468 Page 12 of 13	H. Ghorbaninejad, A. Ghajar

Fig. 9 The frequency response of the band-stop filter, shown in Fig. 8

4 Conclusion

In this paper, a new method has been proposed to design both band-pass and band-stop E-plane waveguide filters. Furthermore, the proposed method can be applied to design waveguide filter with a desired frequency response characteristic. In this method, each conventional resonator is replaced by a longitudinal patterned plane, which can be designed by genetic algorithm optimization, so that the scattering parameters of the structure will be fitted to that of the desired resonator. The proposed method facilitates and accelerates the optimization process in comparison to simulator software. Furthermore, a waveguide filter with a desired frequency response characteristic can be designed, as a single block instead of some cascaded blocks. Moreover, the proposed approach could be helpful to design waveguide filters with higher selectivity features. The performance of the proposed approach has been approved, by some examples, and using comparison between the obtained and simulated results.

Appendix

The electric dyadic Green’s functions derived as follows.

G

¼ m¼0 n¼0

emen

nk2

k2

sin

k x

Þ

cos k y

sin

k x0

Þ

cos k y0

exp

ð

j

z

z0

o

2jxe0abCmn

yy

X X

0

y

x

y

x

y

Cmn

X X emen

ð22Þ

Gxz

Cmnky sin kxx cos kyy

sin kxx0

sin kyy0

exp

Cmn

z z0

¼ m¼0 n¼0

2jxe0abCmn

ð Þ

ð

Þ

ð j jÞ

ð23Þ

123

Genetic algorithm design for E-plane waveguide filters

Page 13 of 13

468

Gzx

¼

XX

emen

Cmnky sin kxx

Þ

sin kyy sin kxx0

Þ

cos kyy0

exp

ð

Cmn

z

z0

m¼0 n¼0 2jxe0abCmn

ð

ð

j

jÞ

ð24Þ

emen

Gzz

X X

sin kxx sin kyy

sin kxx0

Þ

sin

kyy0

Cmn2

þ

k02

ð25Þ

¼ m¼0 n¼0 2jxe0abCmn

ð Þ

ð

2Cmndðz z0Þ& expð Cmnjz z0jÞg

q

where

Cmn ¼

2

2

2

is

the

propagation

2

2

l0e0,

ðmp=aÞ þðnp=bÞ k0

constant, k0

¼ x

kx ¼ mp=a, and ky ¼ np=b. In Eqs. 22, 23, upper and lower sign corresponds to z z0; and z\z0 respectively and the Neumann factor en is given by:

en	¼		1; n ¼		0
			2; n	6¼	0

References

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