Resonant capacitor

Resonant capacitor

A resonant capacitor is an acoustics and electrical engineering term for a frequency resonant inductor. Although they are actually inductors, they are called capacitors because they are capable of storing significant amounts of charge (electrons) in an electrical network (circuit) whereas an inductor stores energy in a magnetic field. Resonant capacitors are typically used to introduce resonant frequencies of a given base frequency to spread signal energy over the frequency spectrum, effectively reducing the energy at the base frequency and increasing tolerance to EMI.

Applications

Frequency Spreading

Resonant capacitors are commonly used in Spread-spectrum clocking designs to spread the resonant clock frequency over a wider frequency spectrum. The electrical resonance of the inductor provides frequency spreading while the capacitive properties keep a majority of the energy in the baseband frequency. The resonance occurs because the inductive reactance and the capacitive reactance of the device are of similar magnitude, causing electrical energy to oscillate between the internal magnetic and electric fields.

Robotics

Designs that incorporate actuators commonly use resonant capacitors. Resonant capactors are used to drive the actuator control signals, providing smooth modulation of the actuating device. The significant capacitive reactance in these devices provides integrated band-pass filtering of the control signal. This filtering solves common problems with actuator designs that tend to result in actuator oscillation due to noise on the input control signal.

Aerospace

Resonant capacitors are increasingly being used in aerospace applications due to their resilience to beta particle and gamma ray interaction. Since these devices store significant amounts of energy in both the electric and magnetic fields, incoming beta particles and gamma rays are effectively absorbed and annihilated. Electrons from β- decay are absorbed in the magnetic field while positrons from β+ decay are absorbed in the electric field. Typical capacators and inductors are unable to absorb gamma rays because they only store their energy in one part of the electromagnetic spectrum, whereas resonant capacitors store energy in the full spectrum allowing them to interact and absorb gamma rays.

Explanation

The structure of resonant capacitors can be approximated as a small resistor (R) in series with an inductor (L) and with a capacitor (C) in parallel to ground.

Start by using Kirchoff's Laws and by evaluating the Thevenin and Norton Equivalent Circuits.

: egin{align}V & = I imes R \V & = L imes frac{dI}{dt} \I & = C imes frac{dV}{dt} \ end{align}

The frequency response can be estimated by looking at the complex impedance.

: egin{align}Z & = R + X \X & = j omega L + frac{1}{j omega C} \ end{align}

Since these devices have R << 1

: Z approx X = j omega L + frac{1}{j omega C}

For low frequency signals, the capacative response dominates the inductive reactance.

: Z approx frac{1}{j omega C}So:: egin{align}V & = I imes Z \frac{dV}{dt} & = frac{dI}{dt} imes Z \frac{I}{C} & = frac{V}{L} imes frac{1}{j omega C} \V & = j omega L imes I \ end{align}

For high frequency signals, the inductive reactance dominates the capacative response.

: Z approx j omega LSo:: egin{align}V & = I imes Z \frac{dV}{dt} & = frac{dI}{dt} imes Z \frac{I}{C} & = frac{V}{L} imes j omega L \V & = frac{1}{j omega C} imes I \ end{align}

Placement

For optimal EMI reduction, resonant capacitors should be placed as closely to the current sinking device as possible. Typical placement is under the integrated circuit across Vcc and ground, near applicable Decoupling capacitors

Trivia

The drawing of the flux capacitor made popular by the movie Back to the Future was based loosely on actual designs of resonant capacitors.

References

* cite web
title = Impedance And Resonant Capacitor Calculator
url = http://www.csgnetwork.com/capimprescalc.html
accessdate = 2007-01-19
* cite web
title = The Physics of Resonance
url = http://intuitor.com/resonance/circuits.html
accessdate = 2007-01-19
* cite web
title = Resonant circuits
url = http://www.tina.com/course/28resonant/resonant.htm
accessdate = 2007-01-19
* cite web
title = Resonant charging
url = http://www.richieburnett.co.uk/resonant.html
accessdate = 2007-01-19


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