Capacitors and ESR

= Capacitor ESR Ratings = == ESR Equivalent Series Resistance == The ESR rating of a capacitor is a rating of quality. = Condensator ESR Evaluări === Rezistenta VSH Equivalent Series == Evaluarea ESR unui condensator este o evaluare de calitate. A theoretically perfect capacitor would be lossless and have an ESR of zero. Un condensator teoretic perfect ar fi fără pierderi și au un ESR de la zero. It would have no in-phase AC resistance. Nu ar avea nici în faza de rezistență AC. We live in the real world and all capacitors have some amount of ESR. Trăim în lumea reală și toate condensatoarele au o anumită cantitate de ESR. To understand why, let us review what a capacitor is, what they are made of, and how we rate them. Pentru a înțelege de ce, să ne revizui ceea ce este un condensator, ceea ce acestea sunt realizate din, și modul în care le-am evalua. == Measuring ESR == You can measure ESR with an analog meter called the Capacitor Wizard From Transtronics, Inc., which is this site's sponsor. == Masurarea ESR == Puteți măsura cu un metru ESR analogic numit Condensator Wizard Din Transtronics, Inc, care este sponsorul acestui site. Other Capacitance meters  == What is a Capacitor? [Http://secure.transtronics.com/Test_Equipment.html metri Alte Capacitance] == Ce este un condensator? == A capacitor consists of two conductive metal plates separated by an insulating dielectric. == Un condensator este format din două plăci de metal conductoare separate printr-un dielectric izolator. The dielectric can be made of glass, ceramic, tantalum oxide, or plastics such as polyethylene or polycarbonate. Dielectrică poate fi confecționat din sticlă, ceramică, oxid de tantal, sau din material plastic, cum ar fi polietilena sau policarbonat. Even air can be used as the dielectric. Chiar de aer poate fi folosit ca dielectric. When the capacitor holds some energy in the form of extra electrons on one plate and electron holes on the other, we say that the capacitor is charged. Atunci când condensatorul deține unele de energie sub formă de electroni suplimentare, pe de o farfurie si gauri de electroni pe de altă parte, spunem că condensatorul este încărcat'. == Farads == Capacitance (C) is the amount of charge per volt of potential that a capacitor holds. == == Farads Capacitate ( C) este cantitatea de taxa pe volt de potențial, care deține un condensator. (C = Q / V, where Q = charge (measured in coulombs) and V = potential difference (measured in volts) Capacitance is measured in Farads, but most often a small fraction of a Farad thus: * micro-Farads uF millionths (10-6) Farads * pico-Farads pF (10-12) Farads (sometimes called "puffs" in engineering slang) The energy stored in a capacitor is E = CV2/2 (E is in joules). Thus, the average power in watts is Pav = CV2 / 2t, where t is the time in seconds. The maximum voltage rating and its capacitance determine the amount of energy a capacitor holds. The voltage rating increases with increasing dielectric strength and the thickness of the dielectric. The capacitance increases with the area of the plates and decreases with the thickness of the dielectric. Thus, the capacitance of a capacitor (C) is related to the plate area (A), plate separation distance (d), and permittivity (ε) of the dielectric by the following equation: $C = \varepsilon A/d$ Here A and d are based on meters as the unit and ε is in Farads per meter (or Coulombs squared per newton-meters squared). Notice the force unit involved—it explains why capacitor microphonics (remember the good old condenser microphone?) and a mechanical failure mode of capacitors). (

, where ε_d is the permittivity of the dielectric and ε₀ is the permittivity of free space Air has nearly the same dielectric value as a vacuum with k = 1.0001. , while the plastics range in the low 2s to low 3s.</span> Teflon, un foarte bun izolator, are o valoare de .</span> Mica primeste-ne un

is 27, and the ceramics' range from 35 to over 6,000.</span> Oxid de aluminiu este de 7, k 
where XC is the capacitive reactance $X_{\rm C} =\frac{1}{\omega C}=\frac{1}{2\pi f C}$ and R is the soon-to-be-defined term of ESR.   Q is proportional to the inverse of the amount of energy dissipated in the capacitor. Thus, ESR rating of a capacitor is inversely related to its quality. == Dissipation Factor == The inverse of Q is the dissipation factor (tan(δ)). Thus, tan(δ) = ESR/XC and the higher the ESR the more losses in the capacitor and the more power we dissipate. If too much energy is dissipated in the capacitor, it heats up to the point that values change (causing drift in operation) or failure of the capacitor. == Ripple Current Rating == The ripple current is sometimes rated for a capacitor in RMS current. Remembering that P = I2R where R in this case is ESR it is plain to see that this is a power dissipation rating. == Dielectric Absorption == This is the phenomenon where after a capacitor has been charged for some time, and then discharged, some stored charge will migrate out of the dielectric over time, thus changing the voltage value of the capacitor. This is extremely important in sample and hold circuit applications. The typical method of observing Dielectric Absorption is to charge up a cap to some known DC voltage for a given time, then discharge the capacitor through a 2 ohm resistor for one second, then watch the voltage on a high-input-impedance voltmeter. The ratio of recovered voltage (expressed in percent) is the usual term for Dielectric absorption. The charge absorption effect is caused by a trapped space charge in the dielectric and is dependent on the geometry and leakage of the dielectric material. == ESL == ESL (Equivalent Series Inductance) is pretty much caused by the inductance of the electrodes and leads. The ESL of a capacitor sets the limiting factor of how well (or fast) a capacitor can de-couple noise off a power bus. The ESL of a capacitor also sets the resonate-point of a capacitor. Because the inductance appears in series with the capacitor, they form a tank circuit. == ESR Defined == ESR is the sum of in-phase AC resistance. It includes resistance of the dielectric, plate material, electrolytic solution, and terminal leads at a particular frequency. ESR acts like a resistor in series with a capacitor (thus the name Equivalent Series Resistance). This resistance often is the cause of failures in capacitor circuits. These circuits look just fine on paper, but the hidden resistance causes failure due to heat buildup. To charge the dielectric material current needs to flow down the leads, through the lead plate junction, through the plates themselves - and even through the dielectric material. The dielectric losses can be thought of as friction of aligning dipoles and thus appear as an increase (or a reduction of the rate of decrease -- this increase is what makes the resistance vs freq line to go flat.) of measured ESR as frequency increases. As the dielectric thickness increases so does the ESR. As the plate area increases, the ESR will go down if the plate thickness remains the same. To test a capacitor's ESR requires something other than a standard capacitor meter. While a capacitor value meter is a handy device, it will not detect capacitor failure modes that raise the ESR. As the years go by, more and more designs rely on low ESR capacitors to function properly. ESR-failed caps can present circuit symptoms that are difficult to diagnose. == Formulas at a glance == ===Dissipation Factor === Where: * δ is the angle between the capacitor's impedance vector and the negative reactive axis. * DF is the Dissipation Factor (sometimes expressed as a percentage). * ESR stands for Equivalent Series Resistance * XC is the capacitive reactance $DF = \tan \delta = \frac{ESR}{|X_{\rm C}|}$ ===Capacitive Reactance === Reactance is used to compute amplitude and phase changes of sinusoidal current. It is denoted by the symbol $\scriptstyle{X}$ and can be used in place of resistance in many calculations - It can be thought of as the effective AC resistance at some frequency. $X_{\rm C} = \frac{-1}{ \omega C} = \frac{-1}{2 \pi fC}$ The -1 above is because the reactance is negative from the following vector math: Both reactance $\scriptstyle{X}$ and resistance $\scriptstyle{R}$ are required to calculate impedance $\scriptstyle{Z}$. In some circuits one of these may dominate, but an approximate knowledge of the minor component is useful to determine if it may be neglected. :$Z = R + jX\,$ where :j2 =  − 1 The 'magnitude' $\scriptstyle{|Z|}$ phase $\scriptstyle{\theta}$ of the impedance depend on the combined action of the resistance and the reactance. $\scriptstyle{|Z|}$ is the ratio of the voltage and current amplitudes, while the $\scriptstyle{\theta}$ is the voltage–current phase difference. :$|Z| = \sqrt{ZZ^*} = \sqrt{R^2 + X^2}$ where Z *  is the complex conjugate of Z :$\theta = \arctan{X \over R}$ * If $\scriptstyle{X > 0}$, the reactance is inductive * If $\scriptstyle{X = 0}$, then the impedance is purely resistive * If $\scriptstyle{X < 0}$, the reactance is capacitive The reciprocal of reactance ( 1 / X) is susceptance - not a term you will likely meet up with. ===Inductive reactance:=== XL = ωL = 2πfL Relationship between angular frequency ω and frequency f: ω = 2πf $I = \frac{E}{\sqrt{R^2 + \left(\omega L -\frac {1}{\omega C}\right)^2}}$ === Resonance Frequency === * Fr =  Frequency of Resonance $F_{\rm r} = \frac{1}{2\pi \sqrt{LC}}$ === Dielectric Constant to Capacitance === Where * k = dielectric constant ($\varepsilon_d/\varepsilon_0$; dimensionless) * A = area (square meters) * t = thickness of the dielectric (meters) * Q = charge (coulombs) * V = potential difference (volts) $C = \frac{\varepsilon_0 kA}{t}$ $C = \frac{Q}{V}$ * $\varepsilon_d$ is the permittivity of the dielectric * $\varepsilon_0$ is the permittivity of free space ($8.85 \cdot 10^{-12} {\rm F}\;{\rm m}^{-1}$) $C = \frac{ \varepsilon A}{t}$ $k = \frac{\varepsilon_d}{\varepsilon_0}$ === Stored Energy === Where energy E (in joules) stored in a capacitor is given by $E = \frac{CV^2}{2}$ === Average power === Thus, the average power in watts where t = time in seconds. $P_{\rm av} = \frac{CV^2}{2t}$ $Z_{\rm C} = \sqrt{ESR^2 + X_{\rm C}^2}$ ==Time Domain Reflectometry (TDR) — Characteristic Impedance of cable formulas == === Discontinuance of transmission characteristic impedance=== Where * Za = characteristic impedance through which the incident wave travels first * Zb = the characteristic impedance through which the incident wave travels next. * Vr = the reflected wave amplitude, * Vi = the incident wave amplitude * Vt is the transmitted wave amplitude. $\frac{V_{\rm r}}{V_{\rm i}} = \frac{Z_{\rm b} -Z_{\rm a}}{Z_{\rm b} + Z_{\rm a}}$ $\frac{V_{\rm r}}{V_{\rm t}} = \frac{2 Z_{\rm b}}{Z_{\rm b} + Z_{\rm a}}$ $Z_{\rm b} = Z_{\rm a}\left( \frac{V_{\rm i} + V_{\rm r}}{V_{\rm i} - V_{\rm r}}\right)$ Where: * Z0 is the characteristic impedance $\tau = RC = \frac{Z_0C}{2}$ == Was this Information Useful? == If you found this information useful - all I ask is to look at our home page and see if we have any products that might be of use to you or a colleague. Link to us if you have a web page. If you have some thing to add to this page please use the edit button.</span> A se vedea [/ kituri /. Secretele ccode.htm ale paginii condensator coduri.] Pentru mai multe informatii == == Rigiditatea dielectrica Rigiditatea dielectrica este o proprietate de dielectric, care este, de obicei, exprimat în volți per mil. (V/.001 ") sau volti pe centimetru (V / cm) este diferența maximă potențial într-o unitate de grosime a dielectricului înainte de a descompune și permite o scânteie. Dacă vom depăși. rigidității dielectrice, un arc electric va "clipi peste" și sudați de multe ori plăci de condensator împreună. == Q sau de calitate Factor ==' Q a unui condensator este importantă în circuitele tunate, deoarece acestea sunt mai atenuate și au un punct de tuning larg ca' Q se duce în jos. < math> Q = \ frac Template:X \ rm C {R} </ math> unde X  C </ sub> este reactanța capacitivă