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Optimizing SNR in Cascaded Filters: Approximate vs. Exact Solutions

Explore the benefits of 1-stage vs. 2-stage filters in terms of decibels and phase shift. Compare the approximate and exact solutions, and discover how to achieve optimal SNR and phase shift for specific frequency ranges with the Rule of 10x. Design a circuit that enhances SNR and maintains phase shift for bass frequencies while shifting the cutoff frequency left by 3 dB.

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Optimizing SNR in Cascaded Filters: Approximate vs. Exact Solutions

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  1. Cascaded Filters Approximate and Exact Solutions

  2. 2 stage lpf • Second stage: • R2 = 500 kW • C2 = 1 mF • Ratios: • R2/R1 = 10 • C2/C1= 1/10 • First stage: • R1 = 50 kW • C1 = 10 mF

  3. 1-stage vs. 2-stage (dB) (deg)

  4. Approximate solution (dB) (deg)

  5. Exact solution (dB) (deg)

  6. Comparison of Approximate and Exact Solutions • Drum Roll Please…

  7. They’re practically the same... (dB) Provided you design properly with Rule of 10x (deg)

  8. What’s it good for?

  9. Get rid of bieber • Beauty and the Beat • Sweet bass line (f <= 150 Hz) • Screechy Bieber vocals (f >= 450 Hz) • Raw song SNR = Bass/Bieber = ½ • Design a circuit that: • increases SNR >= 2 • keeps phase shift for bass frequencies |f|<= 80 deg.

  10. Cutoff freq shifts left -3 dB

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