing to so as you can to a to try and boost your page rankings the idea is to add as many links a site that is linked to many other internet sites.

There are many forms of link spamming. An easy one is named link farming , involving producing areas of pages that refer to each other to be able to bulk up a link index.

Still another tactic is named the Sybil attack where you set up links to unrelated but common sites where visitors won"t see them. Here is the forging of multiple identities for malicious intent, named after the famous person with the multiple personality disorder. This pictorial account website has a pile of majestic aids for why to provide for this enterprise. A spammer may develop multiple the websites at different names of domain that connect to each other, such as artificial blogs referred to as junk blogs. Yet another type is named Wiki junk, which uses links to be placed by the open editing platform of wiki systems on a typical page.

Just one more common technique is Splogging also referred to as junk blogging. This is actually the positioning of links randomly on other sites in blogs, forums, guest books and forums.

Site hijacking is really common it"s ridiculous. Web hosts do it when you forget to continue your domain name. Site hijacking is accomplished by creating a criminal content of a favorite site which shows articles similar to the original to a crawler, but redirects web surfers to unrelated or detrimental sites. Some link spammers check DNS records for domains that will expire soon, and then find them if they expire and replace the pages with links to their pages. If you know any thing, you will likely need to learn about link emporor.

Link Spamming is classified as a top risk method to do effective SEO, you risk having your site banned by Google if you do.. Dig up new resources on our related website by visiting ::Guerra"s Blog:: Ways to get free traffic using link deals - Indyarocks.com.

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