% characteristic impedance of a microstrip line clear er=4.8; d=1/16;% find w/d for given Zo Zref=110; Zo=Zref; A=Zo/60*sqrt((er+1)/2)+(er-1)/(er+1)*(.23+.11/er); B=377*pi/2/Zo/sqrt(er); ratio1=8*exp(A)/(exp(2*A)-2); ratio2=2/pi*(B-1-log(2*B-1)+(er-1)/2/er*(log(B-1)+.39-.61/er)); if ratio1 < 2, ratio=ratio1; end if ratio2 >= 2, ratio=ratio2; end ee=(er+1)/2+(er-1)/2/sqrt(1+12/ratio);% check the impedance using the reverse formulas  if ratio <=1, Z0=60/sqrt(ee)*log(8/ratio+ratio/4); end  if ratio >1, Z0=120*pi/sqrt(ee)/(ratio+1.393+.667*log(ratio+1.444)); end disp('-------------- 50 OHM LINE DIMENSIONS -----------------') disp(['design characteristic impedance (ohms): ',num2str(Zo)]) disp(['relative permittivity: ',num2str(er)]) disp(['substrate thickness, (in): ',num2str(d),', (m): ',num2str(d*.0254)]) disp(['effective relative permittivity: ',num2str(ee)]) disp(['ratio W/d: ',num2str(ratio)]) disp(['line width, W (in): ',num2str(ratio*d),', (m): ',num2str(ratio*d*.0254)]) disp(['computed characteristic impedance (ohms): ',num2str(Z0)])% antenna dimensions f=8.5e9; wavl=3e8/f/sqrt(ee); L=wavl/2; disp('----------------- PATCH DIMENSIONS --------------------') disp(['frequency, f (GHz): ',num2str(f/1e9)]) disp(['patch length, L (m): ',num2str(L)]) disp(['patch length, L (in): ',num2str(L/.0254)])% equal Y power splitter -- recompute new dimensions Zo=Zref*2; A=Zo/60*sqrt((er+1)/2)+(er-1)/(er+1)*(.23+.11/er); B=377*pi/2/Zo/sqrt(er); ratio1=8*exp(A)/(exp(2*A)-2); ratio2=2/pi*(B-1-log(2*B-1)+(er-1)/2/er*(log(B-1)+.39-.61/er)); if ratio1 < 2, ratio=ratio1; end if ratio2 >= 2, ratio=ratio2; end ee=(er+1)/2+(er-1)/2/sqrt(1+12/ratio);% check the impedance using the reverse formulas  if ratio <=1, Z0=60/sqrt(ee)*log(8/ratio+ratio/4); end  if ratio >1, Z0=120*pi/sqrt(ee)/(ratio+1.393+.667*log(ratio+1.444)); end disp('------------ POWER SPLITTER DIMENSIONS ----------------') disp(['design characteristic impedance (ohms): ',num2str(Zo)]) disp(['relative permittivity: ',num2str(er)]) disp(['effective relative permittivity: ',num2str(ee)]) disp(['substrate thickness, (in): ',num2str(d),', (m): ',num2str(d*.0254)]) disp(['ratio W/d: ',num2str(ratio)]) disp(['line width, W (in): ',num2str(ratio*d),', (m): ',num2str(ratio*d*.0254)]) disp(['computed characteristic impedance (ohms): ',num2str(Z0)])