1. RLC CIRCUITS AND RESONANCE
Chapter 13
RLC CIRCUITS
AND RESONANCE

2. IMPEDANCE AND PHASE ANGLE OF SERIES RLC CIRCUITS
A series RLC circuit contains resistance, inductance, and capacitance

3. ANALYSIS OF SERIES RLC CIRCUITS
In a series RLC circuit, the capacitor voltage and the inductor voltage are always 180 out of phase with each other.
Inset picture 13-3
Inset picture 13-6

4. SERIES RESONANCE
In a series RLC circuit, series resonance occurs when XL = XC
The frequency at which resonance occurs is called the resonance frequency and is designed fr

5. XL and XC Cancel at Resonance
At resonance, VL and VC are equal in magnitude and 180° out of phase with each other.
Inset picture 13-11
VCL = VC - VL

6. The Series Resonance Frequency

7. Voltage and Current in a Series RLC Circuit
Inset picture 13-13

8. The Impedance of a Series RLC circuit
At zero frequency, XC and Z are infinitely large and XL is zero
As the frequency increases XC decreases and XL increases
At fr , XC = XL and Z =R
At frequency above fr , XL becomes increasingly larger than XC

9. The Phase Angle of a Series RLC circuit
At f < fr , XC > XL and I leads VS
At f > fr , XC < XL and I lags VS

10. SERIES RESONANT FILTERS
The Band-Pass Filter
A band-pass filter allow signals at the resonant frequency and at frequencies within a certain band to pass from input to output
Inset picture 13-19

11. Bandwidth of the Passband
The bandwidth (BW) of a band-pass filter is the range of frequencies for which the current ( or voltage) is equal to or greater than 70.7% of its value at the resonant frequency.
f1 is called the lower cutoff frequency
f2 is called the upper cutoff frequency
Inset picture

12. Selectivity of a Band-Pass Filter
Selectivity defines how well a resonant circuit responds to a certain frequency and discriminates against all others. The narrow the bandwidth, the greater the selectivity
Inset picture

13. The Quality Factor (Q) of a Resonant Circuit
The quality factor (Q) is the ratio of the reactive power in the inductor to the true power in the winding resistance of the coil and any other resistance in series with the coil.
Inset picture

14. The Band-Stop Filter
The band-stop filter rejects signals with frequencies between the lower and upper cutoff frequencies and pass those signals with frequencies below and above the cutoff values. This type sometimes is called band-elimination, band-reject or notch filter

15. PARALLEL RLC CIRCUITS Impedance and phase angle
When f > fr , XC < XL , the impedance of the circuit is predominantly capacitor because the capacitive current is greater, and Itot leads Vs
When f < fr , XC > XL the impedance of the circuit is predominantly inductive, and Itot lags Vs
Inset picture

16. Current in a Parallel RLC circuit

17. PARALLEL RESONANCE Ideally, parallel resonance occurs when XL= XC
when XL= XC , IL and IC are equal in magnitude, and always 180◦ out of phase with each other, and thus two currents cancel (Itot = 0)

18. The Parallel Resonant Frequency
The frequency at which resonance occurs is determined by

19. Current in a Parallel Resonant Circuit
Below the resonant frequency
XL < XC , IL > IC , Itot decrease
At the resonant frequency
XL = XC , IL = IC , Itot zero , Z is infinite
Above the resonant frequency
XL > XC , IL < IC , Itot increase

20. Tank circuit
The parallel resonant LC circuit is often called a tank circuit
The stored energy is transferred back and forth between the capacitor and the coil

21. PARALLEL RESONANCE FILTERS
The Band-Pass Filter
f < fr , Z is very low, Vout is small
f = fr , Z is maximum, Vout is maximum
f > fr , Z is decrease, Vout is decrease

22. The Band-Stop Filtor
The current is minimum at resonance and increase on both sides of resonance.
The output voltage follows the current, and is across the series load resistor

23. APPLICATIONS Tuned Amplifiers
A tuned amplifier is a circuit that amplifies signals within a specified band

24. APPLICATIONS
TV Receiver

25. APPLICATIONS
Super heterodyne Receiver