微带线分析与综合
本文实现的计算精度可媲美ADS等 专业 电磁计算软件，matlab实现
github地址：https://github.com/yangli0534/microstrip_calc
1 function ms = ms_analysis(substrate, w, l,fc) 2 % MS_ANALYSIS calc electric specification of microstrip line 3 % Author : LEON, yangli0534@yahoo.com 4 % blog : www.cnblogs.com/hiramlee0534 5 % parameters : 6 % substrate is a struct ,('er',varepsilon_r,'h',h,'mur',mu_r, 't',t, 'cond', cond, 'rough',0,'tand',tanD); 7 % w , width of ms 8 % l , length of ms 9 % fc, frequency 10 % ms was a struct, ms = struct('Zc',ms_Zc, 'er_eff',ms_ereff, 'El',ms_el,'beta',ms_beta, 'loss',loss, 'delay',delay, 'delta',skin_depth); 11 % Zc: charateristic impdance 12 % er_eff: effective relative permitivity 13 % El : electric length 14 % 15 %% 16 % constant 17 varepsilon_0 = 8.854187817e-12; 18 mu0 = 4*pi*1e-7; 19 c = 1/sqrt(varepsilon_0*mu0); 20 21 %% 22 %electric parameters 23 %Zc = 50 ;% characteristic impedance. 24 %El = 90;% 25 %fc = 35e9; %center frequency :Hz 26 %% 27 % substate parameters 28 ms_er = substrate.er;%2.2 ; % relative permittivity constant 29 ms_h = substrate.h/1e3;%0.508e-3; % substrate height:m 30 ms_t = substrate.t/1e3;%;0;%metal thickness :m 31 mur = substrate.mur;%1; % ralative permeability constant 32 rough = substrate.rough;%T0 ; % 33 cond = substrate.cond;%5.88e7; % conductivity 34 ms_tand = substrate.tand; 35 %substrate = struct('er',2.2,'h',0.508,'t',0.1,'tand',0.0009,'cond',5.8e7,'rought',0) 36 mu = mur*4*pi*1.0e-7;% permeability 37 %t = float(lineEdit_ms_T.text())/1.0e3 38 %% 39 %freq 40 lambda0 = c/fc;% % wavelengt in free space : m 41 ms_fc = fc; 42 ms_w = w/1e3; 43 ms_l = l/1e3; 44 %% 45 %calc 46 U = ms_w/ms_h; % ratio of trace width to substrate thickness 47 if ms_t > 0 48 T = ms_t/ms_h; %ratio of conductor thickness to substrate thickness 49 %(T/PI)*log(1.0 + 4.0*exp(1.0)/(T*power(coth(sqrt(6.517*u)),2.0))) 50 U1 = U +(T*log(1.0+4.0*exp(1)/T/power(1.0/tanh(sqrt(6.517*U)),2.0)))/pi; % from Hammerstad and Jensen 51 % 0.5*(1.0 + 1.0/cosh(sqrt(er-1.0)))*deltau1 52 Ur = U +(U1-U)*(1.0+1.0/(cosh(sqrt(ms_er-1))))/2.0; % from Hammerstad and Jensen 53 else 54 U1 = U; 55 Ur = U; 56 end 57 Y = ee_HandJ(Ur,ms_er); 58 % %Z0 =z0_HandJ(Ur)/sqrt(Y) 59 %ereff0 = Y*power(Z01_U1/Z01_Ur,2) 60 ereff0 = Y*power(z0_HandJ(U1)/z0_HandJ(Ur),2.0); 61 62 fn = ms_fc*ms_h/1e7; 63 P1 = 0.27488 + (0.6315 + (0.525 / (power((1 + 0.157*fn),20))) )*U - 0.065683*exp(-8.7513*U); 64 P2 = 0.33622*(1 - exp(-0.03442*ms_er)); 65 P3 = 0.0363*exp(-4.6*U)*(1 - exp(-power((fn / 3.87),4.97))); 66 P4 = 1 + 2.751*( 1 - exp(-power((ms_er/15.916),8))); 67 P = P1*P2*power(((0.1844 + P3*P4)*10*fn),1.5763); 68 ms_ereff = (ms_er*P+ereff0)/(1+P); % equavlent ralative dielectric constant 69 ms_Zc = microstrip_z_calc(ms_w,ms_h,ms_l,ms_t,ms_fc,ms_er); 70 z1 = 0.434907*((power(ms_ereff,0.81) + 0.26)/(power(ms_ereff,0.81) - 0.189))*(power(U,0.8544) + 0.236)/(power(U,0.8544) + 0.87); 71 z2 = 1 + (power(U,0.371))/(2.358*ms_er + 1); 72 z3 = 1 + (0.5274*atan(0.084*(power(U,(1.9413 / z2)))))/(power(ms_ereff,0.9236)); 73 z4 = 1 + 0.0377*atan(0.067*(power(U,1.456)))*(6 - 5*exp(0.036*(1-ms_er))); 74 z5 = 1 - 0.218*exp(-7.5*U); 75 deltal = ms_h * z1 * z3 * z5 / z4; 76 v = c/sqrt(ms_ereff); 77 length = ms_l/(v/ms_fc); 78 % delay 79 delay = 1e9*ms_l/v; 80 % dielectric losses 81 ld = pi*ms_fc/v*ms_er/ms_ereff*(ms_ereff-1)/(ms_er-1)*ms_tand ;% unit in nepers/meter 82 ld = 20.0/log(10)*ld ;% unit in dB/meter 83 ld = ld * ms_l; % unit in dB 84 % conduction losses 85 % skin depth in meters 86 skin_depth = sqrt(1/(pi*ms_fc*mu*cond)); 87 if skin_depth <= ms_t 88 Z2 = microstrip_z_calc(ms_w,ms_h,ms_l,ms_t,ms_fc,1); 89 Z1 = microstrip_z_calc(ms_w-skin_depth,ms_h+skin_depth,ms_l,ms_t-skin_depth,ms_fc,1); 90 % conduction losser 91 lc = pi*ms_fc/c*(Z1-Z2)/ms_Zc; 92 elseif ms_t > 0 93 %resistance per meter = 1/(Area*conductivity) 94 res = 1/(ms_w*ms_t*cond); 95 %conduction losses, nepers per meter 96 lc = res/(2.0*ms_Zc); 97 skin_depth = ms_t; 98 else 99 lc = 0; 100 end 101 lc = 20.0/log(10)*lc; 102 lc = lc * ms_l; 103 lc = lc * (1.0+2.0/pi*atan(1.4*power(rough/skin_depth,2))); 104 loss = ld + lc; 105 ms_k0 = 2*pi/c*ms_fc; 106 ms_beta = ms_k0*sqrt(ms_ereff); 107 ms_el = sqrt(ms_ereff)*ms_k0*ms_l/1000/pi*180.0; 108 ms_el = 360*length; 109 % lineEdit_ms_Zc.setText(str(ms_Zc)) 110 % lineEdit_ms_ereff.setText(str(ms_ereff)) 111 % lineEdit_ms_el.setText(str(ms_el)) 112 % lineEdit_ms_beta.setText(str(ms_beta)) 113 % lineEdit_ms_loss.setText(str(loss)) 114 % label_delay.setText('delay = '+str(delay)+' ns') 115 % label_skin_depth.setText('skin depth = '+str(skin_depth)+' m') 116 ms = struct('Zc',ms_Zc, 'er_eff',ms_ereff, 'El',ms_el,'beta',ms_beta, 'loss',loss, 'delay',delay, 'delta',skin_depth); 117 end
1 function ms = ms_synthesis(substrate,Zc,El,fc) 2 % MS_SYSTHESIS calc the width and length of microstrip line 3 % Author : LEON, yangli0534@yahoo.com 4 % blog : www.cnblogs.com/hiramlee0534 5 % parameters : 6 % substrate is a struct ,('er',varepsilon_r,'h',h,'mur',mu_r, 't',t, 'cond', cond, 'rough',0,'tand',tanD); 7 % Zc ,characteristic impedance 8 % El : electric length 9 % fc : frequency Hz 10 % output variable ms is a struct,('w',wx*1e3, 'l',l*1e3,'er_eff',er_eff); 11 % the unit for length is mm 12 % Example 13 %Zc = 50; 14 %El = 90; 15 %f0=35e9; 16 %substrate = struct('er',varepsilon_r,'h',h,'mur',mu_r, 't',t, 'cond', cond, 'rough',0,'tand',tanD); 17 % 18 %ms=ms_synthesis(substrate,Zc,El,f0) 19 %the output result: 20 %ms = 21 % 22 % struct with fields: 23 % 24 % w: 1.543090255176611 25 % l: 1.800407506983852 26 % er_eff: 1.925472337115954 27 %% 28 % constant 29 varepsilon_0 = 8.854187817e-12; 30 mu0 = 4*pi*1e-7; 31 c = 1/sqrt(varepsilon_0*mu0); 32 33 %% 34 %electric parameters 35 %Zc = 50 ;% characteristic impedance. 36 %El = 90;% 37 %fc = 35e9; %center frequency :Hz 38 %% 39 % substate parameters 40 er = substrate.er;%2.2 ; % relative permittivity constant 41 h = substrate.h/1e3;%0.508e-3; % substrate height:m 42 t = substrate.t/1e3;%;0;%metal thickness :m 43 mur = substrate.mur;%1; % ralative permeability constant 44 rough = substrate.rough;%T0 ; % 45 cond = substrate.cond;%5.88e7; % conductivity 46 %substrate = struct('er',2.2,'h',0.508,'t',0.1,'tand',0.0009,'cond',5.8e7,'rought',0) 47 mu = mur*4*pi*1.0e-7;% permeability 48 %t = float(lineEdit_ms_T.text())/1.0e3 49 50 lambda0 = c/fc;% % wavelengt in free space : m 51 lx = 1000*25.4e-6; 52 wmin = 0.01*25.4e-6; 53 wmax = 499.0*25.4e-6; 54 %impedance convergence tolerance (ohms) 55 abstol = 1e-6; 56 reltol = 0.1e-6; 57 maxiters = 50; 58 A = ((er - 1)/(er + 1)) * (0.226 + 0.121/er) + (pi/377.0)*sqrt(2*(er+1))*Zc; 59 w_h = 4/(0.5*exp(A) - exp(-A)); 60 if w_h > 2.0 61 B = pi*377.0/(2*Zc*sqrt(er)); 62 w_h = (2/pi)*(B - 1 - log(2*B - 1) + ((er-1)/(2*er))*(log(B-1) + 0.293 - 0.517/er)); 63 end 64 wx = h * w_h; 65 66 if wx >= wmax 67 wx = 0.95*wmax; 68 end 69 70 if wx <= wmin 71 wx = wmin; 72 end 73 wold = 1.01*wx; 74 Zold = microstrip_z_calc(wold,h,lx,t,fc,er); 75 76 77 if Zold < Zc 78 wmax = wold; 79 else 80 wmin = wold; 81 end 82 83 iters = 0; 84 done = 0; 85 86 while done == 0 87 iters = iters + 1; 88 Z0 = microstrip_z_calc(wx,h,lx,t,fc,er); 89 if Z0 < Zc 90 wmax = wx; 91 else 92 wmin = wx; 93 end 94 if abs(Z0-Zc) < abstol 95 done = 1; 96 elseif abs(wx-wold) < reltol 97 done = 1; 98 elseif iters >= maxiters 99 done = 1; 100 else 101 dzdw = (Z0 -Zold)/(wx-wold); 102 wold = wx; 103 Zold = Z0; 104 wx = wx -(Z0-Zc)/dzdw; 105 if (wx > wmax) || (wx < wmin) 106 wx = (wmin+ wmax)/2.0; 107 end 108 end 109 end 110 111 er_eff = er_eff_calc(wx,h,t,fc,er); 112 v = c/sqrt(er_eff); 113 l = El/360.0*v/fc; 114 %num2str(wx*1.0e3) 115 %num2str(er_eff) 116 %num2str(l*1.0e3) 117 ms = struct('w',wx*1e3, 'l',l*1e3,'er_eff',er_eff); 118 end
1 function Zc = microstrip_z_calc(w,h,l,t,fc,er) 2 3 U = w/h; % ratio of trace width to substrate thickness 4 if t > 0 5 T = t/h; %ratio of conductor thickness to substrate thickness 6 %(T/PI)*log(1.0 + 4.0*exp(1.0)/(T*power(coth(sqrt(6.517*u)),2.0))) 7 U1 = U +(T*log(1.0+4.0*exp(1)/T/power(1.0/tanh(sqrt(6.517*U)),2.0)))/pi; % from Hammerstad and Jensen 8 % 0.5*(1.0 + 1.0/cosh(sqrt(er-1.0)))*deltau1 9 Ur = U +(U1-U)*(1.0+1.0/(cosh(sqrt(er-1))))/2.0; % from Hammerstad and Jensen 10 else 11 U1 = U; 12 Ur = U; 13 end 14 Y = ee_HandJ(Ur,er); 15 Z0 =z0_HandJ(Ur)/sqrt(Y); 16 %ereff0 = Y*power(Z01_U1/Z01_Ur,2) 17 ereff0 = Y*power(z0_HandJ(U1)/z0_HandJ(Ur),2.0); 18 fn = fc*h/1e7; 19 P1 = 0.27488 + (0.6315 + (0.525 / (power((1 + 0.157*fn),20))) )*U - 0.065683*exp(-8.7513*U); 20 P2 = 0.33622*(1 - exp(-0.03442*er)); 21 P3 = 0.0363*exp(-4.6*U)*(1 - exp(-power((fn / 3.87),4.97))); 22 P4 = 1 + 2.751*( 1 - exp(-power((er/15.916),8))); 23 P = P1*P2*power(((0.1844 + P3*P4)*10*fn),1.5763); 24 ereff = (er*P+ereff0)/(1+P); % equavlent ralative dielectric constant 25 %ms_Zc = Z0*power(ereff0/ms_ereff,0.5)*(ms_ereff-1)/(ereff0-1) 26 fn = fc*h/1e6; 27 R1 = 0.03891*(power(er,1.4)); 28 R2 = 0.267*(power(U,7.0)); 29 R3 = 4.766*exp(-3.228*(power(U,0.641))); 30 R4 = 0.016 + power((0.0514*er),4.524); 31 R5 = power((fn/28.843),12.0); 32 R6 = 22.20*(power(U,1.92)); 33 R7 = 1.206 - 0.3144*exp(-R1)*(1 - exp(-R2)); 34 R8 = 1.0 + 1.275*(1.0 - exp(-0.004625*R3*power(er,1.674)*power(fn/18.365,2.745))); 35 R9 = (5.086*R4*R5/(0.3838 + 0.386*R4))*(exp(-R6)/(1 + 1.2992*R5)); 36 R9 = R9 * (power((er-1),6))/(1 + 10*power((er-1),6)); 37 R10 = 0.00044*(power(er,2.136)) + 0.0184; 38 R11 = (power((fn/19.47),6))/(1 + 0.0962*(power((fn/19.47),6))); 39 R12 = 1 / (1 + 0.00245*U*U); 40 R13 = 0.9408*(power( ereff,R8)) - 0.9603; 41 R14 = (0.9408 - R9)*(power(ereff0,R8))-0.9603; 42 R15 = 0.707*R10*(power((fn/12.3),1.097)); 43 R16 = 1 + 0.0503*er*er*R11*(1 - exp(-(power((U/15),6)))); 44 R17 = R7*(1 - 1.1241*(R12/R16)*exp(-0.026*(power(fn,1.15656))-R15)); 45 Zc = Z0*(power((R13/R14),R17));% characteristic impedance 46 end
OPTIMISM, PASSION & HARDWORK
