LTC1164

11

1164fa

Mode 3A

This is an extension of Mode 3 where the highpass and

lowpass output are summed through two external resis-

10. Mode 3A is more versatile than Mode 2 because the

notch frequency can be higher or lower than the center

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

Figure 10 is not always required. When cascading the

sections of the LTC1164, 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 2: 2nd Order Filter Providing Notch, Bandpass, Lowpass

ODES OF OPERATIO

LTC1164 • MOO04

R3

R4

R2

NS

BP

LP

R1

1/4 LTC1164

1 +

1 +

R3/R1;

MODE 2 (100:1):

100

–

+

+

–

Σ

∫

∫

R3

R2

R2

R4

; Q =

; THEN CALCULATE R1 TO SET THE DESIRED GAIN

R3 =

R2

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

50

; Q =

50

R3/R1

1 – (R3/16R4)

+

1.005

Q

R2

R4

R2

16R4

1 +

MODE 2 (50:1):

50

R2

R4

1 + R2

R4

–R2/R1

1 + (R2/R4)

–R2/R1

1 + (R2/R4)

–R2/R1

1 + (R2/R4)

– R2/R1

1 + (R2/R4)

1.005 (

√1 + R2/R4)

(R2/R3) – (R2/16R4)

= – R2/R1

2

()

= – R2/R1

2

()

Figure 10. Mode 3A: 2nd Order Filter Providing Highpass, Bandpass, Lowpass, Notch

LTC1164 • MOO05

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

50

R3/R1

1 – (R3/16R4)

MODE 3A (50:1):

MODE 3A (100:1):

50

R2

R4

R4

R1

; THEN CALCULATE R1 TO SET

THE DESIRED GAIN

R3 =

R2

+

1.005

Q

R2

R4

R2

16R4

R4/R1;

=

2

()

= –R2/R1

100

100

R2

R4

R2

R4

R3

R2

2

(

)

(

)

R3

R4

R2

HP

S

BP

LP

NOTCH

EXTERNAL OP AMP OR

INPUT OP AMP OF THE

LTC1164, SIDE A, B, C, D

R1

AGND

1/4 LTC1164

–

+

+

–

Σ

∫

∫

–

+

; Q =

; Q =

1.005 (√R2/R4)

(R2/R3) – (R2/16R4)

×

R2

R1

×