Combine capacitors and inductors to be frequency independent

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Combining capacitors and inductors to achieve frequency-independent impedance is challenging due to their inherent frequency-dependent characteristics. While an all-pass network can provide transparency across frequencies, it requires resistive terminations to function effectively. An infinitely long transmission line with uniform inductance and capacitance can achieve frequency independence when terminated in its characteristic resistance. Balancing inductance and capacitance alone does not yield frequency independence across a range of frequencies, as their reactance curves do not cancel out. Utilizing amplifiers or gyrator circuits may offer potential solutions for achieving a negative slope in impedance, but practical limitations remain.
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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