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Signals and Networks (SEE 2043) Lecture #17 Topics covered High Pass Filters

Signals and Networks (SEE 2043) Lecture #17 Topics covered High Pass Filters Higher Order Filters (Second order). Objectives. By the end of this lecture, the student must be able to: Understand the characteristics of first order high pass filters.

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Signals and Networks (SEE 2043) Lecture #17 Topics covered High Pass Filters

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  1. Signals and Networks • (SEE 2043) • Lecture #17 • Topics covered • High Pass Filters • Higher Order Filters (Second order)

  2. Objectives • By the end of this lecture, the student must be able to: • Understand the characteristics of first order high pass filters. • Plot the amplitude and phase response of the first order high pass filters • Understand the characteristics of second order filters. • Plot the amplitude and phase response of the second order filters

  3. |H(jω)| stopband passband ωc ω 0 Cutoff frequency High Pass Filter (HPF) The filter passes signals at frequencies higher than the cutoff frequency. Magnitude at cutoff frequency is 3 dB less than the amplitude at passband Ideal magnitude plot of HPF showing passband and stopband, separated by cutoff frequency • Two types of HPF circuits will be examined: • Series RC circuit • Series RL circuit

  4. C + V1(s) R Vo(s) + - - Series RC circuit (HPF) The transfer function for the HPF circuit is: Replacing s=jω;

  5. Continue Maximum value of Hmax=1, when ω>>1/RC. Hence: The cutoff frequency can be designed to any desired value by selecting values for R and C. Bode Plot: Addition of constant, zero at origin and real pole.

  6. Bode Plot (HPF) dB 3 dB { ωc: estimate 20dB/decade 20log10RC+ 20log|jω| ω ωc θ 0.1ωc ωc 10ωc 90o ω -45o/decade 45o 0o

  7. R + V1(s) L Vo(s) + - - Series RL circuit (HPF) The transfer function for the HPF circuit is: Replacing s=jω;

  8. Continue Maximum value of Hmax=1, when ω>>R/L. Hence: The cutoff frequency can be designed to any desired value by selecting values for R and L. Bode Plot: Addition of constant, zero at origin and real pole.

  9. Bode Plot (HPF) dB 3 dB { ωc: estimate 20dB/decade 20log10(R/L)+ 20log|jω| ω ωc θ 0.1ωc ωc 10ωc 90o ω -45o/decade 45o 0o

  10. Example Given a transfer function for a given filter as follows: • Determine type of filter using Bode Plot. • Determine the cut-off frequency.

  11. Higher Order Filters • LPF and HPF filters discussed previously is a first order type. • Rules for constructing Bode plots: 1 filter – slope of 20 dB/decade, 2 cascaded filters – slope of 20+20 dB=40 dB. • In general, higher number of cascaded filters (higher order filters)  transition from passband to the stopband becomes sharper  more efficient in filtering. • The order of a filter is determined by the number of poles in its transfer function. e.g.

  12. Reminder!!!! Depending on the value of ξ, the poles of the transfer function for the second order filter can be either complex or real. Example: Need to consider the Bode Plot for complex poles Need to consider the Bode Plot for real poles

  13. Second Order Filters + VC(s) - R C + V1(s) L VL(s) + - - It can be shown that: Second order HPF Second order LPF

  14. Example From previous slide, obtain the Bode Plot for second order LPF and second order HPF

  15. Vin Vout Second Order Filter Second order LPF Vin Vout Second order HPF

  16. Next Lecture • Band Pass Filter • Band Reject Filter

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