Combine capacitors and inductors to be frequency independent

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Discussion Overview

The discussion revolves around the possibility of combining capacitors and inductors to achieve a total impedance that is independent of frequency. Participants explore theoretical and practical aspects of this concept, including circuit design and the implications of resistance.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants suggest that any combination of parallel capacitors and inductors will have a resonant frequency, indicating that frequency dependence is inherent in such setups.
  • One participant emphasizes the need for the imaginary part of the impedance to cancel out completely, expressing a desire for a frequency-independent behavior.
  • Another participant proposes that using non-harmonically related resonant frequencies could theoretically achieve frequency independence, but notes that this would lead to significant energy dissipation and heat generation in a passive system.
  • A different viewpoint introduces the concept of an all-pass network, which can be frequency transparent but requires resistive terminations, suggesting that some resistance is necessary for achieving frequency independence.
  • It is mentioned that balancing inductance with capacitance cannot yield frequency independence across a range of frequencies, as their reactance curves do not cancel out except at a single frequency.
  • Some participants speculate that using amplifiers or gyrator circuits might allow for achieving a negative slope in impedance, potentially leading to frequency-independent behavior.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of achieving frequency-independent impedance with capacitors and inductors. There is no consensus on a definitive method, and multiple competing ideas are presented.

Contextual Notes

Limitations include the dependence on circuit configurations, the role of resistance, and the challenges of achieving true frequency independence in practical applications.

Kfir Dolev
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Is it possible to combine (possibly infinite) capacitors and inductors to get a total impedance which is independent of frequency. If so, how?
 
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Kfir Dolev said:
Is it possible to combine (possibly infinite) capacitors and inductors to get a total impedance which is independent of frequency. If so, how?

you are a little vague in your setup description

but start with any parallel capacitor/inductor combination will have its resonant frequencyDave
 
The Impedence will be a function of frequency in general. I want the frequency dependence to complete cancel out in the imaginary part of Z(\omega)
 
You could make a circuit where the various resonant frequencies are not harmonically related (try using values of C and L related by surds) , but in a passive system this will dissipate all the energy of the signal very quickly - you will get the big zero you are looking for, but also a lot of waste heat!
 
Kfir Dolev said:
Is it possible to combine (possibly infinite) capacitors and inductors to get a total impedance which is independent of frequency. If so, how?
One circuit is the all-pass netwrok, which is transparent at all frequencies. But it requires resistive terminations. There has to be resistance somewhere to fulfil your request. Frequency independence occurs, for instance, with an infinitely long transmission line having uniformly distributed inductance and capacitance, such as a pair of wires.
If resistance is allowed, we can terminate a lossless line in its charactersitic resistance and the input impedance becomes frequency independent.
If you try to balance inductance with capacitance, it cannot work over range of frequencies, because the the slope of the reactance curve in both cases is positive, so they do not cancel except at one frequency. This is why we cannot make truly frequency independent antennas.
On the other hand, it might be possible to achieve a negative slope using an amplifier, such as a gyrator circuit, or maybe in conjunction with mutual inductance, which can have either "polarity".
 

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