LTC1064

10

1064fb

fO =

1 +

; fn =

; HOHP f→

=

HON(f = fO) = Q

HOLP –

HOHP ; Q =

1064 F09Eq

fO =

; fn =

; HOHP =

; HOBP =

fCLK

100

R2

R4

RH

RL

MODE 3a (100:1):

NOTE: THE 50:1 EQUATIONS FOR MODE 3A ARE DIFFERENT FROM

THE EQUATIONS FOR MODE 3A OPERATION OF THE LTC1059,

LTC1060 AND LTC1061. START WITH fO, CALCULATE R2/R4, SET R4;

FROM THE Q VALUE, CALCULATE R3:

√

R2

R4

√

√

fCLK

100

R2

R4

R3 =

; THEN CALCULATE R1 TO

SET THE DESIRED GAIN.

+

R2

1.005

Q

√

R2

16R4

R2

R1

–

R2

R3

R2

16R4

R2

R4

1.005

√

–

R3

R1

HOBP = –

; HOLP(f = 0) =

Q =

R3

16R4

1 –

R4

R1

–

;

R3

R1

–

;

R3

R2

R4

R1

fCLK

2

()

()()

()( )

RH

RL

√

R2

R4

√

fCLK

50

fCLK

50

MODE 3a (50:1):

R2

R1

–

;

fCLK

2

()

()

HOLP = –

; HON1(f→ 0) =

; HON2 f→

=

;

R4

R1

R2

R1

RG

RL

RG

RL

RG

RH

RG

RH

–

+

∫

∫

LP

+ Σ

AGND

HP

S

1/4 LTC1064

–

BP

R1

R2

VIN

R3

R4

1064 F09

CC

RL

RH

RG

NOTCH

EXTERNAL OP AMP OR INPUT

OP AMP OF THE LTC1064,

SIDE A, B, C, D

–

+

1064 F08Eq

fO =

1 +

; fn =

; Q =

1 +

; HOLP = –

;

fCLK

100

R2

R4

R3

R2

MODE 2 (100:1):

NOTE: THE 50:1 EQUATIONS FOR MODE 2 ARE DIFFERENT FROM THE EQUATIONS

FOR MODE 2 OPERATION OF THE LTC1059, LTC1060 AND LTC1061. START WITH

fO, CALCULATE R2/R4, SET R4; FROM THE Q VALUE, CALCULATE R3:

√

R2

R4

√

R2

R4

√

fO =

1 +

; fn =

; Q =

; HOLP = –

;

fCLK

50

fCLK

50

fCLK

50

MODE 2 (50:1):

R2

R3

R2

16R4

R2

R4

1.005

1 +

√

–

R3

R1

HOBP = –

; HON1(f→ 0) = –

; HON2 = f→

=

R3

16R4

1 –

R2

R4

R3 =

; THEN CALCULATE R1 TO SET THE DESIRED GAIN.

1 +

+

R2

1.005

Q

√

R2

16R4

R2

R1

R2

R4

1 +

R2

R1

–

R2

R1

R2

R4

1 +

R2

R1

R2

R4

1 +

fCLK

2

()

fCLK

2

()

HOBP = –

; HON1(f→ 0) = –

; HON2 f→

= –

R3

R1

R2

R1

R2

R1

R2

R4

1 +

–

+

∫

∫

LP

1064 F08

+ Σ

AGND

NS

1/4 LTC1064

–

R1

R2

VIN

R3

R4

BP

ODES OF OPERATIO

Figure 8. Mode 2: 2nd Order Filter Providing Notch, Bandpass and Lowpass

Mode 3a

This is an extension of Mode 3 where the highpass and

lowpass outputs are summed through two external resis-

tors RH and RL to create a notch. This is shown in Figure 9.

Mode 3a is more versatile than Mode 2 because the notch

frequency can be higher or lower than the center fre-

quency of the 2nd order section. The external op amp of

Figure 9 is not always required. When cascading the

sections of the LTC1064, the highpass and lowpass

outputs can be summed directly into the inverting input of

the next section. The topology of Mode 3a is useful for

elliptic highpass and notch filters with clock-to-cutoff

frequency ratios higher than 100:1. This is often required

to extend the allowed input signal frequency range and to

avoid premature aliasing.

When the internal clock-to-center frequency ratio is set at

50:1, the design equations for Q and bandpass gain are

different from the 100:1 case.

Figure 9. Mode 3a: 2nd Order Filter Providing Highpass, Bandpass, Lowpass and Notch