Balder W. Holst

Hello there!

My name is Balder and this is my personal website. Here i write down what i learn to maybe help others some day. For now i will just act like people are reading my articles, and make them for fun.

This website has three main sections:

I write these articles for fun, and even though i try to make sure that they are correct, i am not a perfect human and there are sure to be mistakes. Below is a list of most recent articles in all categories.

Recent Posts

Timeline Period
0001/01/01 · Notes
Transformation Matrices
Transformation Matrices Transformation from $\set{A}$ to ${\set B}$. $$^A_BT = \left( \begin{array}{cccc} r_{11} & r_{12} & r_{13} & p_x \ r_{21} & r_{22} & r_{23} & p_y \ r_{31} & r_{32} & r_{33} & p_z \ w_x & w_y & w_z & s \ \end{array} \right) $$ In kinematics we only interested in rotation and translation. Shering and scaling is therefore disabled. $$ \left( \begin{array}{cccc} r_{11} & r_{12} & r_{13} & p_x \
0001/01/01 · Notes
Transient Respons
Transient Respons “Transiente kredsløb dør ud” - Jan Man kan ikke snakke om impedans I spoler og kondensatorer er det forskellige størrelser, der ikke kan ændre sig momentant. Kondensator $$I_C(0_{+}) = I_C(0_{-})$$ Spoler $$V_L(0_{+}) = V_L(0_{-})$$ #elektronik
0001/01/01 · Notes
Transistorer
Transistorer En lille strøm styrer en meget større strøm Kan forstærke strømme hvor operationsforstærkere forstærker spænding. Karakteristikker Ideel Praktisk Storsignal Typer Transistorer Bipolar Junktion Transistor - BJT $$I_{E} = I_{B} + I_{C}$$ $L_{E}$ : Emitter strømmen $I_{B}$ : Base strømmen $I_{C}$ : Collector strømmen Arbejdsområder Aktiv $$\beta = \frac{I_{C}}{I_{B}} \arrows I_{C} = \beta \cdot I_{B}$$ $\beta$ : Forstærkningen (af strømmen) Det hvor transistoren fungerer som en diode.
0001/01/01 · Notes
Transmission
Transmission Signal Impairment Attenuation: Loss of energy $$dB = 10 \cdot \log_{10}\left(\frac{P_{2}}{P_{1}}\right)$$ $P_{1}$: Initial power $P_{2}$: Final power $$dB = 20 \cdot \log_{10}\left(\frac{V_{2}}{V_{1}}\right)$$ $V_{1}$: Initial Voltage $V_{2}$: Final Voltage Distortion Different frequencies will be warped (in phase) differently as the signal travels. Therefore the receiver signal will be distorted. ![450](Pasted image 20230912120722.png) Noise Thermal noise: From random movements of electrons in the conductor. Induced noise: Electromagnetic (motors, machines…) Crosstalk: Another wire affects this line Impule noise: lightning, thunderstorms… Signal-to-Noise ratio $$SNR=\frac{\text{average signal power}}{\text{average noise power}}$$ $$SNR_{dB} = 10 \cdot \log_{10}(SNR)$$ !
0001/01/01 · Notes
Tretrinsraketten
Tretrinsraketten En metode til at differentiere funktioner i hånden der gør brug af definitionen af en differentieret funktion#Definition af et Differentiale. I dette eksempel vil jeg bruge funktionen $f(x) = 3x^2$ Trin 1 find $f(x_0 + h) - f(x_0)$ $$f(x_0 + h) - f(x_0) = 3 (x_0+h)^2-3x_0^2 = 3 \cdot (h^2 + 2 \cdot h \cdot x_0 + x_0^2)-3x_0^2 = 3 \cdot h^2 + 6 \cdot h \cdot x_0 + \bcancel{3 \cdot x_0^2} - \bcancel{3 \cdot x_0^2}$$
0001/01/01 · Notes
Tri-State Buffer
Tri-State Buffer See slides [Lesson 3.pdf#page=24#page=24](Lesson 3.pdf) A way to connect different signals to one wire. If signals were connected directly together, it may result in short. The Tri-State buffer prevents this. An enable signal can make the output completely disconnected from the input. Tri-State meaning $\text{HIGH}$, $\text{LOW}$ or $\text{HI-Z}$ (high impedance/disconnected). #microcontrolers
0001/01/01 · Notes
Trigonometri
Trigonometri see also: [Law of Cosines](Law of Cosines). Cosinus og Sinus $$\sin(\theta) = \frac{\text{Modstående}}{\text{Hypotenusen}}$$ $$\cos(\theta) = \frac{\text{Hoslæggende}}{\text{Hypotenusen}}$$ $$\tan(\theta)= \frac{\text{Modstående}}{\text{Hoslæggende}} = \frac{\sin(\theta)}{\cos{(\theta)}}$$ And arctan $$a = \arctan\left(\frac{\sin(a)}{\cos(a)}\right) \pm n\pi, \s n \in \Z$$ Or use atan2 for full $360\degree$ resolution! $$a = \text{arctan2}\left(\frac{\sin(a)}{\cos(a)}\right) \pm n \cdot 2\pi, \s n \in \Z$$ Flere Relationer $$\sin(\theta) = \sin(\pi - \theta)$$ $$\cos(\theta) = \sin\left(\theta + \frac{\pi}{2}\right)$$ $$\cos(\theta) = \cos(-\theta)$$ $$\sin(-\theta) = -\sin(\theta)$$ Den med Tangens $$\tan^{-1}(x)= \int\frac{1}{1+x^2}dx$$
0001/01/01 · Notes
Tyngdeaccelerationen
Tyngdeaccelerationen $$g = 9.815 \frac{m}{s^2} $$ #fysik
0001/01/01 · Notes
Tyngdekraften
Tyngdekraften $$F_g = m \cdot g$$ $F_g$ : Tyngdekraften. $m$ : Massen. $g$ :Tyngdeaccelerationen #fysik
0001/01/01 · Notes