david/ECE_456_Reports
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

finished q1b

Browse Source
This commit is contained in:
pkirwin 2021-02-06 15:55:04 -07:00
parent 9c17fcd819
commit 0b1a5bc9e0
4 changed files with 361 additions and 6 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

99
PS1/doc.tex Normal file
View File

@ -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}

13
PS1/q1b.m
View File

@ -3,8 +3,8 @@ clear all;
%% Constants
% Physical constants
%hbar = 1.052e-34;
%q = 1.602e-19;
hbar = 1.052e-34;
q = 1.602e-19;
%epsilon_0 = 8.854e-12;
%epsilon_r = 4;
%mstar = 0.25 * 9.11e-31;
@ -34,7 +34,7 @@ dE = E(2) - E(1);
cal_E = 0.2;
% Lorentzian density of states, normalized so the integral is 1
D = (gamma_sum / (2*pi)) ./ ( (E-cal_E).^2 + (gamma_sum/2).^2);
D = (gamma_sum / (2*pi)) ./ ( (E-cal_E).^2 + (gamma_sum/2).^2 );
D = D ./ (dE*sum(D));
% Reference no. of electrons in channel
@ -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 = U_P + 0.1 * (tmpU_P - U_P)
%U_P = tmpU_P;
U_P = U_P + 0.1 * (tmpU_P - U_P)
end
% Calculate current based on solved potential.

128
PS1/test.asv Normal file
View File

@ -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]’);

127
PS1/test.m Normal file
View File

@ -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]');