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March 15, 2017 15:17
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| """ | |
| Returns the efficiency of a rectangular microstrip patch as a percentage. Based on ArrayCalc calc_patchr_eff.m. | |
| References: | |
| Microstrip Antennas, I.J Bahl and P.Bhartia, Published Atrech House, Page 60 | |
| Advances in Microstrip and Printed Antennas", Lee and Chen (Ch5) | |
| Some useful numbers : | |
| CONDUCTORS DIELECTRICS | |
| Material Conductivity S/m Material Er Tand | |
| Perfect 9.90E+99 (lossless) FR4_Epoxy 4.4 0.02 | |
| Silver 6.29E+07 Arlon 25FR 3.43 0.0035 | |
| Copper 5.80E+07 Arlon AD300 3.00 0.003 | |
| Pure Alumin. 3.77E+07 Arlon AR1000 10.00 0.0035 | |
| Al. 6063-T832 3.08E+07 Rogers RO3003 3.00 0.0013 | |
| Al. 6061-T6 2.49E+07 Rogers RO3006 6.15 0.0025 | |
| Brass 1.56E+07 Rogers RO3010 10.20 0.0035 | |
| Phospor bronze 9.09E+06 Rogers RO4350 3.48 0.004 | |
| Stainless Steel 302 1.39E+06 Glass 5.5 0.000 | |
| Plexiglass 3.4 0.001 | |
| Polyamide 4.3 0.004 | |
| Polyester 3.2 0.003 | |
| Polyethylene 2.25 0.001 | |
| """ | |
| from math import sqrt, pi | |
| def CalculatePatchEff(Er, W, L, h, tand, sigma, Freq, VSWR): | |
| """ | |
| Er: Relative dielectric constant | |
| W: Patch width (m) | |
| L: Patch length (m) | |
| h: dielectric thickness (m) | |
| tand: Loss tangent of dielectric (units) | |
| sigma: Conductivity of patch (Siemens/m) | |
| Freq: Frequency (Hz) | |
| VSWR: VSWR for bandwidth estimate (ratio). http://www.antenna-theory.com/definitions/vswr.php describes how well the antenna is impedance matched to the line it is connected to. | |
| """ | |
| if Er <= 1.000001: | |
| Er = 1.000001 | |
| if tand <= 0.000001: | |
| tand = 0.000001 | |
| Eo = 8.854185e-12 # Free space dielectric constant | |
| Ee = Eo * Er # Effective dielectric constant | |
| lamba = 3e8 / Freq | |
| """ | |
| % Calculation for space and surface wave efficiency factor, gives roughly the same results. | |
| % Reference : "Advances in Microstrip and Printed Antennas" Lee and Chen(Ch 5) | |
| % Efficiency due to surface wave component, dominant for larger h/lambda values | |
| """ | |
| Mur = 1 | |
| n1 = sqrt(Er * Mur) | |
| ko = 2 * pi * Freq * (sqrt((8.854e-12) * (pi * 4e-7))) | |
| Lo = lamba | |
| Psur = (1 / Lo ** 2) * ((ko * h) ** 3) * (60 * pi ** 3 * Mur ** 3 * (1 - 1 / n1 ** 2) ** 3) # Power radiated as surface wave | |
| c1 = 1 - 1 / n1 ** 2 + (2 / 5) / n1 ** 4 | |
| Pr = (1 / Lo ** 2) * (ko * h) ** 2 * (80 * pi ** 2 * Mur ** 2 * c1) # Total power radiated | |
| Effsw = Pr / (Pr + Psur) # Efficiency factor for surface wave losses | |
| """ | |
| % Efficiency due to ohmic and dielectric losses, dominant for smaller h/lambda values | |
| % *********************************************************************************** | |
| % Reference : "Microstrip Antennas" Bahl and Bartia | |
| """ | |
| if W < lamba: | |
| Rr = 90 * lamba ** 2 / W ** 2 # Radiation resistance for W<lambda | |
| else: | |
| Rr = 120 * lamba / W # Radiation resistance for W>lambda | |
| Qr = (3e8 * sqrt(Ee)) / (2 * (Freq / 1e6) * h) # Quality factor, modified by me, not sure freq was in Ghz, more like MHz !? | |
| Rc = (1 / sigma) * 0.5 * sqrt(Freq) * (L / W) * Qr ** 2 # Equivalent resistance for conductor loss (ohms) | |
| Rd = (30 * tand / Er) * ((h * lamba) / (L * W)) * Qr ** 2 # Equivalent resistance for dielectric loss (ohms) | |
| Rtot = Rr + Rd + Rc # Total resistance (ohms) | |
| Effcd = Rr / Rtot # Efficiency factor for combined dielectric and ohmic losses | |
| Eff1 = Effsw * Effcd | |
| Eff = Eff1 * 100 # Total efficiency including ohmic, dielectric and surface wave losses (percent) | |
| Qt = Qr * Eff1 / (pi) # Ref Balanis p762 ( Qtotal = Qradiated*Efficiency ) Not the pi factor, I added that, seems necassary get sensible results using Qr from above !? | |
| BW = (VSWR - 1) / (Qt * sqrt(VSWR)) | |
| BWf = BW * Freq / 1e6 # Bandwidth as a frequency span in MHz | |
| print("Rectangular patch overall efficency " + str(Eff) + "%") | |
| print("Surface wave efficiency factor " + str(Effsw)) | |
| print("Ohmic and dielectric efficiency factor " + str(Effcd)) | |
| print("BW=" + str(BWf) + "MHz for VSWR=" + str(VSWR) + " at Fo=" + str(Freq / 1e6) + " MHz") | |
| return Eff | |
| if __name__ == "__main__": | |
| """ | |
| Calculates efficiencies for two patches @14GHz, one with FR4 and one RO4350. | |
| """ | |
| import patch | |
| import Directivity | |
| freq = 14e9 # Same parameters for both patches | |
| h = 1.524e-3 | |
| VSWR = 2.0 | |
| sigma = 5.8e7 # Copper | |
| # FR4_Epoxy | |
| Er = 4.4 | |
| tand = 0.02 | |
| print("\n\nCalculating for FR4 patch.") | |
| W, L, h, Er = patch.DesignPatch(Er, h, freq) | |
| eff = CalculatePatchEff(Er, W, L, h, tand, sigma, freq, VSWR) | |
| Directivity.CalcDirectivity(eff, patch.PatchFunction, freq, W, L, h, Er) | |
| # Rogers RO4350 | |
| print("\n\nCalculating for RO4350 patch.") | |
| Er = 3.48 | |
| tand = 0.004 | |
| W, L, h, Er = patch.DesignPatch(Er, h, freq) | |
| eff = CalculatePatchEff(Er, W, L, h, tand, sigma, freq, VSWR) | |
| Directivity.CalcDirectivity(eff, patch.PatchFunction, freq, W, L, h, Er) |
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