The equivalent circuit, which explains the major features of the electrolytic capacitor, is shown in Fig. 2. Shunt resistance R represents the effect of d.c. leakage. A very small amount of power is dissipated in R. but this causes negligible heating compared to that dissipated in the equivalent series resistance ESR. Ripple or a.e. passing through the capacitor produces a power loss in the ESR. This results in heating within the capacitor. The ESR also explains why the capacitor can't behave as a short-circuit at high frequencies. The very wide use of switch-mode power supplies has increased the demand for low-impedance, high-frequency capacitors with high ripple current ratings. Suitable types always have a low ESR, for reasons that will be explained later. L is the self-inductance, which is the result of the physical geometry of the capacitor and its terminations. The magnitude of L is such that electrolytics are ineffective as capacitors at radio frequencies. At these frequencies the inductive reactance is large. Acknowledgement Components list 
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Simple ESR Meter for Electrolytics
by Ray Porter , M.Sc., C.Eng., M.I.E.E.
TELEVISION Servicing Magazine January and April 1993
You can subscribe to TELEVISION magazine or buy it at WH Smith newsagent.
ESR article
Aluminium electrolytic capacitors are widely used where high capacitance values are required. Readers will have noticed that a significant number of equipment faults are caused by their failure. This article provides a historical background then goes on to describe the construction, limitations and failure mechanisms of these components in their miniature PCB-mounted form. With this information electronic project constructors and service engineers will be able to choose the component best suited for a particular purpose - where this is not dictated by physical size or the pitch of the leadout wires.
A Century of Electrolytics
The electrolytic capacitor, or condenser as it was then known, was invented a hundred years ago in Germany. It was first used as a filtering element in battery eliminators during the Twenties, when electronic engineering was almost totally concerned with radio broadcast and receiving equipment. These early versions had a "wet" electrolyte and had to be vertically mounted. This limitation was lifted in 1928 when "dry" electrolyte, i.e. impregnated paper, started to be used.
As a result of enhancements in both design and the manufacturing processes used there have been improvements in performance, size and reliability over the last ten years. Compact, modern consumer electronic products continue to require the most that components can give by way of performance however. Thus component failures do occur.
Construction
Fig. 1 shows the general form of construction. The aluminium electrolytic capacitor consists of two layers of aluminium foil which are separated by paper that's impregnated with an electrolyte gel - the capacitor derives its name from this. The foil and paper sandwich is spirally wound and then enclosed in an aluminium or plastic tube.
Only one of the foil layers is an actual electrode of the capacitor - the positive plate or anode. By etching its surface the effective area of the anode is increased one hundredfold, thus increasing the capacitance value obtained in comparison with that achievable using plain foil. The second electrode, the negative plate, is the electrolyte which is in contact with the anode foil. The second foil serves only to provide a contact with the electrolyte. Aluminium oxide, which is formed on the capacitor's anode electrochemically during manufacture, serves as the dielectric. The relative permittivity of the aluminium oxide is about eight: its thickness, which depends on the forming voltage applied during manufacture, is about 1-5 nanometres per volt. It's because of the dielectric strength of about IMV per mm and the moderate relative permittivity that the aluminium electrolytic achieves the highest CV product within a particular volume of any form of capacitor.
Equivalent Circuit
Fig. 2: Simplified equivalent circuit of an electrolytic capacitor. A and B are the terminals, C is the effective capacitance, R is the shunt resistance (insulation resistance) through which d.c. leakage current flows, ESR is the equivalent series resistance and L the capacitor's self-inductance due to its terminals, electrodes and geometry.
Variations of Characteristics in Use
Fig. 3 shows how the characteristics of aluminium electrolytes vary with applied frequency, changes of internal temperature, increases in applied d.c. voltage and the passage of time. This information can be used as a guide in assessing the suitability of an electrolytic capacitor for use under arduous environmental and electrical conditions.
Fig. 3: How the characteristics of an aluminium electrolytic capacitor vary with temperature, frequency, time and applied voltage.
Effect of Temperature Increase
Increased temperature within an electrolytic capacitor produces a capacitance change that may make it unsuitable for use in a timing circuit. But the most important long-term effect of increased temperature is that the capacitor's life is reduced. This occurs because the electrolyte evaporates, its vapour passing through the end seal which is usually a rubber plug. The loss of electrolyte reduces the capacitance and increases the ESR, since less plate area is then in use. These changes in electrical effectiveness result in equipment failures because filtering and coupling deteriorate. The deterioration reaches the point where correct circuit operating conditions are no longer maintained.
Increased ambient temperature also leads to increased internal temperature. It has been found that because the electrolyte evaporates more rapidly at high temperature the life expectancy of an electrolytic capacitor at 60 C is twice that at 75 C, while at 85 C life is again halved. Extreme increase in internal temperature produces increased internal pressure. This is relieved by a controlled thickness vent in the can, a diaphragm in large cans or by expulsion of the rubber end plug in miniature electrolytics.
Ripple Current Rating
The permissible ripple current is limited by the capacitor's internal temperature which rises because of dissipation due to the ESR. It has been found that temperature rise in C is equal to:
(IxI x ESR x 1.1 x 100000)/can area in sq. mm.
Thus a larger can and/or a lower ESR results in a higher ripple current rating.
Forward Voltage Rating
The forward voltage rating is related to the voltage used while forming the dielectric during manufacture and is the maker's recommended maximum value. At one time the use of an electrolytic capacitor at less than its rated value resulted in deterioration of the dielectric. Use of high purity aluminium foil has solved this problem, and now the effect of using an electrolytic capacitor at less than its rated value is to increase the dielectric's reliability in accordance with a fifth power law, e.g. failure rate at 80 per cent of the rated voltage = (0.8)5 = 0.33 times the failure rate at 100 per cent. Thus the life expectancy of the dielectric is increased three times by a 20 per cent reduction in the applied voltage.
Reverse Voltage
Up to l.5V is an acceptable reverse voltage for aluminium electrolytics. Non-polarised types often have seals at both ends of the can. Because of this the electrolyte vapour leakage is twice that with a single-ended type. So it's worth considering the use of a polarised type even where no bias voltage is normally present in the circuit concerned.
Application of a higher reverse voltage for a long time will result in a loss of capacitance. But application of a significantly higher reverse voltage for a short period of time won't cause failure either in the reverse direction or when the capacitor is subsequently used with the correct forward voltage. Be careful about applying incorrect d.c. voltages to electrolytics: their failure mode can be explosively dangerous when internal pressure is released after an excessive temperature rise.
Expected Life
Manufacturers seem to regard the life of components used in consumer electronic products as being a minimum of three-five years. This is checked by testing at maximum temperature for up to 10,000 hours. But degradation limits with bottom-of-the-range electrolytics are specified for only 500 hours - see Table 1. This means that significant deterioration will occur after say a year if the capacitor is operated with a high internal temperature.
In the UK, ambient temperatures for consumer equipment are normally 20-30 C. The ambient summertime temperature in China is around 40 C, which must shorten the life of electrolytics used there. Long-haul travellers are advised to keep their camcorders cool!
Manufacturers consider the end of an electrolytic capacitor's useful life to be when 40 per cent of the electrolyte has evaporated and escaped through the end seal, but catastrophic failure as described below may occur before this point is reached.
Failure Modes
The most common cause of failure when electrolytic capacitors are being tested for useful life expectancy is a short-circuit through the dielectric because of voltage stress. Open-circuits occur because of mechanical failure of the joint between the foil and capacitor terminals and are much less common. In field servicing the most common cause of failure is the absorption of hydrogenated hydrocarbon cleaners, which attack the aluminium foil, through the end seal. Current "green" practices in industry are to use no-wash or water-washable fluxes while soldering, which should reduce this type of field failure.
Typical Characteristics
Table 1 lists typical electrolytic capacitor characteristics in relation to voltage rating. This shows that capacitors with the same voltage rating and type of construction have the same dissipation factor. A capacitor that will provide better reliability can thus be chosen, since use of one with a higher voltage rating will result in longer dielectric life because of the voltage Berating factor while the drying-up process will be slower because the internal temperature will be lower Internal temperature is reduced because high-voltage capacitors have a larger case size and a lower ESR value. Because of the heat-handling capability of higher-voltage capacitor their ripple current rating increases with voltage rating for given capacitance value.
Table 1: Typical electrolytic capacitor characteristics.
Voltage rating: lOV 16V 25V 35V 50V 63V
Dissipation factor for capacitors with values between 0.47uF- 1,000uF
105C type 0.19 0.16 0.14 0.12 0.1 0.1
Low ESR type 0.15 0.1 0.08 0.07 0.06 0.05
ESR of a 220uF capacitor at 120Hz (Ohms)
105C type 1.15 0.97 0.84 0.72 0.6 0.6
Low ESR type 0.5 0.4 0.32 0.28 0.22 0.21
Maximum ripple current at 120Hz (mA)
105C type 260 320 430 480 540 580
Low ESR type 380 450 600 700 900 1,100
Case size, diameter x length in mm
105Ctype 8x11 lOx12.5 10x16 10x20 12.5x20 12.5x25
Low ESR type 0x16 10x16 12.5x20 12.5x 25 16x 25 16x31.5
Life test data: permitted dissipation factor
105C type, after 500 hours 1.5 x initial value
Low ESR type, after 2,000 hours 2 x initial value
My thanks to Sprague Electric and Rubycon for supplying performance and life data for their ranges of miniature aluminium electrolytic capacitors.
GLOSSARY OF TERMS
Dissipation Factor (DF): The ratio of the effective series resistance (ESR} of a capacitor to its reactance at a specified frequency.
Effective Series Resistance (ERR): This is the "lumped" element that's used for purposes of calculation to explain the power loss within a capacitor when it passes a.c.
Etching: An electrochemical process that roughens the surface of the aluminium foil, thereby increasing its surface area in comparison with unetched foil.
Quality Factor (QF): The ratio of capacitive reactance to ESR at a specified frequency. It's the inverse of DF.
Working Voltage: The maximum d.c. voltage that can be applied to a capacitor for continuous duty at the maximum rated temperature.
ESR METER
In an article in the January 1993 issue I described the way in which the effective series resistance (ESR) of an aluminium electrolytic capacitor can increase so that it no longer acts as a low-impedance component. This explains why a fault is often cleared by replacing an electrolytic capacitor even though its value, when checked with a capacitance meter, is close to that marked on it. In view of this I decided to design a simple meter to measure the ESR of electrolytic capacitors. Its range suits the ESR values of PCB-mounted electrolytics. By checking against standard values (see Fig. 3) you can reject lossy capacitors.
The tester makes use of an operational amplifier as a negative-resistance oscillator. Since the operation of negative-resistance operational-amplifier circuits doesn't seem to be well known a short explanation of the relevant theory is provided later.
Circuit Description
The circuit produces a negative resistance to cancel the ESR of the capacitor being tested so that there is continuous series resonance with a fixed inductor. Fig. 4 shows the circuit diagram of the meter. The negative resistance is produced by IC1b: Cx is the capacitor under test and L1 the fixed inductor. VR1 enables the negative resistance to be adjusted. Rotate it until oscillation stops: the ESR value can then be read from a scale fixed to VR1.
When there is no negative resistance present L1 and Cx
form a series resonant circuit that's damped by L1's resistance and Cx's ESR. This circuit will ring when energised by an impulse. IC1a is used as an oscillator to produce a square wave output at a frequency of a few Hz. This output is differentiated to produce the spikes (impulses) that energise the resonant circuit. When the capacitor's ESR and the resistance of R1 are cancelled by the negative resistance the ringing becomes a continuous oscillation. LED D1 is then on. When the oscillation is stopped by reducing the value of the negative resistance the LED goes off.
If a short-circuit capacitor is connected to the tester the LED comes on with full brightness. When the resonant circuit is oscillating the LED is illuminated on only the positive-going half cycles: it therefore glows at half brightness.
IC1d provides a half-supply voltage reference for IC1b. S1 varies IC1b's gain, changing the negative resistance to provide 0-1, 0-10 and 0-100 ESR ranges.
Construction
The circuit was built on a piece of stripboard which, with a PP3 battery, fits easily into an ABS box. L1 was wound around the four pillars on the inside of the box's lid - see Fig. 8. It consists of 42 turns of 30 s.w.g. enamelled copper wire. This results in a coil with a resistance of 3.2 and an inductance of 90 H. A different wire gauge could be used, but its resistance plus that of R1 must equal IO .
With the coil as specified above a l,OOO F capacitor in
position Cx produces oscillations at 70Hz. A 1uF capacitor increases the frequency to 10kHz. When testing the circuit I connected a crystal earpiece via a l00nF capacitor to R19 to check for oscillation. The clicks of a square wave can be heard when VR1 is set far away from the position that stops oscillation. As the critical setting of VR1 is approached the pure sound of a low-amplitude sine wave is audible.
Calibration
Start by using a known good l,000pF capacitor with a voltage rating of at least 25V in position Cx. Adjust VR1 until the LED goes off. Mark the scale O IQ. Now add known-value resistors in series with Cx and adjust VR1 until the LED just goes off. Mark the scale with the new total resistance value. You may find it convenient to use increments of O IQ on the 1 range and suitably larger increments on the other two ranges.
Interpreting the Results
Fig. 6 shows typical ESR values, based on manufacturers' data and allowing for the fact that ESR measured at 10kHz is usually one third of that measured at 1kHz. The ESR values with lOV normal grade capacitors can be seen to be four times those with low-ESR 63V types. Thus when a low-ESR type has deteriorated to the point where its ESR is the same as that of a normal electrolytic its internal heating will have quadrupled!
If you find that the measured ESR value is more than twice that shown in Fig. 6 the capacitor is past its best. ESR values for capacitors with voltage ratings other than those specified in Fig. 6 will be between the relevant lines on the graph.
Negative Resistance with an Op Amp
When a voltage increase is applied to a negative resistance there's a current decrease, i.e. I = -V/R.
Two operational-amplifier configurations exhibit negative input resistance. They are shown in Figs. 7 and 8. The one to use depends on the source resistance of the circuit to which it's connected. This is because the circuits use negative and positive feedback simultaneously, the source being part of the feedback potential dividers. If the proportion of the output fed back to the non-inverting (+) input in Fig. 7 is too large or the stage gain in Fig. 8 is too great unwanted oscillation will occur and the circuit won't function as a negative resistance.
Conventional current notation is used in the following explanation. In Fig. 7 the values of R2 and R3 are equal. Thus when +V is applied to the input the output rises to +2V. The voltage across R is then V and its direction is such that I must flow out of the input. So the circuit's input resistance is V/-I=-R, which means that the input resistance is of magnitude equal to R but negative in value.
The same analysis can be applied to the circuit shown in Fig. 8. Remember that these circuits will be stable only when the source resistance is as shown, and that operation as described is possible only when the operational amplifier's normal voltage and current ratings are not exceeded.
R1 6.8 R8 47k R15 150k
R2 1k R9 560 R16 1.1k
R3 1M R10 120k R17 2k
R4 100k R11 120k R18 11k
R5 10k R12 33k R19 10k
R6 270k R13 2.2M R20 10k
R7 470k R14 150k All 0.25W 5%
VR1 100k
C1 2.2nF C2 220uF, 15V C3 0.1uF
C4 10nF
IC1 TL084CN Tr1 BC547 Tr2 BC557
TR3 BC547 D1 Red LED
L1 14m of 30g enamelled wire - see text
S1 3--pole 4-way switch
ABS box, stripboard
Fig. 6: Typical ESR values, A 10V normal grade, B 25V normal or 10V low-ESR grade, C 100V normal or 25V low-ESR grade, D 63V low-ESR grade.
Fig. 7 (left): Negative-resistance op-amp circuit when the source resistance is less than R.
Fig. 8 (right): Negative-resistance op-amp circuit when the source resistance is greater than R.
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