Resonant Frequency in
Series Circuits

Section A-001-003

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Take The Res Freq Series Test

Calculating Resonant Frequencies in Series RLC Circuits

The resonant frequency of a series RLC circuit is a critical parameter in electrical engineering, determining the frequency at which the circuit naturally oscillates. It depends on the values of the resistance (R), inductance (L), and capacitance (C) in the circuit.

Advanced Amateur A-001-003 Resonant Frequency in Series RLC Circuits.mp4

Resonant Frequency Formula

The formula for calculating the resonant frequency (f) is:

f = 1 / (2π√(LC))

where:

- L is the inductance in henrys (H)
- C is the capacitance in farads (F)
- π is Pi, approximately 3.14159

Specific Examples

R = 47 ohms, L = 50 microhenrys, C = 40 picofarads
- L = 50 × 10^-6 H
- C = 40 × 10^-12 F
- f = 1 / (2π√(50 × 10^-6 × 40 × 10^-12))
- f ≈ 3.56 MHz
R = 47 ohms, L = 40 microhenrys, C = 200 picofarads
- L = 40 × 10^-6 H
- C = 200 × 10^-12 F
- f = 1 / (2π√(40 × 10^-6 × 200 × 10^-12))
- f ≈ 1.78 MHz
R = 47 ohms, L = 50 microhenrys, C = 10 picofarads
- L = 50 × 10^-6 H
- C = 10 × 10^-12 F
- f = 1 / (2π√(50 × 10^-6 × 10 × 10^-12))
- f ≈ 7.12 MHz
R = 47 ohms, L = 25 microhenrys, C = 10 picofarads
- L = 25 × 10^-6 H
- C = 10 × 10^-12 F
- f = 1 / (2π√(25 × 10^-6 × 10 × 10^-12))
- f ≈ 10.1 MHz
R = 47 ohms, L = 3 microhenrys, C = 40 picofarads
- L = 3 × 10^-6 H
- C = 40 × 10^-12 F
- f = 1 / (2π√(3 × 10^-6 × 40 × 10^-12))
- f ≈ 14.5 MHz
R = 47 ohms, L = 4 microhenrys, C = 20 picofarads
- L = 4 × 10^-6 H
- C = 20 × 10^-12 F
- f = 1 / (2π√(4 × 10^-6 × 20 × 10^-12))
- f ≈ 17.8 MHz
R = 47 ohms, L = 8 microhenrys, C = 7 picofarads
- L = 8 × 10^-6 H
- C = 7 × 10^-12 F
- f = 1 / (2π√(8 × 10^-6 × 7 × 10^-12))
- f ≈ 21.3 MHz
R = 47 ohms, L = 3 microhenrys, C = 15 picofarads
- L = 3 × 10^-6 H
- C = 15 × 10^-12 F
- f = 1 / (2π√(3 × 10^-6 × 15 × 10^-12))
- f ≈ 23.7 MHz
R = 47 ohms, L = 4 microhenrys, C = 8 picofarads
- L = 4 × 10^-6 H
- C = 8 × 10^-12 F
- f = 1 / (2π√(4 × 10^-6 × 8 × 10^-12))
- f ≈ 28.1 MHz
R = 47 ohms, L = 1 microhenry, C = 9 picofarads
- L = 1 × 10^-6 H
- C = 9 × 10^-12 F
- f = 1 / (2π√(1 × 10^-6 × 9 × 10^-12))
- f ≈ 53.1 MHz
Circuit resonant frequency is 14.25 MHz and L is 2.84 microhenrys
- f = 14.25 × 10^6 Hz
- L = 2.84 × 10^-6 H
- Rearranging the formula: C = 1 / (4π²f²L)
- C ≈ 44 picofarads

Conclusion

Understanding the resonant frequency in series RLC circuits is crucial for designing and analyzing circuits in various applications, including radio transmitters, filters, and tuning circuits. The ability to calculate resonant frequency using the values of R, L, and C enables engineers to design circuits that meet specific functional requirements.