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X_2)$ + +Where: +$$ +\begin{flalign} +&Y = \text{Output Voltage}&\\\ +&A_v = \text{Open Loop Gain}\\ +&X_1 = \text{Input V1 (Non Inverting Input)}\\ +&X_2 = \text{Input V2 (Inverting Input)}\\ +\end{flalign} +$$ + +# Regions +Op Amps functions in different regions, just like diodes, and transistors. + +![[op-amp-regions.png|400]] + +**Linear Region** +This is how the Op-Amp normally functions. + +**Saturation Region** +When the output of the op-amp would be higher than $+V_{CC}$ or lower than $-V_{CC}$ the output value is clamped to those values. + +In real life OpAmps have $A_V$ values as high as $10^8$ or $10^9$ due to this even very small input voltages would quickly leave the linear region. That is why we need + +**Negative Feedback** +To use negative feedback we connect the output of the OpAmp to one of its inputs. This connection is modified by a *feedback factor* ($\beta$) which can be in the range $0 \le \beta \le 1$. + +Due to this feedback the new formula for the output $V_O$ is now: + +$$ +\begin{flalign} +&V_o = A_V * V_\Delta&\\\ +\\ +&V_- = \beta * V_o\\ +&\text{Now we can say that }V_\Delta \text{is equal to:}\\ +&V_\Delta = V_+ - \beta *V_o &| \textit{ Solve for }V_o \\ +&V_o = \frac{V_+ - V_\Delta}{\beta} +\end{flalign} +$$ + + + +# Non-Inverting Amplifier + +```circuitjs +$ 64 0.000005 1.0312258501325766 50 5 50 5e-11 +a 192 240 304 240 9 15 -15 1000000 4.9999000019999595 5 100000 +r 192 320 192 400 0 1000 +r 304 320 192 320 0 1000 +w 192 320 192 256 0 +w 304 240 304 320 0 +O 304 240 368 240 1 0 +g 192 400 192 432 0 0 +v 96 352 96 224 0 0 40 5 0 0 0.5 +w 96 224 192 224 2 +g 96 352 96 432 0 0 +b 144 288 289 401 0 +x 264 386 278 389 4 24 β +``` + + +# Buffer (Voltage-Follow) + +```circuitjs +$ 64 0.000005 1.0312258501325766 50 5 50 5e-11 +a 192 240 304 240 9 15 -15 1000000 4.999950000499995 5 100000 +w 192 320 192 256 0 +w 304 240 304 320 0 +O 304 240 368 240 1 0 +v 96 304 96 224 0 0 40 5 0 0 0.5 +w 96 224 192 224 2 +g 96 304 96 352 0 0 +w 192 320 304 320 0 +``` \ No newline at end of file diff --git a/Areas/electricity/active-components/transistor.md b/Areas/electricity/active-components/transistor.md new file mode 100644 index 0000000..aa5bed5 --- /dev/null +++ b/Areas/electricity/active-components/transistor.md @@ -0,0 +1,68 @@ +There are two types of transistors: + +# Bipolar Junctions Transistors (BJT) + +![[bipolar-junction-transistor|200x]] + +The current flowing in from Base controls the much larger current flowing between Collector and Emitter. + +## Rules for NPN Transistors + +**1. Polarity** +The collector must be more positive than the emitter. + +**2. Junctions** +The base$\rightarrow$emitter and base$\rightarrow$collector connections behave like diodes. + +**3. Maximum Ratings** +Any transistor has maximum ratings for $I_C$ ,$I_B$ and $V_{CE}$ that should not be exceded. + +**4. Current Amplifier** +When rules 1-3 are obeyed, $I_C$ is roughly equivalent to $IB$ and can be written like: + +$\displaystyle I_C = \beta I_B$ + +In the following example circuit we can see that for a $\beta$ of 100 the Ic current is aroung 100 times higher than the base current. + +```circuitjs +$ 1 0.000005 11.086722712598126 50 5 43 5e-11 +R 256 16 256 -48 0 0 40 2 0 0 0.5 +g 256 144 256 208 0 0 +t 192 80 256 80 0 1 -1.552 0.44799999999999995 100 default +R 144 80 64 80 0 0 40 0.44799999999999995 0 0 0.5 +w 256 16 256 64 3 +w 256 96 256 144 3 +w 144 80 192 80 1 +x 272 -5 289 -2 4 24 C +x 273 179 289 182 4 24 E +x 96 68 112 71 4 24 B +x 266 82 275 85 4 12 Ic +o 1 16 0 159745 0.0001 0.0001 0 2 1 3 +38 3 F1 0 0 1.4 -1 Voltage +``` + +## NPN vs PNP Transistors + +The names come from the way they are constructed +![[bjt-transistors.png]] + +![[transistors-pnp-npn]] + +# Transistor Modes + +## Saturation +In this mode the transistor acts like a short circuit and current flows freely from emitter to collector. + +## Cut-Off +In this mode the transistor acts like an open circuit and no current flows from emitter to collector. + +When $V_C > V _B < V_E$ then the transistor acts in Cutoff Region + +## Active +The current from collector to emitter is proportional to the current flowing into the base. + +# Field-Effect Transistors (FET) + +![[field-effect-transistor|200x]] + + diff --git a/Areas/electricity/assets/Drawing 2022-03-26 14.04.42.excalidraw.md b/Areas/electricity/assets/Drawing 2022-03-26 14.04.42.excalidraw.md new file mode 100644 index 0000000..eef80b3 --- /dev/null +++ b/Areas/electricity/assets/Drawing 2022-03-26 14.04.42.excalidraw.md @@ -0,0 +1,451 @@ +--- + +excalidraw-plugin: parsed +tags: [excalidraw] + +--- +==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== + + +# Text Elements +%% +# Drawing +```json +{ + "type": "excalidraw", + "version": 2, + "source": "https://excalidraw.com", + "elements": [ + { + "type": "freedraw", + 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-0.00019626553302779068 0 +r 368 48 368 128 0 5.6 +g 368 128 368 144 0 0 +c 144 192 224 192 0 0.000021 0.28247067907643153 0.001 +l 224 192 224 272 0 0.0015 0.05216033478886568 0 +g 224 272 224 304 0 0 +c 224 192 304 192 0 0.000063 0.08798149742233852 0.001 +l 304 192 368 192 0 0.00023999999999999998 0.39364251752638785 0 +l 368 192 432 192 0 0.00007999999999999999 0.2045046909150593 0 +r 432 192 432 272 0 8 +c 368 192 368 272 0 0.0000032999999999999997 2.8540707011819855 0.001 +g 368 272 368 304 0 0 +g 432 272 432 304 0 0 +w 144 192 144 368 0 +c 144 368 256 368 0 0.0000024 1.9379638766674248 0.001 +l 256 368 256 432 0 0.00015 0.07979150824953853 0 +g 256 432 256 480 0 0 +c 256 368 368 368 0 0.000007099999999999999 -0.28883337134377607 0.001 +r 368 368 368 432 0 5.6 +g 368 432 368 480 0 0 +170 144 48 80 48 2 100 20000 5 0.1 +x 422 98 519 101 4 24 LowPass +x 473 237 582 240 4 24 BandPass +x 415 408 517 411 4 24 HighPass +o 22 16 0 x81016 4.493571323078259 0.0001 0 2 3 0 22 3 0.000049999999999999996 0 high +o 13 16 0 x83016 5.606100247506279 0.0001 0 2 3 0 13 3 0.000049999999999999996 0 mid +o 5 16 0 x83016 5.222932005819454 0.0001 0 2 3 0 5 3 0.000049999999999999996 0 low +``` \ No newline at end of file diff --git a/Areas/electricity/circuits/filters/more-types.md b/Areas/electricity/circuits/filters/more-types.md new file mode 100644 index 0000000..29f74b4 --- /dev/null +++ b/Areas/electricity/circuits/filters/more-types.md @@ -0,0 +1,30 @@ +![[Pasted image 20220327155446.png]] + + +# Butterworth Filter +**Good** ++ Steep roll-off ++ Good selectivity +**Bad** +- great delay +- poorer phase linearity + +# Bessel Filter +**Good** +- superior phase shift +- low sensitivity +- superior step response +**Bad** +- doesnt have a sharp cutoff + +# Chebyshev Filter +**Good** ++ Sharp Roll-off +**Bad** +- Ripple in stopband + +# Elliptic Filter +**Good** ++ Sharpest roll-off of all +**Bad** +- Ripple in PassBand and StopBand \ No newline at end of file diff --git a/Areas/electricity/circuits/filters/topology.md b/Areas/electricity/circuits/filters/topology.md new file mode 100644 index 0000000..b704d05 --- /dev/null +++ b/Areas/electricity/circuits/filters/topology.md @@ -0,0 +1,30 @@ + +# L - Topology + +The L filters consist of two reactive elements, one in series with the signal and one in parallel to it. + +**RC Filters** are very cheap and easy to build but are only suited for low power applications as there is a resistor in series with the signal. Also the resistor may introduce thermal noise to the signal. + +**RL Filters** + +![[filter-topology-l.excalidraw]] + +## T-Topology + + +![[filter-topology-t]] + +# $\pi$ - Topology + +![[filter-topolgy-pi]] + + + +pi Topology is mostly used for Low Pass Filters. + +This filter is used a lot to reduce the ripple of Full Bridge Rectifiers. + +Formulas: + +![[formulas#Cutoff Frequency pi Topology Filter|Cutoff Frequency]] + diff --git a/Areas/electricity/circuits/rc-low-pass.md b/Areas/electricity/circuits/rc-low-pass.md index 5fa4105..d0ff2c3 100644 --- a/Areas/electricity/circuits/rc-low-pass.md +++ b/Areas/electricity/circuits/rc-low-pass.md @@ -12,7 +12,7 @@ We can also see that for the RL LowPass Filter the positions of the resistor and Lets design a RC LowPass Filter with a [[glossary#Cutoff Frequency|Cutoff Frequency]] of $15.9kHz$. The Formular for calculating the cutoff frequency is the following: -![[formulas#Cutoff Frequency for RC LowPass]] +![[formulas#Cutoff Frequency for RC Filters]] So, we now have the following formula: @@ -62,4 +62,5 @@ Or we can plot it # Second Order Low Pass Filter -If we place two LPF's in series \ No newline at end of file +If we place two LPF's in series + diff --git a/Areas/electricity/circuits/series-rlc.md b/Areas/electricity/circuits/series-rlc.md new file mode 100644 index 0000000..3041053 --- /dev/null +++ b/Areas/electricity/circuits/series-rlc.md @@ -0,0 +1,34 @@ +![[rlc-series-example.png]] + + +Lets find out the total impedance and current of this circuit: + +$$ +\begin{flalign} +&I = \frac{V}{Z}&\\\ +&Z = R^2 + (X_C-X_C)^2&\\ +&X_C = \frac{1}{\omega C} &\\ +&X_L = \omega C &\\ +\end{flalign} +$$ +Lets put in some numbers + +$$ +\begin{flalign} +&X_C = \frac{1}{2\pi*50*0.0001} \approx 31.830\ohm &\\\ +&X_L = 2\pi*50*0.15 \approx 47.123\ohm&\\ +&Z = \sqrt{12^2+(31.830-47.123)^2} \approx 19.4\ohm\\ +&I = \frac{100}{19.439} \approx 5.14A +\end{flalign} +$$ + +Now lets finally calculate the voltage drops across all the components + +$$ +\begin{flalign} +V_R = 5.14*12 &\approx 61.68V&\\\ +V_L = 5.14*47.13 &\approx 242.24V\\ +V_C = 5.14*31.83 & \approx 163.6V\\ +\end{flalign} +$$ + diff --git a/Areas/electricity/parts/capacitors/smoothing.md b/Areas/electricity/circuits/voltage-divider.md similarity index 100% rename from Areas/electricity/parts/capacitors/smoothing.md rename to Areas/electricity/circuits/voltage-divider.md diff --git a/Areas/electricity/formulas.md b/Areas/electricity/formulas.md index c2313d8..5671568 100644 --- a/Areas/electricity/formulas.md +++ b/Areas/electricity/formulas.md @@ -96,7 +96,7 @@ $\displaystyle f_{c} = \frac{R}{2\pi L}$ ## Signal Response of an RC Filter -Xc = [[#Capacitive Reactance]] +$X_c$ = [[#Capacitive Reactance]] || [[#Inductive Reactance]] $\displaystyle V_{out} = V_{in}(\frac{X_{c}}{\sqrt{R^2+X_{c}^2}})$ @@ -106,6 +106,47 @@ $\displaystyle f_{(-3db)} = f_{c}\sqrt{2^{(\frac{1}{n})}-1}$ Where $n$ = Number if **identical** filters -# Center Frequency for RLC Low Pass Filter +# Resonance Frequency for RLC Low Pass Filter -$\displaystyle f_{o} = \frac{1}{2\pi \sqrt{LC}}$ \ No newline at end of file +$\displaystyle f_{o} = \frac{1}{2\pi \sqrt{LC}}$ + +# Center Frequency with Fc and Fh + +$f_{c} = \sqrt{f_{h}*f_{l}}$ + +## Filter Response for RC Filters + +$V_{out} = V_{in}(\frac{X_c}{\sqrt{R_{1}^2+X_{c}^2}})$ + +## Cutoff Frequency $\pi$ Topology Filter + +When the two capacitors have the same capacitance, it can be calculated like this: + +$\displaystyle f_c = \frac{1}{4\pi\sqrt{LC}}$ + +## Voltage Divider + +$V_{out} = V_{in}(\frac{R_{1}}{R_1+R_2})$ + + +# Angular Frequency ($\omega$) + +$\omega = 2\pi f = \frac{2\pi}{T}$ ^4ad7fc + +# RLC Series Response + +This is basically Ohms Law: + +$\displaystyle V = IZ$ + +Where $Z$ is the impedance: + +$Z = \sqrt{R^2 + (X_L - X_C)^2}$ + + +# Current through a transistor + +$\displaystyle I_{EQ} = \frac{V_{BB}-{V_{BE}}}{\frac{R_B}{(\beta+1)}+R_E}$ + + +# Non-Inverting Amplifier Gain \ No newline at end of file diff --git a/Areas/electricity/glossary.md b/Areas/electricity/glossary.md index 6bca649..5a27f1e 100644 --- a/Areas/electricity/glossary.md +++ b/Areas/electricity/glossary.md @@ -9,6 +9,9 @@ In [electrical engineering](https://en.wikipedia.org/wiki/Electrical_engineering ## Output Impedance ($Z_{out}$) +## Reactance (X) +Reactance is resistance related to frequency + ## Voltage (V) **Voltage**, **electric potential difference**, **electric pressure** or **electric tension** is the difference in [electric potential](https://en.wikipedia.org/wiki/Electric_potential "Electric potential") between two points. @@ -52,12 +55,33 @@ A component is a **reactive component** when it resists to changes in current or ## Millmans Theorem -## Cutoff Frequency +## Cutoff Frequency ($f_{c}$) $\rightarrow$ [[filters]] The frequency at which the output strength of a filter is 3dB lower than the input strength. When this frequency is passed the output signal is $V_{Peak} \frac{1}{\sqrt{2}}$ the strength of the input signal. +# High/Low Cutoff Frequency ($f_{H}/f_{L}$) + +# Center Frequency +$\rightarrow$ [[formulas#Center Frequency for RLC Low Pass Filter | Formula 1]] $\rightarrow$ [[formulas]] +The midpoint between the High and the Low Cutoff Frequency, + # Pass-Band The Pass-Band is the frequency range which is allowed to pass through a filter without changes. # Stop-Band The stopband is the frequency range which is attenuated by a filter. + +# Pass-Band Ripple + +![[frequency-response.png]] + + +# Transfer Function + +The Transfer function is a mathematical model of some analog filter that represents the input strength to output strength related to the frequency of the input. + + +# Angular Frequency ($\omega$) + + +![[formulas#^4ad7fc]] \ No newline at end of file diff --git a/Areas/electricity/parts/op-amp.md b/Areas/electricity/parts/op-amp.md deleted file mode 100644 index fbd4178..0000000 --- a/Areas/electricity/parts/op-amp.md +++ /dev/null @@ -1,3 +0,0 @@ -![[op-amp-basic-schematic-symbol.svg]] - -The operational amplifier has a very high input impedance which makes it very good for amplifying low voltage signals. \ No newline at end of file diff --git a/Areas/electricity/parts/capacitors.md b/Areas/electricity/passive-components/capacitors.md similarity index 100% rename from Areas/electricity/parts/capacitors.md rename to Areas/electricity/passive-components/capacitors.md diff --git a/Areas/electricity/parts/capacitors/coupling.md b/Areas/electricity/passive-components/capacitors/coupling.md similarity index 100% rename from Areas/electricity/parts/capacitors/coupling.md rename to Areas/electricity/passive-components/capacitors/coupling.md diff --git a/Areas/electricity/parts/capacitors/impedance-reactance.md b/Areas/electricity/passive-components/capacitors/impedance-reactance.md similarity index 100% rename from Areas/electricity/parts/capacitors/impedance-reactance.md rename to Areas/electricity/passive-components/capacitors/impedance-reactance.md diff --git a/Areas/electricity/parts/capacitors/rc-time-constant.md b/Areas/electricity/passive-components/capacitors/rc-time-constant.md similarity index 100% rename from Areas/electricity/parts/capacitors/rc-time-constant.md rename to Areas/electricity/passive-components/capacitors/rc-time-constant.md diff --git a/Areas/electricity/passive-components/capacitors/smoothing.md b/Areas/electricity/passive-components/capacitors/smoothing.md new file mode 100644 index 0000000..e69de29 diff --git a/Areas/electricity/parts/coax-cable.md b/Areas/electricity/passive-components/coax-cable.md similarity index 100% rename from Areas/electricity/parts/coax-cable.md rename to Areas/electricity/passive-components/coax-cable.md diff --git a/Areas/electricity/parts/diodes.md b/Areas/electricity/passive-components/diodes.md similarity index 100% rename from Areas/electricity/parts/diodes.md rename to Areas/electricity/passive-components/diodes.md diff --git a/Areas/electricity/parts/diodes/example.md b/Areas/electricity/passive-components/diodes/example.md similarity index 100% rename from Areas/electricity/parts/diodes/example.md rename to Areas/electricity/passive-components/diodes/example.md diff --git a/Areas/electricity/parts/filters.md b/Areas/electricity/passive-components/filters.md similarity index 89% rename from Areas/electricity/parts/filters.md rename to Areas/electricity/passive-components/filters.md index 1881e10..045974f 100644 --- a/Areas/electricity/parts/filters.md +++ b/Areas/electricity/passive-components/filters.md @@ -10,7 +10,7 @@ There are two different types of filters: # Passive Filters -Passive filters use passive components to filter a signal, like resistors, capacitors or inductors. +Passive filters use passive components like resistors, capacitors or inductors. # Active Filters @@ -58,4 +58,7 @@ Now lets calculate the cutoff frequency when we place three of those filters in ![[formulas#Cutoff Frequency for multiple Low Pass Filters]] $f_{(-3db)} = 530.51 \sqrt{2^{(\frac{1}{3})}-1}$ -$\displaystyle f_{(-3db)} \approx 270.467010633$ \ No newline at end of file +$\displaystyle f_{(-3db)} \approx 270.467010633$ + + +![[Drawing 2022-03-26 14.04.42.excalidraw]] \ No newline at end of file diff --git a/Areas/electricity/parts/inductors.md b/Areas/electricity/passive-components/inductors.md similarity index 100% rename from Areas/electricity/parts/inductors.md rename to Areas/electricity/passive-components/inductors.md diff --git a/Areas/electricity/parts/inductors/back-emf.md b/Areas/electricity/passive-components/inductors/back-emf.md similarity index 100% rename from Areas/electricity/parts/inductors/back-emf.md rename to Areas/electricity/passive-components/inductors/back-emf.md diff --git a/Areas/electricity/parts/led.md b/Areas/electricity/passive-components/led.md similarity index 100% rename from Areas/electricity/parts/led.md rename to Areas/electricity/passive-components/led.md diff --git a/Areas/electricity/passive-components/relays.md b/Areas/electricity/passive-components/relays.md new file mode 100644 index 0000000..2d5c130 --- /dev/null +++ b/Areas/electricity/passive-components/relays.md @@ -0,0 +1,6 @@ +A relay is basically a switch that is controled by voltage. + +# Mechanical Relay + +# Solid State Relay + diff --git a/Areas/electricity/parts/resistors.md b/Areas/electricity/passive-components/resistors.md similarity index 100% rename from Areas/electricity/parts/resistors.md rename to Areas/electricity/passive-components/resistors.md diff --git a/Areas/electricity/parts/rlc-series-response.md b/Areas/electricity/passive-components/rlc-series-response.md similarity index 100% rename from Areas/electricity/parts/rlc-series-response.md rename to Areas/electricity/passive-components/rlc-series-response.md diff --git a/Areas/electricity/parts/transformers.md b/Areas/electricity/passive-components/transformers.md similarity index 100% rename from Areas/electricity/parts/transformers.md rename to Areas/electricity/passive-components/transformers.md diff --git a/Areas/electricity/parts/voltage-dividers.md b/Areas/electricity/passive-components/voltage-dividers.md similarity index 100% rename from Areas/electricity/parts/voltage-dividers.md rename to Areas/electricity/passive-components/voltage-dividers.md diff --git a/Areas/optimizing/dev.md b/Areas/optimizing/dev.md index ec9db64..a8b50ac 100644 --- a/Areas/optimizing/dev.md +++ b/Areas/optimizing/dev.md @@ -3,23 +3,22 @@ ## ~~ Nested tmux sessions ~~ Adding this: -```config + +```yaml RequestTTY true RemoteCommand tmux new -A -s ssh ``` to the ssh config if the specific hosts will automatically start tmux when connected If i ssh into a remote machine with tmux started as well I have some problems: - - ~~ Duplicate tmux bar ~~ - - ~~ Shortcuts don't work in remote ~~ + - ~~Duplicate tmux bar~~ + - ~~Shortcuts don't work in remote~~ - This works by hitting the prefix key twice, e.g. ctrl-a-a ## ~~ Debian Gnome sometimes comma key doesn't work ~~ - Has not happened in a while ## ~~ Neovim shortcut to comment out ~~ - Fixed this by installing the NerdCommenter Plugin ## ~~ Neovim Auto fix problems shortcut + hover window ~~ @@ -27,5 +26,13 @@ Fixed this by installing the NerdCommenter Plugin ## ~~ Better git merging in Neovim, like in VScode ~~ ## ~~ Copying between neovim, tmux and ssh sessions does not work ~~ + ## Learn how to use splits and buffers in neovim + ## Fix the dictionary for neovim ltex-ls + +# Linux + +## Power Management +I want to set the Power Mode e.g. Power/Normal/Energy Saver. +Maybe with a waybar integration, but not that important. diff --git a/Areas/upv/classes/analog-electricity/Exam 01.md b/Areas/upv/classes/analog-electricity/Exam 01.md new file mode 100644 index 0000000..5c953fb --- /dev/null +++ b/Areas/upv/classes/analog-electricity/Exam 01.md @@ -0,0 +1,44 @@ + +```circuitjs +$ 1 0.000005 10.20027730826997 50 5 43 5e-11 +R 80 336 16 336 0 0 40 20 0 0 0.5 +t 192 320 240 320 0 1 1.9615942922422976e+59 1.9615942922422976e+59 100 default +r 240 336 240 400 0 870.13 +g 240 400 240 432 0 0 +R 240 304 240 256 0 0 40 15 0 0 0.5 +w 240 336 320 336 0 +w 320 336 320 176 0 +w 320 176 80 176 0 +w 80 176 80 304 0 +R 320 336 384 336 0 0 40 5 0 0 0.5 +409 80 320 192 320 1 0.6 0 25 0 +R 128 288 128 256 0 0 40 15 0 0 0.5 +g -16 368 -16 416 0 0 +R 128 352 128 416 0 0 40 -15 0 0 0.5 +o 1 16 6 159746 0.0001 0.0001 0 1 +38 2 F1 0 1 1000 -1 Resistance +38 0 F1 0 -20 20 -1 Voltage +``` + + + +```circuitjs +$ 1 0.000005 382.76258214399064 50 5 43 5e-11 +g -16 368 -16 416 0 0 +v -16 368 -16 272 0 1 159 1 0 0 0.5 +r -16 272 80 272 0 10000 +c 80 176 192 176 0 1e-8 11.574895081799204 0.001 +w 80 272 80 176 0 +w 80 176 80 96 0 +r 80 96 192 96 0 100000 +w 192 96 192 176 0 +409 80 288 192 288 1 0.6 29.037879762735045 0.023100000000000002 0 +R 128 256 128 208 0 0 40 -15 0 0 0.5 +R 128 320 128 368 0 0 40 15 0 0 0.5 +w 80 304 80 368 0 +r 80 368 80 432 0 10000 +g 80 432 80 464 0 0 +w 192 288 192 176 0 +O 192 288 272 288 0 0 +o 15 16 0 159754 13.6659683006871 0.0001 0 1 +``` \ No newline at end of file diff --git a/Untitled.md b/Untitled.md new file mode 100644 index 0000000..e69de29

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