smith圆图软件包matlab设计教程
前 言
Smith圆图是P.H.Smith于1939年在贝尔实验室发明的，它主要用于计算微波网络的阻抗、导纳及网络阻抗匹配设计，还可用于设计微波元器件。Smith圆图软件不仅适用于微波
工程
路基工程安全技术交底工程项目施工成本控制工程量增项单年度零星工程技术标正投影法基本原理
设计，亦可用于电磁场、微波技术及天线与电波传播等课程相关内容的教学。
多年来，Smith圆图作为一个不可缺少的设计工具，在高频和微波领域发挥了重要作用。掌握了Smith圆图的原理和特性，并熟悉其阻抗匹配技术，将使设计人员的设计能力大为加强。尽管目前微波电路CAD技术已进入了设计领域，人们仍大量使用圆图作为设计工具。究其原因，一是因为现有的大部分CAD软件在设计时要求用户提供初始电路(包括拓扑和元件值)，因此仍需借助于Smith圆图进行图解设计;另一方面，对于窄带情形，利用圆图通常可直接完成设计不 必进一步进行优化而且目前不少大型软件价格昂贵，CAD技术尚未普及，因而一款Smith圆图工具的设计仍然是非常有必要的。
微波网络的正弦稳态分析含有复数计算，运算十分繁琐和耗时。在计算机运算速度和内存不够发达以前，图解分析法得到长足发展，其中多年来应用最广的是Smith圆图。在计算微波传输线输入阻抗、导纳及阻抗匹配等问题时，它不仅能避开繁琐的
公式
小学单位换算公式大全免费下载公式下载行测公式大全下载excel公式下载逻辑回归公式下载
及复数运算，使工程设计中相关计算简单便捷，而且图解过程物理概念清晰，所得结果直观形象。随着计算机技术的飞速发展，图解法在计算精度上的固有缺陷日益显现，因为，圆图的计算精度取决于圆图中必须有足够的圆周数，而过多的圆周会导致图线过于密集，不便将阻抗、反射系数、
行波系数及电长度等相关数据从图上直接读出。通过对圆图构成的基本原理和应用问题的分析，利用现代计算机技术可以解决圆图计算精度等方面存在的问题，为此设计的Smith圆图软件既保留圆图计算直观、便捷的大众性，又满足工程设计中相关参数的计算精度。在计算机应用日益普及的今天，该软件特别适合电磁场、微波技术与天线等领域的教学和工程设计相关参数计算使用。
目 录
摘 要„„„„„„„„„„„„„„„„„„„„„„„„„4 第,章 概述 „„„„„„„„„„„„„„„„„„„„„„5 第,章 Smith圆图软件构成的基本原理 „„„„„„„„„„7
2.1 阻抗圆图软件构成的基本原理„„„„„„„„„„„„„7
2.3 圆图软件的设计特点 „„„„„„„„„„„„„„„„„8
2.3 圆图的基本应用„„„„„„„„„„„„„„„„„„„10 第,章 仿真与调试„„„„„„„„„„„„„„„„„„„11
3.1 调试„„„„„„„„„„„„„„„„„„„„„„„„11
3.2 仿真„„„„„„„„„„„„„„„„„„„„„„„„12
3.3 仿真结果验算„„„„„„„„„„„„„„„„„„„„13 第,章 设计小结 „„„„„„„„„„„„„„„„„„„„14
致谢 „„„„„„„„„„„„„„„„„„„„„„15
参考文献 „„„„„„„„„„„„„„„„„„„„16
附录 源程序代码„„„„„„„„„„„„„„„„„17
基于MATLAB语言的Smith圆图软件设计
[摘 要]:Smith圆图是从事微波工程实验和天线设计的重要工具。应用MATLAB作为开发平台研制的Smith圆图应用软包，使圆图的应用和计算变得更加方便、快捷，该软件具有用户图形界面，简单易用，而且计算精度高。
[关键词]: MATLAB;GUI;Smith圆图;
第1章 概述
Smith圆图的基本在于以下的算式:
式中的Г代表其线路的反射系数，即阻抗匹配时, [S]矩阵里的S11，zL是归一化负载抗，即ZL / Z0。其中，ZL是电路的负载值Z0是传输线的特性阻抗值，通常会使用50
Ω。图1-1中的圆形
线代表电阻抗力的
实数值，即电阻值，
中间的横线与向上
和向下散出的线则
代表电阻抗力的虚
数值，即由电容或
电感在高频下所产
生的阻力，当中向
上的是正数，向下
的是负数。圆图图
最中间的点(1+j0)
代表一个已匹配的图1-1 Smith圆图
电阻数值(ZL)，同时其反射系数的值会是零。图表的边缘代表其反射系数的长度是1，即100%反射。在图边的数字代表反射系数的角度(0-180度)和波长(由零至半个波长)。有一些图表是以导纳值来表示，把上述的阻抗值旋转180度即可。
自从有了计算机后，此种图表的使用率随之而下，但仍常用来表示特定的资料。对于就读电磁学及微波电子学的学生来说，在解决课本问题仍然很实用，因此史密斯图至今仍是重要的教学用具。
本设计是运用MATLAB编写SMITH圆图仿真程序，整个圆图软件分为用户图形界面模块、圆图计算模块、画图演示模块。圆图计算模块分为输入阻抗计算、
反射系数计算、行波系数、驻波比计算以及整个Smith圆图;画图演示模块分为等归一化电阻圆、等归一化电抗圆、反射系数圆;确定阻抗值在圆图上的位置、圆图的基本应用、求输入阻抗及其在圆图上的位置。
具体实现:
1、 本程序能读出圆图上的任意一点对应的各个值，并能够根据输入的
归一化阻抗画出相应的圆图、显示对应的值;
2、 当在MATLAB环境下运行程序后，会显示完整的圆图工具界面，在
整个界面的右半部分画出完整的Smith圆图;
3、 当在“输入数据”文本框里分别输入负载阻抗的实部及虚部，点击
“确定”按钮，会在绘图区域内画出圆图，并显示相应的阻抗、反
射系数、驻波比、行波系数的值。
第2章 Smith圆图软件构成的基本原理
2.1 阻抗圆图软件构成的基本原理
圆图运算的基础是反射系数 ( Г=U+jV ) 。Smith圆图由反射系数平面上的
等归一化反射系数圆族、等归一化电阻圆族、等归一化电抗圆族构成。利用已知
的归一化阻抗zL=R+jX，实现等反射系数圆族程序如下:
R=R;X=X;%输入归一化阻抗
U= ( R^2+X^2-1) / ( R^2+23R+1+X^2) ;
V= ( 23X) / ( R^2+23R+1+X^2) ;
tr=23pi3 ( 00.011) ;
Г=sqrt (U^2+V^2) ;%等反射系数圆的半径 plot ( r3cos ( tr) ，r3sin ( tr) ，’y’ )
%画等反射系数圆
实现等归一化电阻圆族程序如下:
For rr=1/ ( 1+R) ;cr=1-rr;%画电阻圆
plot ( cr+rr3cos ( tr) ，rr3sin ( tr) ，’m’ ) 实现等归一化电抗圆族程序如下:
forx=X;%画电抗圆
rx=1/x;cx=rx;
iftx
2)
max_bound =
%equations were derived using the symbolic (-1+5^2+R^2)/(5^2+R^2+2*R+1); toolbox as follows else
%solve('R=(1-Gr^2-Gi^2)/((1-Gr)^2+Gi^2)','Gi') if(mod(R,.2)==0) %bound was derived as follows max_bound =
%solve('1/(R+1)*(-(R+1)*(R-2*R*Gr+R.*Gr^2-1+(-1+5^2+R^2)/(5^2+R^2+2*R+1); Gr^2))^(1/2)=0','Gr') else
for R = interval2, max_bound =
min_bound1 = (R-1)/(R+1); (-1+2^2+R^2)/(2^2+R^2+2*R+1);
end
if(R<.2) end
if(mod(R,.1)==0) elseif(R<10)
max_bound = if(mod(R,2)==0)
(-1+2^2+R^2)/(2^2+R^2+2*R+1); max_bound =
elseif(mod(R,.02)==0) (-1+20^2+R^2)/(20^2+R^2+2*R+1);
max_bound = else
(-1+.5^2+R^2)/(.5^2+R^2+2*R+1); max_bound =
else (-1+10^2+R^2)/(10^2+R^2+2*R+1);
max_bound = end
(-1+.2^2+R^2)/(.2^2+R^2+2*R+1); else
if(R==.05 | (R<.151 & R>.149)) if(R==10|R==20)
min_bound2 = max_bound =
(-1+.5^2+R^2)/(.5^2+R^2+2*R+1); (-1+50^2+R^2)/(50^2+R^2+2*R+1);
max_bound2 = elseif(R==50)
(-1+1^2+R^2)/(1^2+R^2+2*R+1); max_bound = 1;
end elseif(R<20)
end max_bound =
elseif(R<1) (-1+20^2+R^2)/(20^2+R^2+2*R+1);
if(mod(R,.2)==0) else
max_bound = max_bound =
(-1+5^2+R^2)/(5^2+R^2+2*R+1); (-1+50^2+R^2)/(50^2+R^2+2*R+1);
elseif(mod(R,.1)==0) end
max_bound = end
(-1+2^2+R^2)/(2^2+R^2+2*R+1);
elseif(R==.25 | R==.35 | R==.45) index = ceil((min_bound1+1)*(MAX-1)/2+1);
temp = actual_value = Gr(index); (-1+.5^2+R^2)/(.5^2+R^2+2*R+1); if(actual_valuemax_bound)
else index = index - 1;
max_bound = end
(-1+1^2+R^2)/(1^2+R^2+2*R+1);
end MIN2 = ceil((min_bound2+1)*(MAX-1)/2+1);
elseif(R<5) actual_value = Gr(MIN2);
if(actual_value.149 & R<.151))
%fix resolution issues in .2-.5 range
plot(Gr(MIN2:MAX2),r_L_a2(length(Gr(MIN2:M
if(~(R>.2 & R<.5 & ~(mod(R,.02)==0))) AX2))-length(r_L_a2)+1:length(r_L_a2)),'b');
if(R==1)
color = 'r'; plot(Gr(MIN2:MAX2),r_L_b2(length(Gr(MIN2:M
else AX2))-length(r_L_b2)+1:length(r_L_b2)),'b');
color ='b';
end end
plot(Gr(MIN:index),r_L_a(1:index-MIN+1),color,end
Gr(MIN:index), r_L_b(1:index-MIN+1),color);
if(R<=1) %equations were derived using the symbolic
if(mod(R,1)==0) toolbox as follows
word = [num2str(R) '.0']; %solve('2*Gi/((1-Gr)^2+Gi^2)=x','Gi')
else %bound was derived as follows
word = num2str(R); %solve('1-X^2+2*X^2*Gr-X^2*Gr^2=0','Gr')
%solve('1/2/X*(2+2*(1-X^2+2*X^2*Gr-X^2*Gr^2(-1+X^2+5^2)/(X^2+5^2+2*5+1); )^(1/2))=(1-Gr^2)^(1/2)','Gr') elseif(mod(X,.1)==0) for X = interval, max_bound =
inter_bound = (-1+X^2+2^2)/(X^2+2^2+2*2+1); (-1+X^2)/(X^2+1); %intersection with unit circle: elseif(X<.5)
all values must be less than this\ max_bound =
imag_bound = (-1+X)/X; %boundary of (-1+X^2+.5^2)/(X^2+.5^2+2*.5+1); imagination: all values must be greater than this else
angle_point = 0; max_bound =
if(inter_bound ~= 0) (-1+X^2+1^2)/(X^2+1^2+2*1+1);
angle_point = end
sqrt(1-inter_bound^2)/inter_bound; elseif(X<5)
end if(mod(X,2)==0)
max_bound =
imag_bound_y = (-1+X^2+20^2)/(X^2+20^2+2*20+1); 1/2/X*(-2+2*(1-X^2+2*X^2.*inter_bound-X^2.*i elseif(mod(X,1)==0) nter_bound.^2).^(1/2)); max_bound =
(-1+X^2+10^2)/(X^2+10^2+2*10+1);
imag_rad = (imag_bound^2 + elseif(X>2)
imag_bound_y^2)^(1/2); max_bound =
condition = imag_rad < 1; (-1+X^2+5^2)/(X^2+5^2+2*5+1);
if(inter_bound > 1) else
inter_bound = 1; if(mod(X,.2)==0)
elseif(inter_bound < -1) max_bound =
imag_bound=-1; (-1+X^2+5^2)/(X^2+5^2+2*5+1);
end else
max_bound =
if(imag_bound > 1) (-1+X^2+2^2)/(X^2+2^2+2*2+1);
imag_bound = 1; end
elseif(imag_bound < -1) end
imag_bound=-1; elseif(X<10)
end if(mod(X,2)==0)
max_bound =
%used solve function to find intersection of (-1+X^2+20^2)/(X^2+20^2+2*20+1); appropriate circle with corresponding else
hyperbolics max_bound =
%solve('-1/(R+1)*(-(R+1)*(R-2*R*Gr+R*Gr^2(-1+X^2+10^2)/(X^2+10^2+2*10+1); -1+Gr^2))^(1/2)=1/2/X*(-2+2*(1-X^2+2*X^2*Gr-X end
^2*Gr^2)^(1/2))','Gr') else
%The following conditional tree creates the if(X==10|X==20) internal bounding between the two types of max_bound =
curves for variable resolution (-1+X^2+50^2)/(X^2+50^2+2*50+1);
if(X<.2) elseif(X==50)
if(mod(X,.1)==0) max_bound = 1;
max_bound = elseif(X<20)
(-1+X^2+2^2)/(X^2+2^2+2*2+1); max_bound =
elseif(mod(X,.02)==0) (-1+X^2+20^2)/(X^2+20^2+2*20+1);
max_bound = else
(-1+X^2+.5^2)/(X^2+.5^2+2*.5+1); max_bound =
else (-1+X^2+50^2)/(X^2+50^2+2*50+1);
max_bound = end
(-1+X^2+.2^2)/(X^2+.2^2+2*.2+1); end
end
elseif(X<1) inter_index =
if(mod(X,.2)==0) ceil((inter_bound+1)*(MAX-1)/2+1);
max_bound = imag_index =
ceil((imag_bound+1)*(MAX-1)/2+1); X^2.*Gr(MIN2:MAX3).^2).^(1/2)));
index4 = ceil((max_bound+1)*(MAX-1)/2+1); x_L_c=
real(1/2/X*(2+2*(1-X^2+2*X^2.*Gr(MIN:MAX2)-
index1 = X^2.*Gr(MIN:MAX2).^2).^(1/2))); max(inter_index,imag_index); %maximum index x_L_d=
for c,d real(1/2/X*(-2-2*(1-X^2+2*X^2.*Gr(MIN:MAX2)-
index2 = X^2.*Gr(MIN:MAX2).^2).^(1/2))); min(imag_index,inter_index); %minimum index
for c,d if(MIN2 -1 & check1 == check2)
plot(Gr(MIN:MAX2),x_L_c,'g')
if((actual_value1 > inter_bound & index1 == plot(Gr(MIN:MAX2),x_L_d,'g') inter_index)|(actual_value1 > imag_bound & end
index1 == imag_index))
index1 = index1 - 1; plot(Gr(MIN2:MAX3),x_L_a,'g')
end plot(Gr(MIN2:MAX3),x_L_b,'g')
if((actual_value2 < inter_bound & index2 ==
inter_index)|(actual_value2 < imag_bound & condition = Gr(MIN2)^2 + x_L_d(1)^2 > .985; index2 == imag_index)) if(X<=1)
index2 = index2 + 1; if(mod(X,.1)==0)
end if(mod(X,1)==0)
if((actual_value3 < inter_bound & index3 == word = [num2str(X) '.0']; inter_index)|(actual_value3 < imag_bound & else
index3 == imag_index)) word = num2str(X);
index3 = index3 + 1; end
end if(X==1)
if(actual_value4 > max_bound) angle = 90;
index4 = index4 - 1; else
end angle =
-atan(angle_point)*180/pi;
MIN=index2; end
MAX2=index1;
MAX3=index4; set(text(Gr(MIN2),x_L_d(1),word),'Rotation',ang
MIN2 = index3; le,'VerticalAlignment','bottom','HorizontalAlign
ment','left');
% actual_value1 = Gr(MIN);
% actual_value2 = Gr(MAX2); set(text(Gr(MIN2),-x_L_d(1),word),'Rotation',-an
% MIN=1; gle+180,'HorizontalAlignment','right','VerticalAli
% MAX2=MAX; gnment','bottom');
% MIN2=1; if(mod(X,.2)==0)
xval=X^2/(X^2+4);
x_L_a = yval =
real(1/2/X*(-2+2*(1-X^2+2*X^2.*Gr(MIN2:MAX31/2/X*(-2+2*(1-X^2+2*X^2*xval-X^2*xval^2)^(1/)-X^2.*Gr(MIN2:MAX3).^2).^(1/2))); 2));
x_L_b = angle =
real(1/2/X*(2-2*(1-X^2+2*X^2.*Gr(MIN2:MAX3)--atan(yval/(.5-xval))*180/pi;
-atan(angle_point)*180/pi+180;
set(text(xval,yval,word),'Rotation',angle,'H
orizontalAlignment','left','VerticalAlignment','bo set(text(Gr(MAX2),x_L_d(length(x_L_d)),[nttom'); um2str(X)
'.0']),'Rotation',angle,'VerticalAlignment','bottoset(text(xval,-yval,word),'Rotation',-angle+180,'m','HorizontalAlignment','left'); HorizontalAlignment','right','VerticalAlignment','
bottom') set(text(Gr(MAX2),-x_L_d(length(x_L_d)),[n
end um2str(X)
end '.0']),'Rotation',-angle+180,'HorizontalAlignment
elseif(X<=2) ','right','VerticalAlignment','bottom');
if(mod(X,.2)==0) end
if(mod(X,1)==0) end
word = [num2str(X) '.0']; else
else if(mod(X,10)==0)
word = num2str(X); if(condition)
end angle =
if(condition) -atan(angle_point)*180/pi+180;
angle =
-atan(angle_point)*180/pi+180; set(text(Gr(MIN2),x_L_a(1),num2str(X)),'Ro
tation',angle,'VerticalAlignment','bottom','Horizset(text(Gr(MIN2),x_L_a(1),word),'Rotation',anglontalAlignment','left');
e,'VerticalAlignment','bottom','HorizontalAlignm
ent','left'); set(text(Gr(MIN2),-x_L_a(1),num2str(X)),'R
otation',-angle+180,'HorizontalAlignment','right'set(text(Gr(MIN2),-x_L_a(1),word),'Rotation',-an,'VerticalAlignment','bottom'); gle+180,'HorizontalAlignment','right','VerticalAli else
gnment','bottom'); angle =
else -atan(angle_point)*180/pi+180;
angle =
-atan(angle_point)*180/pi+180; set(text(Gr(MAX2),x_L_d(length(x_L_d)),num2st
r(X)),'Rotation',angle,'VerticalAlignment','botto
set(text(Gr(MAX2),x_L_d(length(x_L_d)),wm','HorizontalAlignment','left'); ord),'Rotation',angle,'VerticalAlignment','botto
m','HorizontalAlignment','left'); set(text(Gr(MAX2),-x_L_d(length(x_L_d)),n
um2str(X)),'Rotation',-angle+180,'HorizontalAlig
set(text(Gr(MAX2),-x_L_d(length(x_L_d)),wnment','right','VerticalAlignment','bottom'); ord),'Rotation',-angle+180,'HorizontalAlignment' end
,'right','VerticalAlignment','bottom'); end
end end
end end
elseif(X<=5) %plot imaginary axis
if(mod(X,1)==0) plot(zeros(1,length(Gr)),Gr,'r');
if(condition)
angle =
-atan(angle_point)*180/pi+180; wavelengths = 0:.01:.5;
angle = linspace(pi,-pi,length(wavelengths));
set(text(Gr(MIN2),x_L_a(1),[num2str(X) wave_circle = 1.05*exp(j*phaseAngle); '.0']),'Rotation',angle,'VerticalAlignment','bottoplot(real(wave_circle),imag(wave_circle),'r'); m','HorizontalAlignment','left');
for i=1:length(wavelengths)-1,
set(text(Gr(MIN2),-x_L_a(1),[num2str(X) x=real(1.025*exp(j*angle(i))); '.0']),'Rotation',-angle+180,'HorizontalAlignment y=imag(1.025*exp(j*angle(i))); ','right','VerticalAlignment','bottom'); if(x>0)
else rot_angle=atan(y/x)*180/pi-90;
angle = else
rot_angle=atan(y/x)*180/pi+90;
end function edit2_Callback(hObject, eventdata,
if(wavelengths(i)==0) handles)
word = '0.00'; % hObject handle to edit2 (see GCBO)
elseif(mod(wavelengths(i),.1)==0) % eventdata reserved - to be defined in a
word = [num2str(wavelengths(i)) '0']; future version of MATLAB
else % handles structure with handles and user
word = num2str(wavelengths(i)); data (see GUIDATA)
end
% Hints: get(hObject,'String') returns contents of set(text(x,y,word),'Rotation',rot_angle,'VerticalAedit2 as text
lignment','middle','HorizontalAlignment','center' % str2double(get(hObject,'String')) end returns contents of edit2 as a double
guidata(hObject, handles);
%plot reflection coefficient and line of
intersection only if arguments are present
% --- Executes on button press in pushbutton1. % Choose default command line output for function pushbutton1_Callback(hObject, smith eventdata, handles)
handles.output = hObject; % --- Executes on button press in radiobutton5.
% hObject handle to pushbutton1 (see % Update handles structure GCBO)
guidata(hObject, handles); % eventdata reserved - to be defined in a
future version of MATLAB
% UIWAIT makes smith wait for user response % handles structure with handles and user (see UIRESUME) data (see GUIDATA)
% uiwait(handles.figure1); %%%%%%%%%%%%%%%%%%%%%%%%%%%
r=str2num(get(handles.edit1,'String')); % --- Outputs from this function are returned to x=str2num(get(handles.edit2,'String')); the command line. Tx=(r^2+x^2-1)/((r+1)^2+x^2); function varargout = smith_OutputFcn(hObject, Ty=(2*x)/((r+1)^2+x^2);
eventdata, handles) Tr=(Tx^2+Ty^2)^(0.5);
% varargout cell array for returning output PP=(1+Tr)/(1-Tr);
args (see VARARGOUT); K=1/PP;
% hObject handle to figure Yr=(1-Tx^2-Ty^2)/((1+Tx)^2+Ty^2); % eventdata reserved - to be defined in a Yi=(-2*Ty)/((1+Tx)^2+Ty^2);
future version of MATLAB
% handles structure with handles and user set(handles.text1,'String',Yr); data (see GUIDATA) set(handles.text2,'String',Yi);
set(handles.text3,'String',PP); % Get default command line output from set(handles.text4,'String',Tr); handles structure set(handles.text5,'String',K); varargout{1} = handles.output; %%%%%%%%%%%%%%%%%%%%%%%%%%%
function edit1_Callback(hObject, eventdata, global fig1 fig2 fig3 fig4 fig5 fig6 fig7 fig8 fig9 handles) fig10 fig11 fig12
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a if fig1~=0
future version of MATLAB delete(fig1);
% handles structure with handles and user end
data (see GUIDATA) if fig2~=0
delete(fig2);
% Hints: get(hObject,'String') returns contents of end
edit1 as text if fig3~=0
% str2double(get(hObject,'String')) delete(fig3);
returns contents of edit1 as a double end
guidata(hObject, handles); if fig4~=0
delete(fig4); XX=Tr*exp(j*Angle); end fig3=plot(XX,'ko'); if fig5~=0 else Angle=0.5*pi;
delete(fig5); XX=Tr*exp(j*Angle); end fig4=plot(XX,'ko'); if fig6~=0 wavelengths = 0:.01:.5;
delete(fig6); Angle =
end linspace(0.5*pi,1.5*pi,length(wavelengths)); if fig7~=0 XX=Tr*exp(j*Angle);
delete(fig7); fig5=plot(real(XX),imag(XX),'k'); end Angle=-pi;
if fig8~=0 XX=Tr*exp(j*Angle);
delete(fig8); fig6=plot(XX,'ro'); end end
if fig9~=0 else Angle=atan(Ty/Tx);
delete(fig9); if Ty>0
end XX=Tr*exp(j*Angle); if fig10~=0 fig7=plot(XX,'ro');
delete(fig10); wavelengths = 0:.01:.5; end NAngle =
if fig11~=0 linspace(Angle-pi,Angle,length(wavelengths));
delete(fig11); XX=Tr*exp(j*NAngle); end fig8=plot(real(XX),imag(XX),'k'); if fig2~=0 Angle=Angle-pi;
delete(fig2); XX=Tr*exp(j*Angle); end fig9=plot(XX,'ko'); if fig12~=0 else XX=Tr*exp(j*Angle);
delete(fig12); fig10=plot(XX,'ko'); end wavelengths = 0:.01:.5;
if Tx==0; NAngle =
if Ty>0 linspace(Angle,Angle+pi,length(wavelengths));
Angle=0.5*pi; XX=Tr*exp(j*NAngle);
XX=Tr*exp(j*Angle); fig11=plot(real(XX),imag(XX),'k');
fig1=plot(XX,'ro'); Angle=Angle+pi;
wavelengths = 0:.01:.5; XX=Tr*exp(j*Angle);
Angle = fig12=plot(XX,'ro'); linspace(-0.5*pi,0.5*pi,length(wavelengths)); end
XX=Tr*exp(j*Angle); end
fig2=plot(real(XX),imag(XX),'k');
Angle=-pi;
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