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Elliptic Band Reject Filter (ELBRF_KP, ELBRF_FS, ELBRF_N)

Elliptic Band Reject Filter (ELBRF_KP, ELBRF_FS, ELBRF_N)

Properties	Description	Units	Default	Range
AMAX	Maximum ripple in the pass band	dB	Required	>0
AMIN	Minimum ripple in the stop band	dB	Required	>0
FA	Lower pass band edge	Hz	Required	>FL
FB	Upper pass band edge	Hz	Required	>FA
FL	Lower stop band edge, ELBRF_FS only	Hz	FA*FB/FH	>0
FH	Upper stop band edge, ELBRF_FS only	Hz	FA*FB/FL	>FB
KP	Steepness of descent (Sharpness), ELBRF_KP only		Required for ELBRF_KP	[0,1)
N	Order of filter, ELBRF_N only		Required for ELBRF_N	[2,15]
R1	Reference resistance at node 1	Ohm	50.	³0
R2	Reference resistance at node 2	Ohm	50	³0
IL	Insertion loss in dB		0	³0

Notes

1. The model ELBRF has been separated into three components: ELBRF_KP, ELBRF_N, and ELBRF_FS. The parameters FL & FH, KP, and N may not be used concurrently.

2. The elliptic filter is equiripple in the pass band and the stop band (it has equal loss maxima in the pass band and equal loss minima in the stop band). The elliptic filter is used when a sharp transition region is desired for the lowest possible order (which defines the number of reactive elements needed for the filter implementation).

3. In the case ELBRF_KP, KP is a required parameter.

4. In the case ELBRF_N, N is a required parameter.

5. In the case ELBRF_FS, either FL or FH must be provided as inputs. If only FL or FH is given, then the corresponding values for FH and FL are calculated such that a geometrically symmetrical filter is defined:

6. If both FL and FH are defined such that the filter is not geometrically symmetrical, then^1,2:

Case _:A new upper stop band edge and a new upper pass band edge are defined, according to:

_and

_.Case _:A new lower stop band edge and lower pass band edge is defined as:

7. The normalized low pass model poles are then calculated for f_c=1, and f_S=(f_H-f_L)/(f_B-f_A) (where fc is the pass band cutoff frequency, and f_s is the stopband edge frequency - see low pass elliptical filter model description).

8. The band reject model is described by the following^1,2:

, where A(f) is the loss in dB, and R_n is the n^th order Tschebycheff rational function,
_,and
_.where w=2pf.

9. The magnitude of the transfer function, |H(jw)| is equal to the inverse of the loss:

10. Range for N: 2 < N < 15

Netlist Form

ELBRF:NAME n1 n2 AMAX=val AMIN=val {FA=val FB=val [FL=val|FH=val] | FA=val FB=val KP=val | FA=val FB=val N=val}

Netlist Example

ELBRF:1 1 2 FA=2ghz FB=4GHZ FL=2.02GHz FH=3.96GHZ AMAX=0.01 AMIN=40

ELBRF:2 1 2 FA=2GHZ FB=4GHZ N=12 AMAX=0.01 AMIN=40

ELBRF:3 1 2 FA=2GHZ FB=4GHZ KP=0.99 AMAX=0.01 AMIN=40

References

1. Approximate Methods for Electronic Filter Design, Richard W. Daniels, Bell Telephone Laboratories, Inc., McGraw-Hill Book Company, 1974.

2. Handbook of Filter Synthesis, Anatol I. Zverev, John Wiley & Sons, 1967.

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