Circuits and YOU!

We've covered the 3 fundamental components the basis for electrical systems. Lets do a quick review over some terms

AC: Alternating current, circuit that deal with a cyclic harmonic change in potential over time. Us outlets are 110 VRMS 60HZ which means the average voltage put out is 110 volts and it oscillates as a 60HZ sine wave.

DC: Direct current, current is steady and a fixed potential is across two points. We use DC for most circuits.

Voltage: Potential difference across two points, Voltage is the work a circuit is capable of doing and is the product of an electrostatic attraction between two points.

Current: Is the charge that actually "flows" in a circuit. Voltage is the work capable current is what does that work.

The Three Fundamental components:

The Resistor: The resistor allows you to control current in a circuit, it is probably the most essential component. (V=IR)

Capacitor: Two plates separated by some sort of dielectric, Holds a charge and useful in storing energy and filtering signals.

Inductor: Coil of wire that holds energy in a magnetic field. Any current flowing through a wire produces a magnetic field around it.

The Fourth fundamental component?:

Resistors, Capacitors and Inductors are all useful things but it wasn't until semiconductors that we truly were able to create high speed circuits of today.

I've already done a writeup on semiconductors here:

http://mcuplace.com/mcu/blog4.php/2008/08/20/semiconduct-this

What is circuitry?

Circuitry is the process of taking these components and making circuits that do useful things. We can make sensors that record data, Counters, Timers, Computers, Calculators, Robots. We can make pretty much anything you want to with these components.

What we will be covering in this blog is a hodgepodge of information from digital circuits, to circuit analysis to schematic design and introduction to software suites.

Basic Symbols:

Part of reading a schematic is understanding what the symbols mean and how to interpret them.

Voltage Source / EMF

A battery or DC voltage source is denoted by parallel lines of varying size. The longer line denotes + and smaller line denotes -

Passive Components:

The symbol for a resistor is a zig-zag line.

Potentiometers or variable resistors are a resistor symbol with an arrow through it

The symbol for a capacitor is two separated parallel lines

Electrolytic capacitors may have a curved line or a + sign to denote polarity

The symbol for an inductor is a half coil

Semiconductors

The symbol for a diode is a triangle with a line at the tip, the triangle *points* where the current flows and the line is usually on the negative part of the diode.

The symbol for an LED is a diode symbol with arrows coming out from the triangle denoting it produces light.

Transistors

NPN Bi-polar Junction Transistors are denoted by the following symbol

PNP transistors are denoted by

NPN can be remember because the arrow is Not Pointing iN, and PNP is the complement of NPN

MOSFET transistors share a different symbol than BJT transistors.

NMOS transistors are denoted by:

PMOS are denoted by a NMOS symbol with a complement dot in the front.

MOSFET transistors also have different symbols but all use the same basic shape.

There are many other symbols out there for electric components, however these are the most common. As we demonstrate more circuits we will go over the symbols as we get to them.

We will be going over some basic circuits so we can get the hang of designing circuits and doing analysis.

Magnetism and electricity have been proven to be fundamentally linked. A magnetic flux will create a current in a wire just as a current in a wire will create a magnetic flux. This property is called Lenz's law and is the basis for how an inductor functions. The reason why this happens can be explained through conservation of energy, when a force (magnetic field) acts upon a wire, there is no way for that wire to store the energy, so that force turns into electric current and we get an EMF. Lenz's law can be explained by Faraday's law of induction:

Faraday's law of induction states that the EMF produced is the result of a change in magnetic flux with respect to time.

An inductor is nothing more than a piece of copper wire wound as a coil which makes it more permeable to magnetic flux.

An inductors job in a circuit is very similar to a capacitor it stores energy for later use. As current flows through an inductor, the current builds a magnetic flux around the inductor. This magnetic flux was the product of induction and will try and resist any change in current due to Lenz's law.

An inductor is a very simple and crude device, it is used in very similar applications to a capacitor.

LRC Circuits

a very popular application to an inductor is the creation of an oscillator using a capacitor and an inductor. Putting these two components in series with one another will create an oscillator at a certain frequency, this was primarily used in radio tuning as you had an inductor hooked up to a variable capacitor to turn into certain frequencies. LRC circuits can get much more complicated, but that is for another time.

Transformers

The principle role for an inductor is the transformer, a device that is used to modulate voltage across two circuits.

A Transformer is simply two inductors coupled via a piece of iron.

A transformer only works with an alternating current as a constant DC current will not produce a changing magnetic flux and thus wont create an EMF.

The voltage change across the transformer is proportional to the number of turns difference across the transformer.

N = Number of turns

Note about Inductors

Now, just as a capacitor is any break in your circuit, an inductor is ANY connection in your circuit. This is another problem that plagues analog circuits. Every wire is going to be creating a magnetic flux and every wire is going to be inductively coupled some how. This wont destroy your circuits, but it is something to be keen of when designing a circuit.

Formula Sheet

Faraday's Law

Transformers

The capacitor is another fundamental component. The prime role for the capacitor is to hold charge and store energy for later use. This property makes a capacitor very useful for filtering and storing power. The capacitor works by electrostatic attraction, when you have a potential across any two points the opposite charge attracts each other. As long as there is a potential across the capacitor charge will keep building up until the potential across the capacitor equals the potential across the circuit. Once this happens current ceases to flow. You can think of a capacitor as a break in a circuit, once the electrostatic force between the two points is at an equilibrium with the source, there is no force to drive this attraction of charge. No flow of charge means no current; because of this a capacitor is known to block DC current. A capacitor in series once charged will stop current flow. This also give a capacitor a complex impedance, the more a capacitor charge the more the electrostatic force resists flow and increases resistance across the capacitor. A capacitor in series will allow AC to pass through the capacitor since the capacitor is constantly charging and discharging.

The capacitance is a unit of how much a capacitor can "hold" which is a product of permittivity and area by the distance of the plates. Thus as area increases capacitance increases and as distance between the plates increases, capacitance decreases. Capacitors are measured in farads with one farad being 1 coulomb of charge across a capacitor with a potential of 1 volt across it. A coulomb is a large amount of charge so capacitors are usually measured in microfarads

The permittivity is a product of the material between the plates, in simple cases it is air, other cases it can be a sophisticated dielectric.

Now capacitance is a product of any two points in a circuit with a potential across them, separated by any distance. Although when d is a large value, capacitance is low, this still has an effect on a circuit. It is an important consideration how capacitance will affect your circuit since everything is a capacitor. Besides causing some unwanted affects, a capacitor can be a useful component.

Conservation of charge:
A Capacitor holds charge, unlike potential which is the product of an electrostatic force, charge is a "physical" thing, you cannot lose charge. This is very important since charge is a principle part of a capacitor.

Capacitor in Series:

Capacitors in series the capacitance add as the inverse so:

One advantage to using capacitors in series is that you can pass higher voltages across lower voltage capacitors (I.e you can pass 200V through 2 100V capacitors in series)

Capacitors in Parallel:

Capacitors in parallel the capacitance adds across the capacitors.

Capacitance is determined by the area of the capacitor, naturally more capacitors in parallel will have more area, which is why capacitance adds.

Work and Energy:

Capacitors can hold a charge, which means they can store energy. The energy associated with a capacitor is defined as:

This is useful in finding how much energy is stored in a capacitor, Power is the rate consumption of energy, thus by finding the energy stored in a capacitor you can find how much power it has.

Timing:

The largest use of a capacitor is in timing. It takes time to charge the capacitor, which can be used to your advantage as a timing source. The most simple resonator is a RC circuit. Capacitors are used in oscillating circuits which are used to produce specific frequencies. Also capacitors can modulate frequency due to the fact that charging a capacitor is time dependent.

This is a basic intro to the capacitor, I hope to go over more in the future.

Formula Sheet:

Capacitance:

Capacitor in series:

Capacitor in parallel:

Potential energy of a capacitor:

One of the most fundamental components is the resistor. The resistor allows one to control the current flow in a circuit. The base unit for a resistor is the ohm which is denoted by a capital omega.

The fundamental formula for a resistor is ohm's law which states V=IR.

The simplest circuit one can construct is a resistor across a voltage source.

A 1Kohm resistor across a source. The resistor is denoted by a squiggly line and the power source is denoted by the parallel lines. In this circuit we have a 1Kohm resistor across a varying DC source, at 10 volts the resistor will have 10miliamps running through it.

Ohm's law is shown by the following graph which shows current vs voltage. The slope is resistance.

(Y axis is in mA while X is in Volts)

This is very simple circuit yet, most complicated circuits can be redrawn as a equivalence circuit involving a single power source and a single resistor.

Resistors can be hooked up two ways, series and parallel.

Series:

Series is a type of circuit where everything is hooked up in a line, the charge that goes through one device goes through all the rest in that line, since charge has to conserved. The voltages across all the devices are not the same as they all add up to the source voltage.

In series, resistance adds up so that:

In this setup the two 1Kohm resistors act like 1 2Kohm resistor.

Other facts in series, the current through resistors in series is all the same, the current into one the device is the same as the other. The voltage is not the same though each device (unless same values). Two Resistors in series is known as a voltage divider.
The Vout is found by the following formula

This states that resistances in series add up, those two 1Kohm resistors form an equivalence 2Kohm resistor.

Parallel

In parallel the circuit branches off into two or more components. In parallel the voltages are the same across two devices, however the current is not.

The following circuit shows two resistors in parallel, their values are 1Kohm and 2Kohm respectively.

They both have the same potential through them, however their resistances draw differing amounts of current. Their equivalence resistance is shown by the following

As you can see the current through each resistor is different, however they add up to the total current through them

Parallel is useful when you want the same potential across many components. In parallel components can draw more power than in series.

The Resistor is a fundamental part of all circuits, it is essential to be able control current and source the correct amount of power to parts in your circuit.

Formula Sheet.
Ohm's Law

Power

Resistor in Series

Resistor in Parallel

Voltage Divider

I'd like to start off by defining electricity and its basic components.

Electricity is the flow of charge that can do useful work. Charge can be either positive or negative. A negative charge exists where there is an excess of electrons, a positive is where we have a deprivation of electrons. Electricity isn't always just the flow of electrons, it can be also considered the flow of ions or other charged sources. This flow of charge is caused by the interaction of charge on the atomic level. Remembering that like charges repel and opposites attract. These attractions and repulsions form the basis for electricity and the movement of charge. Conductors are materials that allow charge to flow freely through it, insulators do not. When we work with circuitry we use conductors to channel the flow of charge through our circuit to do useful work. One unit of charge is the Coulomb(C) which is 6.24 * 10^18 elementary (electron) charges. We also use Q to denote charge.

Charge is going to try and equalize itself when possible and minimize the energy of a system to reach equilibrium. opposite charges are going to cancel each other and like charges are going to spread out so that charge distribution is even throughout a system. This can be demonstrated by having two spheres, with +1Q charge and -1Q charge respectively, touching them and separating them will yield two spheres with 0Q charge on them. Likewise if you were to take two spheres with +3Q and +5Q each and touched them, they would both have +4Q charge each after this interaction.

Two charged spheres separated by a distance r will exert a force on each other. The electrostatic force is the force due to two charged particles and is the product of the magnitude of charge over the square of the distance between them and a constant k. This force is what drives electricity and makes charge want to flow.

Every charged particle has an electric field surrounding it, which propagates out positive and into negative charge. This field is useful in defining the force charged systems have on each other. We can find the electric field of a surface by applying Gauss's law which states that the electric field through an area A is equal to the charge enclosed divided by the permittivity of free space.

With a force, you can do work. Voltage (Electric potential) is the work due to a charge in an electric field and is defined by the dot product of electric field and distance.

Voltage is one of the fundamental components of useful electricity, its a definition that allows us not to worry about the sub atomic interactions of charge and allows us to work on a circuit on the macroscopic scale. Voltage is the work done by an electric field.

Another fundamental component is Current, which is the flow of charge per unit time (Q/t). For a potential (Voltage) to do meaningful work, charge must flow. The unit of current is the Ampere (I) and is the equivalence of 1 Coulomb of charge per Second.

The last meaningful definition is Resistance. If a circuit didn't have resistance the charge would flow from one terminal to another as fast a possible. This will give you an almost infinite current, and your circuit would vaporize. By adding a device that provides resistance, you can control your circuit and measure voltage and current at points in your system and even use them as variables to control you system.

All three fundamental components of electricity come together in Ohm's law which states that the voltage across a circuit is the product of the current through it by the resistance of your circuit.

With this definition you can control every aspect of your circuit.

Another useful definition is Power (Work per unit time) which is defined as

With these two equations you know how to control your system and how much power it is using to operate, the two essential parts to making a useful circuit.

With this basic knowledge in place you'll be able to understand even the most complicated systems.

Formula Sheet.

Formulas are simplified only to demonstrate principle, please look them up if you plan on doing meaningful calculations.

Dot Product =

Electrostatic Force (Coulomb's Law)

Electric Field

Gauss's Law

1 Amp = 1 Coulomb / Second
1 Omh = Resistance of a device with a potential of 1 volt across it and current 1 Amp flowing through it