%% HW01 Problem #4A

% Define some constants
alpha=pi/2;   % 180° saturation pulse [rad]
gamma=40.05;  % 19F gyromagnetic ratio in [Hz/µT]
B1_max=25;    % Max B1 amplitude in [µT]h
B0=3;       % B0 in [T]

t_RF=(alpha*pi)/(2*2*pi*gamma*1e6*B1_max*1e-6)%1e6*alpha/(2*pi*gamma*B1_max);  % Shortest RF pulse duration in [µs]

w_RF=2*pi*gamma*B0*1e6;              % RF pulse carrier frequence in [rad/s]

t=linspace(0,t_RF,1000000);          % Time vector [µs]
B1=B1_max*sin(pi*t/t_RF).*exp(-i*w_RF*t);            % B1 pulse


% NOTE: The complete solution must be written out for full credit.  This
% code just helps calculate some values...

% Plot the components of the resultant B1 pulse amplitude in the laboratory 
% frame as a function of time. 
figure; hold on;
  plot(t,real(B1),'r','linewidth',1.5);
  plot(t,imag(B1),'b','linewidth',1.5);
  axis([0 0.001 -30 30]);
  xlabel('Time [s]');
  ylabel('B1 Amplitude [µT]');
  title('90-deg 19F B1-Pulse @ 25µT');
  set(gcf,'Color','w');
  set(gca,'Color','w','XColor','k','YColor','k');
  set(gca,'Color','w','XColor','k','YColor','k','LineWidth',1.25,'Fontsize',11,'Fontweight','bold');
  set(get(gca,'Title'),'Color','k','FontSize',16);
  set(get(gca,'Xlabel'),'FontSize',14,'fontweight','bold');
  set(get(gca,'Ylabel'),'FontSize',14,'fontweight','bold');
  grid('on')
  print2desktop('/Users/pmagrath/desktop/','HW1_P4_19F_1B')
  
figure; hold on;
  plot(t,real(B1),'r','linewidth',1.5);
  plot(t,imag(B1),'b','linewidth',1.5);
  axis([.0003 0.0003005 -16 16]);
  xlabel('Time [s]');
  ylabel('B1 Amplitude [µT]');
  %title('90-deg 1H B1-Pulse @ 25µT');
  legend('Real','Imaginary')
  title('90-deg 19F B1-Pulse @ 25µT');
  set(gcf,'Color','w');
  set(gca,'Color','w','XColor','k','YColor','k');
  set(gca,'Color','w','XColor','k','YColor','k','LineWidth',1.25,'Fontsize',11,'Fontweight','bold');
  set(get(gca,'Title'),'Color','k','FontSize',16);
  set(get(gca,'Xlabel'),'FontSize',14,'fontweight','bold');
  set(get(gca,'Ylabel'),'FontSize',14,'fontweight','bold');
  grid('on')
  
  print2desktop('/Users/pmagrath/desktop/','HW1_P4_19F_2B')