1. ABE425 Engineering Measurement Systems Filters Dr. Tony E. Grift
Dept. of Agricultural & Biological Engineering
University of Illinois

2. Agenda Recap complex numbers
Relationship Laplace, frequency (Fourier) domain
Relationship time, s and frequency domains
decibel notation (dB)
RC circuit as a Low-Pass and High-Pass filter
Bode plots
Combination filters

3. Complex number in complex plane
Argument of s
Absolute value of s (aka Modulus or Magnitude)

4. Operations on complex numbers cont.
Multiplication/division
using Euler’s notation

5. Operations on complex numbers cont.
Complex conjugate
Multiplying a complex number by its conjugate
gives a real number

6. Relation Laplace and Fourier Transform
Time domain
Time domain
s-domain (Laplace Domain)
-domain (Frequency Domain)
Transient response
(step, impulse, ramp)
Frequency response
(filters)

7. Relation time, s and frequency ( ) domain
Time domain i
Laplace (s)-domain
-domain

8. Concept of impedance (Capacitor)
Laplace transform

9. Concept of impedance (Inductor (coil))
Laplace transform

10. Low-Pass filter using RC network

11. Derivation transfer function with impedance

12. Decibel notation Addition is much simpler than multiplication
Notation in Bel (after Alexander Graham Bell)
For Power
For Voltages (Power ~ Voltage2)
In deciBel (0.1 Bel)

13. The transfer function of a RC circuit is a complex number

14. First order system analysis in standard notation (laborious)

15. First order system analysis in standard notation (laborious)

16. First order system analysis in Euler’s notation

17. First order system analysis in Euler’s notation

18. RC circuit as a Low-Pass filter
Transfer function has an
Absolute value (Magnitude of complex number)
Phase (argument of complex number)
Analyze three points:
Very low frequencies
‘Corner’ frequency
Very high frequencies

19. Filter response at very low frequency
Magnitude
Magnitude in dB
Phase (argument)

20. Filter response at corner frequency
Magnitude
Magnitude in dB
Phase (argument)

21. Filter response at very high frequency
Magnitude
Magnitude in dB
Phase (argument)

22. Summary 1st order low pass filter characteristics

23. Bode plot of a Low-Pass filter for t = 1s
MatLab: bode([0 1],[1 1])

24. High-pass filter using RC network

25. High-Pass filter characteristics

26. RC circuit as a High-Pass filter
Filter response has a
Absolute value (Magnitude of complex number) and
Phase (argument of complex number)

27. 1st order High Pass filter characteristics

28. Bode plot of a High-Pass filter for t = 1s
MatLab: bode([1 0],[1 1])

29. Band-Pass filter through cascading

30. Cascade of High-Pass and Low-Pass filters to obtain a Band-Pass filter
Since the sections are separated by a buffer: Add absolute values in dB;s. Add phase angles
Buffer

31. ABE425 Engineering Measurement Systems Filters The End
Dept. of Agricultural & Biological Engineering
University of Illinois