Download - Cascaded Filters
CASCADED FILTERSApproximate and Exact Solutions
2 STAGE LPF
First stage:R1 = 50 kWC1 = 10 mF
Second stage:R2 = 500 kWC2 = 1 mF
Ratios:R2/R1 = 10C2/C1 = 1/10
1-STAGE VS. 2-STAGE
-5 -4 -3 -2 -1 0 1 2 3 4-120
-100
-80
-60
-40
-20
0
log10
()
G(
) =
20
log 10
|H(
)|
2-stage
1-stage
-5 -4 -3 -2 -1 0 1 2 3 4
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
log10
()
(
)
2-stage
1-stage
(dB
)
(deg)
APPROXIMATE SOLUTION
-5 -4 -3 -2 -1 0 1 2 3 40
0.2
0.4
0.6
0.8
1
log10
()
|H(
)|
-5 -4 -3 -2 -1 0 1 2 3 4-120
-100
-80
-60
-40
-20
0
log10
()
G(
) =
20
log 10
|H(
)|
-5 -4 -3 -2 -1 0 1 2 3 4
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
log10
()
(r
ad)
(deg)
(dB
)
EXACT SOLUTION
-5 -4 -3 -2 -1 0 1 2 3 40
0.2
0.4
0.6
0.8
1
log10
()
|H(
)|
-5 -4 -3 -2 -1 0 1 2 3 4-120
-100
-80
-60
-40
-20
0
log10
()
G(
) =
20
log 10
|H(
)|
-5 -4 -3 -2 -1 0 1 2 3 4
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
log10
()
(r
ad)
(deg)
(dB
)
COMPARISON OF APPROXIMATE AND EXACT SOLUTIONS Drum Roll Please…
THEY’RE PRACTICALLY THE SAME...
-5 -4 -3 -2 -1 0 1 2 3 4-120
-100
-80
-60
-40
-20
0
log10
()
G(
) =
20
log
10 |H
()|
-5 -4 -3 -2 -1 0 1 2 3 4
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
log10
()
(r
ad)
-5 -4 -3 -2 -1 0 1 2 3 40
0.2
0.4
0.6
0.8
1
log10
()
|H(
)|Provided you design properly
with Rule of 10x(deg)
(dB
)
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.
CUTOFF FREQ SHIFTS LEFT
-1 -0.5 0 0.5 1
-20
-15
-10
-5
0
log10
()
2-stage
1-stage
-3 dB
