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9. Frequency Response

9. Frequency Response. CIRCUITS by Ulaby & Maharbiz. Overview. 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. Other Transfer Functions. Voltage Gain. Magnitude Phase.

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9. Frequency Response

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  1. 9. Frequency Response CIRCUITS by Ulaby & Maharbiz

  2. Overview

  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. Other Transfer Functions Voltage Gain Magnitude Phase

  4. Filters

  5. RC Low Pass To determine corner frequency:

  6. RC High Pass

  7. Filter Terminology Zin1= R + jωL. Im [Zin1] = 0 when ω = 0 Im [Zin2] = 0 requires that ZL = −ZC or, equivalently, ω2 = 1/LC

  8. 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.

  9. dB Scale

  10. RL Filter --Magnitude Log scale for ω and dB scale for M

  11. RL Filter--Phase Log scale for ω and linear scale for φ(ω)

  12. Bode Plots: Straight line approximations Bode Magnitude Slope= 20N dB per decade Bode Phase Slope= 45N degrees per decade 1 decade 1 decade

  13. Bode Plots Bode Magnitude Slope= 40dB per decade Bode Phase Slope= 90 degrees per decade

  14. Bode Factors

  15. 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

  16. Example 9-5: More Bode Plots

  17. Example 9-6:Given Bode Plot, Obtain Expression

  18. Bandpass RLC Filter

  19. Bandpass RLC Filter (cont.) Quality Factor Q: characterizes degree of selectivity of a circuit where Wstoris the maximum energy that can be stored in the circuit at resonance (ω = ω0), and Wdissis the energy dissipated by the circuit during a single period T.

  20. Bandpass RLC Filter (cont.) • Derivation of Q Resonant frequency Bandwidth

  21. Bandpass Filter

  22. Example 9-7: Bandpass Filter Design

  23. Highpass Filter Lowpass Filter

  24. Bandreject Filter

  25. Filter Order

  26. Active Filters ̶Lowpass

  27. Active Filters ̶Highpass

  28. Cascading Active Filters

  29. Example 9-10: Third-Order Lowpass Filter

  30. Cont.

  31. Example 9-11 cont.

  32. Cont.

  33. Signal Modulation

  34. Superheterodyne receiver Frequency of received signal is “down-converted” to a lower intermediate frequency, while retaining the modulation ( which contains the message information) intact

  35. Multisim Analysis of RLC Circuit

  36. Multisim Analysisof Active Filters

  37. Tech Brief 17: Bandwidth and Data Rate Signal-to-noise ratio

  38. Tech Brief: Bandwidth and Data Rate Shannon-Hartley Theorem Channel capacity (data rate) in bits/s Bandwidth in Hz Note: A high data rate can be achieved even if the signal power is smaller than the noise, so long as sufficient bandwidth is available.

  39. Summary

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