Chapter 11 Frequency Response and Filters

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Transcript of Chapter 11 Frequency Response and Filters

chapter11WEBChapter 11: Outline







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Frequency Response
Frequency Response
l Frequency response is the forced response of a circuit to a sinusoid ac waveform of a particular frequency. Amplitude ratio and phase shift are typically used to characterize frequency response.
l Transfer function vs. phasor analysis:
)()( ωjHsH →
L L
Example 11.1: A Frequency-Selective Network
)4.82300cos(32.1)6.2620cos(94.8)(
300,20
Frequency Response Curves
( ) ( )[ ] ( ) ( )[ ]
aj aj

−=



−=∠=
==
−−−
A: Waveform Distortion
50020 )25(20
frequencies but suppress/reject the others. l Four common categories: lowpass, highpass, bandpass and
notch. l A positive gain constant K is assumed. l Ideal lowpass filter, ideal highpass filter, cutoff frequency,
passband and stop band.
ω=2πf ω/ ω co=f/fco
First-Order Filter Networks
/ ,
RC K
RC j
RC j
j jH
RC s
Design a low pass filter with fco around 4 KHz
co
co
Ls
s
Ls
s
s
out
Bandpass and Notch Filters
Bandpass and Notch Filters
l Ideal bandpass filter, ideal notch filter (band-reject filter), lower cutoff frequency, upper cutoff frequency and bandwidth.
bandwidth
)2/1(cos
180,180
Resonant Circuits l Resonant circuits for bandpass and notch filters.
L C
R L
R CRQ
C L
RCRR L
2
( ) ↑↓
=
=<<
=
==
==
0
Bode Plots
Bode Plots l Amplitude ratio and frequency are converted to a
logarithmic scale. l Factored functions and decibels:
L)()()( 21 sHsKHsH =
Amplitude vs. dB Gain
Ramp Function
0
Example 11.8: (Cont.)
First-Order Bode Plots
l Products of first-order factors: Bode plots of any transfer functions consisting entirely of first-order factors and powers of first-order factors can be constructed using the additive property of gain and phase. The important elements include: break frequencies, asymptotic gain and phase using straight line approximations and constants . and KKdB ∠
Example 11.9: Frequency Response of a Bandpass Amplifier
dBK
2,5.0, /49
16 log10
200,50,4.275.1log10
14
100,145log20
)5,100;()100;(14)(
1.0 2 1