Finding the inductor value with a frequency range

In summary, the frequency range assigned to a television channel is 53.2 to 57.2 MHz. Using a 15.8 pF capacitor, a series RLC tuning circuit in a TV receiver resonates at the middle of this range. The inductance value can be calculated using the equation 1/(2*pi*sqrt(LC)).
  • #1
cummi3em
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0

Homework Statement


A television channel is assigned the frequency range 53.2 to 57.2 MHz. A series RLC tuning circuit in a TV receiver resonates in the middle of this frequency range. The circuit uses a 15.8 pF capacitor. What is the value of the inductor (in mH)?


Homework Equations



1/(2*pi*sqrt(LC))

The Attempt at a Solution


I tried using the above equation to solve for L using the lowest, highest, and middle frequency
 
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  • #2
What have you got for the middle frequency?

ehild
 
  • #3
55.2 MHz
 
  • #4
Sorry, :) I meant the inductance at the middle frequency.

ehild
 
  • #5
thank you but i got it i was using the wrong units
 

1. How do I calculate the inductor value with a given frequency range?

To calculate the inductor value, you will need to use the formula L = (2πf)^-1, where L is the inductor value in Henries, π is a mathematical constant (approximately 3.14), and f is the frequency in Hertz. First, determine the frequency range you need the inductor to operate within, then use this formula to calculate the required inductor value.

2. Can I use any inductor with a given frequency range?

No, the inductor used must have a high enough self-resonant frequency (SRF) to operate within the given frequency range. The SRF is the frequency at which the inductor's parasitic capacitance causes it to behave as a parallel-tuned circuit, and it should be at least three times higher than the highest frequency in the range.

3. How do I determine the frequency range that an inductor can operate within?

The frequency range of an inductor depends on its inductance value and its self-resonant frequency (SRF). You can use the formula f = (2πL)^-1 to calculate the frequency range, where f is the frequency in Hertz and L is the inductance in Henries. If the SRF is not mentioned in the inductor's specifications, it can be calculated using SRF = 1/(2π√(LC)), where C is the inductor's parasitic capacitance in Farads.

4. What other factors should I consider when choosing an inductor for a specific frequency range?

Besides the self-resonant frequency, you should also consider the inductor's quality factor (Q), which determines its ability to store energy. A higher Q factor means that the inductor will have lower losses and better performance within the given frequency range. You should also consider the inductor's tolerance, as a lower tolerance will result in a more accurate inductance value.

5. Is it possible to use multiple inductors to cover a wider frequency range?

Yes, you can use multiple inductors in series or parallel to cover a wider frequency range. In series, the total inductance is the sum of each individual inductor's value, while in parallel, the total inductance is the reciprocal of the sum of the reciprocals of each inductor's value. However, it is essential to consider the tolerance and SRF of each inductor when using this method to ensure optimal performance within the desired frequency range.

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