1. C ASCADED F ILTERS Approximate and Exact Solutions

2. 2 STAGE LPF First stage: R 1 = 50 k  C 1 = 10  F Second stage: R 2 = 500 k  C 2 = 1  F Ratios: R 2 /R 1 = 10 C 2 /C 1 = 1/10

3. 1- STAGE VS. 2- STAGE (dB) (deg)

4. A PPROXIMATE SOLUTION (deg) (dB)

5. E XACT SOLUTION (deg) (dB)

6. C OMPARISON OF A PPROXIMATE AND E XACT S OLUTIONS Drum Roll Please…

7. T HEY ’ RE PRACTICALLY THE SAME... Provided you design properly with Rule of 10x (deg) (dB)

8. W HAT ’ S IT GOOD FOR ?

9. G ET 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 |  |<= 80 deg.

10. C UTOFF FREQ SHIFTS LEFT -3 dB