Harmonics

It's the magic of tuned circuits.

http://en.wikipedia.org/wiki/RLC_circuit

Yep. I recommend taking a function generator, a power amp, a scope and a tuned circuit and just playing with it. Nothing beats seeing it.

If you have a series circuit involving R (resistance), C (capacitance) and L (inductance), the total voltage drop along the circuit is obtained by adding the voltage drops along the R,L,C portions. But since there is a phase difference between voltages along R,L,C, those cannot be added arithmetically, but geometrically (that means that the total sum is less than the sum of the components). An ideal capacitance Xc(no R component) is oriented at 90 degrees from the resistance, while the inductance XL is oriented also at 90 degrees but in the opposite direction.

Since both XL and XC are dependent on the frequency, there is a frequency at which the 2 components neutralize themselves (XL = XC). This is the resonance frequency.

Since XC = XL can occur at any value of L and C (very high or very low, but at a resultant frequency), the same resonance frequency implying only that L*C = constant, the voltage along XC (UC = I * XC) (and also along XL) (UL = I * XL) can be very high, much greater than the voltage measured at the circuit terminals (U = I * Z = I * R).

As an example, for a voltage U = 120V, and a frequency of 60 Hz, the series circuit consists of a resistance R = 2 ohm, an inductance XL= 10 ohm and a capacitance XC = 10 ohm. The resulting current I = 120/2 = 60A. For a series circuit, the current is the same along all components. So the voltage measured along XL and also XC is:

UL = I*XL = 10 * 60 = 600V equal (but in the opposite direction) to UC = I*XC = 10 * 60 = 600V.

Sorry--I want eaves drop on this thread--Sounds interesting.

Hello ngcamub

A simple example should suffice.

Consider a child on a swing, and you are pushing the swing periodically.

If you time your push to the resonant frequency of the swing (A Pendulum) the push adds to the kinetic energy, and the swing goes higher and higher, because there needs to be only a small amount of input energy from each push to increase swing momentum.

If, however, you push randomly, that swing is not going to increase momentum very much.

Thus it is with resonant tuned circuits, and is the way that radio waves can be impressed onto telephone lines, while filters keep the audio frequency of the telephone from interfering with the radio waves.

Thus too, Power-line carrier circuits can take voice frequency signals (telephone talking)on EHV (110kV upwards) circuitry without the people using the telephones becoming turned into charred carbon - tuned resonant filters keep the High Voltage out of the telephone circuitry.

Basically, Resonance is caused by the timed arrival of a "push" which adds to the energy level of the system, whether that "push" force is electrical, mechanical, or other force.

In the radio field, resonance is used to correctly size transmitting antennas, circuits, transmission lines, tuners and the like.

In the mechanical field, resonance is used for grandfather clocks (pendulum), mechanical watches (escapement) and other purposes.

Harmonics can be extremely destructive, in a manner similar to resonantly pushing that child on the swing until the swing plus child goes right over the top of the overhead support bar and down the other side.

If you're still wondering, reply here.

Kind Regards....

The matter is quite simple, Both the capacitor and the Inductance of the circuit store energy, only at opposite phases ie when one discharges energy stored, other starts storing. The rate (or frequency) of this phenomenon is governed by wL = 1/wC So in a perfect resistance free circuit, the stored energy is circulating inside these two components (the resistance in circuit slowly dissipates this into heat energy) In a circuit connected to power source, this exchange dowe not matter since over a time, the energy inflow and outflow equates. However if the power supply frequency equals this frequency then the system keeps on adding the energy, ie let us say when the capacitor is being charged by inductor, it is getting additionally charged by the power supply, and this hapens in every cycle and the energy keeps on increasing in the storage (L or C) This is the resonance (in fact in our early classes may be some 35 years back we have been taught this by tunig fork-piano wire example)

Series Resonent circuit @ fo is called Accepter Cct. & has zero ZO, so across L & C individually will be theoratically infinite voltage, but opposite in phase.

Regards

Hajee,

I think that, since XL = 2* pi * f * L and thus UL = I * XL can be infinite only if L = infinite and conversely XC = 1/ (2 * pi * f * C) with UC = I * XC = infinite only if C = 0, for I <>0. This is considering ideal L and C (no resistive component).

Do you consider a purely L-C circuit without R ? For such circuit I = infinite. and theoretically UC = UL = infinite.

Regards.

Exactly if considering R= 0. due to zero R Infinite current flows So XL*I or XC* =

? Infinite. Theoratically!

As Xl & Xc are opposite to each other so the Impedance = zero & considering of the circuit zero the current @ fo = infinite.

infinite * anything [except zero] is infinite & Xl & Xc has finite values & = @ fo so

Xl * Infinite = infinite & Xc * infinite = infinite.

or practically voltage across C & L will be very-Hi but opposite in phase.

Acceptor circuit are SHORT-CIRCUITs & source may be damaged if series resistor is not present.

This is a general concept, but in practice R never =s zero.

Everyone is talking about resonant circuits. If you happen to be experiencing harmonics relating to power lines or loads associated with 3 phase power, you need totaly different advice. Could you provide more information about the issue that got you looking into this?