Resonance — The Sweet Spot

What is Resonance?

Resonance happens when you combine an inductor and capacitor, and at one specific frequency, their reactances become equal and cancel each other out. At that frequency, the circuit behaves as if it's purely resistive — no reactance at all.

This is hugely important in radio because it's how we select one frequency and reject all others.

Radio example: The tuned circuits in your receiver use resonance to select the station you want to hear and reject everything else. Your antenna is resonant at a specific frequency — that's where it works best.

The Resonant Frequency Formula

\( f_r = \frac{1}{2\pi\sqrt{LC}} \)

This tells you: for a given inductor (L) and capacitor (C), there's exactly one frequency where they resonate. This formula appears constantly in radio — learn it well!

Example: A 10 μH inductor and a 100 pF capacitor resonate at about 5.03 MHz — right in the middle of the 60-metre band.

Series vs Parallel Resonance

There are two ways to arrange L and C, and they behave oppositely at resonance:

Series LCParallel LC
At resonance, impedance is...Minimum (just R)Maximum
At resonance, current is...MaximumMinimum from source
Used for...Passing a desired frequencyBlocking a desired frequency (or selecting it in a tuned circuit)

Radio example: A series-resonant circuit in an antenna trap passes the trap's frequency through, while a parallel-resonant circuit in a receiver's IF stage presents high impedance at the desired frequency, developing a large signal voltage across it.

Q Factor — How Sharp is the Tuning?

The Q factor tells you how selective a resonant circuit is. High Q = very sharp tuning (narrow bandwidth). Low Q = broad tuning.

\( Q = \frac{f_r}{\text{Bandwidth}} \)

Think of it this way: A high-Q circuit is like a sniper rifle — it targets one frequency precisely. A low-Q circuit is like a shotgun — it covers a wide range.

For a series RLC circuit: \( Q = \frac{X_L}{R} \). So less resistance = higher Q = sharper selectivity.

FrequencySignal StrengthHigh Q — sharp(crystal filter, IF stage)Low Q — broad(antenna, wideband amp)Resonant freq
Bandwidth rule: Bandwidth = fr / Q. So a circuit with Q = 100 at 7 MHz has a bandwidth of 70 kHz — enough to cover a portion of the 40m band. A crystal filter with Q = 50,000 at 9 MHz has a bandwidth of just 180 Hz — perfect for CW.
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