RLC CIRCUITS AND RESONANCE Chapter 13 RLC CIRCUITS AND RESONANCE

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

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

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

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

The Series Resonance Frequency

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

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

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

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

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 13- 21

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- 22

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 13- 23

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

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 13- 30

Current in a Parallel RLC circuit

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)

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

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

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

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

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

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

APPLICATIONS TV Receiver

APPLICATIONS Super heterodyne Receiver