However, for the wireless excitation of a microstrip patch antenna this impedance matching dependence is not required because the patch antenna is not excited using a transmission line (such as a coaxial cable). The quality factor of an antenna can be defined as a representation of the antenna losses . According to  the total quality factor for a circular microstrip patch antenna can be calculated from the following equation:1Qt=1Qrad+1Qc+1Qd+1Qsw(2)Figure 1 shows the geometry of the CMPA sensor. For very thin substrates (h<<��0), the loss due to surface waves, 1/Qsw, is very small and can be neglected in calculation of the total quality factor . This indicates that by reducing the thickness of the patch antenna the quality factor due to the surface waves can be improved and as a result of that the total quality factor of the antenna can be improved.
The other quality factors can be calculated using following equations :Qc=h��f��0��(3)Qd=1tan��(4)and for the dominant mode of operation :Qrad=30[(ka)2?1]hf��0(k0a)2I1(5)where:I1=��0��/2[J1��2(k0asin��)+cos2��J12(k0asin��)/(k0asin��)2]sin��d��(6)Figure 1.Geometry of the CMPA sensor.The quality factor due to dielectric losses can be improved by using low loss materials for the antenna substrate. From Equation (3), the conductive loss can be reduced by increasing the conductivity of the patch and the ground plane. In practice, the Qc will be lower than Equation (3) because of the surface roughness of the patch and the ground plane. According to , for very thin substrates the dominant factor is the radiation quality factor.
This part of the total quality factor is proportional to the substrate dielectric constant and the inverse of the substrate thickness.2.1. Effect of Substrate Material on Quality FactorIn order to improve the quality factor of the CMPA, a numerical investigation into the effect of each parameter of the total quality factor was carried out. To this end, two commercially available substrates were selected, namely a FR4 (��r = 4.5, tan�� = 0.025) and Rogers? RT/duroid 6010.2LM? (��r = 10.2, tan�� = 0.0023 ; Rogers Corporation, Brooklyn, CT, USA). The FR4 substrate was selected because it was used in previous studies on CMPA sensors [8�C10,17] and the Rogers? substrate (which is called high Q material in the rest of the paper) was used because it has much lower tangent loss and much higher permittivity compared to FR4.
For the numerical study the thickness of each substrate was varied within the range of commercially Cilengitide available laminate thicknesses, i.e., 0.127, 0.254, 0.635, 1.27, 1.90, 2.50 mm for high Q material and 0.8, 1.0, 1.2, 1.5, 2.0, 2.4 mm for FR4. The antennas were designed to resonate at 1.5 GHz (similar to previous studies on CMPAs [8�C10,17]).