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Capacitors & Capacitance Calculations

Capacitors are passive devices used in electronic circuits to store energy in the form of an electric field. They are the compliment of inductors, which store energy in the form of a magnetic field. An ideal capacitor is the equivalent of an open circuit (infinite ohms) for direct currents (DC), and presents an impedance (reactance) to alternating currents (AC) that depends on the frequency of the current. The reactance (opposition to current flow) of a capacitor is inversely proportional to the frequency of the current flowing through it. Capacitors were originally referred to as "condensers" for a reason that goes back to the days of the Leyden Jar where electric charges were thought to accumulate on plates through a condensation process.

The property of capacitance that opposes current flow is exploited for the purpose of conducting signals with a higher frequency component while preventing signals of lower frequency components to pass. A common application of a capacitor is in an RF (radio frequency) circuit is where a DC bias voltage needs to be blocked from flowing through a circuit while allowing the RF signal to pass.

Series LC circuit - RF CafeParallel LC tank circuit - RF CafeWhen used in series (left) or parallel (right) with its circuit compliment, an inductor, the inductor-capacitor combination forms a circuit that resonates at a particular frequency that depends on the values of each component.  In the series circuit, the impedance to current flow at the resonant frequency is zero with ideal components. In parallel circuits (right), the impedance to current flow is infinite with ideal components.

Real-world inductor model with resistance, inductance, and capacitance - RF CafeReal-world capacitors made of physical components exhibit more than just a pure capacitance when present in an AC circuit. A common circuit simulator model is shown to the right. It includes the actual ideal capacitor with a parallel resistive component that responds to alternating current. The DC resistive component is in series with the ideal capacitor, and an inductor is connected in series with the entire assembly and represents the inductance of the component leads and plates.

Equations (formulas) for combining capacitors in series and parallel are given below. Additional equations are given for capacitors of various configurations.

As these figures and formulas indicate, capacitance is a measure of the ability of two surfaces to store an electric charge. Separated and isolated by a dielectric (insulator), a net positive charge is accumulated on one surface and a net negative charge is stored on the other surface.

In an ideal capacitor, charge would be stored indefinitely; however, real world capacitors gradually lose their charge due to leakage currents through the non-ideal dielectric.

Additionally, an inductive component is present due to metal leads (if present) and characteristics of the plate surfaces. This inductance, in combination with the capacitance, creates a resonant frequency where the capacitor looks like a pure resistance.

Series Capacitors

1 =  1  +  1 + · · · +  1
CS   C1     C2            Cn

Series capacitors - RF Cafe
Capacitive Reactance

RF Cafe - Capacitive reactance formula

Parallel Capacitors

Cp = C1 + C2 + · · · + Cn
Parallel capacitors - RF Cafe
Parallel Plates
Capacitor parallel plates drawing - RF Cafe Parallel plate capacitance - RF Cafe
                                W = Energy (J)
RF Cafe - Voltage across capacitor
RF Cafe - Capacitance reactance
Coaxial Cable
Coaxial cable drawing - RF Cafe Coaxial cable capacitance equation - RF Cafe
A = Area of plates
C = Capacitance (F)
D = Distance between plates (m)
a = Inner radius (m)
b = Outer radius (m)
q = Charge (Coulombs)
x = Length (m)
W = Energy (J)
εr = Relative permittivity
ε0 = 8.85 x 10-12 F/m
D.F. = Dissipation Factor = 1/q
C =  q
 V
D.F. =  1
 q
 
Equivalent Capacitor (total model)
Capacitor equivalent model drawing - RF Cafe
Old Capacitor Color Code Chart
Old rectangular or square package capacitor color code table - RF Cafe
Old ceramic axial lead package capacitor color code table - RF Cafe

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