Bandpass Filter Terminology

Attenuation @ fr

Rejection Bandwidth @ Ar

Upper and Lower Rejection Frequencies

Shape Factor @ Ar : SF = Br(Ar)/Bp

Center FrequencyUpper and Lower Cutoff Frequencies (3 dB)

PassbandInsertion LossRipple

Bandwidth (3 dB Passband)

Note: An attenuation must be specified in order to determine shape factor:“Shape Factor at 30 dB attenuation.”

Pole Placement and Pass Band

Bandpass Filter MathHorizontal axis is Logarithmic: fp+/f0 = f0/fp- and fr+/f0 = f0/fr-

Center Frequency is Geometric Mean f02 = fp+fp- = fr+fr-

20 0 0

0

0

0

0

0

( )( )

( )

( )

( )

R r r rr

P P

r r rr

P P r

r rr L

r r

r rr L

r r

B A f fSF A

B B

f f f f f fSF A

B B f f

f A fSF A Q

f f A

ASF A Q

A

Standard Design Curves

Attenuation vs Shape Factor

Separate Curves for different Ripple

Inside Passband

Outside passband

Separate sets of curves for different Number of Poles (3 poles shown)

DO NOT USE qMIN ON CHARTS

Use Loss Curve to Determine Qu(MIN)

Figure 7-14 QL/Qu vs Insertion Loss Per Pole

Loss/Pole -10log 1 2 L

u

Q

Q

Filter Specs• Center Frequency

• Passband

• Allowable Passband Insertion Loss/Ripple

• Required Out of Band Attenuation

• Rejection Bandwidth

• Number of Poles

• Design Ripple

• Component Unloaded Q

Use Curves to Determine

Use Tables (p 230) to determine k and q values . . .

C1A

C1,2

C1B

C4A

C4B

C3C2

C2,3 C3,4

LLL L

Four Pole, Parallel, Capacitive, Top Coupled Filter

00

1Let L

Node

TNode

X LC

LX

C

RS RL

1,21,2 2,3 C =Node

L

kC C

Q

1 11 1,2

1 1

1 11

1 1 1

A BNode

A B

B

A A B

C CC C C

C C

C C

C C C

3 2,3 3,4NodeC C C C

Coupling Capacitors

Tank Capacitors End Loading

4 4

24

4

24

4

1 1

1 1

L T L coil

L T L u T

L

T L u

R q Q X R R

q Q X R Q X

R

X q Q Q

This is what the author refers to as the “design impedance level”

21

1

1 1S

T L u

R

X q Q Q

Equation 7-20 for = 1, (used by author to compute XT = XL)

Design ExampleFM IF Filter – 200 Khz Channel Spacing

Requirements:1. Center Frequency – 10.7 Mhz2. Acceptance ( 3 dB) Bandwidth – 160 Khz3. Rejection – 30 dB at 240 Khz BW; SF(30 dB) = 1.54. Max Insertion Loss – 4 dB5. Ripple – 0.1 dB max6. RS = 75 RL = 50

200 Khz

160 Khz

240 Khz

4 dB

3 dB

30 dB

10.7 Mhz

200 Khz 200 Khz0 dBf

Determine Poles, Ripple, Qu(min), k, q

160 Khz

240 Khz

4 dB

3 dB

30 dB

10.7 Mhz

0 dB f

Appendix B: Want > 30 dB attenuation at SF = 1.5• Not possible for 2,3,4 poles• 5 poles, curve 6 – 1 dB ripple . . . Too much• 6 poles, curve 4 – 0.01 dB ripple OK• We could choose curve 5, 0.1 dB ripple and 32 dB @ SF = 1.5

Fig 7-14• Loss Per pole = 4 dB/6 poles = 0.66 dB/pole• QL/Qu(min) = 0.075

• QL = 10.7/0.16 = 66.875

• Qu(min) = 891 (Difficult!!)

Table 7-1 0.01 dB Chebychev, n = 6

• q1,n = 0.937

• k1,2 = k5,6 = 0.809

• k2,3 = k4,5 = 0.550

• k3,4 = 0.518

Determine Component ValuesChoose XT in the range of 50 – 500 - - Lets pick 135 (just for fun)

0 0

12 110

2 2T

NT

XL nH C pF

f f X

1,21,2 5,6

2,3 4,5

3,4

0.809110 1.3

66.875

0.9

0.85

NL

kC C pF pF C

Q

C pF C

C pF

1 1,2 6

2 1,2 2,3 5

3 2,3 3,4 4

110 1.3 108.7

110 1.3 0.9 107.8

108.25

N

N

N

C C C pF C

C C C C pF C

C C C C pF C

Determine Taps for End Loading

26

6

6

1

1 1 50 1 1

135 .937 66.875 891

0.074

0.091

L

T L u

R

X q Q Q

C6A = 1460 pF C6B = 117 pF

C1A = 1195 pF C1B = 119 pF

These could also be implemented as autotransformer tap points on the input/output inductors.

Critique of Author’s Methodology

• “design impedance level” is really not a design choice, but a threshold for limiting tank reactance based on an arbitrary lower limit for inductors (50 uH).

• The author’s method requires equal source and load resistances, which is not always possible or desirable.

• Using the author’s method, the tank reactance is determined by the source and load impedances. The use of reactive voltage dividers on the input and output tanks allows the tank reactance to be chosen independently.