# KEHlecture22

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### EEE 302 Electrical Networks II:

Lecture 22 1 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001

### Resonant Circuits:

Lecture 22 2 Resonant Circuits Resonant frequency : the frequency at which the impedance of a series RLC circuit or the admittance of a parallel RLC circuit is purely real, i.e., the imaginary term is zero (ωL=1/ωC) For both series and parallel RLC circuits, the resonance frequency is At resonance the voltage and current are in phase, (i.e., zero phase angle) and the power factor is unity

### Quality Factor (Q):

Lecture 22 3 Quality Factor (Q) An energy analysis of a RLC circuit provides a basic definition of the quality factor (Q) that is used across engineering disciplines, specifically: The quality factor is a measure of the sharpness of the resonance peak; the larger the Q value, the sharper the peak where BW =bandwidth

### Bandwidth (BW):

Lecture 22 4 Bandwidth (BW) The bandwidth (BW) is the difference between the two half-power frequencies BW = ω HI – ω LO =  0 / Q Hence, a high-Q circuit has a small bandwidth Note that:  0 2 = ω LO ω HI See Figs. 12.23 and 12.24 in textbook (p. 692 & 694)

### Series RLC Circuit:

Lecture 22 5 Series RLC Circuit For a series RLC circuit the quality factor is

### PowerPoint Presentation:

Lecture 22 6 Class Examples Extension Exercise E12.8 Extension Exercise E12.9 Extension Exercise E12.10 Extension Exercise E12.11 Extension Exercise E12.12

### Parallel RLC Circuit:

Lecture 22 7 Parallel RLC Circuit For a parallel RLC circuit, the quality factor is

### PowerPoint Presentation:

Lecture 22 8 Class Example Extension Exercise E12.13

### Scaling:

Lecture 22 9 Scaling Two methods of scaling: 1) Magnitude (or impedance) scaling multiplies the impedance by a scalar, K M resonant frequency, bandwidth, quality factor are un affected 2) Frequency scaling multiplies the frequency by a scalar, ω'=K F ω resonant frequency, bandwidth, quality factor are affected

### Magnitude Scaling:

Lecture 22 10 Magnitude Scaling Magnitude scaling multiplies the impedance by a scalar, that is, Z new = Z old K M Resistor: Z R’ = K M Z R = K M R R’ = K M R Inductor: Z L’ = K M Z L = K M j  L L’ = K M L Capacitor: Z C’ = K M Z C = K M / ( j  C ) C’ = C / K M

### Frequency Scaling:

Lecture 22 11 Frequency Scaling Frequency scaling multiplies the frequency by a scalar, that is, ω new = ω old K F but Z new = Z old Resistor: R ” = Z R = R R” = R Inductor: j (  K F ) L = Z L = j  L L” = L / K F Capacitor: 1 / [ j (  K F ) C ] = Z C = 1 / ( j  C ) C” = C / K F

### PowerPoint Presentation:

Lecture 22 12 Class Example Extension Exercise E12.15 