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| In [[electronics]], when describing a [[voltage]] or [[current (electricity)|current]] [[step function]], '''rise time''' is the time taken by a [[Signal (electrical engineering)|signal]] to change from a specified low value to a specified high value. Typically, in [[analog electronics]], these values are 10% and 90% of the step height: in control theory applications, according to {{harvtxt|Levine|1996|p=158}}, rise time is defined as "the time required for the response to rise from x% to y% of its final value", with 0%-100% rise time common for underdamped second order systems, 5%-95% for critically damped and 10%-90% for overdamped.<ref name="risedef">Precisely, {{harvtxt|Levine|1996|p=158}} states: "''The rise time is the time required for the response to rise from x% to y% of its final value. For [[Damping ratio|overdamped]] [[Control system|second order system]]s, the 0% to 100% rise time is normally used, and for [[damping ratio|underdamped systems]]...the 10% to 90% rise time is commonly used''". See also the textbook {{harvnb|Nise|2008}}.</ref> The output signal of a [[system]] is characterized also by [[fall time]]: both parameters depend on rise and fall times of input signal and on the characteristics of the [[system]].
| | Some consumers of computer are aware which their computer become slower or have certain errors following using for a while. But most folks don't understand how to accelerate their computer and some of them don't dare to operate it. They always find some experts to keep the computer in wise condition however, they have to spend certain funds on it. Actually, we can do it by oneself. There are numerous registry cleaner software that you can get 1 of them online. Some of them are free plus you merely should download them. After installing it, this registry cleaner software might scan the registry. If it found these mistakes, it may report we plus you are able to delete them to keep your registry clean. It is simple to operate plus it is the best method to repair registry.<br><br>Carry out window's program restore. It is extremely important to do this because it removes wrong changes that have happened inside the system. Some of the errors outcome from inability of your system to create restore point frequently.<br><br>Over time the disk could furthermore receive fragmented. Fragmentation causes a computer to slow down because it takes windows much longer to find a files location. Fortunately, a PC has a built in disk defragmenter. You can run this program by clicking "Start" - "All Programs" - "Accessories" - "System Tools" - "Disk Defragmenter". You can have the way to choose that drives or partition we want to defragment. This action could take we several time so it is very advised to do this on a regular basis so because to avoid further fragmentation and to accelerate your windows XP computer.<br><br>Always see with it which you have installed antivirus, anti-spyware plus anti-adware programs plus have them up-to-date on a regular basis. This can help stop windows XP running slow.<br><br>Google Chrome crashes on Windows 7 when the registry entries are improperly modified. Missing registry keys or registry keys with wrong values could cause runtime mistakes and thereby the problem occurs. You are recommended to scan the entire program registry and review the outcome. Attempt the registry repair task using third-party [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities] software.<br><br>Why this problem arises frequently? What are the causes of it? In fact, there are 3 major causes which could lead to the PC freezing problem. To solve the problem, you should take 3 steps in the following paragraphs.<br><br>The 'registry' is merely the central database which shops all the settings plus options. It's a truly important piece of the XP system, meaning that Windows is regularly adding plus updating the files inside it. The problems occur whenever Windows actually corrupts & loses several of these files. This makes a computer run slow, as it attempts hard to find them again.<br><br>Registry products have been designed to fix all the broken files inside the program, allowing a computer to read any file it wants, whenever it wants. They work by scanning from the registry plus checking each registry file. If the cleaner sees it is corrupt, then it may substitute it automatically. |
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| == Overview ==
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| Rise time is an analog parameter of fundamental importance in [[electronics|high speed electronics]], since it is a measure of the ability of a circuit to respond to fast input signals. Many efforts over the years have been made to reduce the rise times of generators, analog and digital circuits, measuring and data transmission equipment, focused on the research of faster [[electronic device|electron devices]] and on techniques of reduction of stray circuit parameters (mainly capacitances and inductances). For applications outside the realm of high speed [[electronics]], long (compared to the attainable state of the art) rise times are sometimes desirable: examples are the [[Dimmer|dimming]] of a light, where a longer rise-time results, amongst other things, in a longer life for the bulb, or digital signals apt to the control of analog ones, where a longer rise time means lower capacitive feedthrough, and thus lower coupling [[noise]].
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| == Simple examples of calculation of rise time ==
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| The aim of this section is the calculation of rise time of [[step response]] for some simple systems: all notations and assumptions required for the following analysis are listed here.
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| *<math>t_r\,</math> is the '''rise time''' of the analyzed system, measured in [[second]]s.
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| *<math>f_L\,</math> is the ''low frequency cutoff'' (-3 dB point) of the analyzed system, measured in [[hertz]].
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| *<math>f_H\,</math> is ''high frequency cutoff'' (-3 dB point) of the analyzed system, measured in hertz.
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| *<math>h(t)\,</math> is the ''[[impulse response]]'' of the analyzed system in the time domain.
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| *<math>H(\omega)\,</math> is the ''[[frequency response]]'' of the analyzed system in the frequency domain.
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| *The [[Bandwidth (signal processing)|bandwidth]] is defined as
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| :<math>BW = f_{H} - f_{L}\,</math>
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| :and since the low frequency cutoff <math>f_L</math> is usually several decades lower than the high frequency cutoff <math>f_H</math>,
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| :<math>BW\cong f_H\,</math>
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| *All systems analyzed here have a [[frequency response]] which extends to 0 (low-pass systems), thus
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| :<math>f_L=0\,\Leftrightarrow\,f_H=BW</math> exactly.
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| *All systems analyzed are thought as [[electrical network]]s and all the signals are thought as [[voltage]]s for the sake of simplicity: the input is a [[step function]] of <math>V_0</math> [[volt]]s.
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| === Gaussian response system ===
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| A system is said to have a [[Gaussian]] response if it is characterized by the following frequency response
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| :<math>|H(\omega)|=e^{-\frac{\omega^2}{\sigma^2}} </math>
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| where <math>\sigma>0</math> is a constant, related to the high frequency cutoff by the following relation:
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| :<math>f_H = \frac{\sigma}{2\pi} \sqrt{\frac{3}{20\log e}} \cong 0.0935 \sigma</math>
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| The corresponding [[impulse response]] can be calculated using the inverse [[Fourier transform]] of the shown [[frequency response]]
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| :<math>\mathcal{F}^{-1}\{H\}(t)=h(t)=\frac{1}{2\pi}\int\limits_{-\infty}^{+\infty} {e^{-\frac{\omega^2}{\sigma^2}}e^{i\omega t}} d\omega=\frac{\sigma}{2\sqrt{\pi}}e^{-\frac{1}{4}\sigma^2t^2}</math>
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| Applying directly the definition of [[step response]]
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| :<math>V(t) = V_0{H*h}(t) = \frac{V_0}{\sqrt{\pi}}\int\limits_{-\infty}^{\frac{\sigma t}{2}}e^{-\tau^2}d\tau = \frac{V_0}{2}\left[1+\mathrm{erf}\left(\frac{\sigma t}{2}\right)\right]\Leftrightarrow\frac{V(t)}{V_0}=\frac{1}{2}\left[1+\mathrm{erf}\left(\frac{\sigma t}{2}\right)\right]</math>
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| Solving for ''t'''s the two following equations by using known properties of the [[error function]]
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| :<math>0.1=\frac{1}{2}\left[1+\mathrm{erf}\left(\frac{\sigma t_1}{2}\right)\right]
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| \qquad0.9=\frac{1}{2}\left[1+\mathrm{erf}\left(\frac{\sigma t_2}{2}\right)\right]</math>
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| the value <math>t=-t_1=t_2</math> is then known and since <math>t_r=t_2-t_1=2t</math>
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| :<math>t_r=\frac{4}{\sigma}{\mathrm{erf}^{-1}(0.8)}\cong\frac{0.3394}{f_H}</math>
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| and then
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| :<math>t_r\cong\frac{0.34}{BW}\quad\Longleftrightarrow\quad BW\cdot t_r\cong 0.34</math>
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| ===One stage low pass RC network===
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| For a simple one stage low pass [[RC circuit|RC network]], the 10% to 90% rise time is proportional to the network time constant <math>\tau=RC</math>:
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| :<math>t_r\cong 2.197\tau\,</math>
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| The proportionality constant can be derived by using the output response of the network to a [[unit step function]] input signal of <math>V_0</math> amplitude, aka its [[step response]]:
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| :<math>V(t) = V_0 \left(1-e^{-\frac{t}{\tau}} \right)</math>
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| Solving for ''t'''s
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| :<math>\frac{V(t)}{V_0}=\left(1-e^{-\frac{t}{\tau}}\right)</math>
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| :<math>\frac{V(t)}{V_0}-1=-e^{-\frac{t}{\tau}}</math>
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| :<math>1-\frac{V(t)}{V_0}=e^{-\frac{t}{\tau}}</math>
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| :<math>\ln\left(1-\frac{V(t)}{V_0}\right)=-\frac{t}{\tau}</math>
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| :<math> t = -\tau \; \ln\left(1-\frac{V(t)}{V_0}\right)</math>
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| We call t<sub>1</sub> the time needed to go from 0% to 10% of the steady-state value, and t<sub>2</sub> the one to 90%.
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| Thus t<sub>1</sub> is such that <math>\frac{V(t)}{V_0}=0.1</math> and t<sub>2</sub> is such that <math>\frac{V(t)}{V_0}=0.9</math>.
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| Solving the previous equation for these two values we find the analitical expression for t<sub>1</sub> and t<sub>2</sub>:
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| :<math> t_1 = -\tau\;\ln\left(1-0.1\right) = -\tau \; \ln\left(0.9\right) = -\tau\;\ln\left(\frac{9}{10}\right) = \tau\;\ln\left(\frac{10}{9}\right) = \tau({\ln 10}-{\ln 9})</math>
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| We obtain t<sub>2</sub> in the same way, resulting in
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| :<math>t_2=\tau\ln{10}\,</math> | |
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| Subtracting <math>t_1</math> from <math>t_2</math> we obtain the rise time, whis is therefore proportional to the time constant:
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| :<math>t_r = t_2-t_1 = \tau\cdot\ln 9\cong\tau\cdot 2.197</math>
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| Now, noting that
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| :<math>\tau = RC = \frac{1}{2\pi f_H}</math>
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| (see [[Time_constant#Relation of time constant to bandwidth|here]] for the proof of the previous equation) then
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| :<math>t_r\cong\frac{2.197}{2\pi f_H}\cong\frac{0.349}{f_H}</math>
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| and since the high frequency cutoff is equal to the bandwidth
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| :<math>t_r\cong\frac{0.35}{BW}\quad\Longleftrightarrow\quad BW\cdot t_r\cong 0.35</math>
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| This formula implies that if the bandwidth of an [[oscilloscope]] is 350 [[hertz|MHz]], its 10% to 90% risetime is 1 nanosecond.
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| === Rise time of cascaded blocks ===
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| Consider a system composed by <math>n</math> cascaded non interacting blocks, each having a rise time <math>\scriptstyle{t_{r_i}}</math> and no [[overshoot (signal)|overshoot]] in their [[step response]]: suppose also that the input signal of the first block has a rise time whose value is <math>\scriptstyle{t_{r_S}}</math>. Then its output signal has a rise time <math>\scriptstyle{t_{r_O}}</math> equal to
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| :<math>t_{r_O}=\sqrt{t_{r_S}^2+t_{r_1}^2+\dots+t_{r_n}^2}</math>
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| This result is a consequence of the [[central limit theorem]], as reported in {{Harvnb|Valley|Wallman|1948|pp=77–78}} and proved by [[Henry Wallman]] in {{Harvnb|Wallman|1950}}.<ref>This beautiful one-page paper does not contain any calculation. [[Henry Wallman]] simply sets up a table he calls [[dictionary]] paralleling concepts from [[electronics engineering]] and [[probability theory]]: the key of the process is the use of [[Laplace transform]]. Then he notes that, following the correspondence of concepts established by the [[dictionary]], that the [[step response]] of a cascade of blocks corresponds to the [[central limit theorem]] and states that: "''This has important practical consequences, among them the fact that if a network is free of overshoot its time-of-response inevitably increases rapidly upon cascading, namely as the square-root of the number of cascaded network''".{{harv|Wallman|1950|p=91}}</ref>
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| == Factors affecting rise time ==
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| Rise time values in a resistive circuit are primarily due to stray [[capacitance]] and [[inductance]] in the circuit. Because every [[electrical network|circuit]] has not only [[electrical resistance|resistance]], but also [[capacitance]] and [[inductance]], a delay in voltage and/or current at the load is apparent until the [[Steady state theory|steady state]] is reached. In a pure [[RC circuit]], the output risetime (10% to 90%), as shown above, is approximately equal to <math>2.2 RC</math>.
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| == Rise time in control applications ==
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| In control theory, for overdamped systems, rise time is commonly defined as the time for a waveform to go from 10% to 90% of its final value.<ref name="risedef"/>
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| The [[quadratic function|quadratic]] [[approximation]] for normalized '''rise time''' for a 2nd-order system, [[step response]], no zeros is:
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| :<math> t_r \cdot\omega_0= 2.230\zeta^2-0.078\zeta+1.12\,</math>
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| where ζ is the [[damping ratio]] and ω<sub>0</sub> is the [[natural frequency]] of the network.
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| However, the proper calculation for rise time from 0 to 100% of an under-damped 2nd-order system is:
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| :<math> t_r \cdot\omega_0= \frac{1}{\sqrt{1-\zeta^2}}\left ( \pi - \tan^{-1}\left ( {\frac{\sqrt{1-\zeta^2}}{\zeta}} \right )\right )</math>
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| where ζ is the damping ratio and ω<sub>0</sub> is the natural frequency of the network.
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| == See also ==
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| *[[Fall time]]
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| *[[Frequency response]]
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| *[[Impulse response]]
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| *[[Step response]]
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| *[[Transition time]]
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| *[[Settling time]]
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| ==Notes==
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| {{reflist|30em}}
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| == References ==
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| *{{Citation
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| | first = William S.
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| | last = Levine
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| | title = The control handbook
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| | publisher = [[CRC Press]]
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| | place = [[Boca Raton, FL]]
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| | year = 1996
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| | isbn= 0-8493-8570-9
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| | pages = 1548
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| }}.
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| *{{Citation
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| | last = Nise
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| | first = Norman S.
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| | author-link =
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| | title = Control Systems Engineering
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| | place =
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| | publisher = [[John Wiley & Sons]]
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| | series =
| |
| | volume =
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| | year = 2008
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| | edition = Fifth
| |
| | pages = xvii+880
| |
| | language =
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| | url =
| |
| | doi =
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| | id =
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| | isbn = 978-0-471-79475-2
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| }}
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| *[[United States]] [[Federal Standard 1037C]]: Glossary of Telecommunications Terms
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| *{{Citation
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| | last = Valley
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| | first = George E., Jr.
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| | author-link =
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| | last2 = Wallman
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| | first2 = Henry
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| | author2-link = Henry Wallman
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| | title = Vacuum Tube Amplifiers
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| | series = MIT Radiation Laboratory Series
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| | volume = 18
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| | publisher = [[McGraw-Hill]].
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| | place = [[New York]]
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| | year = 1948
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| | pages =xvii+743
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| }} Paragraph 2 of chapter 2 and paragraphs 1 to 7 of chapter 7 .
| |
| *{{Citation
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| | last = Wallman
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| | first = Henry
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| | author-link = Henry Wallman
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| | title = Transient response and the central limit theorem of probability
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| | journal =[http://www.ams.org/cgi-bin/bookstore/bookpromo/psapmseries Proceedings of Symposia in Applied Mathematics]
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| | volume = 2
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| | page = 91
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| | publisher = [[American Mathematical Society|AMS]].
| |
| | place = [[Providence, Rhode Island|Providence]]
| |
| | year=1950
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| | id=
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| | mr= 0034250
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| | zbl= 0035.08102
| |
| }}.
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| [[Category:Electronics]]
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| [[Category:Transient response characteristics]]
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Some consumers of computer are aware which their computer become slower or have certain errors following using for a while. But most folks don't understand how to accelerate their computer and some of them don't dare to operate it. They always find some experts to keep the computer in wise condition however, they have to spend certain funds on it. Actually, we can do it by oneself. There are numerous registry cleaner software that you can get 1 of them online. Some of them are free plus you merely should download them. After installing it, this registry cleaner software might scan the registry. If it found these mistakes, it may report we plus you are able to delete them to keep your registry clean. It is simple to operate plus it is the best method to repair registry.
Carry out window's program restore. It is extremely important to do this because it removes wrong changes that have happened inside the system. Some of the errors outcome from inability of your system to create restore point frequently.
Over time the disk could furthermore receive fragmented. Fragmentation causes a computer to slow down because it takes windows much longer to find a files location. Fortunately, a PC has a built in disk defragmenter. You can run this program by clicking "Start" - "All Programs" - "Accessories" - "System Tools" - "Disk Defragmenter". You can have the way to choose that drives or partition we want to defragment. This action could take we several time so it is very advised to do this on a regular basis so because to avoid further fragmentation and to accelerate your windows XP computer.
Always see with it which you have installed antivirus, anti-spyware plus anti-adware programs plus have them up-to-date on a regular basis. This can help stop windows XP running slow.
Google Chrome crashes on Windows 7 when the registry entries are improperly modified. Missing registry keys or registry keys with wrong values could cause runtime mistakes and thereby the problem occurs. You are recommended to scan the entire program registry and review the outcome. Attempt the registry repair task using third-party tuneup utilities software.
Why this problem arises frequently? What are the causes of it? In fact, there are 3 major causes which could lead to the PC freezing problem. To solve the problem, you should take 3 steps in the following paragraphs.
The 'registry' is merely the central database which shops all the settings plus options. It's a truly important piece of the XP system, meaning that Windows is regularly adding plus updating the files inside it. The problems occur whenever Windows actually corrupts & loses several of these files. This makes a computer run slow, as it attempts hard to find them again.
Registry products have been designed to fix all the broken files inside the program, allowing a computer to read any file it wants, whenever it wants. They work by scanning from the registry plus checking each registry file. If the cleaner sees it is corrupt, then it may substitute it automatically.