Combine capacitors and inductors to be frequency independent

In summary, it is possible to create a circuit where the total impedance is independent of frequency, but it requires resistive terminations. This can be achieved with an all-pass network or by terminating a lossless line in its characteristic resistance. However, trying to balance inductance and capacitance will not work over a range of frequencies. It may be possible to achieve a negative slope using an amplifier or mutual inductance.
  • #1
Kfir Dolev
5
0
Is it possible to combine (possibly infinite) capacitors and inductors to get a total impedance which is independent of frequency. If so, how?
 
Physics news on Phys.org
  • #2
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
 
  • #3
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)
 
  • #4
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!
 
  • #5
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".
 

1. What is the purpose of combining capacitors and inductors to be frequency independent?

The purpose of combining capacitors and inductors is to create a circuit that has a constant impedance over a wide range of frequencies. This is commonly referred to as a frequency independent circuit.

2. How do capacitors and inductors work together to achieve frequency independence?

Capacitors and inductors have opposite reactions to changes in frequency. By combining them in a circuit, the effects of capacitive and inductive reactance can cancel each other out, resulting in a constant impedance regardless of frequency.

3. Why is frequency independence important in electronic circuits?

Frequency independence is important because it allows for consistent performance of electronic circuits over a wide range of frequencies. This is especially crucial in applications such as filters, amplifiers, and oscillators.

4. Can any combination of capacitors and inductors achieve frequency independence?

No, not all combinations of capacitors and inductors can achieve frequency independence. The circuit must be designed carefully, taking into account the values and placement of the components, in order to achieve the desired frequency independent behavior.

5. Are there any drawbacks to using combined capacitors and inductors for frequency independence?

One potential drawback is that the circuit may become more complex and may require more components. Additionally, there may be some trade-offs in terms of other circuit parameters, such as cost, size, and power consumption, in order to achieve frequency independence.

Similar threads

B LC resonance with high Q factor, Inductor with non magnetic core
    • Electromagnetism
Replies
4
Views
426
Charging and Discharging of a capacitor in an LC circuit
    • Electromagnetism
2
Replies
50
Views
12K
Formula for Resonant Frequency of 2 Metal Coaxial Cylinders?
    • Electrical Engineering
Replies
10
Views
1K
Battery connected to a pure inductor with a Zero-resistance wire
    • Electromagnetism
Replies
10
Views
1K
Why is impedance given as a simple Ohms unit when it's frequency dependent?
    • Electrical Engineering
Replies
10
Views
472
Exploring LRC AC Series Circuits
    • Electrical Engineering
Replies
25
Views
2K
B Antenna induction, oscillating circuit generating EM Waves
    • Electromagnetism
Replies
1
Views
64
Some questions about capacitor discharging
    • Electromagnetism
Replies
7
Views
934
Charges of capacitors in series and in parallel
    • Electromagnetism
Replies
7
Views
1K
Why does my inductor coil have no effect on my circuit
    • Electromagnetism
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top