From 50a968d642ae703e5205ab283c1c230e5f0e2c59 Mon Sep 17 00:00:00 2001 From: MK2020 Date: Tue, 14 Mar 2017 03:26:42 +0000 Subject: graphs done --- Part 1/Figures/heun_exponential1.fig | Bin 0 -> 841735 bytes Part 1/Figures/heun_exponential2.fig | Bin 0 -> 840517 bytes Part 1/Figures/heun_heaviside.fig | Bin 0 -> 302550 bytes Part 1/Figures/heun_heaviside_current.fig | Bin 0 -> 683359 bytes Part 1/Figures/heun_sawtooth(T=0.000015).fig | Bin 0 -> 587690 bytes Part 1/Figures/heun_sawtooth(T=0.0004).fig | Bin 0 -> 614848 bytes Part 1/Figures/heun_sawtooth(T=0.0011).fig | Bin 0 -> 643142 bytes Part 1/Figures/heun_sawtooth.fig | Bin 0 -> 659055 bytes Part 1/Figures/heun_sawtoothwave(T=0.00015).fig | Bin 0 -> 593536 bytes Part 1/Figures/heun_sinewave(T=0.000015).fig | Bin 0 -> 552589 bytes Part 1/Figures/heun_sinewave(T=0.00015)fig.fig | Bin 0 -> 537761 bytes Part 1/Figures/heun_sinewave(T=0.0004).fig | Bin 0 -> 563427 bytes Part 1/Figures/heun_sinewave(T=0.0011).fig | Bin 0 -> 595598 bytes 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0000000..2286205 Binary files /dev/null and b/Part 1/Figures/ralston_squarewave(T=0.0011).fig differ diff --git a/Part 1/Figures/ralston_squarewave.fig b/Part 1/Figures/ralston_squarewave.fig new file mode 100644 index 0000000..b9f199b Binary files /dev/null and b/Part 1/Figures/ralston_squarewave.fig differ diff --git a/Part 1/heun_script.m b/Part 1/heun_script.m index fdf9a62..012c75a 100644 --- a/Part 1/heun_script.m +++ b/Part 1/heun_script.m @@ -14,7 +14,7 @@ Vout = zeros(1, N); current = zeros(1,N); %input voltage -% step function of 5 volt +% step function of 3.5 volt Vin = @(t)3.5*heaviside(t); %the initial condition @@ -40,6 +40,12 @@ xlabel({'Time', '(seconds)'}); ylabel({'V_{out}', '(volt)'}); title('(Heaviside) V_{out} versus time'); +figure(8); +plot(t, current); +xlabel({'Time', '(seconds)'}); +ylabel({'V_{out}', '(volt)'}); +title('V_{out} versus time (Heaviside)'); + %--------------------------------------------------------------------------------------------- %initailise the circuits at the top @@ -73,12 +79,10 @@ figure(2); plot(Vout); xlabel({'Time', '(seconds)'}); ylabel({'V_{out}', '(volt)'}); -title('(Exponential #1) V_{out} versus time'); +title('V_{out} versus time (Exponential square function #1)'); %----------------------------------------------------------------------------------------------- -%initailise the circuits at the top - %initailise the container at the top %input voltage @@ -108,10 +112,10 @@ figure(3); plot(Vout); xlabel({'Time', '(seconds)'}); ylabel({'V_{out}', '(volt)'}); -title('#(Exponential #2) V_{out} versus time'); +title('V_{out} versus time (Exponential #2)'); -%------------------------------------------------------------------------------------------- +% %------------------------------------------------------------------------------------------- %initailise the circuits at the top @@ -126,7 +130,9 @@ current = zeros(1,N); %input voltage % step function of 5 volt -Vin = @(t)4*sin(2*pi*6000*t); +% T= 0.00015, 0.000015, 0.0004, 0.0011 +T = 0.0011; +Vin = @(t)4*sin(2*pi*t/T); %the initial condition t(1) = 0; @@ -149,7 +155,7 @@ figure(4); plot(Vout); xlabel({'Time', '(seconds)'}); ylabel({'V_{out}', '(volt)'}); -title('(Sine wave) V_{out} versus time '); +title('V_{out} versus time (T=0.0011)(Sine wave)'); %----------------------------------------------------------------------------------------- @@ -162,7 +168,7 @@ title('(Sine wave) V_{out} versus time '); %input voltage % step function of 5 volt A = 4; -T = 0.0015; +T = 0.0011; Vin = @(t) A * square(2*pi*t/T); @@ -187,7 +193,7 @@ figure(5); plot(Vout); xlabel({'Time', '(seconds)'}); ylabel({'V_{out}', '(volt)'}); -title('(Square wave) V_{out} versus time'); +title('V_{out} versus time (T=0.0011) (Square wave)'); %-------------------------------------------------------------------------------------- %initailise the circuits at the top @@ -197,7 +203,7 @@ title('(Square wave) V_{out} versus time'); %input voltage % step function of 5 volt A = 4; -T = 0.0015; +T = 0.000015; Vin = @(t) A * sawtooth(2*pi*t/T); @@ -222,6 +228,6 @@ figure(6); plot(Vout); xlabel({'Time', '(seconds)'}); ylabel({'V_{out}', '(volt)'}); -title('(Sawtooth wave) V_{out} versus time'); +title('V_{out} versus time (T=0.0011) (Sawtooth wave)'); end \ No newline at end of file diff --git a/Part 1/midpoint_script.m b/Part 1/midpoint_script.m index 35ace43..196cb90 100644 --- a/Part 1/midpoint_script.m +++ b/Part 1/midpoint_script.m @@ -3,99 +3,104 @@ ts = 0; % set initial value of x_0 is = 0; h = 0.0001; % set step-size tf = 0.03; % stop here + R = 0.5; L = 0.0015; -vin = @(t) 3.5; -func = @(t, iout) (vin(t) - iout*R) / L; % define func -[t, iout ] = midpoint(func, ts, tf, is, h); - -vout = vin(t) - iout * R; -plot(t,vout); -xlabel({'Time', '(seconds)'}); -ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (original function)'); +% vin = @(t) 3.5; +% func = @(t, iout) (vin(t) - iout*R) / L; % define func +% [t, iout ] = midpoint(func, ts, tf, is, h); +% +% vout = vin(t) - iout * R; +% figure(1); +% plot(t,vout); +% xlabel({'Time', '(seconds)'}); +% ylabel({'V_{out}', '(volt)'}); +% title('V_{out} versus time (Heaviside)'); +% %____________________________________________________________________ +% h = 0.0001; +% tf = 0.03; +% figure; +% A = 3.5; +% tau = 0.00015; +% +% vin = @(t) A * exp(-t.^2/tau); +% func = @(t, iout) (vin(t) - iout*R) / L; % define func +% [t, iout ] = midpoint(func, ts, tf, is, h); +% +% vout = vin(t) - iout * R; +% figure(2); +% plot(t,vout); +% xlabel({'Time', '(seconds)'}); +% ylabel({'V_{out}', '(volt)'}); +% title('V_{out} versus time (Exponential square function #1)'); %____________________________________________________________________ -h = 0.0001; -tf = 0.03; -figure; -A = 3.5; -tau = 0.000150; - -vin = @(t) A * exp(-t.^2/tau); -func = @(t, iout) (vin(t) - iout*R) / L; % define func -[t, iout ] = midpoint(func, ts, tf, is, h); +% h = 0.0001; +% tf = 0.03; +% figure; +% A = 3.5; +% tau = 0.00015; +% +% vin = @(t) A * exp(-t/tau); +% func = @(t, iout) (vin(t) - iout*R) / L; % define func +% [t, iout ] = midpoint(func, ts, tf, is, h); +% +% vout = vin(t) - iout * R; +% figure(3); +% plot(t,vout); +% xlabel({'Time', '(seconds)'}); +% ylabel({'V_{out}', '(volt)'}); +% title('V_{out} versus time (Exponential function #2)'); -vout = vin(t) - iout * R; -plot(t,vout); -xlabel({'Time', '(seconds)'}); -ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (exponential square funtion)'); %____________________________________________________________________ -h = 0.0001; -tf = 0.03; -figure; -A = 3.5; -tau = 0.000150; - -vin = @(t) A * exp(-t/tau); -func = @(t, iout) (vin(t) - iout*R) / L; % define func -[t, iout ] = midpoint(func, ts, tf, is, h); - -vout = vin(t) - iout * R; -plot(t,vout); -xlabel({'Time', '(seconds)'}); -ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (exponential function)'); - +% h = 0.0001; +% tf = 0.03; +% figure; +% A = 4; +% T = 0.0011; +% +% vin = @(t) A * sin(2*pi*t/T); +% func = @(t, iout) (vin(t) - iout*R) / L; % define func +% [t, iout ] = midpoint(func, ts, tf, is, h); +% +% vout = vin(t) - iout * R; +% figure(4); +% plot(t,vout); +% xlabel({'Time', '(seconds)'}); +% ylabel({'V_{out}', '(volt)'}); +% title('V_{out} versus time (T=0.0011) (Sine wave)'); %____________________________________________________________________ -h = 0.0001; -tf = 0.03; -figure; -A = 4; -T = 0.0015; - -vin = @(t) A * sin(2*pi*t/T); -func = @(t, iout) (vin(t) - iout*R) / L; % define func -[t, iout ] = midpoint(func, ts, tf, is, h); - -vout = vin(t) - iout * R; -plot(t,vout); -xlabel({'Time', '(seconds)'}); -ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (sine function)'); -%____________________________________________________________________ -h = 0.0001; -tf = 0.03; -figure; -A = 4; -T = 0.0015; - -vin = @(t) A * square(2*pi*t/T); -func = @(t, iout) (vin(t) - iout*R) / L; % define func -[t, iout ] = midpoint(func, ts, tf, is, h); - -vout = vin(t) - iout * R; -plot(t,vout); -xlabel({'Time', '(seconds)'}); -ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (square function)'); +% h = 0.0001; +% tf = 0.03; +% A = 4; +% T = 0.0011; +% +% vin = @(t) A * square(2*pi*t/T); +% func = @(t, iout) (vin(t) - iout*R) / L; % define func +% [t, iout ] = midpoint(func, ts, tf, is, h); +% +% vout = vin(t) - iout * R; +% figure(5); +% plot(t,vout); +% xlabel({'Time', '(seconds)'}); +% ylabel({'V_{out}', '(volt)'}); +% title('V_{out} versus time (T=0.0011) (Square wave)'); %____________________________________________________________________ h = 0.0001; tf = 0.03; -figure; A = 4; -T = 0.0015; +T = 0.0011; vin = @(t) A * sawtooth(2*pi*t/T); func = @(t, iout) (vin(t) - iout*R) / L; % define func [t, iout ] = midpoint(func, ts, tf, is, h); vout = vin(t) - iout * R; +figure(6); plot(t,vout); xlabel({'Time', '(seconds)'}); ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (sawtooth function)'); +title('V_{out} versus time (T=0.0011) (Sawtooth wave)'); diff --git a/Part 1/midpoint_squarewave(T=0.00015).fig b/Part 1/midpoint_squarewave(T=0.00015).fig new file mode 100644 index 0000000..a032340 Binary files /dev/null and b/Part 1/midpoint_squarewave(T=0.00015).fig differ diff --git a/Part 1/ralston_script.m b/Part 1/ralston_script.m index 91da2a9..4e9ee70 100644 --- a/Part 1/ralston_script.m +++ b/Part 1/ralston_script.m @@ -6,86 +6,86 @@ tf = 0.03; % stop here R = 0.5; L = 0.0015; -vin = @(t) 3.5; -func = @(t, iout) (vin(t) - iout*R) / L; % define func -[t, iout ] = ralston(func, ts, tf, is, h); +% vin = @(t) 3.5; +% func = @(t, iout) (vin(t) - iout*R) / L; % define func +% [t, iout ] = ralston(func, ts, tf, is, h); +% +% vout = vin(t) - iout * R; +% plot(t,vout); +% xlabel({'Time', '(seconds)'}); +% ylabel({'V_{out}', '(volt)'}); +% title('V_{out} versus time (original function)'); +% %____________________________________________________________________ +% h = 0.0001; +% tf = 0.03; +% figure; +% A = 3.5; +% tau = 0.00015; +% +% vin = @(t) A * exp(-t.^2/tau); +% func = @(t, iout) (vin(t) - iout*R) / L; % define func +% [t, iout ] = ralston(func, ts, tf, is, h); +% +% vout = vin(t) - iout * R; +% plot(t,vout); +% xlabel({'Time', '(seconds)'}); +% ylabel({'V_{out}', '(volt)'}); +% title('V_{out} versus time (exponential square funtion)'); +% %____________________________________________________________________ +% h = 0.0001; +% tf = 0.03; +% figure; +% A = 3.5; +% tau = 0.00015; +% +% vin = @(t) A * exp(-t/tau); +% func = @(t, iout) (vin(t) - iout*R) / L; % define func +% [t, iout ] = ralston(func, ts, tf, is, h); +% +% vout = vin(t) - iout * R; +% plot(t,vout); +% xlabel({'Time', '(seconds)'}); +% ylabel({'V_{out}', '(volt)'}); +% title('V_{out} versus time (exponential function)'); -vout = vin(t) - iout * R; -plot(t,vout); -xlabel({'Time', '(seconds)'}); -ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (original function)'); -%____________________________________________________________________ -h = 0.0001; -tf = 0.03; -figure; -A = 3.5; -tau = 0.000150; - -vin = @(t) A * exp(-t.^2/tau); -func = @(t, iout) (vin(t) - iout*R) / L; % define func -[t, iout ] = ralston(func, ts, tf, is, h); - -vout = vin(t) - iout * R; -plot(t,vout); -xlabel({'Time', '(seconds)'}); -ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (exponential square funtion)'); -%____________________________________________________________________ -h = 0.0001; -tf = 0.03; -figure; -A = 3.5; -tau = 0.000150; - -vin = @(t) A * exp(-t/tau); -func = @(t, iout) (vin(t) - iout*R) / L; % define func -[t, iout ] = ralston(func, ts, tf, is, h); - -vout = vin(t) - iout * R; -plot(t,vout); -xlabel({'Time', '(seconds)'}); -ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (exponential function)'); - -%____________________________________________________________________ -h = 0.0001; -tf = 0.03; -figure; -A = 4; -T = 0.0015; - -vin = @(t) A * sin(2*pi*t/T); -func = @(t, iout) (vin(t) - iout*R) / L; % define func -[t, iout ] = ralston(func, ts, tf, is, h); - -vout = vin(t) - iout * R; -plot(t,vout); -xlabel({'Time', '(seconds)'}); -ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (sine function)'); -%____________________________________________________________________ -h = 0.0001; -tf = 0.03; -figure; -A = 4; -T = 0.0015; - -vin = @(t) A * square(2*pi*t/T); -func = @(t, iout) (vin(t) - iout*R) / L; % define func -[t, iout ] = ralston(func, ts, tf, is, h); - -vout = vin(t) - iout * R; -plot(t,vout); -xlabel({'Time', '(seconds)'}); -ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (square function)'); %____________________________________________________________________ +% h = 0.0001; +% tf = 0.03; +% figure; +% A = 4; +% T = 0.000015; +% +% vin = @(t) A * sin(2*pi*t/T); +% func = @(t, iout) (vin(t) - iout*R) / L; % define func +% [t, iout ] = ralston(func, ts, tf, is, h); +% +% vout = vin(t) - iout * R; +% plot(t,vout); +% xlabel({'Time', '(seconds)'}); +% ylabel({'V_{out}', '(volt)'}); +% title('V_{out} versus time (T=0.000015) (sine function)'); +% % ____________________________________________________________________ +% h = 0.0001; +% tf = 0.03; +% figure; +% A = 4; +% T = 0.0011; +% +% vin = @(t) A * square(2*pi*t/T); +% func = @(t, iout) (vin(t) - iout*R) / L; % define func +% [t, iout ] = ralston(func, ts, tf, is, h); +% +% vout = vin(t) - iout * R; +% plot(t,vout); +% xlabel({'Time', '(seconds)'}); +% ylabel({'V_{out}', '(volt)'}); +% title('V_{out} versus time (T=0.0011) (square function)'); +% %____________________________________________________________________ h = 0.0001; tf = 0.03; figure; A = 4; -T = 0.0015; +T = 0.0011; vin = @(t) A * sawtooth(2*pi*t/T); func = @(t, iout) (vin(t) - iout*R) / L; % define func @@ -95,7 +95,7 @@ vout = vin(t) - iout * R; plot(t,vout); xlabel({'Time', '(seconds)'}); ylabel({'V_{out}', '(volt)'}); -title('V_{out} versus time (sawtooth function)'); +title('V_{out} versus time (T=0.0011)(sawtooth function)'); diff --git a/Part 1/ralston_sinewave(T=0.0004).fig b/Part 1/ralston_sinewave(T=0.0004).fig new file mode 100644 index 0000000..1e57840 Binary files /dev/null and b/Part 1/ralston_sinewave(T=0.0004).fig differ -- cgit