INC 212 Signals and systems Lecture#8: Analog filter design Assoc. - - PowerPoint PPT Presentation

INC 212 Signals and systems

Lecture#8: Analog filter design

• Assoc. Prof. Benjamas Panomruttanarug

benjamas.pan@kmutt.ac.th

Filter

• Filter ≡ system
• Can be either continuous or discrete time
• By “distortionless transmission” we mean that the
• utput signal of the system is an exact replica of the

input signal, except, possibly, for two minor modifications:

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LTI system, h(t), H(j) x(t), X(j) y(t) = x(t)  h(t) Y(j) = X(j) H(j)

1) A scaling of amplitude 2) A constant time delay

Time‐domain condition for distortionless transmission of a signal through an LTI system.

A signal x(t) is transmitted through the system without distortion if the output signal y(t) is defined by where constant C accounts for a change in amplitude and constant t0 accounts for a delay in transmission.

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) ( ) ( t t Cx t y   ) )

jωt

Y(j CX(jω e 



 ) ) )

jωt

Y(jω H(jω Ce X(jω



  ) ( C ) t ( t t h   

8.3 Ideal Low‐Pass Filters

• The frequency response of a filter is

characterized by a passband and a stopband, which are separated by a transition band.

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p  ; v  

8.3 Ideal Low‐Pass Filters (cont.)

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0,

( ) , 0,

j t c c

e H j



    



       

Practical low‐pass filter: the passband, transition band, and stopband are shown for positive frequencies.

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d  ; e  ; v   Maximum passband attenuation

• r ripple in passband

Maximum stopband magnitude or stopband attenuation Passband edge frequency Stopband edge frequency

8.4 Design of Filters

Analog filter

– Butterworth filter – Elliptic filter – Chebyshev filter (type I and II)

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Analog filter

• Butterworth filter(butter):

– Maximally flat magnitude response – Number of poles = number of filter’s order – No zero

• Elliptic filter (ellip):

– Equiripple magnitude response on both bands

• Chebyshev filter:

– Type I (cheby1): ripples on passband – Type II (cheby2): ripples on stopband

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Example

Design analog Butterworth, Elliptic, and Chebyshev type I and II filters satisfying the following conditions:

– Low‐pass filter with a cutoff at 1 rad/sec – Order of filter = 10 – Maximum ripple in the passband is 6 dB – Stopband attenuation is 50 dB

(Hint: use Matlab command ‘bode’ to plot the frequency responses of the filters)

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Practical use of an analog filter

Analog filter can be built from a passive filter!!!

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Low‐pass Butterworth filters driven from ideal current source: (a) order K = 1 and (b) order K = 3.

Example

Use the designed filters to filter the signal below:

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) 5 ( sin 7 . ) 3 . cos( 2 . 1 ) ( t t t s  

99 .   t