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pkirwin 2021-02-06 16:05:14 -07:00
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159
PS1/doc.tex
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@ -11,12 +11,22 @@
\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
}
\lstset{language=Matlab,%
%basicstyle=\color{red},
breaklines=true,%
morekeywords={matlab2tikz},
keywordstyle=\color{blue},%
morekeywords=[2]{1}, keywordstyle=[2]{\color{black}},
identifierstyle=\color{black},%
stringstyle=\color{mylilas},
commentstyle=\color{mygreen},%
showstringspaces=false,%without this there will be a symbol in the places where there is a space
numbers=left,%
numberstyle={\tiny \color{black}},% size of the numbers
numbersep=9pt, % this defines how far the numbers are from the text
emph=[1]{for,end,break},emphstyle=[1]\color{red}, %some words to emphasise
%emph=[2]{word1,word2}, emphstyle=[2]{style},
}
\title{ECE 456 - Problem Set 1}
\date{2021-02-06}
@ -35,29 +45,14 @@
\singlespacing
\pagenumbering{arabic}
\section{Introduction}
\section{Question 1}
\subsection{(a)}
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.
\begin{equation}
N = $\int_{-\infty}^{\infty}$
\end{equation}
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}
@ -70,30 +65,112 @@
The VHDL architecture below was written to implement this circuit in hardware.
\begin{lstlisting}[language=MATLAB]
U0 = 0.25;
\begin{lstlisting}[language=Matlab]
clear all;
%% Constants
% Physical constants
hbar = 1.052e-34;
% Single-charge coupling energy (eV)
U_0 = 0.25;
% (eV)
kBT = 0.025;
% Contact coupling coefficients (eV)
gamma_1 = 0.005;
gamma_2 = gamma_1;
gamma_sum = gamma_1 + gamma_2;
% Capacitive gate coefficient
a_G = 0.5;
% Capacitive drain coefficient
a_D = 0.5;
a_S = 1 - a_G - a_D;
% Central energy level
mu = 0;
% Energy grid, from -1eV to 1eV
NE = 501;
E = linspace(-1, 1, NE);
dE = E(2) - E(1);
% TODO name this better
cal_E = 0.2;
% Capacitance parameters
% Lorentzian density of states, normalized so the integral is 1
D = (gamma_sum / (2*pi)) ./ ( (E-cal_E).^2 + (gamma_sum/2).^2 );
D = D ./ (dE*sum(D));
alpha_G = 0.5;
alpha_D = 0.5;
alpha_S = 1 - alpha_G - alpha_D;
% Reference no. of electrons in channel
N_0 = 0;
% Energy grid in eV, from -1 eV to 1 eV
voltages = linspace(0, 1, 101);
NE = 501;
E = linspace(-1,1,NE);
dE = E(2) - E(1);
% Terminal Voltages
V_G = 0;
V_S = 0;
% Gamma parameters, in eV
for n = 1:length(voltages)
% Set varying drain voltage
V_D = voltages(n);
gamma_1 = 0.005;
gamma_2 = 0.005;
gamma = gamma_1 + gamma_2;
% Shifted energy levels of the contacts
mu_1 = mu - V_S;
mu_2 = mu - V_D;
% Laplace potential, does not change as solution is found (eV)
% 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;
% Assume large rate of change
dU_P = 1;
% Run until we get close enough to the answer
while dU_P > 1e-6
% source Fermi function
f_1 = 1 ./ (1 + exp((E + U_L + U_P - mu_1) ./ kBT));
% drain Fermi function
f_2 = 1 ./ (1 + exp((E + U_L + U_P - mu_2) ./ kBT));
% Update channel electrons against potential
N(n) = dE * sum( ((gamma_1/gamma_sum) .* f_1 + (gamma_2/gamma_sum) .* f_2) .* D);
% Re-update Poisson portion of potential
tmpU_P = U_0 * ( N(n) - N_0);
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)
end
% Calculate current based on solved potential.
% Note: f1 is dependent on changes in U but has been updated prior in the loop
I(n) = q * (q/hbar) * (gamma_1 * gamma_1 / gamma_sum) * dE * sum((f_1-f_2).*D);
end
%%Plotting commands
figure(1);
h = plot(voltages, 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(voltages, I,'k');
grid on;
set(h,'linewidth',[2.0]);
set(gca,'Fontsize',[18]);
xlabel('Drain voltage [V]');
ylabel('Current [A]');
\end{lstlisting}
\newpage
\end{document}

4
PS1/q1b.m
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@ -4,10 +4,6 @@ clear all;
% Physical constants
hbar = 1.052e-34;
q = 1.602e-19;
%epsilon_0 = 8.854e-12;
%epsilon_r = 4;
%mstar = 0.25 * 9.11e-31;
% Single-charge coupling energy (eV)
U_0 = 0.25;

109
PS1/q1c.m Normal file
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@ -0,0 +1,109 @@
clear all;
%% Constants
% Physical constants
hbar = 1.052e-34;
q = 1.602e-19;
%epsilon_0 = 8.854e-12;
%epsilon_r = 4;
%mstar = 0.25 * 9.11e-31;
% Single-charge coupling energy (eV)
U_0 = 0.25;
% (eV)
kBT = 0.025;
% Contact coupling coefficients (eV)
gamma_1 = 0.005;
gamma_2 = gamma_1;
gamma_sum = gamma_1 + gamma_2;
% Capacitive gate coefficient
a_G = 0.5;
% Capacitive drain coefficient
a_D = 0.5;
a_S = 1 - a_G - a_D;
% Central energy level
mu = 0;
% Energy grid, from -1eV to 1eV
NE = 501;
E = linspace(-1, 1, NE);
dE = E(2) - E(1);
% TODO name this better
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 = D ./ (dE*sum(D));
% Reference no. of electrons in channel
N_0 = 0;
voltages = linspace(0, 1, 101);
% Terminal Voltages
V_G = 0;
V_S = 0;
for n = 1:length(voltages)
% Set varying drain voltage
V_D = voltages(n);
% Shifted energy levels of the contacts
mu_1 = mu - V_S;
mu_2 = mu - V_D;
% Laplace potential, does not change as solution is found (eV)
% 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;
% Assume large rate of change
dU_P = 1;
% Run until we get close enough to the answer
while dU_P > 1e-6
% source Fermi function
f_1 = 1 ./ (1 + exp((E + U_L + U_P - mu_1) ./ kBT));
% drain Fermi function
f_2 = 1 ./ (1 + exp((E + U_L + U_P - mu_2) ./ kBT));
% Update channel electrons against potential
N(n) = dE * sum( ((gamma_1/gamma_sum) .* f_1 + (gamma_2/gamma_sum) .* f_2) .* D);
% Re-update Poisson portion of potential
tmpU_P = U_0 * ( N(n) - N_0);
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)
end
% Calculate current based on solved potential.
% Note: f1 is dependent on changes in U but has been updated prior in the loop
I(n) = q * (q/hbar) * (gamma_1 * gamma_1 / gamma_sum) * dE * sum((f_1-f_2).*D);
end
%%Plotting commands
figure(1);
h = plot(voltages, 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(voltages, I,'k');
grid on;
set(h,'linewidth',[2.0]);
set(gca,'Fontsize',[18]);
xlabel('Drain voltage [V]');
ylabel('Current [A]');