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Understanding Frequency Response and System Concepts

Explore the characteristics of circuits like low-pass, high-pass, and band-pass filters, and learn about system modeling and responses in physical systems. Visualize plots showing magnitude and phase responses for various filters and equivalent circuits. Discover the behavior of noisy sinusoidal voltages through filter circuits such as Wheatstone bridge and RC filters.

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Understanding Frequency Response and System Concepts

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  1. C H A P T E R 6 C H A P T E R Frequency Response and System Concepts

  2. I L S S 1 + + V V 2 L S L CD Player Amplifier Speakers – (Source) (Circuit) (Load) A physical system A circuit model Figure 6.1 A circuit model I

  3. RC low-pass filter. The circuit preserves lower frequencies while attenuating the frequencies above the cutoff frequency, = 1/ RC . 0 The voltages V and V are the i o filter input and output voltages, respectively. R + + V C V i o _ _ Figure 6.9 A simple RC filter

  4. 1 0.8 0.6 Amplitude 0.4 0.2 0 2 1 0 1 2 3 4 10 10 10 10 10 10 10 Radian frequency (logarithmic scale) Phase response of RC low-pass filter 0 _ 20 _ 40 Phase, degrees _ 60 _ 80 10 10 10 10 10 10 10 Radian frequency (logarithmic scale) Figure 6.10 Magnitude and phase response plots for RC filter Magnitude response of RC low-pass filter

  5. Filter capacitor c R T + V R R _ noise 1 3 + a b + V V _ V V C T out a b _ C + _ V R R S 2 4 Wheatstone bridge equivalent circuit d _ V = V V out a b Figure 6.14 Wheatstone bridge with equivalent circuit and simple capacitive filter

  6. Noisy sinusoidal voltage 10 5 Volts 0 _ 5 _ 10 0 0.08 0.16 0.24 0.32 t (s) Filtered noisy sinusoidal voltage 10 5 Volts 0 _ 5 _ 10 0 0.08 0.16 0.24 0.32 t (s) Figure 6.15 Unfiltered and filtered bridge output

  7. RC high-pass filter. The circuit preserves higher frequencies while attenuating the frequencies below the cutoff frequency, = 1/ RC . 0 C + + V V R i o _ _ Figure 6.16 High-pass filter

  8. 1 80 0.8 60 0.6 Amplitude 40 0.4 20 0.2 0 0 – 2 – 1 0 1 2 3 4 – 2 – 1 0 1 2 3 4 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Radian frequency (logarithmic scale) Radian frequency (logarithmic scale) Figure 6.17 Frequency response of a high-pass filter Phase, degrees

  9. RLC band-pass filter. The circuit preserves frequencies within a band. C L + + V V R i o _ _ Figure 6.19 RLC band-pass filter

  10. Band-pass filter amplitude response 1 0.8 0.6 Amplitude 0.4 0.2 0 10 3 10 2 10 1 10 0 10 1 10 2 10 3 Radian frequency (logarithmic scale) Band-pass filter phase response 50 Phase, degrees 0 _ 50 10 3 10 2 10 1 10 0 10 1 10 2 10 3 Radian frequency (logarithmic scale) Figure 6.20 Frequency response of RLC band-pass filter

  11. R L 1 i ( t ) O + v ( t ) v ( t ) C R i 2 C – Z Z 1 L + V ( s ) V ( s ) Z I ( s ) Z i C C O 2 – Figure 6.32 A circuit and its Laplace transform domain equivalent

  12. 6 4 2 Imaginary part 0 – 2 – 4 – 6 – 10 – 5 0 5 Real part Figure 6.33 Zero-pole plot for the circuit of Figure 6.32

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