The Capacitor GENERAL INFORMATION A capacitor is a component which is capable of storing electrical energy. It consists of two conductive plates (electrodes) separated by insulating material which is called the dielectric. A typical formula for determining capacitance is: C = .224 KA t C = capacitance (picofarads) K = dielectric constant (Vacuum = 1) A = area in square inches t = separation between the plates in inches (thickness of dielectric) .224 = conversion constant (.0884 for metric system in cm) Capacitance – The standard unit of capacitance is the farad. A capacitor has a capacitance of 1 farad when 1 coulomb charges it to 1 volt. One farad is a very large unit and most capacitors have values in the micro (10-6), nano (10-9) or pico (10-12) farad level. Potential Change – A capacitor is a reactive component which reacts against a change in potential across it. This is shown by the equation for the linear charge of a capacitor: Iideal = C dV dt where I = Current C = Capacitance dV/dt = Slope of voltage transition across capacitor Thus an infinite current would be required to instantly change the potential across a capacitor. The amount of current a capacitor can “sink” is determined by the above equation. Equivalent Circuit – A capacitor, as a practical device, exhibits not only capacitance but also resistance and inductance. A simplified schematic for the equivalent circuit is: RP Dielectric Constant – In the formula for capacitance given above the dielectric constant of a vacuum is arbitrarily chosen as the number 1. Dielectric constants of other materials are then compared to the dielectric constant of a vacuum. Dielectric Thickness – Capacitance is indirectly proportional to the separation between electrodes. Lower voltage requirements mean thinner dielectrics and greater capacitance per volume. Area – Capacitance is directly proportional to the area of the electrodes. Since the other variables in the equation are usually set by the performance desired, area is the easiest parameter to modify to obtain a specific capacitance within a material group. Energy Stored – The energy which can be stored in a capacitor is given by the formula: E = 1⁄2CV2 L RS C C = Capacitance Rs = Series Resistance L = Inductance Rp = Parallel Resistance Reactance – Since the insulation resistance (Rp) is normally very high, the total impedance of a capacitor is: Z= where 冑 R + (X - X ) 2 S 2 C L Z = Total Impedance Rs = Series Resistance XC = Capacitive Reactance = 1 2 π fC XL = Inductive Reactance = 2 π fL The variation of a capacitor’s impedance with frequency determines its effectiveness in many applications. E = energy in joules (watts-sec) V = applied voltage C = capacitance in farads 2 Phase Angle – Power Factor and Dissipation Factor are often confused since they are both measures of the loss in a capacitor under AC application and are often almost identical in value. In a “perfect” capacitor the current in the capacitor will lead the voltage by 90°. The Capacitor Insulation Resistance – Insulation Resistance is the resistance measured across the terminals of a capacitor and consists principally of the parallel resistance RP shown in the equivalent circuit. As capacitance values and hence the area of dielectric increases, the I.R. decreases and hence the product (C x IR or RC) is often specified in ohm farads or more commonly megohm microfarads. Leakage current is determined by dividing the rated voltage by IR (Ohm’s Law). I (Ideal) I (Actual) Loss Angle Phase Angle f V IR s In practice the current leads the voltage by some other phase angle due to the series resistance RS. The complement of this angle is called the loss angle and: Power Factor (P.F.) = Cos f or Sine Dissipation Factor (D.F.) = tan for small values of the tan and sine are essentially equal which has led to the common interchangeability of the two terms in the industry. Equivalent Series Resistance – The term E.S.R. or Equivalent Series Resistance combines all losses both series and parallel in a capacitor at a given frequency so that the equivalent circuit is reduced to a simple R-C series connection. Dielectric Strength – Dielectric Strength is an expression of the ability of a material to withstand an electrical stress. Although dielectric strength is ordinarily expressed in volts, it is actually dependent on the thickness of the dielectric and thus is also more generically a function of volts/mil. Dielectric Absorption – A capacitor does not discharge instantaneously upon application of a short circuit, but drains gradually after the capacitance proper has been discharged. It is common practice to measure the dielectric absorption by determining the “reappearing voltage” which appears across a capacitor at some point in time after it has been fully discharged under short circuit conditions. Corona – Corona is the ionization of air or other vapors which causes them to conduct current. It is especially prevalent in high voltage units but can occur with low voltages as well where high voltage gradients occur. The energy discharged degrades the performance of the capacitor and can in time cause catastrophic failures. CERAMIC CAPACITORS E.S.R. C Dissipation Factor The DF/PF of a capacitor tells what percent of the apparent power input will turn to heat in the capacitor. Dissipation Factor = E.S.R. = (2 π fC) (E.S.R.) XC The watts loss are: Watts loss = (2 π fCV2) (D.F.) Very low values of dissipation factor are expressed as their reciprocal for convenience. These are called the “Q” or Quality factor of capacitors. Multilayer ceramic capacitors are manufactured by mixing the ceramic powder in an organic binder (slurry) and casting it by one technique or another into thin layers typically ranging from about 3 mils in thickness down to 1 mil or thinner. Metal electrodes are deposited onto the green ceramic layers which are then stacked to form a laminated structure. The metal electrodes are arranged so that their terminations alternate from one edge of the capacitor to another. Upon sintering at high temperature the part becomes a monolithic block which can provide extremely high capacitance values in small mechanical volumes. Figure 1 shows a pictorial view of a multilayer ceramic capacitor. Multilayer ceramic capacitors are available in a wide range of characteristics, Electronic Industries Association (EIA) and the military have established categories to help divide the 3 The Capacitor CERAMIC LAYER ELECTRODE TERMINATE EDGE TERMINATE EDGE END TERMINATIONS ELECTRODES MARGIN Figure 1 EIA Temperature Compensating Ceramic temperature characteristics in accordance with EIA-198. 4 basic characteristics into more easily specified classes. The basic industry specification for ceramic capacitors is EIA specification RS-198 and as noted in the general section it specifies temperature compensating capacitors as Class 1 capacitors. These are specified by the military under specification MIL-PRF-20. General purpose capacitors with non-linear temperature coefficients are called Class 2 capacitors by EIA and are specified by the military under MIL-C-11015 and MIL-PRF-39014. The new high reliability military specification, MIL-PRF-123 covers both Class 1 and Class 2 dielectrics. Class 1 – Class 1 capacitors or temperature compensating capacitors are usually made from mixtures of titanates where barium titanate is normally not a major part of the mix. They have predictable temperature coefficients and in general, do not have an aging characteristic. Thus they are the most stable capacitor available. Normally the T.C.s of Class 1 temperature compensating capacitors are C0G (NP0) (negative-positive 0 ppm/°C). Class 1 extended temperature compensating capacitors are also manufactured in T.C.s from P100 through N2200. Class 2 – General purpose ceramic capacitors are called Class 2 capacitors and have become extremely popular because of the high capacitance values available in very small size. Class 2 capacitors are “ferro electric” and vary in capacitance value under the influence of the environmental and electrical operating conditions. Class 2 capacitors are affected by temperature, voltage (both AC and DC), frequency and time. Temperature effects for Class 2 ceramic capacitors are exhibited as non-linear capacitance changes with temperature. The Capacitor Table 2: MIL and EIA Temperature Stable and General Application Codes EIA CODE Percent Capacity Change Over Temperature Range MIL CODE Symbol Temperature Range A -55°C to +85°C B -55°C to +125°C C -55°C to +150°C Cap. Change Zero Volts Cap. Change Rated Volts R +15%, -15% +15%, -40% W +22%, -56% +22%, -66% X +15%, -15% +15%, -25% Y +30%, -70% +30%, -80% Z +20%, -20% +20%, -30% Symbol Temperature characteristic is specified by combining range and change symbols, for example BR or AW. Specification slash sheets indicate the characteristic applicable to a given style of capacitor. In specifying capacitance change with temperature for Class 2 materials, EIA expresses the capacitance change over an operating temperature range by a 3 symbol code. The first symbol represents the cold temperature end of the temperature range, the second represents the upper limit of the operating temperature range and the third symbol represents the capacitance change allowed over the operating temperature range. Table 2 provides a detailed explanation of the EIA system. Effects of Voltage – Variations in voltage affects only the capacitance and dissipation factor. The application of DC voltage reduces both the capacitance and dissipation RS198 Temperature Range X7 X5 Y5 Z5 -55°C to +125°C -55°C to +85°C -30°C to +85°C +10°C to +85°C Code Percent Capacity Change D E F P R S T U V ±3.3% ±4.7% ±7.5% ±10% ±15% ±22% +22%, -33% +22%, - 56% +22%, -82% EXAMPLE – A capacitor is desired with the capacitance value at 25°C to increase no more than 7.5% or decrease no more than 7.5% from -30°C to +85°C. EIA Code will be Y5F. factor while the application of an AC voltage within a reasonable range tends to increase both capacitance and dissipation factor readings. If a high enough AC voltage is applied, eventually it will reduce capacitance just as a DC voltage will. Figure 2 shows the effects of AC voltage. Capacitor specifications specify the AC voltage at which to measure (normally 0.5 or 1 VAC) and application of the wrong voltage can cause spurious readings. Figure 3 gives the voltage coefficient of dissipation factor for various AC voltages at 1 kilohertz. Applications of different frequencies will affect the percentage changes versus voltages. D.F. vs. A.C. Measurement Volts AVX X7R T.C. 10.0 50 Dissipation Factor Percent Capacitance Change Percent Cap. Change vs. A.C. Volts AVX X7R T.C. 40 30 20 10 0 12.5 Figure 2 25 37.5 Volts AC at 1.0 KHz Curve 1 - 100 VDC Rated Capacitor 8.0 Curve 2 - 50 VDC Rated Capacitor Curve 3 - 25 VDC Rated Capacitor 6.0 Curve 3 Curve 2 4.0 2.0 Curve 1 0 .5 1.0 1.5 2.0 2.5 AC Measurement Volts at 1.0 KHz 50 Figure 3 5 The Capacitor Capacitance Change Percent Cap. Change vs. D.C. Volts AVX X7R T.C. 2.5 0 Capacitance Change Percent 1600 1200 800 AVX X7R T.C. 0 -5 -7.5 10 KHz 100 KHz 1 MHz 10 MHz 100 MHz 1 GHz Frequency 25% 50% 75% Percent Rated Volts 100% Effects of Frequency – Frequency affects capacitance and dissipation factor as shown in Figures 6 and 7. Variation of impedance with frequency is an important consideration for decoupling capacitor applications. Lead length, lead configuration and body size all affect the impedance level over more than ceramic formulation variations. (Figure 8) +20 Effects of Time – Class 2 ceramic capacitors change capacitance and dissipation factor with time as well as temperature, voltage and frequency. This change with time is known as aging. Aging is caused by a gradual re-alignment of the crystalline structure of the ceramic and produces an exponential loss in capacitance and decrease in dissipation factor versus time. A typical curve of aging rate for semistable ceramics is shown in Figure 9 and a table is given showing the aging rates of various dielectrics. +10 0VDC 0 RVDC -10 -20 -30 -55 -35 -15 +5 +25 +45 +65 +85 +105 +125 Temperature Degrees Centigrade Figure 5 Cap. Change vs. Frequency AVX C0G (NP0) T.C. 0 AVX X7R T.C. -10 -20 1 KHz 10 KHz 100 KHz 1 MHz Frequency Figure 6 1 KHz Figure 7 -10 -30 AVX C0G (NP0) T.C. 400 Typical Cap. Change vs. Temperature AVX X7R T.C. Capacitance Change Percent 2000 -2.5 Figure 4 6 “Q” vs. Frequency "Q" Factor The effect of the application of DC voltage is shown in Figure 4. The voltage coefficient is more pronounced for higher K dielectrics. These figures are shown for room temperature conditions. The combination characteristic known as voltage temperature limits which shows the effects of rated voltage over the operating temperature range is shown in Figure 5 for the military BX characteristic. 10 MHz 100 MHz 1 GHz If a ceramic capacitor that has been sitting on the shelf for a period of time, is heated above its curie point, (125°C for 4 hours or 150°C for 1⁄2 hour will suffice) the part will de-age and return to its initial capacitance and dissipation factor readings. Because the capacitance changes rapidly, immediately after de-aging, the basic capacitance measurements are normally referred to a time period sometime after the de-aging process. Various manufacturers use different time bases but the most popular one is one day or twenty-four hours after “last heat.” Change in the aging curve can be caused by the application of voltage and other stresses. The possible changes in capacitance due to de-aging by heating the unit explain why capacitance changes are allowed after test, such as temperature cycling, moisture resistance, etc., in MIL specs. The application of high voltages such as dielectric withstanding voltages also tends to de-age capacitors and is why re-reading of capacitance after 12 or 24 hours is allowed in military specifications after dielectric strength tests have been performed. The Capacitor Typical Curve of Aging Rate X7R Dielectric Impedance vs. Frequency Effect of Capacitance – AVX SpinGuards +1.5 0 1.00 .001mF .01mF 0.10 .1mF .33mF 0.01 1 10 100 Log Frequency, MHz 1000 Capacitance Change Percent Log Impedance, Ohms 10.00 -1.5 -3.0 -4.5 -6.0 -7.5 Impedance vs. Frequency Effect of Dielectric – AVX DIPGuards 1 1000 10,000 100,000 Hours Max. Aging Rate %/Decade None 2 3 5 Figure 9 .0 R F X7 47 .0 F R 22 X7 Z5U F 0.1 .22 Log Impedance, Ohms ) F 1 .0 0 (NP G F C0 01 .0 R X7 R X7 F 0.1 1 10 100 200 Log Frequency, MHz Impedance vs. Frequency Effect of Lead Length – Military CKR05 .01mF 100.0 Log Impedance, Ohms 100 Characteristic C0G (NP0) X7R Z5U Y5V 10.0 1.0 10 Effects of Mechanical Stress – High “K” dielectric ceramic capacitors exhibit some low level piezoelectric reactions under mechanical stress. As a general statement, the piezoelectric output is higher, the higher the dielectric constant of the ceramic. It is desirable to investigate this effect before using high “K” dielectrics as coupling capacitors in extremely low level applications. Reliability – Historically ceramic capacitors have been one of the most reliable types of capacitors in use today. The approximate formula for the reliability of a ceramic capacitor is: .500" .250" .062" 0" 10.0 Lo = Lt 共共 Vt Vo X 共共 Tt To Y where Lo = operating life T t = test temperature and To = operating temperature in °C L t = test life V t = test voltage Vo = operating voltage X,Y = see text 1.0 0.1 1 10 100 Log Frequency, MHz Figure 8 1000 Historically for ceramic capacitors exponent X has been considered as 3. The exponent Y for temperature effects typically tends to run about 8. 7 The Capacitor General Electrical and Environmental Specifications Many AVX ceramic capacitors are purchased in accordance with Military Specifications, MIL-PRF-39014, MIL-C-11015, MIL-PRF-20, MIL-PRF-55681, and MIL-PRF-123 or according to individual customer specification. When ordered to these specifications, the parts will meet the requirements set forth in these documents. The General Electrical and Environmental Specifications listed below detail test conditions which are common to the foregoing and to most ceramic capacitor specifications. If additional information is needed, AVX Application Engineers are ready to assist you. Capacitance – Capacitance shall be tested in accordance with Method 305 of MIL-STD-202. Class 1 dielectric to 1000 pF measured at 1 MHz, ± 100 KHz, > 1000 pF measured at 1 KHz ± 100 Hz both at 1.0 ± 0.2 VAC. Class 2 dielectrics (except High K) to 100 pF shall be measured at 1 MHz ± 100 KHz, > 100 pF measured at 1 KHz ± 100 Hz both at 1.0 ± 0.2 VAC. High K dielectrics measured at 1 KHz ± 100 Hz with less than 0.5 VAC or less applied. Dissipation Factor – D.F. shall be measured at the same frequency and voltage as specified for capacitance. Dielectric Strength – The dielectric strength shall be measured in accordance with Method 301 of MIL-STD-202 with a suitable resistor in series with the power supply to limit the charging current to 50 ma. max. Insulation Resistance – Insulation Resistance shall be measured in accordance with Method 302 of MIL-STD-202 with rated voltage or 200 VDC whichever is less applied. The current shall be limited to 50 ma. max. and the charging time shall be 2.0 minutes maximum. Burn-In – (Where specified.) 100% of the parts shall be subjected to 5 cycles of Thermal Shock per Method 107 Test Condition A of MIL-STD-202 followed by voltage conditioning at twice rated voltage and maximum rated temperature for 100 hours or as specified. After Burn-In, parts shall meet all initial requirements. Barometric Pressure – Capacitors shall be tested in accordance with Method 105 of MIL-STD-202 Test Condition D (100,000 ft.) with 100% rated voltage applied for 5 seconds with current limited to 50 ma. No evidence of flashover or damage is permitted. Solderability – Capacitors shall be tested in accordance with Method 208 of MIL-STD-202 with 95% coverage of new solder. 8 Vibration – Capacitors shall be tested in accordance with Method 208 Test Condition D of MIL-STD-202 with the bodies rigidly clamped. The specimens shall be tested in 3 mutually perpendicular planes for a total of 8 hours with 125% rated DC voltage applied. No evidence of opens, intermittents or shorts is permitted. Shock – Capacitors shall be tested in accordance with Method 213 Condition 1 (100 Gs) of MIL-STD-202 with the bodies rigidly clamped. No evidence of opens, intermittents or shorts is permitted. Thermal Shock and Immersion – Capacitors shall be tested in accordance with Method 107 Condition A of MIL-STD-202 with high test temperature (maximum rated operating temperature) followed by Method 104 of MIL-STD-202 Test Condition B. Moisture Resistance – Capacitors shall be tested in accordance with Method 106 of MIL-STD-202 with rated voltage or 100 VDC whichever is less applied for the first 10 cycles. Resistance to Solder Heat – Capacitors shall be tested in accordance with Method 210 of MIL-STD-202 with immersion to .050 of body. AVX Ceralam capacitors are manufactured with solder which melts at a temperature greater than 450°F. General Considerations – The application of voltage or temperature usually causes temporary changes in the capacitance of Class 2 ceramic capacitors. These changes are normally in the positive direction and may cause out-oftolerance capacitance readings. If a capacitance reading is made immediately after a dielectric strength or insulation resistance test and parts are high capacitance, they should be re-read after a minimum wait of 12 hours. The Capacitor BASIC CAPACITOR FORMULAS I. Capacitance (farads) English: C = .224 K A TD .0884 KA Metric: C = TD XI. Equivalent Series Resistance (ohms) E.S.R. = (D.F.) (Xc) = (D.F.) / (2 π fC) XII. Power Loss (watts) Power Loss = (2 π fCV2) (D.F.) XIII. KVA (Kilowatts) KVA = 2 π fCV2 x 10 -3 II. Energy stored in capacitors (Joules, watt - sec) E = 1⁄2 CV2 XIV. Temperature Characteristic (ppm/°C) T.C. = Ct – C25 x 106 C25 (Tt – 25) III. Linear charge of a capacitor (Amperes) dV I=C dt XV. Cap Drift (%) C1 – C2 C.D. = C1 IV. Total Impedance of a capacitor (ohms) Z= 冑R 2 + (XC - XL )2 V. Capacitive Reactance (ohms) 1 xc = 2 π fC S XVI. Reliability of Ceramic Capacitors Vt L0 X Tt Y = Lt Vo To ( ) ( ) VI. Inductive Reactance (ohms) xL = 2 π fL XVII. Capacitors in Series (current the same) Any Number: 1 = 1 + 1 --- 1 CT C1 C2 CN C1 C2 Two: CT = C1 + C2 VII. Phase Angles: Ideal Capacitors: Current leads voltage 90° Ideal Inductors: Current lags voltage 90° Ideal Resistors: Current in phase with voltage XVIII. Capacitors in Parallel (voltage the same) CT = C1 + C2 --- + CN VIII. Dissipation Factor (%) D.F.= tan (loss angle) = E.S.R. = (2 πfC) (E.S.R.) Xc IX. Power Factor (%) P.F. = Sine (loss angle) = Cos (phase angle) f P.F. = (when less than 10%) = DF XIX. Aging Rate A.R. = % XX. Decibels Pico Nano Micro Milli Deci Deca Kilo Mega Giga Tera X 10-12 X 10-9 X 10-6 X 10-3 X 10-1 X 10+1 X 10+3 X 10+6 X 10+9 X 10+12 D C/decade of time db = 20 log V1 V2 X. Quality Factor (dimensionless) Q = Cotan (loss angle) = 1 D.F. METRIC PREFIXES x 100 SYMBOLS K = Dielectric Constant f = frequency Lt = Test life A = Area L = Inductance Vt = Test voltage TD = Dielectric thickness = Loss angle Vo = Operating voltage V = Voltage f = Phase angle Tt = Test temperature t = time X & Y = exponent effect of voltage and temp. To = Operating temperature Rs = Series Resistance Lo = Operating life 9