Inductors, capacitors and resonance

Frequency-dependent opposition

An ideal inductor has reactance XL = 2πfL, increasing with frequency. An ideal capacitor has XC = −1/(2πfC), whose magnitude decreases as frequency rises. The sign indicates the phase relationship; it does not mean a capacitor has negative resistive loss.

The formulas expect hertz, henries and farads. One microhenry is 10⁻⁶ H and one picofarad is 10⁻¹² F. The calculators handle these conversions. When calculating manually, confused prefixes are a common cause of results that are wrong by many orders of magnitude.

When reactances cancel

At f₀ = 1/(2π√LC), the two ideal reactances have equal magnitude. In series they cancel. For 1 µH and 100 pF, this occurs at about 15.915 MHz. Ideal series impedanceImpedance×Impedance is complex opposition to alternating current: it includes resistance and a frequency-dependent reactance. Antenna input impedance is therefore more than a DC resistance reading.Example & full explanation → becomes zero there; a real circuit retains its loss resistance.

In an ideal parallel circuit, the reactive parts of admittance cancel instead, making impedance very large in the lossless model. Series and parallel circuits must therefore not be treated as identical despite sharing the ideal resonance formula. Loading and losses determine what an installed resonator actually does.

RF components are not ideal

An inductor also has capacitance and resistance; a capacitor also has parasitic inductance. Above self-resonance, expected behaviour can reverse. Check the data sheet, tolerance and suitable frequency range. Quality factor and connected loads determine bandwidthBandwidth×Bandwidth is the width of a frequency range. A receiver filter limits the analysed range; the signal’s occupied bandwidth is a separate quantity.Example & full explanation →; the simple LC formula does not.