RectPatch.py

""" Functions dealing with rectangular patch antenna."""
import math
import matplotlib.pyplot as plt
import numpy as np
from sph2cart1 import sph2cart1
from cart2sph1 import cart2sph1
from math import cos, sin, sqrt
from mpl_toolkits.mplot3d import Axes3D


def PatchFunction(thetaInDeg, phiInDeg, Freq, W, L, h, Er):
    """
    Taken from Design_patchr
    Calculates total E-field pattern for patch as a function of theta and phi
    Patch is assumed to be resonating in the (TMx 010) mode.
    E-field is parallel to x-axis

    W......Width of patch (m)
    L......Length of patch (m)
    h......Substrate thickness (m)
    Er.....Dielectric constant of substrate

    Refrence C.A. Balanis 2nd Edition Page 745
    """
    lamba = 3e8 / Freq

    theta_in = math.radians(thetaInDeg)
    phi_in = math.radians(phiInDeg)

    ko = 2 * math.pi / lamba

    xff, yff, zff = sph2cart1(999, theta_in, phi_in)                            # Rotate coords 90 deg about x-axis to match array_utils coord system with coord system used in the model.
    xffd = zff
    yffd = xff
    zffd = yff
    r, thp, php = cart2sph1(xffd, yffd, zffd)
    phi = php
    theta = thp

    if theta == 0:
        theta = 1e-9                                                              # Trap potential division by zero warning

    if phi == 0:
        phi = 1e-9

    Ereff = ((Er + 1) / 2) + ((Er - 1) / 2) * (1 + 12 * (h / W)) ** -0.5        # Calculate effictive dielectric constant for microstrip line of width W on dielectric material of constant Er

    F1 = (Ereff + 0.3) * (W / h + 0.264)                                        # Calculate increase length dL of patch length L due to fringing fields at each end, giving total effective length Leff = L + 2*dL
    F2 = (Ereff - 0.258) * (W / h + 0.8)
    dL = h * 0.412 * (F1 / F2)

    Leff = L + 2 * dL

    Weff = W                                                                    # Calculate effective width Weff for patch, uses standard Er value.
    heff = h * sqrt(Er)

    # Patch pattern function of theta and phi, note the theta and phi for the function are defined differently to theta_in and phi_in
    Numtr2 = sin(ko * heff * cos(phi) / 2)
    Demtr2 = (ko * heff * cos(phi)) / 2
    Fphi = (Numtr2 / Demtr2) * cos((ko * Leff / 2) * sin(phi))

    Numtr1 = sin((ko * heff / 2) * sin(theta))
    Demtr1 = ((ko * heff / 2) * sin(theta))
    Numtr1a = sin((ko * Weff / 2) * cos(theta))
    Demtr1a = ((ko * Weff / 2) * cos(theta))
    Ftheta = ((Numtr1 * Numtr1a) / (Demtr1 * Demtr1a)) * sin(theta)

    # Due to groundplane, function is only valid for theta values :   0 < theta < 90   for all phi
    # Modify pattern for theta values close to 90 to give smooth roll-off, standard model truncates H-plane at theta=90.
    # PatEdgeSF has value=1 except at theta close to 90 where it drops (proportional to 1/x^2) to 0

    rolloff_factor = 0.5                                                       # 1=sharp, 0=softer
    theta_in_deg = theta_in * 180 / math.pi                                          # theta_in in Deg
    F1 = 1 / (((rolloff_factor * (abs(theta_in_deg) - 90)) ** 2) + 0.001)       # intermediate calc
    PatEdgeSF = 1 / (F1 + 1)                                                    # Pattern scaling factor

    UNF = 1.0006                                                                # Unity normalisation factor for element pattern

    if theta_in <= math.pi / 2:
        Etot = Ftheta * Fphi * PatEdgeSF * UNF                                   # Total pattern by pattern multiplication
    else:
        Etot = 0

    return Etot

def GetPatchFields(PhiStart, PhiStop, ThetaStart, ThetaStop, Freq, W, L, h, Er):
    """"
    Calculates the E-field for range of thetaStart-thetaStop and phiStart-phiStop
    Returning a numpy array of form - fields[phiDeg][thetaDeg] = eField

    W......Width of patch (m)
    L......Length of patch (m)
    h......Substrate thickness (m)
    Er.....Dielectric constant of substrate
    """
    fields = np.ones((PhiStop, ThetaStop))                                      # Create initial array to hold e-fields for each position

    for phiDeg in range(PhiStart, PhiStop):
            for thetaDeg in range(ThetaStart, ThetaStop):                       # Iterate over all Phi/Theta combinations
                eField = PatchFunction(thetaDeg, phiDeg, Freq, W, L, h, Er)     # Calculate the field for current Phi, Theta
                fields[phiDeg][thetaDeg] = eField                               # Update array with e-field

    return fields


def PatchEHPlanePlot(Freq, W, L, h, Er, isLog=True):
    """
    Plot 2D plots showing E-field for E-plane (phi = 0°) and the H-plane (phi = 90°).
    """

    fields = GetPatchFields(0, 360, 0, 90, Freq, W, L, h, Er)                                                   # Calculate the field at each phi, theta

    Xtheta = np.linspace(0, 90, 90)                                                                             # Theta range array used for plotting

    if isLog:                                                                                                   # Can plot the log scale or normal
        plt.plot(Xtheta, 20 * np.log10(abs(fields[90, :])), label="H-plane (Phi=90°)")                          # Log = 20 * log10(E-field)
        plt.plot(Xtheta, 20 * np.log10(abs(fields[0, :])), label="E-plane (Phi=0°)")
        plt.ylabel('E-Field (dB)')
    else:
        plt.plot(Xtheta, fields[90, :], label="H-plane (Phi=90°)")
        plt.plot(Xtheta, fields[0, :], label="E-plane (Phi=0°)")
        plt.ylabel('E-Field')

    plt.xlabel('Theta (degs)')                                                                                  # Plot formatting
    plt.title("Patch: \nW=" + str(W) + " \nL=" + str(L) +  "\nEr=" + str(Er) + " h=" + str(h) + " \n@" + str(Freq) + "Hz")
    plt.ylim(-40)
    plt.xlim((0, 90))

    start, end = plt.xlim()
    plt.xticks(np.arange(start, end, 5))
    plt.grid(b=True, which='major')
    plt.legend()
    plt.show()                                                                                                  # Show plot

    return fields                                                                                               # Return the calculated fields


def SurfacePlot(Fields, Freq, W, L, h, Er):
    """Plots 3D surface plot over given theta/phi range in Fields by calculating cartesian coordinate equivalent of spherical form."""

    print("Processing SurfacePlot...")

    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')

    phiSize = Fields.shape[0]                                                                                   # Finds the phi & theta range
    thetaSize = Fields.shape[1]

    X = np.ones((phiSize, thetaSize))                                                                           # Prepare arrays to hold the cartesian coordinate data.
    Y = np.ones((phiSize, thetaSize))
    Z = np.ones((phiSize, thetaSize))

    for phi in range(phiSize):                                                                                  # Iterate over all phi/theta range
        for theta in range(thetaSize):
            e = Fields[phi][theta]

            xe, ye, ze = sph2cart1(e, math.radians(theta), math.radians(phi))                                   # Calculate cartesian coordinates

            X[phi, theta] = xe                                                                                  # Store cartesian coordinates
            Y[phi, theta] = ye
            Z[phi, theta] = ze

    ax.plot_surface(X, Y, Z, color='b')                                                                         # Plot surface
    plt.ylabel('Y')
    plt.xlabel('X')                                                                                             # Plot formatting
    plt.title("Patch: \nW=" + str(W) + " \nL=" + str(L) +  "\nEr=" + str(Er) + " h=" + str(h) + " \n@" + str(Freq) + "Hz")
    plt.show()


def DesignPatch(Er, h, Freq):
    """
    Returns the patch_config parameters for standard lambda/2 rectangular microstrip patch. Patch length L and width W are calculated and returned together with supplied parameters Er and h.

    Returned values are in the same format as the global patchr_config variable, so can be assigned directly. The patchr_config variable is of the following form [Er,W,L,h].
    Usage: patchr_config=design_patchr(Er,h,Freq)
    Er.....Relative dielectric constant
    h......Substrate thickness (m)
    Freq...Frequency (Hz)

    e.g. patchr_config=design_patchr(3.43,0.7e-3,2e9)
    """
    Eo = 8.854185e-12

    lambd = 3e8 / Freq
    lambdag = lambd / sqrt(Er)

    W = (3e8 / (2 * Freq)) * sqrt(2 / (Er + 1))

    Ereff = ((Er + 1) / 2) + ((Er - 1) / 2) * (1 + 12 * (h / W)) ** -0.5                              # Calculate effictive dielectric constant for microstrip line of width W on dielectric material of constant Er

    F1 = (Ereff + 0.3) * (W / h + 0.264)                                                 # Calculate increase length dL of patch length L due to fringing fields at each end, giving actual length L = Lambda/2 - 2*dL
    F2 = (Ereff - 0.258) * (W / h + 0.8)
    dL = h * 0.412 * (F1 / F2)

    lambdag = lambd / sqrt(Ereff)
    L = (lambdag / 2) - 2 * dL

    print('Rectangular Microstrip Patch Design')
    print("Frequency: " + str(Freq))
    print("Dielec Const, Er : " + str(Er))
    print("Patch Width,  W: " + str(W) + "m")
    print("Patch Length,  L: " + str(L) + "m")
    print("Patch Height,  h: " + str(h) + "m")

    return W, L, h, Er

if __name__ == "__main__":
    """Some example patches with various thickness & Er."""
    print("Patch.py")

    freq = 14e9
    Er = 3.66                                                           # RO4350B

    h = 0.101e-3
    W, L, h, Er = DesignPatch(Er, h, freq)
    fields = PatchEHPlanePlot(freq, W, L, h, Er)
    SurfacePlot(fields, freq, W, L, h, Er)

    h = 1.524e-3
    W, L, h, Er = DesignPatch(Er, h, freq)                              # RO4350B
    fields = PatchEHPlanePlot(freq, W, L, h, Er)
    SurfacePlot(fields, freq, W, L, h, Er)

    fields = PatchEHPlanePlot(freq, 10.7e-3, 10.47e-3, 3e-3, 2.5)                # Random
    SurfacePlot(fields, freq, W, L, h, Er)

I can't find these packages sph2cart1 ,cart2sph1. Where can i get the same ?

Hi

I was having the same issue when trying to play around with this nice piece of python work. I found substitute functions at https://stackoverflow.com/questions/30084174/efficient-matlab-cart2sph-and-sph2cart-functions-in-python

Not sure that they do the right thing but the script runs now ..

UPDATE: Looking at the E and H field plots then something is surely wrong as I get something completely different from what is illustrated here by John..

Hi

Just as a follow-up .. the below definitions are needed

def cart2sph1(x,y,z):
r = np.sqrt(x2 + y2 + z**2)
phi = np.arctan2(y,x)
th = np.arccos(z/r)
return r, th, phi

def sph2cart1(r,th,phi):
x = r * np.cos(phi) * np.sin(th)
y = r * np.sin(phi) * np.sin(th)
z = r * np.cos(th)
return x, y, z

Hello,

sph2cart1 and cart2sph1 come from John's Patch.py script. So, if you have that file in the same directory, change the imports to:

from Patch import sph2cart1
from Patch import cart2sph1

Or, add the definitions (don't forget to include acos and atan2 in the math import):

def sph2cart1(r, th, phi):
x = r * cos(phi) * sin(th)
y = r * sin(phi) * sin(th)
z = r * cos(th)

return x, y, z

def cart2sph1(x, y, z):
r = sqrt(x2 + y2 + z**2) + 1e-15
th = acos(z / r)
phi = atan2(y, x)

return r, th, phi