            ### Technical Handbook ### Capacitors 1 ### Capacitors and Capacitance1     ### Reversible Electrolytic Capacitors2  Click on a subject in the right-hand column or scroll down to read everything

### A Brief History of Capacitance

The unit of capacitance is the Farad (symbol F), named after the English physicist Michael Faraday (1791 - 1867). Son of a poor blacksmith and farrier, he became an apprentice bookbinder at the age of 13; at 22 he joined the staff of Sir Humphrey Davy's laboratory, where he began his experimental work in electricity and magnetism. With no formal training in this field, but as a deeply religious man, convinced that observable events were governed by certain natural laws, he set himself the task of discovering and verifying those rules. His achievements included the design of the first dynamo based on his theory and subsequent proof that an electromotive force is set up within a conductor when it is moved through a magnetic field, cutting the lines of magnetic force. Virtually all today's electro-mechanical engineering is based on his theories.

Algebraically, capacitance is usually represented as 'C'.

### Units of Capacitance

The unit of capacitance is the Farad, which, in practical terms, is too large to be used in normal circumstances. Capacitance is therefore normally specified in smaller units as appropriate:

 1 µF = 1,000 nF = 1,000,000 pF 1 nF = 0.001 µF = 1,000 pF 1 pF = 0.001 nF = 0.000001 µF

### Capacitors Connected in Parallel

Connecting capacitors in parallel results in a total capacitance which is the sum of the two capacitors - so connecting two 5µF in parallel gives a total capacitance of 10µF;  1µF in parallel with 4.7µF results in 5.7µF.

Ctotal = C1 + C2

There is also a slight reduction in ESR and increase in ripple current capability.

The combined voltage rating will be equivalent to the lower rated of the two capacitors.

### Capacitors Connected in Series

Not normally recommended. For situations where such connection is unavoidable, the combined capacitance may be calculated as: ESR will increase to approximately the sum of that of the two individual capacitors; DF will approximate to the higher of the two values and ripple current will be equivalent to the lower of the two values.

The combined voltage rating will be equivalent to the lower rated of the two capacitors.

### AC and DC Voltage Relationships

The numerical relations of a sine wave are

 r.m.s. 0.707 x peak value peak value 1.414 x r.m.s. value mean value 0.636 x peak value peak value 1.572 x mean value mean value 0.899 x r.m.s. r.m.s. 1.111 x mean value

For practical applications using reversible electrolytics it is generally sufficient to derive an AC working voltage from the stated DC voltage using the rms value;  so a 50V DC rating could be accepted as equivalent to 35V AC (50 x 0.707 = 35.35).

This holds true up to about 5KHz.  At high frequencies (RF) considerable derating is required, as losses increase and heating results.

• These are theoretical equivalents, and should be used only as a guide. In practical applications, other parameters may intrude.
• Regardless of its AC rating, no capacitor should ever be connected to mains circuits unless it is expressly stated as being suitable for mains applications.

### Ripple Current

Ripple current is a parameter which, in practice, only applies to electrolytic capacitors. It represents the AC signal element in a voltage with a DC offset as would be seen by a conventional polar electrolytic capacitor. In the case of reversible electrolytics used in loudspeaker crossover circuits, where there is no DC offset voltage, it follows that ripple current will be identical to the AC current passed by the capacitor.

The effective series resistance (ESR) of any electrolytic capacitor is sufficiently high to generate heat if excessive AC/ripple current is allowed to pass - resulting, ultimately, in failure of the component.

With film capacitors, and especially polypropylene film types, the ESR is so small that there is virtually no heat build up even at very high currents - far higher than should be found in a loudspeaker crossover.

### Dissipation Factor and 'Q'

Some people prefer to discuss the dissipation factor of a capacitor in terms of 'Q' - probably to parallel the concept as correctly applied to inductors.

Q is defined as the reciprocal of DF - thus the higher the Q, the 'better' the capacitor and the lower the dissipation factor.  See also Effective Series Resistance and Dissipation Factor.

 DF =   5% º Q = 20 DF = 10% º Q = 10 DF = 20% º Q =  5

### Matching Capacitor Type to Application

Of the wide range of available capacitor types, those particulary applicable to audio may be divided into two main categories: Reversible Electrolytic and Metallized Film - both of which are available from Expotus Components in configurations appropriate for use in loudspeakers and other critical applications.

The type of capacitor to be used in a given application may usually be decided in terms of working voltage  versus dissipation factor. In general, the lower the dissipation factor, the better the signal transmission, i.e. the better the perceived audio performance.

The following graph displays the relative merits of the various capacitor types available from ECL. 