A novel method of support vector machine to compute the resonant frequency of annular ring compact microstrip antennas

Figures & data

Figure 1. The geometry of ARCMA.

Table 1. Physical and electrical parameters of simulated ARCMAs

Simulation numbers	Antenna dimensions (mm)			εr
	ao	ai	h
4 × 25	15	2, 4, 6, 8, 10	0.640	4.50
	20	3, 6, 9, 12, 15	0.640	4.50
	25	4, 8, 12, 16, 20	0.640	4.50
	30	5, 10, 15, 20, 25	0.640	4.50
	35	6, 12, 18, 24, 30	0.640	4.5
	15	2, 4, 6, 8, 10	1.570	2.33
	20	3, 6, 9, 12, 15	1.570	2.33
	25	4, 8, 12, 16, 20	1.570	2.33
	30	5, 10, 15, 20, 25	1.570	2.33
	35	6, 12, 18, 24, 30	1.570	2.33
	15	2, 4, 6, 8, 10	2.500	9.80
	20	3, 6, 9, 12, 15	2.500	9.80
	25	4, 8, 12, 16, 20	2.500	9.80
	30	5, 10, 15, 20, 25	2.500	9.80
	35	6, 12, 18, 24, 30	2.500	9.80
	15	2, 4, 6, 8, 10	3.175	2.20
	20	3, 6, 9, 12, 15	3.175	2.20
	25	4, 8, 12, 16, 20	3.175	2.20
	30	5, 10, 15, 20, 25	3.175	2.20
	35	6, 12, 18, 24, 30	3.175	2.20

Figure 2. Block diagram of the SVM Model.

Table 2. The SVM parameters

Parameters	Set type/value
Kernel function	Gaussian
Kernel function coefficient (σ)	30
Penalty weight (C)	100000
Slack variables (ξ)	0.001
Number of input	4
Number of output	1

Figure 3. The comparative results of simulation and SVM for training phase.

Table 3. Physical and electrical parameters of 10 simulated ARCMAs for test process

Antenna number	Antenna parameters
	Patch dimensions (mm)			εr	h/λd
	ao	ai	h
1	15	4	2.5	9.8	0.045
2	15	6	1.57	2.33	0.027
3	15	10	3.175	2.2	0.056
4	20	3	0.64	4.5	0.009
5	20	6	1.57	2.33	0.021
6	20	15	2.5	9.8	0.027
7	25	4	3.175	2.2	0.035
8	25	12	1.57	2.33	0.015
9	30	10	0.64	4.5	0.005
10	30	20	3.175	2.2	0.024
11	35	12	0.64	4.5	0.005
12	35	24	2.5	9.8	0.015

Table 4. The resonant frequencies and APE values for test process

Antenna number	Resonant frequencies (GHz)						Percentage errors (%)
	fIE3D	SVM	Calculated by
			Pintzos and Pregla (1978)	Wu and Rosenbaum (1973)	Bahl and Stuchly (1992)	Kumar and Dhubkarya (2011)	SVM	Pintzos and Pregla (1978)	Wu and Rosenbaum (1973)	Bahl and Stuchly (1992)	Kumar and Dhubkarya (2011)
1	1.734	1.733	1.735	1.814	1.813	2.888	0.029	0.058	4.614	4.556	66.551
2	3.323	3.285	3.265	3.181	3.181	3.749	1.149	1.745	4.273	4.273	12.820
3	3.563	3.496	2.917	2.843	2.844	2.396	1.882	18.131	20.208	20.180	32.753
4	2.006	2.023	1.995	2.025	2.025	5.234	0.825	0.548	0.947	0.947	160.917
5	2.594	2.573	2.576	2.534	2.535	3.700	0.829	0.694	2.313	2.274	42.637
6	1.033	1.030	1.041	1.027	1.026	0.804	0.339	0.774	0.581	0.678	22.168
7	2.258	2.249	2.135	2.354	2.355	5.748	0.400	5.447	4.252	4.296	154.562
8	1.833	1.830	1.832	1.785	1.785	1.854	0.179	0.055	2.619	2.619	1.146
9	1.189	1.197	1.193	1.160	1.159	1.564	0.697	0.336	2.439	2.523	31.539
10	1.547	1.616	1.420	1.395	1.395	1.175	4.461	8.209	9.825	9.825	24.047
11	1.021	1.016	0.960	0.920	0.936	0.901	0.490	5.975	9.892	8.325	11.753
12	0.582	0.571	0.542	0.689	0.495	0.786	1.890	6.873	18.385	14.948	35.052
APE							1.098	4.070	6.696	6.287	49.662

Table 5. Physical and electrical parameters of of ARCMAs published earlier in literature

	Patch dimensions (mm)			εr	h/λd
	ao	ai	h
Dahele, Lee, and Wong (1987)	50	25	1.59	2.32	0.007
Bahl et al. (1980)	20	10	3.18	2.32	0.040
Fan and Lee (1991)	50	25	1.59	2.32	0.007
Liu and Hu (1996b)	14.2	7.1	0.355	2.65	0.006
Kumar and Dhubkarya (2011)	17.2	8.6	1.6	4.2	0.022
Dahele and Lee (1982)	70	35	1.59	2.32	0.005
Lee et al. (1983)	70	35	1.59	2.3	0.005
Row (2004)	30	10	0.8	4.4	0.007
Shinde et al. (2010)	35	17.5	1.53	4.3	0.010
Shinde et al. (2010)	17.5	8.75	1.53	4.3	0.021
This study	13	2	2.54	4.5	0.054

Table 6. The measured and calculated resonant frequencies for ARCMAs

		Resonant frequencies (GHz)
	fmeasured	Simulated		fSVM		Calculated by
		IE3D™	HFSS™			Pintzos and Pregla (1978)	Wu and Rosenbaum (1973)	Bahl and Stuchly (1992)	Kumar and Dhubkarya (2011)
Dahele, Lee, and Wong (1987)	0.878	0.880	0.880		0.880	0.886	0.850	0.854	0.877
Bahl et al. (1980)	2.450	2.500	2.410		2.539	2.337	2.171	2.149	2.297
Fan and Lee (1991)	0.891	0.880	0.880		0.880	0.886	0.850	0.854	0.877
Liu and Hu (1996b)	2.880	2.880	2.890		2.878	2.907	2.790	2.811	2.882
Kumar and Dhubkarya (2011)	1.989	2.030	1.980		2.046	2.035	1.850	1.855	1.997
Dahele and Lee (1982)	0.625	0.620	0.620		0.617	0.627	0.600	0.609	0.622
Lee et al. (1983)	0.626	0.630	0.620		0.623	0.629	0.610	0.612	0.625
Row (2004)	1.243	1.210	1.200		1.210	1.213	1.150	1.171	1.590
Shinde et al. (2010)	0.940	0.950	0.940		0.947	0.954	0.890	0.897	0.941
Shinde et al. (2010)	1.960	1.970	1.910		1.970	1.972	1.790	1.801	1.936
This study	3.000	3.030	2.970		3.050	2.800	3.070	2.518	8.392
APE (%)					1.393	1.940	5.530	6.150	19.820

Figure 4. The simulated and measured return loss plots.

Figure 5. The simulated radiation patterns of fabricated ARCMA at 3 GHz for (a)

E_ϕ for θ = 90°, (b)

E_θ ϕ = 0° and

ϕ = 90°.

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