Yıldız Technical University
Cascaded FirstOrder Filters
Introduce cascaded first-order op-amp filters
Faculty of Electrical and Electronic Engineering
Lesson Objectives
Introduce cascaded filters
Introduce bandpass filter characteristics
Introduce second-order transfer functions
2
First-Order LPF and HPF
3
Cascaded Filter
Input
First-Order Output
LPF
Input
First-Order Output
HPF
4
Cascaded Filter
5
Bandpass Filter Characteristics
6
Transfer Function
Second-Order Filter
Standard Form:
7
Cascaded Bandpass Filters
8
Question
Is it possible to form a cascaded band-reject
filter?
9
Summary
Cascaded Filters
Bandpass Transfer Functions
10
Second-Order
Transfer Functions
Introduce second-order filter transfer functions
Lesson Objectives
Introduce second-order filter transfer functions
Examine features of transfer functions
12
Filter Transfer Function
Ratio of output voltage to input
voltage as a function of frequency
For any frequency, the transfer
function is a complex number that
indicates how the filter modifies
the magnitude and phase of the
input to produce the output
13
First-Order Low-Pass Filter
14
Second-Order Low-Pass Filter
15
Effect of Quality Factor (Q)
16
High-Pass Filters
17
Band-Pass Filters
18
Butterworth and Chebyshev
Types of transfer functions
For second-order filters, the type is
determined by the Q value
Butterworth (Maximally Flat)
Chebyshev
19
Chebyshev Filters
20
Butterworth Filters
21
Fourth-Order Butterworth vs. Chebyshev
22
Summary
Introduced second-order transfer functions
Examined features of transfer functions
23
Second-Order
Transfer Functions
Introduce second-order filter transfer functions
Faculty of Electrical and Electronic Engineering
Lesson Objectives
Introduce second-order filter transfer functions
Examine features of transfer functions
25
Filter Transfer Function
Ratio of output voltage to input
voltage as a function of frequency
For any frequency, the transfer
function is a complex number that
indicates how the filter modifies
the magnitude and phase of the
input to produce the output
26
First-Order Low-Pass Filter
27
Second-Order Low-Pass Filter
28
Effect of Quality Factor (Q)
29
High-Pass Filters
30
Band-Pass Filters
31
Butterworth and Chebyshev
Types of transfer functions
For second-order filters, the type is
determined by the Q value
Butterworth (Maximally Flat)
Chebyshev
32
Chebyshev Filters
33
Butterworth Filters
34
Fourth-Order Butterworth vs. Chebyshev
35
Summary
Introduced second-order transfer functions
Examined features of transfer functions
36
Second-Order
Filter Circuits
Introduce second-order Sallen-Key filter circuits
Lesson Objectives
Introduce second-order filter circuits
Design second-order filters
38
Sallen-Key Low-Pass Filter
Vi
Vo
39
Lowpass Design Equations
Special Case 1
(K = 1, Solve for C’s)
Special Case 2
(K = 1, Solve for R’s)
Can simplify with
R1 and R2 are interchangeable
Special Case 3
(R’s equal and C’s equal)
40
Sallen-Key Highpass Filter
Vi
Vo
41
Highpass Design Equations
Special Case 1
(K = 1, C1 = C2 = C)
Special Case 2
(R’s equal and C’s equal)
42
Sallen-Key Bandpass Filter
Vi
Vo
43
Bandpass Design Equations
Special Case
(R’s equal and C’s equal)
44
Notch Filters
45
Example Design
Butterworth 2nd Order LPF
Special Case 1
(K = 1, Solve for C’s)
Can simplify with
46
Example Design
47
Summary
Introduced second-order filter circuits
Designed a second-order lowpass filter
48
Filtering
Demonstration
Dr. İbrahim Beklan
Küçükdemiral
Department of Control and
Automation Engineering
Demonstrate filtering of signals
Lesson Objectives
Examine frequency spectra of signals
Demonstrate filtering by a second-order filter circuit
50
Spectrum of Sine Wave
51
Spectrum of Sum of Two Sine Waves
52
Spectrum of Square Wave
53
Spectrum of Square Wave
54
Relaxation Oscillator
55
Measurements
1kHz Square
Wave
Relaxation Oscillator
Vo
f0 = 1kHz Q=5 Sallen-Key BPF
56
Total Harmonic Distortion (THD)
57
Summary
Introduced frequency spectra
Examined physical circuit filtering performance
58