диафрагмированные волноводные фильтры / 201eab41-7127-4480-b776-d7a9624de251

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To illustrate the double resonance mechanism another resonator (Figure 9), consisting of the resonating slot (slot 1) and one of the asymmetric slots (slot 2 / slot 3), has been simulated. The frequency responses are show in Figure 10, which can be explained as follows. In Figure 9 (a) slot 2 behaves as an inductor throughout the band whereas the resonator slot (slot 1) behaves as an inductor below the transmission pole and capacitor above the transmission pole. Therefore below the transmission pole the

equivalent circuit of Figure 9 (a) behaves as a series combination of two inductors and no resonance (hence TZ) occurs. However, above the transmission pole, it becomes a series LC resonator and a TZ is observed. Figure 10 (b) can be similarly explained. However for this case slot 3 behaves as a capacitor. Therefore the equivalent circuit of Figure 9 (b) is a series LC network below the transmission pole and a series combination of two capacitors above the transmission poles. Thus we get a TZ below the transmission pole and no TZ above the transmission pole. In summary it can be said that if the asymmetric slot length is shorter than the resonating slot, TZ will be placed at upper side (or above the centre frequency), and if the asymmetric slot dimension is longer than the resonating slot, TZ will be placed at lower side (or below the centre frequency).

	Manuscript
(a)	(b)
Accepted

Figure 9. Schematic diagram of (a) waveguide loaded with slot 1 and slot 2 of Figure 6 and (b) waveguide loaded with slot 1 and slot 3 of Figure 6.

(a) (b)

Figure 10. Frequency response of the circuit of (a) Figure 9. (a) and (b) Figure 9. (b).

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To demonstrate the independent control	of the st pband TZ s, the circ it of
Figure 6 (b) has been simulated for different val	es of LAS1 and LAS2. Initially LA 1 has

been	varied from 11 to 15 mm keeping LAS2 c nstant and then LAS2 has been varied
from	7 to 9.5 m m keeping LAS1 cons tant. In both the cases the positio ns of lower and
upper TZs have been noted and plotted in Figure 11. Th e figure i mplies that with
incre ase in LAS2 , the upper TZ remains almost co nstant at 11.55 GHz b ut the low er TZ

varie s from 8.445 to 9.39 GHz, wher eas with in crease in	AS1, the lower TZ re mains
Manuscript
almo st constant at 8.64 GHz but the u pper TZ var ies from 9.	98 to 13.12 GHz. Therefore
by varying LAS1 / LAS2, th e upper / lower TZ can be plac ed at the		desired location,
without affecting the others. The figu re also reveals that irre spective of		the variation of
LAS1 / LAS2 the c enter frequency also remains almost constant.

Accepted	(a)

(b)

Figure 11. The variations o f the TZs with variations in asym metric slot length (a) LAS2 Varied ( onstant: LRS = 10.6, WRS= 1, LAS1 = 8.6, WAS1 = 1), and (b) LAS1 Varied ( Constant: L RS = 10.6, LAS2 = 15.4, WRS = 1, WAS2= 1). All dime nsions are in mm.

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To	vali date	the simulation t hree differ nt asymmetric	slot loaded resonator
structures	(Fig re	6 (b)) have been fabricated and measured	usin g Keysoft PNA

network analyzer (Model: N5221A). The mea ured frequency respo nses have been com pared with the respe ctive simulated frequency responses in Figure 12, hich reve als good agreement be ween them.

		Manuscript
The simulated	scattering parameters of the eq uivalent circuit (Figur e 8) and HFSS
model (Figure 6	(b)) have been plotte d and compared in Figure 13, which shows a good
Accepted
agre ement between them.

Figure 12. Com parison of the simul ated and m easured fr quency re sponses of three

asym metric slot loaded str uctures (Resonator 1: LRS = 10.6, LAS1 = 7, L AS2 = 15.4, WRS = WAS1 = WAS2 = 1, Resonator 2: LRS = 10.6, L AS1 = 8, LAS 2 = 13.4, W RS = AS2 = WAS3 = 1, and Reson ator 3: LRS = 10.6, LA S1 = 8.6, L S2 = 11.4, WRS= WAS 2 = WAS3 = 1 (in mm).

Figure 13. Com parison of the frequency response of the circuits in Figure 6. (b) and Figure 8.

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2. Third Order Bandpass Filter with Multiple Transmission Zeros

The proposed third order bandpass filter has been designed by placing three asymmetric slot loaded resonators on the transverse plane of a WR-90 waveguide, as shown in Figure 14 (a). The dimensions of the slots are tabulated in Table I. The resonators have been placed at a distance (l) 9.2 mm. In the figure “h+c” is the thickness of the dielectric substrate and copper (0.797mm). To analyze the coupling between resonators and its effect on the frequency response of the filter, parametric analysis of the structure is carried out with different value of “l”. The result shown in Figure 15. The parametric analysis reveals that an acceptable frequency response can be achieved for l=9.2 mm. The equivalent circuit of the filter is shown in Figure 14 (b). The values of lumped elements of Figure 14 (b) have been tabulated in Table II. Comparison of the frequency responses of the circuit model (Figure 14 (b)) and waveguide model (Figure 14 (a)) is shown in Figure 16. The results are in close agreement.

Table I final dimensions of the three asymmetrical slot resonator.

	Resonator			First			Second		Third
	Resonator Slot		LRS = 10.6 mm				LRS = 10.6 mm		LRS= 10.6 mm
			WRS= 1 mm				WRS= 1 mm		WRS = 1 mm
							Manuscript
	Asymmetric Slot 1		LAS1 = 7 mm				LAS1 = 8 mm		LAS1 = 8.6 mm
			WAS1		= 1 mm		WAS1 = 1 mm		WAS1 =1 mm
	Asymmetric Slot 2		LAS2 = 15.4 mm				LAS2 = 13.4 mm		LAS2 = 11.4 mm
			WAS2		= 1 mm		WAS2 = 1 mm		W AS2 = 1 mm
		Table II Lumped Elemental Values of Figure 14 (b).
		Resonator 1			Resonator 2			Resonator 3
		LS1 = 0.70693 nH			LS3 = 0.36091 nH			LS5 = 0.24665 nH
		CS1 = 0.67982 pF			CS3 = 1.0245 pF			CS5 = 1.2679 pF
Accepted					Lp	= 0.8199 nH		Lp = 0.8199 nH
		Lp = 0.8199 nH
		Cp = 0.3035 pF			Cp = 0.3035 pF			Cp = 0.3035 pF
		LS2 = 0.23132 nH			LS4 = 0.55816 nH			LS6 = 1.1428 nH
		CS2 = 0.53549 pF			CS4 = 0.27570 pF			CS6 = 0.1430 pF

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		Manuscript
		(a)
Accepted		(b)
Figure 14.	Schematic diagram of the proposed filter (a) wave guide model, and (b)
lump ed element equivalent circuit.
Figure 15.	Para metric anal sis of the structure for different l ength (l).

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Figure 16. Comparison of the frequency responses of the circuit model (Figure 14. (b)) and waveguide model (Figure 14. (a)).

.

4. Fabrication and Measurement

Based on the above analysis, the proposed filter has been fabricated and measured within the X–band frequency range using Keysoft PNA network analyzer (Model: N5221A). Keysight 85520A calibration kit is used to calibrate the VNA before taking

Manuscript

measurement with standard calibration procedure. Initially the slot resonators and WR– Accepted90 waveguide were fabricated separately. Then the resonators were manually placed inside the waveguide, to construct the filter. The experimental set up for the

measurement of scattering parameters is shown in Figure 17 and fabricated front view and side view are shown in Figure 18. The comparison between the simulated and measured frequency responses is shown in Figure 19 (a), which shows a good agreement between them. The magnified view of the passband insertion loss is shown in Figure 19 (b). The measured results shows centre frequency 9.98 GHz, lower cut-off frequency 9.49 GHz, higher cut-off frequency 10.51 GHz, fractional bandwidth of 10.27 % and insertion loss 1 dB. The measured TZs are located at 8.23, 8.70, 9.16, 10.9, 11.6 and 13.115 GHz. The slight difference between the simulated and measured result are due to the losses in waveguide to coaxial adaptor and fabrication tolerances.

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Figure 17.	Experimental setup for the	Manuscript
		measurement S-parameters of the fabricated filter.
Accepted
Figure 18.	Front view and ide view of the fabric ated filter.

(a)

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Figure 19. Comparison the simulated and measured frequency response (a) over 8 – 13.5 GHz and (b) over 9.5 – 10.5 GHz.

A comparison between the proposed and some of the reported waveguide filters is summarized in Table III, whereas the comparison of simulated and measured filter characteristics is provided in Table IV. Table III reveals that the proposed filter has higher bandwidth than [1, 22, 23], better return loss than [1, 3, 4], better insertion loss than [22] and compact than [3]. Though some of the properties of the filters presented in

Manuscript(b)

[1 – 4] are better than the proposed filter, they do not have TZs at their stopband. Therefore the passband to stopband transition of the proposed filter is better than those in [1 – 4]. Some properties of the filters presented in [22, 23] are also better than the proposed filter, but their bandwidths are smaller than the proposed filter. At this point it may be noted that the proposed filter allows independent control of centre frequency and TZs, which the other filters do not.

Table III Comparison of the characteristics of the proposed bandpass filter with other reported waveguide filter.

	Refrence	Center	Bandwidth	RL in	IL in	Length	No. of
		Frequecy in	In GHz	dB	dB	in mm	TZs
	Accepted
		GHz
	[1]	11.95	0.5	10	0.5	15.02	–
	[2]	10.03	1.88	15.21	0.49	20.33	–
	[3]	9.25	1.5	13	0.5	92.76	–

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[4]	10.15	1.43	13	0.7	20.33	–
[22]	10	0.4	17	1.7	20.42	6
[23]	10	0.4	20	0.58	19.875	6
Proposed	9.98	1.02	13.25	1	20.33	6

	Table IV Comparison of the Simulated and Measured Filter Characteristics.
resonator. The proposed method providesManuscriptthe flexibility to insert TZs at the
		Center	3-dB	RL in	IL in dB	TZs location
		Frequecy in	BW In	dB		(GHz)
		GHz	GHz
	Simulated	10	1.0774	14	0.5	8.23/8.69/9.155/1
						0.89/11.62/13.15
	Measured	9.98	1.02	13.25	1	8.23/8.7/9.16/10.9
						/11.6/13.115

4. Conclusion

This paper presents a simple and efficient way to design a compact waveguide

bandpass filter with multiple stopband TZs using asymmetric slot loaded Accepteddesired locations using simple modifications in the structure. It also provides the flexibility to control the centre frequency and bandwidth as per requirement with

simple modifications in the slot resonator. The controls of the centre frequency, bandwidth and individual TZs are independent of each other. The insertion of the TZs at the desired locations helps to suppress the interference more efficiently and therefore the filter is useful in the microwave systems that are prone to be affected by interfering signals, for example, radar, radio location and radio navigation systems. Detailed design procedures and equivalent circuit models of the proposed filter have been provided and validated.

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