1. MALVINO
Electronic
PRINCIPLES
SIXTH EDITION

2. Active Filters
Chapter 21

3. Ideal filter responsesfc A
Ideal
filter
responses
Low-pass
Bandpass BW f f1 f2 A f
All-pass A A
High-pass
Bandstop f f fc f1 f2

4. Real filter response Ideal (brickwall) filters do not exist.
Real filters have an approximate response.
The attenuation of an ideal filter is  in the stopband.
Real filter attenuation is vout/vout(mid):
3 dB = 0.5
12 dB = 0.25
20 dB = 0.1

5. The order of a filter
In an LC type, the order is equal to the number of inductors and capacitors in the filter.
In an RC type, the order is equal to the number of capacitors in the filter.
In an active type, the order is approximately equal to the number of capacitors in the filter.

6. Filter approximations
Butterworth (maximally flat response): rolloff = 20n dB/decade where n is the order of the filter
Chebyshev (equal ripple response): the number of ripples = n/2
Inverse Chebyshev (rippled stopband).
Elliptic (optimum transition)
Bessel (linear phase shift)

7. Real low-pass filter responses Inverse Chebyshev
Butterworth f f A f
Bessel
Inverse
Chebyshev A A
Elliptic f f
Note: monotonic filters have no ripple in the stopband.

8. Real bandpass filter responses Inverse Chebyshev
Butterworth f f A f
Bessel
Inverse
Chebyshev A A
Elliptic f f

9. A second-order low-pass LC filter1
fr = L
Q = XL R C R
600 W
vout
vin
L C fR Q
9.55 mH mF kHz
47.7 mH nF kHz
135 mH nF kHz

10. The effect of Q on second-order response
Q = 10 (underdamped) A
Q = 2 (underdamped)
20 dB
6 dB
Q = (critically damped)
0 dB
a = Q 1
rolloff = 40 dB/decade f
fR or f0
The Butterworth response is critically damped.
The Bessel response is overdamped (Q = … not graphed).
The damping factor is a.

11. Sallen-Key second-order low-pass filter
vout
vin C1
Q = 0.5 C2 C1
Av = 1
2pR
C1C2 1
fp =
= pole frequency

12. Second-order responses
Butterworth: Q = 0.707; Kc = 1
Bessel: Q = 0.577; Kc = 0.786
Cutoff frequency: fc = Kcfp
Peaked response: Q > 0.707
f0 = K0fp (the peaking frequency)
fc = Kcfp (the edge frequency)
f3dB = K3fp

13. Higher-order filters
Cascade second-order stages to obtain even-order response.
Cascade second-order stages plus one first-order stage to obtain odd-order response.
The dB attenuation is cumulative.
Filter design can be tedious and complex.
Tables and filter-design software are used.

14. Sallen-Key equal-component filter
vout
vin C
Av = R2 R1 R2 R1
Q = 1
3 - Av
As Av approaches
3, this circuit
becomes impractical.
2pRC 1
fp =

15. Sallen-Key second-order high-pass filter
vout C C
vin R1
Q = 0.5 R1 R2
Av = 1
2pC
R1R2 1
fp =

16. Tunable MFB bandpass filter with constant bandwidth
vout C
vin R3 f0 Q
BW =
Av = -1
2pC 1
f0 =
2R1(R1 R3)
R1+R3
Q = 0.707 R3

17. Sallen-Key second-order notch filter
vin
vout C C R R 2C R2
Av = R2 R1 R1
Q =
0.5
2 - Av
2pRC 1
f0 =
As Av approaches
2, this circuit
becomes impractical.

18. First-order all-pass lag filter
vout
vin R C
f0 =
2pRC 1
f = -2 arctan f f0
Av = 1

19. First-order all-pass lead filter
vout
vin R C f0
f0 =
2pRC 1
Av = -1
f = 2 arctan f

20. Linear phase shift Required to prevent distortion of digital signals
Constant delay for all frequencies in the passband
Bessel design meets requirements but rolloff might not be adequate
Designers sometimes use a non-Bessel design followed by an all-pass filter to correct the phase shift

21. State variable filter R2 R vin R +1 R R1 Av = Q = 3 C R C R1 R 1 f0 =HP
output LP
output
f0 =
2pRC 1 R2 BP
output