射频电路设计--理论与应用matlab程序

% % This program computes the small-signal impedance of % a Si-based pn-junction diode % % Copyright (c) 1999 by P.Bretchko and R.Ludwig % "RF Circuit Design: Theory and Practice" % close all; % close all opened graphs clear all; % clear all variables % first we define all parameters for the transistor and the circuit Z0=50; % characteristic imedance of the system Vcc=3.6; % power supply voltage Vce=2; % collector voltage Ic=10e-3; % collector current T=300; % ambient temperature (300K) % transistor parameters (they are very similar to BFG403W) beta=145; % current gain Is=5.5e-18; % saturation current VAN= 30; % forward Early voltage tau_f=4e-12; % forward transition time rb=125; % base resistance rc=15; % collector resistance re=1.5; % emitter resistance Lb=1.1e-9; % base inductance Lc=1.1e-9; % collector inductance Le=0.5e-9; % emitter inductance Cjc=16e-15; % collector junction capacitance at zero applied voltage mc=0.2; % collector junction grading coefficient Cje=37e-15; % emitter junction capacitance at zero applied voltage me=0.35; % emitter junction grading coefficient phi_be=0.9; % base-emitter diffusion potential phi_bc=0.6; % base-collector diffusion potential Vbe=phi_be; % base-emitter voltage % some physical constants k=1.38e-23; % Boltzmann's constant q=1.6e-19; % elementary charge VT=k*T/q; % thermal potential % compute the values for the biasing resistors s=sprintf('\n\nDC biasing parameters\n\n'); Ib=Ic/beta; s=sprintf('%s DC base current: Ib=%.2f uA\n',s,Ib/1e-6); Rc=(Vcc-Vce)/Ic; s=sprintf('%s Collector biasing resistor: Rc=%.f Ohm\n',s,Rc); Rb=(Vcc-Vbe)/Ib; s=sprintf('%s Base biasing resistor: Rb=%.f kOhm\n',s,Rb/1e3); % computing small signal model parameters s=sprintf('%s\n\nSmall-signal hybrid-pi model parameters\n\n',s); r_pi=VT/Ib; s=sprintf('%s r_pi=%.f Ohm\n',s,r_pi); r0=VAN/Ic; s=sprintf('%s r0=%.f kOhm\n',s,r0/1e3); gm=beta/r_pi; s=sprintf('%s gm=%.f mS\n',s,gm/1e-3); Vbc=Vbe-Vce; Cmu=Cjc*(1-Vbc/phi_bc)^(-mc); s=sprintf('%s\n Base-collector capacitance: Cmu=%.2f fF\n',s,Cmu/1e-15); s=sprintf('%s\n Base-emitter capacitance:\n',s); % compute equivalent pi capacitance if(Vbe<0.5*phi_be) Cpi_junct=Cje*(1-Vbe/phi_be)^(-me); else C_middle=Cje*0.5^(-me); k_middle=1-0.5*me; Cpi_junct=C_middle*(k_middle+me*Vbe/phi_be); end; s=sprintf('%s Junction capacitance: Cpi_junct=%.2f fF\n',s,Cpi_junct/1e-15); Cpi_diff=Is*tau_f/VT*exp(Vbe/VT); s=sprintf('%s Differential capacitance: Cpi_diff=%.2f fF\n',s,Cpi_diff/1e-15); Cpi=Cpi_junct+Cpi_diff; s=sprintf('%s Total capacitance: Cpi=%.2f fF\n',s,Cpi/1e-15); % compute Miller capacitances C_miller=Cmu*(1+gm*r_pi/(r_pi+rb)*Z0*r0/(r0+rc+Z0)); s=sprintf('%s\n\n Miller capacitance: C_miller=%.2f fF\n',s,C_miller/1e-15); C_input=Cpi+C_miller; s=sprintf('%s Total input capacitance: C_input=%.2f fF\n',s,C_input/1e-15); s %******************************************************** % now we are able to compute the frequency response % for Zin, S11, and S21 of the transistor die % % define frequency range f_min=1e6; % lower limit f_max=100e9; % upper limit N=200; % number of points in the graph f=f_min*((f_max/f_min).^((0:N)/N)); % compute frequency points on log scale w=2*pi*f; % compute h-parameters h11=r_pi./(1+j*w*(Cpi+Cmu)*r_pi); h12=j*w*Cmu*r_pi./(1+j*w*(Cpi+Cmu)*r_pi); h21=r_pi*(gm-j*w*Cmu)./(1+j*w*(Cpi+Cmu)*r_pi); h22=1/r0+j*w*Cmu.*(1+j*w*Cpi*r_pi+gm*r_pi)./(1+j*w*(Cpi+Cmu)*r_pi); h=zeros(2,2,N+1); for n=1:N+1 h(:,:,n)=[h11(n),h12(n);h21(n),h22(n)]; end; % convert h-parameters of transistor in die into ABCD form ABCD_die=H_to_ABCD(h); % find corresponding S and Z-parameters s_param=ABCD_to_S(ABCD_die,Z0); z_param=ABCD_to_Z(ABCD_die); % obtain S11 and S21 dim=size(s_param); s11=zeros([1 dim(3)]); s21=zeros([1 dim(3)]); s11(:)=s_param(1,1,:); s21(:)=s_param(2,1,:); % plot S11 on the Smith Chart m_s11=smith_chart; % create a new figure for the Smith Chart display hold on; plot(real(s11),imag(s11),'r','linewidth',2); % plot S21 on the polar graph p_s21=figure; % create polar plot for S21 polar(angle(s21),abs(s21),'r'); hold on; % extract Z11 and Z22 dim=size(z_param); z11=zeros([1 dim(3)]); z22=zeros([1 dim(3)]); z11(:)=z_param(1,1,:); z22(:)=z_param(2,2,:); % plot Z11 m_z11=figure; % create a new graph for Z11 semilogx(f, abs(z11),'r','linewidth',2); hold on; % plot Z22 m_z22=figure; % create a new graph for Z22 semilogx(f, abs(z22),'r','linewidth',2); hold on; %*************************************************** % next base and collector leads are attached to % the transistor die % %find ABCD parameters of the base lead ABCD_base=zeros(2,2,N+1); Z=rb+j*w*Lb; for n=1:N+1 ABCD_base(:,:,n)=[1,Z(n);0,1]; end; %find ABCD parameters of the collector lead ABCD_collector=zeros(2,2,N+1); Z=rc+j*w*Lc; for n=1:N+1 ABCD_collector(:,:,n)=[1,Z(n);0,1]; end; % compute ABCD parameters of the transistor die with % base and collector leads attached ABCD_bc=zeros(2,2,N+1); for(n=1:N+1) ABCD_bc(:,:,n)=ABCD_base(:,:,n)*ABCD_die(:,:,n)*ABCD_collector(:,:,n); end; %find S-parameters of the transistor with base and collector leads S_bc=ABCD_to_S(ABCD_bc,Z0); s_param=S_bc; dim=size(s_param); s11=zeros([1 dim(3)]); s21=zeros([1 dim(3)]); s11(:)=s_param(1,1,:); s21(:)=s_param(2,1,:); % plot S11 figure(m_s11); plot(real(s11),imag(s11),'b','linewidth',2); % plot S21 figure(p_s21); polar(angle(s21),abs(s21),'b'); % find corresponding Z-parameters Z_bc=ABCD_to_Z(ABCD_bc); z_param=Z_bc; dim=size(z_param); z11=zeros([1 dim(3)]); z22=zeros([1 dim(3)]); z11(:)=z_param(1,1,:); z22(:)=z_param(2,2,:); % plot input impedance Z11 figure(m_z11); semilogx(f, abs(z11),'b','linewidth',2); % plot output impedance Z22 figure(m_z22); semilogx(f, abs(z22),'b','linewidth',2); %************************************************ % finally emitter lead is attached to the rest % of the transistor % % find Z parameters of the emitter lead Z_emitter=zeros(2,2,N+1); Z=re+j*w*Le; for n=1:N+1 Z_emitter(:,:,n)=[Z(n),Z(n);Z(n),Z(n)]; end; % compute Z-parameters for the entire transistor Z_tr=zeros(2,2,N+1); for(n=1:N+1) Z_tr(:,:,n)=Z_bc(:,:,n)+Z_emitter(:,:,n); end; %find the S-parameters of the entire transistor S_tr=Z_to_S(Z_tr,Z0); s_param=S_tr; dim=size(s_param); s11=zeros([1 dim(3)]); s21=zeros([1 dim(3)]); s11(:)=s_param(1,1,:); s21(:)=s_param(2,1,:); % plot S11 in the Smith Chart figure(m_s11); plot(real(s11),imag(s11),'g','linewidth',2); title('\bfInput reflection coefficient S_{11}'); %print -deps 'fig7_22a.eps' % plot S21 in polar plot form figure(p_s21); polar(angle(s21),abs(s21),'g'); title('\bfForward transistor gain S_{21}'); %print -deps 'fig7_22b.eps' % compute corresponding Z-parameters z_param=Z_tr; dim=size(z_param); z11=zeros([1 dim(3)]); z22=zeros([1 dim(3)]); z11(:)=z_param(1,1,:); z22(:)=z_param(2,2,:); % plot input impedance figure(m_z11); semilogx(f, abs(z11),'g','linewidth',2); axis([1e6 1e11 0 600]); title('\bfInput impedance'); xlabel('Frequency {\itf}, Hz'); ylabel('Input impedance |Z_{11}|, \Omega'); legend('transistor die', 'with base and collector', 'complete transistor',1); %print -deps 'fig7_21a.eps' % plot output impedance figure(m_z22); semilogx(f, abs(z22),'g','linewidth',2); title('\bfOutput impedance'); xlabel('Frequency {\itf}, Hz'); ylabel('Output impedance |Z_{22}|, \Omega'); legend('transistor die', 'with base and collector', 'complete transistor',1); %print -deps 'fig7_21d.eps'