WRITE THE TEXMAKER CODE OF ABOVE ELECTRICAL ENGINEERING C=capacitance of equival
ID: 2293626 • Letter: W
Question
WRITE THE TEXMAKER CODE OF ABOVE
ELECTRICAL ENGINEERING
C=capacitance of equivalent ckt. [7] 2h where L-inductance of equivalent ckt.7 ? L=additional series inductance Zo1 Z02 ZoiandZg2 are the characteristics impedances of microstrip lines with width of wandw respectively.The values Zol = 120T,/?+ 1.393 + 0.667 ln + 1.444)) Z02-120r/(m + 1.393 + 0.667 ln(72 + 1.444)) where and The AC between center win g and side wing is calculated as gap + 0.0130F (5) 4h where The resonance resistance of the two resonators are given by 11 TX 1,2=24Explanation / Answer
documentclass{article} usepackage{array} usepackage{tabulary} usepackage{amsmath} egin{document} C=capacitance of equivalent ckt.[7] egin{equation} C=dfrac{epsilon_{ef}epsilon_{o}L_{e}W}{2 h} F end{equation} where egin{center} $F=cos ^{ - 2} ({pi}X_{f}/L)$ end{center} L=inductance of equivalent ckt.[7] egin{equation} L= rac{1}{({2pi}f_{r})^{2}C} end{equation} $Delta L$=additional series inductance egin{equation} Delta L= rac{Z_{01}+Z_{02}}{16pi{f_{r}}F} tan(pi{f_{r}{L_{n}}}/C) end{equation} $Z_{01} and Z_{02}$ are the characteristics impedances of microstrip lines with width of $w_{1} and w_{2}$ respectively.The values egin{equation} Z_{01}=120pi/( rac{w_{1}}{h}+1.393+0.667ln( rac{w_{1}}{h}+1.444)) end{equation} $$ Z_{02}=120pi/( rac{w_{2}}{h}+1.393+0.667ln( rac{w_{2}}{h}+1.444)) $$ where $$w_{1}=w-2{P_{s}}-W_{s}$$ and $$w_{2}=2{P_{s}}-W_{s}$$ The capacitance$Delta C$ between center wing and side wing is calculated as gap capacitance. egin{equation} Delta C=2L_{n}dfrac{epsilon_{0}}{pi} left[lnleft(2 rac{1+sqrt{k^{'}}}{1-sqrt{k^{'}}} ight)+lncothleft( rac{{pi}S}{4h} ight)+0.013C_{f}dfrac{h}{s} ight]F end{equation} where $$K^{'}=sqrt{1-K^{2}}$$ $$K^{2}= rac{1+ rac{W_{1}}{S}+ rac{W_{2}}{S}}{left(1+ rac{W_{1}}{S} ight)left(1+ rac{W_{2}}{S} ight)}$$ The resonance resistance of the two resonators are given by [11] egin{equation} R_{1,2}= rac{1}{2(G_{1}+G_{12})}cos^{2}( rac{pi{X_{f}}}{l}) end{equation} $$G_{1}= rac{1}{{120}pi^{2}}int_{0}^{pi}left[ rac{sinleft(kwcos rac{ heta}{2} ight)}{cos{ heta}} ight](sin{ heta})^{3}d{ heta}$$ $$G_{12}= rac{1}{{120}pi^{2}}int_{0}^{pi}left[ rac{sinleft(kwcos rac{ heta}{2} ight)}{cos{ heta}} ight]J_{0}(klsin{ heta})(sin{ heta})^{3}d{ heta}$$ where $k$ is the wave numbers at center wing resonance frequency $f_{r}$ and side wings resonance frequency $f_{r}^{'}$ , which are given by $$fr= rac{1}{sqrt{LC}}$$ $${f}r^{'}= rac{1}{sqrt{L^{'}C^{'}}}$$ where $L^{'}=L+Delta L$ and $C^{'}={C{Delta C}}/{(C+Delta C)} $\ Coupling factor $C_{P}$ between two resonator is given as egin{equation} C_{P}={1}/{sqrt{Q_{T}Q^{'}_{T}}} end{equation} Coupling capacitance $C_{c}$ is defined as egin{equation} C_{c}= -(C+C^{'})+sqrt{left(left(C+C^{'} ight)^{2}-4CC^{'}left(1- rac{1}{C^{2}_{P}} ight) ight)} end{equation} Input impedance of ESPA egin{equation} Z_{in}=jwL_{P}+ rac{Z_{1}Z_{2}}{(Z_{1}+Z_{2})} end{equation} where $Z_{1}$ and $Z_{2}$ are $$Z_{1}= rac{JwLR_{1}}{R_{1}-w^{2}LCR_{1}+JwL} + rac{1}{jwC_{c}} $$ and $$Z_{2}= rac{JwL^{'}R_{2}}{R_{2}-w^{2}L^{'}C^{'}R_{2}+JwL^{'}}$$ $$L_{P}= rac{60{h}}{C}ln(C/{0.2886pi{f_{r}}})$$ reflection coefficient $$Gamma=dfrac{Z_{in}-50}{Z_{in}+50}$$ Return loss egin{equation} return loss=20log_{10} mid{Gammamid} end{equation} end{document}
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