Introduction to Filters

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					Introduction to Filters

    Section 14.1-14.2
             Application of Filter




Application: Cellphone      Adjacent       Use a filter to remove
Center frequency: 900 MHz   interference   interference
Bandwidth: 200 KHz
                   Filters
• Classification
   – Low-Pass
   – High-Pass
   – Band-Pass
   – Band-Reject
• Implementation
   – Passive Implementation (R,L, C)
   – Active Implementation (Op-Amp, R, L, C)
   – Continuous time and discrete time
             Filter Characteristics
                                  Not desirable.
                                  Alter Frequency content.




Must not alter
the desired signal!                          Affect selectivity
                  Sharp Transition
                  in order to attenuate
                  the interference
Low-Pass Example




How much attenuation is provided by the filter?
              Answer




How much attenuation is provided by the filter? 40 dB
        High-Pass Filter




What filter stopband attenuation is necessary in order
to ensure the signal level is 20 dB above the interference?
  High-Pass Filter (Solution)




What filter stopband attenuation is necessary in order
to ensure the signal level is 20 dB above the interference? 60 dB @60 Hz
Bandpass
  Replace a resistor with a
        capacitor!




How do you replace a resistor with a switch and a capacitor?
Resistance of a Switched
    Capacitor Circuit




            (315A, Murmann, Stanford)
What is the equivalent
continuous time filter?
Filter Transfer Function




 (Increase filter order in order to increase filter selectivity!)
Low Pass Filter Example
Adding a Zero
Complex Poles and Zero at the
           Origin
RC Low Pass (Review)




     A pole: a root of the denomintor
     1+sRC=0→S=-RC
      Laplace Transform/Fourier
             Transform

(Laplace Transform)                                      Complex s plane




          (Fourier Transform)

                                           -p
           p=1/(RC)

                                Location of the zero in the left complex
                                plane
Rules of thumb: (applicable to a pole)
Magnitude:
•20 dB drop after the cut-off frequency
•3dB drop at the cut-off frequency
Phase:
•-45 deg at the cut-off frequency
•0 degree at one decade prior to the cut-frequency
•90 degrees one decade after the cut-off frequency
RC High Pass Filter (Review)




        A zero at DC.
        A pole from the denominator.
        1+sRC=0→S=-RC
      Laplace Transform/Fourier
             Transform

(Laplace Transform)                                      Complex s plane




          (Fourier Transform)

                                           -p
           p=1/(RC)
           Zero at DC.
                                Location of the zero in the left complex
                                plane
Zero at the origin.
Thus phase(f=0)=90 degrees.
The high pass filter has a cut-off frequency of 100.
RC High Pass Filter (Review)




        R12=(R1R2)/(R1+R2)
        A pole and a zero in the left complex plane.
      Laplace Transform/Fourier
     Transform (Low Frequency)

(Laplace Transform)                                      Complex s plane




          (Fourier Transform)

                                         -p
           z=1/(RC)                           -z
           p=1/(R12C)
                                Location of the zero in the left complex
                                plane
     Laplace Transform/Fourier
    Transform (High Frequency)

(Laplace Transform)                                      Complex s plane




          (Fourier Transform)

                                         -p
           z=1/(RC)                           -z
           p=1/(R12C)
                                Location of the zero in the left complex
                                plane
Stability Question




Why the poles must lie in the left half plane?
                               Answer




Recall that the impulse response of a system contains terms such as .


If , these terms grow indefinitely with time while oscillating at
a frequency of

				
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posted:4/11/2014
language:English
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