# Radiation pattern of single patch, E-plane looks unusual.

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#### Terminator3 I am trying to calculate radiation pattern of a patch antenna using this formulas:
C=299792458;
Freq=10.525*10^9;

'wavelength in free space (in mm)
L0=1000*C/Freq
L0 = 28.48384399

'width of patch (mm / mm)
w=8.8/L0
w = 0.308947065

'length of patch (between radiating edges)
l=6.03/L0
l = 0.211698955

'substrate height
h=1.6/L0
h = 0.056172194

Hplane(x)=Sin( (2*Pi*w/2) *Cos(x) ) / ( (2*Pi*w/2)*Cos(x)) *Sin(x)
Function Hplane(x) is defined

Eplane(x)=Sin( (2*Pi*h/2) *Cos(x) ) / ( (2*Pi*h/2)*Cos(x)) *Cos((2*Pi*l/2)*Cos(x) )
Function Eplane(x) is defined

Plot(20*Log10(Hplane(Pi/2+x*Pi/180)),xMin=-90,xMax=90)
Plot done

Plot(20*Log10(Eplane(Pi/2+x*Pi/180)),xMin=-90,xMax=90)
Plot done
It can be directly pasted to freeware program called SpeqMath.
(https://www.speqmath.com/)

Here is radiation patterns for E and H planes: As you can see E-plane red curve looks not right (as i think).
I searched for some radiation pattern images in internet and found out that E-plane and H-plane pattern does not differ so much as on my image. Also i checked formulas many times and all seems to be ok. What's wrong here with red curve?

#### Terminator3 -3dB patch beamwidth for H-plane looks normal (86deg pattern), while E-plane never reaches -3dB, so beamwidth is 180deg! In real antennas i saw parameters around 90 deg for both planes of single patch antenna. I need to know this parameter more precisely.

#### vfone • Terminator3

### Terminator3

Points: 2

#### Terminator3 Thank for posting. On your image E-plane looks nice, there is -3dB at about +-45deg, so -3dB beamwidth is 90deg. When i use formula it is never gets lower than -2dB. Formula is almost the same everywhere (books, papers). But also I convert to dB using 20*Log10. For example, when i calculate array factor (AF), beamwidth and side beams looks perfect (at -3dB level). But when i come to single element pattern, it is a little strange. I multiply AF by E-plane pattern, but as it is a little wrong, side beams too big, or i get 180deg beamwidth for single patch. I am going to found some paper with results on E-plane and calculate it using this formula to check the difference..

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