1. 9. FREQUENCY RESPONSE CIRCUITS by Ulaby & Maharbiz All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

2. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

3. Transfer Function Transfer function of a circuit or system describes the output response to an input excitation as a function of the angular frequency ω. Voltage Gain Other Transfer Functions Magnitude Phase All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

4. Filters All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

5. RC Low Pass To determine corner frequency: All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

6. RC High Pass All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

7. Filter Terminology Z in 1 = R + j ω L. Im [Z in 1 ] = 0 when ω = 0 Im [Z in 2 ] = 0 requires that Z L = − Z C or, equivalently, ω 2 = 1/LC All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

9. Scaling Scaling is used to configure a prototype version of the intended practical scaled circuit such that in the prototype circuit, element values are on the order of ohms, henrys and farads. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

10. dB Scale All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

11. RL Filter --Magnitude Log scale for ω and dB scale for M All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

12. RL Filter -- Phase Log scale for ω and linear scale for φ ( ω ) All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

13. Bode Plots: Straight line approximations Bode Magnitude Slope= 20N dB per decade Bode Phase Slope= 45N degrees per decade 1 decade All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

14. Bode Plots Bode Magnitude Slope= 40dB per decade Bode Phase Slope= 90 degrees per decade All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

15. Bode Factors All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

16. Example 9-4: Bode Plots Standard form Numerator: simple zero of second order with corner frequency 5 rad/s Denominator: pole @ origin, and simple pole with corner frequency 50 rad/s All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

17. Example 9-5: More Bode Plots All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

18. Example 9-6:Given Bode Plot, Obtain Expression First segment: Second segment: All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

19. Bandpass RLC Filter All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

20. Bandpass RLC Filter (cont.) Quality Factor Q: characterizes degree of selectivity of a circuit where W stor is the maximum energy that can be stored in the circuit at resonance ( ω = ω 0 ), and W diss is the energy dissipated by the circuit during a single period T. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

21. Bandpass RLC Filter (cont.)  Derivation of Q Resonant frequency Bandwidth All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

22. Bandpass Filter All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

24. Example 9-7: Bandpass Filter Design All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

25. Highpass FilterLowpass Filter All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

26. Bandreject Filter All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

27. Filter Order All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

28. Active Filters ̶ Lowpass All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

29. Active Filters ̶ Highpass All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

30. Cascading Active Filters All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

31. Example 9-10: Third-Order Lowpass Filter All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

32. Cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

33. Example 9-11 cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

34. Cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

35. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

36. Signal Modulation All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

37. Superheterodyne receiver Frequency of received signal is “down-converted” to a lower intermediate frequency, while retaining the modulation ( which contains the message information) intact All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

38. Multisim Analysis of RLC Circuit All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

39. Multisim Analysis of Active Filters All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

40. Summary All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press