finished q1b

PS1/doc.tex

@@ -0,0 +1,99 @@
+\documentclass{article}
+
+\usepackage{graphicx}
+\usepackage{setspace}
+\usepackage{listings}
+\usepackage{color}
+\usepackage{circuitikz}
+\usepackage{float}
+
+\definecolor{dkgreen}{rgb}{0,0.6,0}
+\definecolor{gray}{rgb}{0.5,0.5,0.5}
+\definecolor{mauve}{rgb}{0.58,0,0.82}
+
+\lstset{basicstyle=\small,
+        keywordstyle=\color{mauve},
+        identifierstyle=\color{dkgreen},
+        stringstyle=\color{gray},
+        numbers=left
+        }
+
+\title{ECE 456 - Problem Set 1}
+\date{2021-02-06}
+\author{David Lenfesty \\ lenfesty@ualberta.ca
+    \and Phillip Kirwin \\ pkirwin@ualberta.ca}
+
+\setcounter{tocdepth}{2} % Show subsections
+
+\begin{document}
+
+    \doublespacing
+    \pagenumbering{gobble}
+    \maketitle
+    \newpage
+
+    \singlespacing
+    \pagenumbering{arabic}
+
+    \section{Introduction}
+
+    The purpose of this lab was to design control circuits according to the provided
+    specifications, and then verify their operation using a simulation or an FPGA.
+
+    In the first part of the lab, a series of boolean expressions
+    were designed to implement a Multiplexer/Demultiplexer circuit,
+    intended to route data from one of three radio recievers to one
+    of three engineers, and signal which engineer was currently
+    recieving data.
+    First, Xilinx Vivado Software was used to produce a circuit
+    to fulfill this objective. Then, using the same software,
+    the circuit was simulated against input combinations which
+    would be encountered during normal use, for verification.
+
+    For the second part of the lab, an Access Control circuit was to be designed,
+    allowing lab entry only if a valid ID was provided alongside a proper keypad
+    combination. Otherwise, an alarm signal was to be sent out.
+    The method of designing this circuit was very similar to the method in part one:
+    Again using Xilinx Vivado, the circuit was designed and simulated against inputs
+    to verify if the outputs matched those in the specification.
+    However, for this section, the design was also uploaded to a physical FPGA board
+    where various could be manually tested and validated.
+
+    \section{Design Section}
+
+    In order to design the desired systems, the Xilinx Vivado software was
+    used to write VHDL code that described the operation of each circuit.
+
+    \newpage
+    \paragraph{MUX / DEMUX Circuit}
+    To implement the multiplexing/demultiplexing system, the following circuit had to be written in VHDL.
+
+    The VHDL architecture below was written to implement this circuit in hardware.
+
+    \begin{lstlisting}[language=MATLAB]
+U0 = 0.25;
+kBT = 0.025;
+mu = 0;
+cal_E = 0.2;
+
+% Capacitance parameters
+
+alpha_G = 0.5;
+alpha_D = 0.5;
+alpha_S = 1 - alpha_G - alpha_D;
+
+% Energy grid in eV, from -1 eV to 1 eV
+
+NE = 501;
+E = linspace(-1,1,NE);
+dE = E(2) - E(1);
+
+% Gamma parameters, in eV
+
+gamma_1 = 0.005;
+gamma_2 = 0.005;
+gamma = gamma_1 + gamma_2;
+    \end{lstlisting}
+    \newpage
+
+\end{document}

PS1/q1b.m

@@ -3,8 +3,8 @@ clear all;
 %% Constants
 
 % Physical constants
-%hbar = 1.052e-34;
+hbar = 1.052e-34;
-%q = 1.602e-19;
+q = 1.602e-19;
 %epsilon_0 = 8.854e-12;
 %epsilon_r = 4;
 %mstar = 0.25 * 9.11e-31;
@@ -55,7 +55,8 @@ for n = 1:length(voltages)
     mu_2 = mu - V_D;
 
     % Laplace potential, does not change as solution is found (eV)
-    U_L = - (a_G*V_G - a_D*V_D - a_S*V_S);
+    % q is factored out here, we are working in eV
+    U_L = - (a_G*V_G) - (a_D*V_D) - (a_S*V_S);
 
     % Poisson potential must change, assume 0 initially (eV)
     U_P = 0;
@@ -78,8 +79,8 @@ for n = 1:length(voltages)
         dU_P = abs(U_P - tmpU_P);
 
         % Unsure why U_P is updated incrementally, perhaps to avoid oscillations?
-        U_P = tmpU_P;
+        %U_P = tmpU_P;
-        % U_P = U_P + 0.1 * (tmpU_P - U_P)
+        U_P = U_P + 0.1 * (tmpU_P - U_P)
     end
 
     % Calculate current based on solved potential.

PS1/test.asv

@@ -0,0 +1,128 @@
+clear all;
+
+% Physical constants in MKS units
+
+hbar = 1.054e-34;
+6 q = 1.602e-19;
+
+% Energy parameters in eV; included are the single-electron charging
+% energy U0; the kBT product; the equilibrium Fermi level mu; and the
+ % energy level cal_E, which is short-form for "calligraphic E"
+
+ % Please especially note that ALL ENERGY VARIABLES IN THIS CODE
+ % ARE IN eV (NOT joules); the equations from class must be adjusted
+ % accordingly, multiplying or dividing appropriate terms by a factor of q
+
+ U0 = 0.25;
+ kBT = 0.025;
+ mu = 0;
+ cal_E = 0.2;
+
+ % Capacitance parameters
+
+ alpha_G = 0.5;
+ alpha_D = 0.5;
+ alpha_S = 1 - alpha_G - alpha_D;
+
+ % Energy grid in eV, from -1 eV to 1 eV
+
+ NE = 501;
+E = linspace(-1,1,NE);
+ dE = E(2) - E(1);
+
+ % Gamma parameters, in eV
+
+ gamma_1 = 0.005;
+ gamma_2 = 0.005;
+ gamma = gamma_1 + gamma_2;
+
+ % Lorentzian density of states, normalized so that its integral is unity
+
+ D = (gamma/(2*pi))./((E-cal_E).ˆ2+(gamma/2)ˆ2);
+ D = D./(dE*sum(D));
+
+ % Reference number of electrons in the channel, assumed to be zero in
+ % this code
+
+ N0 = 0;
+
+ % Voltage values to consider for the final plots
+ 
+ NV = 101;
+ VV = linspace(0,1,NV);
+ dV = VV(2) - VV(1);
+
+ % Loop over voltage values and compute number of electrons and current
+ % for each voltage value in a self-consistent manner
+
+ for count = 1:NV
+
+ % Set terminal voltages
+
+ VG = 0;
+ VD = VV(count);
+ VS = 0;
+
+ % Values of mu1 and mu2; notice that the usual factor of q multiplying
+ % the voltages is omitted, because in this code, energy is in eV
+
+ mu1 = mu - VS;
+ mu2 = mu - VD;
+
+ % Value of Laplace potential in eV
+
+ UL = - (alpha_G*VG) - (alpha_D*VD) - (alpha_S*VS);
+
+ % Initial value of Poisson part in eV
+ UP = 0;
+
+ % Iterate until self-consistent potential is achieved by monitoring
+ % the Poisson part (the Laplace part does not change)
+
+ dUP = 1;
+ while dUP > 1e-6
+
+ % Compute source and drain Fermi functions
+
+ f1 = 1./(1+exp((E + UL + UP - mu1)./kBT));
+ f2 = 1./(1+exp((E + UL + UP - mu2)./kBT));
+
+ % Compute number of channel electrons
+
+ N(count) = dE*sum( ((gamma_1/gamma).*f1 + (gamma_2/gamma).*f2).*D );
+
+ % Newly calculated Poisson part of self-consistent potential
+
+ UPnew = U0*( N(count) - N0 );
+
+ % Change in Poisson part between iterations
+
+ dUP = abs(UP - UPnew);
+
+% New guess for next iteration, found by adding a fraction of the
+% difference between iterations to the old guess
+105
+106 UP = UP + 0.1*(UPnew - UP);
+107
+108 end
+109
+110 % Compute the current in A after the self-consistent potential
+111 % has been achieved; notice the extra factor of q preceding the
+112 % equation, which is needed since the gammas are in eV
+113
+114 I(count) = q*(q/hbar)*(gamma_1*gamma_2)/(gamma) ...
+115 *dE*sum((f1-f2).*D);
+116
+117 end
+118
+119 % Plotting commands, including lines to modify the linewidth
+120 % and Fontsize, just to make the plots look nicer; you don’t
+ % need to worry about how these work
+
+ figure(1); h = plot(VV,N,’k’); grid on;
+ set(h,’linewidth’,[2.0]); set(gca,’Fontsize’,[18]);
+ xlabel(’DRAIN VOLTAGE [V]’); ylabel(’NUMBER OF ELECTRONS’);
+
+ figure(2); h = plot(VV,I,’k’); grid on;
+ set(h,’linewidth’,[2.0]); set(gca,’Fontsize’,[18]);
+ xlabel(’DRAIN VOLTAGE [V]’); ylabel(’CURRENT [A]’);

PS1/test.m

@@ -0,0 +1,127 @@
+clear all;
+
+% Physical constants in MKS units
+
+hbar = 1.054e-34;
+q = 1.602e-19;
+
+% Energy parameters in eV; included are the single-electron charging
+% energy U0; the kBT product; the equilibrium Fermi level mu; and the
+% energy level cal_E, which is short-form for "calligraphic E"
+
+% Please especially note that ALL ENERGY VARIABLES IN THIS CODE
+% ARE IN eV (NOT joules); the equations from class must be adjusted
+% accordingly, multiplying or dividing appropriate terms by a factor of q
+
+U0 = 0.25;
+kBT = 0.025;
+mu = 0;
+cal_E = 0.2;
+
+% Capacitance parameters
+
+alpha_G = 0.5;
+alpha_D = 0.5;
+alpha_S = 1 - alpha_G - alpha_D;
+
+% Energy grid in eV, from -1 eV to 1 eV
+
+NE = 501;
+E = linspace(-1,1,NE);
+dE = E(2) - E(1);
+
+% Gamma parameters, in eV
+
+gamma_1 = 0.005;
+gamma_2 = 0.005;
+gamma = gamma_1 + gamma_2;
+
+% Lorentzian density of states, normalized so that its integral is unity
+
+D = (gamma/(2*pi))./((E-cal_E).^2+(gamma/2)^2);
+D = D./(dE*sum(D));
+
+% Reference number of electrons in the channel, assumed to be zero in
+% this code
+
+N0 = 0;
+
+% Voltage values to consider for the final plots
+
+NV = 101;
+VV = linspace(0,1,NV);
+dV = VV(2) - VV(1);
+
+% Loop over voltage values and compute number of electrons and current
+% for each voltage value in a self-consistent manner
+
+for count = 1:NV
+
+    % Set terminal voltages
+
+    VG = 0;
+    VD = VV(count);
+    VS = 0;
+
+    % Values of mu1 and mu2; notice that the usual factor of q multiplying
+    % the voltages is omitted, because in this code, energy is in eV
+
+    mu1 = mu - VS;
+    mu2 = mu - VD;
+
+    % Value of Laplace potential in eV
+
+    UL = - (alpha_G*VG) - (alpha_D*VD) - (alpha_S*VS);
+
+    % Initial value of Poisson part in eV
+    UP = 0;
+
+    % Iterate until self-consistent potential is achieved by monitoring
+    % the Poisson part (the Laplace part does not change)
+
+    dUP = 1;
+    while dUP > 1e-6
+
+        % Compute source and drain Fermi functions
+
+        f1 = 1./(1+exp((E + UL + UP - mu1)./kBT));
+        f2 = 1./(1+exp((E + UL + UP - mu2)./kBT));
+
+        % Compute number of channel electrons
+
+        N(count) = dE*sum( ((gamma_1/gamma).*f1 + (gamma_2/gamma).*f2).*D );
+
+        % Newly calculated Poisson part of self-consistent potential
+
+        UPnew = U0*( N(count) - N0 );
+
+        % Change in Poisson part between iterations
+
+        dUP = abs(UP - UPnew);
+
+        %New guess for next iteration, found by adding a fraction of the
+        %difference between iterations to the old guess
+
+        UP = UP + 0.1*(UPnew - UP);
+
+    end
+
+    % Compute the current in A after the self-consistent potential
+    % has been achieved; notice the extra factor of q preceding the
+    % equation, which is needed since the gammas are in eV
+
+    I(count) = q*(q/hbar)*(gamma_1*gamma_2)/(gamma)*dE*sum((f1-f2).*D);
+
+end
+
+% Plotting commands, including lines to modify the linewidth
+% and Fontsize, just to make the plots look nicer; you don’t
+% need to worry about how these work
+
+figure(1); h = plot(VV,N,'k'); grid on;
+set(h,'linewidth',[2.0]); set(gca,'Fontsize',[18]);
+xlabel('DRAIN VOLTAGE [V]'); ylabel('NUMBER OF ELECTRONS');
+
+figure(2); h = plot(VV,I,'k'); grid on;
+set(h,'linewidth',[2.0]); set(gca,'Fontsize',[18]);
+xlabel('DRAIN VOLTAGE [V]'); ylabel('CURRENT [A]');