LMF100_15 Datasheet, PDF (20/40 Pages) Texas Instruments – LMF100 Dual High-Performance Switched Capacitor Filters

LMF100
SNOSBG9B – JULY 1999 – REVISED JUNE 2015
www.ti.com
Device Functional Modes (continued)
H_ON = gain of notch at f
= f₀
=
Q
æ
ççè
R_g
R_l
H_OLP
-
R_g
R_h
H_OHP
ö
÷÷ø
(49)
H_n1
=
gain
of
notch
(as
f
®
0)=
R_g
R_l
´ H_OLP
(50)
H_n2
=
gain
of
notch
æ
çè ^as
f
®
f_CLK
2
ö
÷ø
=
R_g
R_h
´ H_OHP
(51)
*In Mode 3, the feedback loop is closed around the input summing amplifier; the finite GBW product of this op amp
causes a slight Q enhancement. If this is a problem, connect a small capacitor (10 pF−100 pF) across R4 to provide
some phase lead.
Figure 44. MODE 3
Figure 45. MODE 3a
8.4.1.7 MODE 4: Allpass, Bandpass, Lowpass Outputs (See Figure 46)
f₀
=
center
frequency
=
f_CLK
100
or
f_CLK
50
;f_z *
=
center
frequency
of
the
complex
zero
»
f₀
(52)
Q = ^f0 ´ ^R3 ; Qz = quality factor of the complex zero pair - ^R3
BW R2
R1
(53)
For AP output make R1 = R2
(54)
H_OAP *
=
Allpass
gain
æ
ç ^at
è
0
-f
=
f_CLK
2
ö
÷
ø
=
- ^R2
R1
=
-1
(55)
H_OLP
=
Lowpass
gain
(as
f
®
0) =
-
æ
çè
R2
R1
+ 1^ö÷ø
=
-2
(56)
H_OBP
=
Bandpass
gain
(at
f
®
f₀ ) =
-
R3
R2
æçè₁₊
R2 ö
R1 ^÷ø
=
-2
æ
çè
R3
R2
ö
÷ø
(57)
Circuit dynamics : H_OBP = H_OLP ´ Q = (H_OAP + 1)Q
(58)
*Due to the sampled data nature f the filter, as light mismatch for f_z and f₀ occurs, causing a 0.4-dB peaking
around f₀ of the allpass filter amplitude response (which theorectically should be a straight line). If this is
unacceptable, TI recommends Mode 5.
8.4.1.8 MODE 5: Numerator Complex Zeros, BP, LP (See Figure 47)
f₀ =
R2
1+
f_CLK
´
or
1+ ^R2 ´ ^fCLK
R4 100
R4 50
(59)
f_z =
1- ^R1 ´ ^fCLK or 1- ^R1 ´ ^fCLK
R4 100
R4 50
(60)
20
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