Table 4 Predicted (Pred) and simulated (Sim) \(S_{11}\) and gain for different substrates at 6 GHz and 9 GHz with their absolute errors (AEs) and relative errors (REs).

From: Design of rectangular patch antennas through machine learning

Material

6 GHz – \(S_{11}\) (dB)

6 GHz – Gain (dB)

9 GHz – \(S_{11}\) (dB)

9 GHz – Gain (dB)

Pred

Sim

AE

RE

Pred

Sim

AE

RE

Pred

Sim

AE

RE

Pred

Sim

AE

RE

\(\varepsilon _r=4.6\), \(t=1.6\) mm

− 10.72

− 10.82

0.1

0.009

3.77

3.79

0.002

0.005

− 11.09

− 10.5

0.41

0.03

2.91

2.92

0.01

0.003

\(\varepsilon _r=4.6\), \(t=2\) mm

− 11.03

− 11.34

0.31

0.02

3.44

3.46

0.002

0.005

− 11.62

− 12.13

0.51

0.04

1.9

1.88

0.02

0.01

\(\varepsilon _r=4.6\), \(t=2.4\) mm

− 11.73

− 11.83

0.1

0.008

2.93

2.93

0.000

0.000

− 11.10

− 11.59

0.49

0.04

0.87

0.86

0.01

0.01

\(\varepsilon _r=6.45\), \(t=1.27\) mm

− 11.86

− 11.91

0.05

0.004

2.69

2.88

0.19

0.06

− 13.64

− 13.51

0.13

0.01

3.32

3.15

0.07

0.02

\(\varepsilon _r=6.45\), \(t=1.9\) mm

− 13.92

− 14.49

0.57

0.03

2.71

2.65

0.06

0.02

− 13.28

− 13.06

0.22

0.02

0.74

0.60

0.09

0.14

\(\varepsilon _r=6.6\), \(t=1.28\) mm

− 12.17

− 12.17

0.00

0.000

3.13

3.16

0.03

0.01

− 13.57

− 13.70

0.13

0.01

2.6

2.77

0.17

0.06