27.03.2023 - 16:51

A 2.2 mH inductor is connected in parallel with a variable capacitor. The capacitor can be varied from 100 pF to 200 pF.

Question:

A {eq}2.2 mH {/eq} inductor is connected in parallel with a variable capacitor. The capacitor can be varied from {eq}100 pF {/eq} to {eq}200 pF {/eq}.

What is the minimum oscillation frequency for this circuit?

What is the maximum oscillation frequency for this circuit?

Answers (1)
  • FSB
    April 11, 2023 в 05:00

    The minimum oscillation frequency for this circuit can be calculated using the formula:

    {eq}f_{min} = \frac{1}{2pisqrt{LC}} {/eq}

    where L is the inductance in henries, and C is the capacitance in farads.

    Substituting the given values, we get:

    {eq}f_{min} = \frac{1}{2pisqrt{(2.2 \times 10^{-3} , mathrm{H})(200 \times 10^{-12} , mathrm{F})}} \approx 2.27 , mathrm{MHz} {/eq}

    Therefore, the minimum oscillation frequency for this circuit is \approx imately 2.27 MHz.

    Similarly, the maximum oscillation frequency can be calculated using the same formula:

    {eq}f_{max} = \frac{1}{2pisqrt{LC}} {/eq}

    Substituting the minimum value of capacitance, we get:

    {eq}f_{max} = \frac{1}{2pisqrt{(2.2 \times 10^{-3} , mathrm{H})(100 \times 10^{-12} , mathrm{F})}} \approx 3.14 , mathrm{MHz} {/eq}

    Therefore, the maximum oscillation frequency for this circuit is \approx imately 3.14 MHz.

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