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#130626 09/14/06 10:42 PM
Joined: Sep 2006
Posts: 5
Junior Member
how the parallel RLC ckt behaves for DC & AC supplies and what is the output?
if resistor is removed from above ckt how the L & C behaves for above supplies seperately and output response?

Joined: Aug 2001
Posts: 7,520
The full, detailed explanation to that question is quite long, but let's try a quick answer.

If we apply D.C. to a capacitor, there will be a brief pulse of current as the capacitor charges, then the current will taper off until it reaches zero when the capacitor is fully charged. The time taken to charge will depend upon the actual value of capacitance and the overall resistance of the circuit (including the source).

We define the time constant as the time it takes for the voltage on the capacitor to reach 63.2% of its final value, and it can be calculated as:

t = R * C

where R is the resistance in ohms and C is the capacitance in farads. For most practical purposes, we can consider the capacitor to be fully charged after a period of 5t.

Applying D.C. to an inductor gives us a somewhat different result. The inductor tries to oppose changes of current, so the current starts low and we see it increase gradually. Again, we define the time constant as the period it takes for the current to reach 63.2% of its final value:

t = L / R

where L is the inductance in henrys.

After approx. 5t seconds the current will have reached its final, maximum value, which will be determined by the overall resistance of the circuit (including the inherent resistance of the coil).

Applying A.C. results in a rather different result, since the A.C. waveform is continually varying.

For an inductor, we can determine the reactance ("A.C. resistance" if you will) of the coil from the formula:

X = 2 * pi * f * L

where f is the frequency. That means that for any given coil, as you increase the frequency the reactance will increase and thus the current will decrease.

For a capacitor, the relationship is the inverse:

X = 1 / (2 * pi * f * C)

So for a capacitor, an increase in frequency results in a decrease in reactance, with a corresponding increase in current.

When we put capacitance and inductance together in a parallel combination, it follows that the voltage across each component at any given moment must be the same.

However, that charging action means that in a purely capacitive circuit the current leads the voltage waveform by 90 degrees. Similarly, the current in a pure inductance lags 90 degrees behind the voltage. That means that for a parallel LC circuit, the current in the L section is 180 deg. out of phase with that in the C section.

The currents oppose each other, and therefore the overall reactance of the circuit is the difference between that of the coil and that of the capacitor.

Because inductive reactance increases with frequency while capacitive reactance decreases, there will be some specific frequency at which XL and XC are equal. This is the resonant frequency of the LC combination, and at this frequency the currents in L and C are exactly equal. because they are 180 out of phase though, they completely cancel out as far as the external circuit is concerned.

Thus at the resonant frequency, the parallel LC circuit appears as an infinitely high impedance and no current will flow. (In a theoretically perfect circuit that is -- In practice, of course, we can never quite achieve that.)

The resonant frequency can be calculated from:

f = 1 / ( 2 * pi * SQRT(L * C) )

Now, altering the value of the parallel resistance will have no effect on the actual resonant frequency of the circuit, but it will change the overall characteristic, since of course there will always be a parallel path for the current around the tuned circuit.

The lower the value of the parallel resistance, the less sharply defined will be the dip in current at the resonant frequency. A parallel resistance is often used across an LC combination in this way in radio circuits to deliberately broaden the frequency response.

[This message has been edited by pauluk (edited 09-16-2006).]

Joined: Nov 2005
Posts: 827
Well Paul, I think it is a pure shame if you haven't had the chance to teach in the past because I know you would be fantastic at it! I would add that the the amount of parallel resistance effects what they call the Q, or Quality Factor of the resonant circuit. You will hear the term, "3dB bandwith" for power, or "6dB bandwidth" for voltage, or "half power point". Adding that parallel resistance is one way to broaden response. Another common way is to combine LC networks that are tuned towards the high and low ends of a desired bandwidth, or "stagger tuned" for a network. The areas where the response falls off on the sides are sometimes called "skirts", which got my attention.

Now, you also mentioned the network across a DC supply, which for most of the time would look like a short circuit.

As you get higher in frequency, everything gets interesting. The series inductance of capacitor leads starts showing up in a meaningful way, as does the capacitance between turns of an inductor. Look inside a UHF tuner if you want to see something that makes no sense if you're used to living in a low frequency world. I used to tune UHF diplexors, and to this day, have no clue as to how things I did to flatten response worked, just that they did work.

Joined: Oct 2000
Posts: 2,722
Broom Pusher and
Excellent job, Paul, on the descriptions and formulas!!!
[Linked Image] [Linked Image]

Also would like to thank Joe for your interesting input, regarding UHF!
Being a "Low Frequency" guy myself, the first time I cracked open an Impedance Matching Transformer for a Television's RF input (300 Ohm twinlead to 75 Ohm Coax, 54-890 MHz), it caught me off guard to see the distinct separations between the Primary and Secondary windings!
A few days with my nose "buried in the books" explained that whole thing!

Anyhow, as said before, my dealings with AC items is of the Low Frequency areas. The highest Frequency I have dealt with (as far as Engineering goes), is the upper limit of the Audio Frequency Spectrum - basically around 20 kHz (or 32 kHz for ultrasonic filtering limits) - but for the most part, 20 kHz is the highest end, with Frequencies of 8 to 12 kHz being the norm.

In the designing of Passive Crossover Networks for Audio Systems' Loudspeakers - most of which are a combination of Series LC and Parallel RLC Networks, the design will reflect the AC Audio output from the Power Amplifier, along with whatever Coupled DC component will be available from the Power Amplifier.

Frequency range is around 20 Hz through 20 kHz, separated into 10 Octaves.

The Low Pass Filters - for the range of 20 Hz through 500 Hz, for driving the large Woofer/Subwoofer Voice Coil of a 3 way speaker, will consist from a single Air-Core Inductor (for a 1st order Network), to an array of 2 Inductors in Series, and 2 Capacitors, in Parallel (for a 4th order Network).

The Band Pass Filters - for the range of 250 Hz through 4000 Hz, for driving the Medium sized Mid-Range Voice Coil of a 3 way speaker, will consist from a single Air-Core Inductor + Capacitor in Series (for a 1st order Network), to an array of 2 Inductors + 2 Capacitors, in Series with the Voice Coil, + 2 sets of LC Series, in Parallel of the Voice Coil (for a 4th order Network).

The High Pass Filters - for the range of 2000 Hz through 20,000 Hz, for driving the small tweeter Voice coil of a 3 way speaker, will consist from a single Polypropylene Capacitor in Series with the Voice Coil (for a 1st order Network), to an array of 2 Capacitors in Series, and 2 Inductors, in Parallel (for a 4th order Network).

Additional Filters have been used with these Passive designs, most of which are for "Taming Peaks" (Notch Filters), and for Impedance Equalization.
These take the form of Series and Parallel RLC, RL, RC and LC Filters.

Another "Tweek" was used to "Boost" Frequency Response of a Driver, due to reductions from "Step Response".

To "Boost" the higher Frequency Response on Tweeters, a Parallel RC Filter is placed in line with the Tweeter.
An additional Mylar Capacitor was placed in Series with the Voice Coil, with a Shunt Resistor around it (the Resistor is Parallel to the Capacitor).
Capacitor value - in microfarads, is based on the figure for a 1st order Crossover's Capacitor.

The Resistor is equal to the rated Impedance of the Tweeter's Voice Coil.

To "Boost" the lower Frequency Response on Woofers, a Parallel RL Filter is placed in line with the Woofer.
An additional Inductor was placed in Series with the Voice Coil, with a Shunt Resistor around it (the Resistor is Parallel to the Inductor).
Inductor value - in millihenrys, is based on the figure for a 1st order Crossover's Inductor.

Similarly, the Resistor is equal to the rated Impedance of the Woofer's Voice Coil.

None of this stuff takes place in the Speaker Circuits for Active Crossover Networks, as all the Frequency Tweeking takes place on the Line-Level inputs of an Amplifier - similar to the Active Filtering done on each Octave of a Graphic Equalizer.

An example of the Filter for a single Octave of a "Tunable" multi-band Graphic Equalizer, consists of fixed RLC components, and an "adjustable R Component", which is a "Slide Pot" (Sliding type of Potentiometer, as opposed to a dial type of Pot).
These Elements work in conjunction with an Op-Amp (Operational Amplifier), most commonly and currently used would be something in a DIP type of an IC.

Just wanted to add a little more to the thread.


Scott " 35 " Thompson
Just Say NO To Green Eggs And Ham!
Joined: Feb 2005
Posts: 693
The only thing I'd add to Scott's post is that, for each increase in the "order", the crossover slope increases by 6 db/octave. In other words, a 1st order crossover has a 6 db/octave slope, a 2nd order crossover has a 12db/octave slope, etc.

That means that, for a 1st-order 1kHz crossover, at 2kHz (for low-pass), or at 500Hz (for high-pass), the signal will be 6db lower than at the crossover point (typically defined as the -3db point, because both drivers contribute to the sound where they overlap)

Larry Fine
Fine Electric Co.
Joined: Feb 2005
Posts: 693
I should also add that, for power circuits, most of this is moot, because the frequency is fixed at 60 Hz.

Larry Fine
Fine Electric Co.

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