Category Archives: hardware

Hardware related topics

Airbrush

Finally got in the mail my most recent acquisition. An small air compressor that will enable me to airbrush a model kit I bought a few years ago. The model is a Gato Class US submarine from World war 2. Because the surface to be painted is rather large (the model has over 1 meter in length) airbrushing it should be a way to not spend much paint and the results should be better.

IMG_0342

On glitch was that the compressor has a Iwata compatible output, and the airbrush I have is a proinsa double action airbrush with a badger compatible connection. So I had to get a converter from 8 inch iwata female to M5x0,45 female.

IMG_0343

The airbrush is pretty cool. Already tried it with water. Now I have to get the paint to spray on the model. Here’s the brush :

IMG_0344

With this tool I will be able to paint the model with some weathering effects on it. I will be posting here the build as it goes along

Node voltage analysis – an example

Continuing with the method for node voltage analysis of circuits with current sources.

Consider the following circuit :

circuit

Stating the KCL (Kirchoffs current law) at each of the four nodes gives us the following system of equations :

equation

That we can solve for the three voltages va, vb and vc, knowing that vd = 0 and given the values for i1 and i7 and the resistances.

Node voltage analysis of a circuit

In this post I will talk about a method for finding node voltages in a specific general type of resistive circuit. Consider the circuit in the following diagram :

circuit

To find the node voltage at node a we take node b as the reference node. According to the KCL (Kirchoff’s current law) we have at node a :

equation_1

then,

equation_2

, because the voltage at point b is zero (its the reference point), we have :

equation_3 or equation_4

 

We will see in future posts how this analysis can be generalised to these types of circuits (resistive with current sources).

Kirchoff’s voltage and current laws

Gustav Robert Kirchoff, a professor at the University of Berlin, stated two laws that relate the current and the voltage in a circuit with two or more resistors.

Kirchoff’s current law states that the algebraic sum of the currents into a node at any instant is zero. We can illustrate this with the following diagram of a circuit node :

KCL

 

i1 -i2 + i3 – i4 = 0, meaning that the sum of currents entering a node is equal to the sum of the currents leaving the node.

Kirchoff’s voltage law states that the algebraic sum of all the voltages in a closed path is zero at all times. Take for example the following circuit :

KVL

 

vc -va-vb = 0 (note the polarity on each element of the circuit)

These rules are very useful in circuit analysis. It allows the setup of a system of equations that can be solved for obtaining voltages at each element and currents on each branch of the circuit.

Integration of the power flowing through an element

I am currently learning about electric circuits and came across some math procedures that I have not used in a long time. Such as integrating a exponential function of the eulers number.

Take an electric element that is subjected to a current and therefore a voltage between its terminals.
We know that :

  • the voltage across its terminals is a function of time, v=2e-t
  • the current flowing through it is also a function of time, i=3e-t

We want to know the amount of electrical charge goes into to element in a time period from 0 to 10 seconds. We know that power is the time rate of change of the charge :

equation_1

Then the charge can be found by integrating the power in a time period:

equation_2

Substituting the power by its constituents, voltage and current we get :

equation_3

To integrate the function of t define u as a function of t :

(1)equation_4

Substituting the function in the integral yields :

(2)equation_5

Then, by derivating both sides of the equation (1) we get :

Substituting into the equation (2) :

equation_7

Then, to calculate the amount of charge between instants 0 and 10 just :

equation_8