TABLE I
TABLE II
PHYSICAL PARAMETERS OF THE
CONVENTIONAL MICROSTRIP
STEPPED-IMPEDANCE LOW-PASS
FILTER
i Z (V) w (mm)
1 15 11. 22
2 120 0.45
3
15
11. 22
F
Iter
l (mm)
2.06
8. 54
7. 70
K0, S0
Koch
Sierpinski
4
5
6
120
15
120
0.45
11. 22
0.45
11. 65
5. 64
3.1
0
1
2
1
2
SUMMARY OF RESULTS
Simulation Results
CF SL 2H-IL
234 14. 53 -1.75
238 14. 17 -2.00
237 14.05 -2.98
235 14.2 -2.86
238 14.0 -2.91
Experiment Results
CF SL 2H-IL
234 14. 45 -2.12
243 14. 12 -2.76
236 14.0 -2.65
233 14. 3 -2.72
235 13. 75 -2.77
MRL
- 19. 8
- 26.2
NULL
- 26. 4
- 30. 35
2H-F
8. 45
7. 95
7. 80
8. 35
8. 3
F
Iter
be demonstrated that the sharp current discontinuities of the high-low microstrip steps can be greatly smoothed,
when the low-impedance microstrip-lines are made with fractal shapes.
K0, S0
Koch
Sierpinski
0
1
2
1
2
MRL
- 17. 8
- 23.2
- 28. 6
- 23. 87
- 28. 8
2H-F
8. 60
7. 65
7. 95
8. 25
8. 3
Design of the Fractal-shaped
Microstrip Stepped-impedance
Low-pass Filters
Based on the construction law of
the Koch islands and Sierpinski carpets mentioned above, the fractal-shaped stepped-impedance low-pass
filters were designed in microstrip
technology. The specifications are
given by the cut-off frequency (fc =
2.5 GHz), filter order (sixth-order)
and frequency response (maximally
flat Butterworth). The design of the
structure is a two-step process.
First, the conventional layout of
the filter is obtained according to
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the standard procedure. To this end,
the characteristic impedances of the
high and low impedance sections
have been set to Zh = 120 V and Zl
= 15 V, respectively. From these
values, the electrical length of each
transmission line section has been
obtained following the standard
design formulas.1 By using a commercial transmission line calculator
(Agilent LineCalc), the geometry of
the filter has been determined for
a Rogers RT/Duroid 5880 substrate
with a thickness h = 0.78 mm and a
dielectric constant e = 2.2. To provide space for the connectors, 50
V access lines have been cascaded
at the input and output ports. The
physical parameters of the designed
conventional microstrip stepped-impedance low-pass filters are listed in Table 1, where i is the filter
section number, Z is the impedance
of the section, and w and l are the
width and length of the microstrip
line, respectively.
The second step consists of constructing the low-impedance sections, where the conductor strip
width is substantial, as Koch islands
and Sierpinski carpets of different
iteration numbers, to enhance the
passband of the filter. The iteration
orders of the fractals are limited
to two because of manufacturing
tolerance. Thus, the Koch and Sierpinski fractal-shaped microstrip
stepped-impedance low-pass filters
with different iteration orders are
determined.
