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narrower, high impedance line required for impedance matching. The simple formula for the impedance of the quarter-wavelength transmission line may be written: Eq. 7 For a typical value of R in = 200 W and Z in = 50 W: Eq. 8 Radiation Intensity Patterns The two-slot radiation model is utilized in predicting the E-plane and H-plane radiation patterns. The radiation intensity of the rectangular microstrip antenna of width W, length L, and height h, may be calculated using the following equations: 10 For the E-plane radiation pattern: f = 0 and - p /2 < q < p /2 (planes have been redefined to comply with reference) Eq. 9 For the H-plane radiation pattern: f = p /2 and - p /2 < q < p /2 (planes have been redefined to comply with reference) Eq. 10 Bancroft 11 provides reduced complexity expressions for the E-plane and H-plane radiation patterns; however, accuracy is modestly compromised due to elimination of the height, h, as a dependent variable. Microstrip Antenna Directivity The two-slot radiation model is also utilized to predict the directivity of the rectangular microstrip antenna. Figure 5 represents graphic definition in conjunction with the microstrip antenna dimensions as previously defined. Although the equation for directivity of a single slot requires the condition k o h << 1, the expression provides reasonable accuracy upon comparison with actual measurement if the condition is moderately violated. The directivity of a single slot may be written: 12 Eq. 11 The directivity of a two-slot array, i.e. the microstrip antenna, may be written using the following expression: 13 10 Carver, K. and Mink, J., Microstrip Antenna Technology, IEEE Transactions, Antennas and Propagation, January, 1981. 11 Bancroft, R., Microstrip and Printed Antenna Design, 2nd Ed., Scitech Publishing, Raleigh, NC, 2009, p. 30. 12 Balanis, C. A., Antenna Theory, 3rd Ed., John Wiley and Sons, Hoboken, NJ, 2005, p. 840. 13 Balanis, C. A., Antenna Theory, 3rd Ed., John Wiley and Sons, Hoboken, NJ, 2005, p. 841. in in R Z Z o 2 = W = × = × = 100 50 200 in in o Z R Z ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 2 , 2 2 2 0 l p f f q f q f q q e f q = × ÷ ÷ ø ö ç ç è æ × × × × × ÷ ÷ ø ö ç ç è æ × × × ÷ ÷ ø ö ç ç è æ × = = k cos cos sin L k cos sin sin W k sin sin W k sin cos h k cos , P o o o r o E ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 2 , 2 2 2 2 l p f q f q f q f q q e p f q = × × ÷ ÷ ø ö ç ç è æ × × × × × ÷ ÷ ø ö ç ç è æ × × × ÷ ÷ ø ö ç ç è æ × = ÷ ø ö ç è æ = k sin cos cos sin L k cos sin sin W k sin sin W k sin cos h k cos , P o o o r o H ( ) q q q q l p p d sin cos cos W k sin I I W D o o 3 0 2 1 1 2 1 2 1 2 × ú ú ú ú û ù ê ê ê ê ë é ÷ ø ö ç è æ = × ÷ ÷ ø ö ç ç è æ = ò where Microstrip Antenna Design 8 www.cadence.com/go/awr