Post on 04-Jun-2018
transcript
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
1/27
Introduction to Filters
Section 14.1-14.2
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
2/27
Application of Filter
Application: CellphoneCenter frequency: 900 MHzBandwidth: 200 KHz
Adjacentinterference
Use a filter to removeinterference
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
3/27
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
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
4/27
Filter Characteristics
Must not alterthe desired signal!
Sharp Transition
in order to attenuatethe interference
Not desirable.Alter Frequency content.
Affect selectivity
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
5/27
Low-Pass Example
How much attenuation is provided by the filter?
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
6/27
Answer
How much attenuation is provided by the filter?40 dB
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
7/27
High-Pass Filter
What filter stopband attenuation is necessary in orderto ensure the signal level is 20 dB above the interference?
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
8/27
High-Pass Filter (Solution)
What filter stopband attenuation is necessary in orderto ensure the signal level is 20 dB above the interference? 60 dB @60 Hz
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
9/27
Bandpass
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
10/27
Replace a resistor with a
capacitor!
How do you replace a resistor with a switch and a capacitor?
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
11/27
Resistance of a Switched
Capacitor Circuit
(315A, Murmann, Stanford)
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
12/27
What is the equivalent
continuous time filter?
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
13/27
Filter Transfer Function
(Increase filter order in order to increase filter selectivity!)
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
14/27
Low Pass Filter Example
1 1
1( )
1aH s
R C s
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
15/27
Adding a Zero
1 1
1( )
1aH s
R C s
1
11 2
1
( )1 1b
C sH s
RC s C s
1 2
1 1 2
1
( ) 1
R C s
R C C s
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
16/27
Complex Poles and Zero at the
Origin
1 1
1 1
1
( )( )
1( )
c
L s RH s
L s RC s
1
2
1 1 1 1 1
C s
R L C s L s R
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
17/27
RC Low Pass (Review)
A pole: a root of the denomintor1+sRC=0S=-RC
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
18/27
Laplace Transform/Fourier
Transform
p=1/(RC)
(Fourier Transform)
(Laplace Transform)
-p
Location of the zero in the left complexplane
Complex s plane
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
19/27
Rules of thumb: (applicable to a pole)Magnitude:1. 20 dB drop after the cut-off frequency2. 3dB drop at the cut-off frequencyPhase:1. -45 deg at the cut-off frequency
2. 0 degree at one decade prior to the cut-frequency3. 90 degrees one decade after the cut-off frequency
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
20/27
RC High Pass Filter (Review)
A zero at DC.A pole from the denominator.1+sRC=0S=-RC
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
21/27
Laplace Transform/Fourier
Transform
p=1/(RC)Zero at DC.
(Fourier Transform)
(Laplace Transform)
-p
Location of the zero in the left complexplane
Complex s plane
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
22/27
Zero at the origin.Thus phase(f=0)=90 degrees.The high pass filter has a cut-off frequency of 100.
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
23/27
RC High Pass Filter (Review)
R12=(R1R2)/(R1+R2)A pole and a zero in the left complex plane.
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
24/27
Laplace Transform/Fourier
Transform (Low Frequency)
z=1/(RC)p=1/(R12C)
(Fourier Transform)
(Laplace Transform)
-p
Location of the zero in the left complexplane
Complex s plane
-z
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
25/27
Laplace Transform/Fourier
Transform (High Frequency)
z=1/(RC)p=1/(R12C)
(Fourier Transform)
(Laplace Transform)
-p
Location of the zero in the left complexplane
Complex s plane
-z
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
26/27
Stability Question
Why the poles must lie in the left half plane?
8/13/2019 ES330 Fall 2012 Lecture 6 Filter Intro
27/27
Answer
Recall that the impulse response of a system contains terms such as .
If , these terms grow indefinitely with time while oscillating ata frequency of
exp( ) exp( ) exp( )k k kp t t j t