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 LPF Output Input First-Order HPF Output 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 V i V o 39
Lowpass Design Equations Special Case 1 (K = 1, Solve for C s) Special Case 2 (K = 1, Solve for R s) Special Case 3 (R s equal and C s equal) Can simplify with R 1 and R 2 are interchangeable 40
Sallen-Key Highpass Filter V i V o 41
Highpass Design Equations Special Case 1 (K = 1, C 1 = C 2 = C) Special Case 2 (R s equal and C s equal) 42
Sallen-Key Bandpass Filter V i V o 43
Bandpass Design Equations Special Case (R s equal and C s equal) 44
Notch Filters 45
Example Design Butterworth 2 nd 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 V o Relaxation Oscillator f 0 = 1kHz Q=5 Sallen-Key BPF 56
Total Harmonic Distortion (THD) 57
Summary Introduced frequency spectra Examined physical circuit filtering performance 58