- Resonant capacitor
A

**resonant capacitor**is anacoustics andelectrical engineering term for a frequency resonantinductor . Although they are actually inductors, they are called capacitors because they are capable of storing significant amounts of charge (electrons ) in anelectrical 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. Theelectrical 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 filter ing 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 andgamma 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.

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

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

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

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:: $egin\{align\}V\; =\; I\; imes\; Z\; \backslash frac\{dV\}\{dt\}\; =\; frac\{dI\}\{dt\}\; imes\; Z\; \backslash frac\{I\}\{C\}\; =\; frac\{V\}\{L\}\; imes\; frac\{1\}\{j\; omega\; C\}\; \backslash V\; =\; j\; omega\; L\; imes\; I\; \backslash \; end\{align\}$

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

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

**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 applicableDecoupling capacitor s**Trivia**The drawing of the

flux capacitor made popular by the movieBack 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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