Bandpass Filter Terminology Center Frequency Upper and Lower

Bandpass Filter Terminology Center Frequency Upper and Lower Cutoff Frequencies (3 d. B) Passband Insertion Loss Ripple Bandwidth (3 d. B Passband) Attenuation @ fr Rejection Bandwidth @ Ar Upper and Lower Rejection Frequencies Shape Factor @ Ar : SF = Br(Ar)/Bp Note: An attenuation must be specified in order to determine shape factor: “Shape Factor at 30 d. B attenuation. ”

Pole Placement and Pass Band

Bandpass Filter Math Horizontal axis is Logarithmic: fp+/f 0 = f 0/fp- and fr+/f 0 = f 0/fr- Center Frequency is Geometric Mean f 02 = fp+fp- = fr+fr-

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 q. MIN ON CHARTS

Use Loss Curve to Determine Qu(MIN) Figure 7 -14 QL/Qu vs Insertion Loss Per Pole

Filter Specs • • • Center Frequency Passband Allowable Passband Insertion Loss/Ripple Required Out of Band Attenuation Rejection Bandwidth Use Curves to Determine • Number of Poles • Design Ripple • Component Unloaded Q

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

Four Pole, Parallel, Capacitive, Top Coupled Filter Coupling Capacitors C 1, 2 C 2, 3 C 3, 4 C 1 B C 4 B L L C 2 RS C 1 A L C 3 Tank Capacitors This is what the author refers to as the “design impedance level” Equation 7 -20 for a = 1, (used by author to compute XT = XL) L C 4 A End Loading RL

Design Example FM IF Filter – 200 Khz Channel Spacing Requirements: 1. Center Frequency – 10. 7 Mhz 2. Acceptance ( 3 d. B) Bandwidth – 160 Khz 3. Rejection – 30 d. B at 240 Khz BW; SF(30 d. B) = 1. 5 4. Max Insertion Loss – 4 d. B 5. Ripple – 0. 1 d. B max 6. RS = 75 W RL = 50 W 10. 7 Mhz 0 d. B 200 Khz f 200 Khz 4 d. B 3 d. B 160 Khz 30 d. B 240 Khz 200 Khz

Determine Poles, Ripple, Qu(min), k, q Appendix B: Want > 30 d. B attenuation at SF = 1. 5 • • Not possible for 2, 3, 4 poles 5 poles, curve 6 – 1 d. B ripple. . . Too much 6 poles, curve 4 – 0. 01 d. B ripple OK We could choose curve 5, 0. 1 d. B ripple and 32 d. B @ SF = 1. 5 Fig 7 -14 • • Loss Per pole = 4 d. B/6 poles = 0. 66 d. B/pole QL/Qu(min) = 0. 075 QL = 10. 7/0. 16 = 66. 875 Qu(min) = 891 (Difficult!!) 10. 7 Mhz 0 d. B Table 7 -1 0. 01 d. B Chebychev, n = 6 • q 1, n = 0. 937 • k 1, 2 = k 5, 6 = 0. 809 • k 2, 3 = k 4, 5 = 0. 550 • k 3, 4 = 0. 518 4 d. B 3 d. B 160 Khz 30 d. B 240 Khz f

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

Determine Taps for End Loading C 6 A = 1460 p. F C 6 B = 117 p. F C 1 A = 1195 p. F C 1 B = 119 p. F 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 u. H). • 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.