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How Resonant RF Circuits Work:

Resonant RF (radio-frequency) circuits—also called LC resonant or tuned circuits—use an inductor (L) and a capacitor (C) to create a natural oscillation at a specific frequency.

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1. Core Components

• Inductor (L): stores energy in a magnetic field
• Capacitor (C): stores energy in an electric field

Energy moves back and forth between these two components when they are connected.

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2. Resonant Frequency

The natural frequency of oscillation is:

f0 = 1 / ( 2 * pi * sqrt(L * C) )

This is the frequency the circuit “likes” to oscillate at.

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3. Types of Resonant Circuits

Series LC Circuit

• L and C in series
• At resonance:
  • Total impedance is minimum
  • Current is maximum
• Acts like a band-pass filter

Parallel LC Circuit

• L and C in parallel
• At resonance:
  • Impedance is maximum
  • Current drawn is minimum
• Acts like a notch filter or a voltage resonator

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4. Energy Oscillation (Intuition)

1. Capacitor charges → electric field stores energy
2. Capacitor discharges through inductor → energy becomes magnetic
3. Magnetic field collapses → induces current back into capacitor
4. Capacitor charges with opposite polarity
5. Cycle repeats

This produces a sinusoidal oscillation, gradually decaying unless externally driven.

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5. Q Factor (Quality Factor)

Q describes how “sharp” the resonance is:

Q = f0 / bandwidth

High Q → narrow bandwidth, strong frequency selectivity.

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6. Uses in RF Systems

• Radio receivers: tuning to a single station
• Transmitters: setting oscillator frequency
• Filters: band-pass or band-stop networks
• Impedance matching: transforming impedances at RF
• Antenna systems: creating resonant matching with antenna elements

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7. Mechanical Analogy

An LC circuit behaves exactly like a mass–spring system:

• Capacitor ↔ spring
• Inductor ↔ mass

Both obey the same second-order differential equation and have a natural resonant frequency.

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