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resonant frequency. 7 Utilization of the cavity model yields the following equations for the calculation of the resonant input resistance of the rectangular microstrip resonator: 8 Note that the ± sign refers to the specific mode field configuration of the cavity resonance beneath the conductor [3]. Eq. 5 Microstrip Antenna Feed Line The resonant input resistance at the edge of the microstrip conductor is generally greater than the feed line characteristic impedance and requires an impedance matching structure in order to reduce the mismatch loss and thereby improve the antenna efficiency. There are two common feed line techniques which facilitate the impedance matching required to achieve an efficient rectangular microstrip antenna as illustrated in Figure 7. a. Inset Feed Matching b. Quarter Wavelength Matching Figure 7 – Impedance Matching Feed Line Techniques The inset feed technique utilizes the reduction in electric field strength to effectively 'tap' a lower impedance drive point, while the quarter-wave transformer uses the transmission line formula which provides the geometric mean of the input resistance and the characteristic impedance of the quarter-wave transmission line. Coaxial probes beneath the conductor or a vertically offset feed along the width are also used on occasion. A useful equation to achieve the optimum inset length, y o , is available: 9 Eq. 6 Although quite convenient and easily implemented, the inset feed distorts the equivalent slot radiation due to the change in geometry. The quarter-wavelength feed minimizes the equivalent slot field distortion due to the 7 The diligent readers are encouraged to indulge their curiosity in one or more of the cited references. 8 Although the expressions appear quite complex, they are rendered tractable using computational programs such as MathCad® and Matlab®. The data analysis feature of Excel may also be employed to provide a reasonable estimate. 9 Balanis, C. A., Antenna Theory, 3rd Ed., John Wiley and Sons, Hoboken, NJ, 2005, pp. 824-825. ( ) ( ) ( ) q q q q q p q q q q p p p d sin sin L k J cos cos W k sin G d sin cos cos W k sin I I G G G R o o o in × × ú ú ú ú û ù ê ê ê ê ë é ÷ ø ö ç è æ × = × ú ú ú ú û ù ê ê ê ê ë é ÷ ø ö ç è æ = = ± = ò ò 3 0 2 0 2 12 3 0 2 1 2 1 1 12 1 2 120 1 2 120 2 1 where ( ) ( ) ( ) ÷ ø ö ç è æ × = = ÷ ø ö ç è æ × + = = o o in o o in y L cos y R y L cos G G y y R p p 2 2 12 1 0 2 1 Microstrip Antenna Design 7 www.cadence.com/go/awr