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FHSST Physics/Electrostatics/Electric Fields

= Electric Fields =

We have learnt that objects that carry charge feel forces from all other charged objects. It is useful to determine what the effect of a charge would be at every point surrounding it. To do this we need some sort of reference.

We know that the force that one charge feels due to another depends on both charges (Q1 and Q2). How then can we talk about forces if we only have one charge? The solution to this dilemma is to introduce a test charge. We then determine the force that would be exerted on it if we placed it at a certain location. If we do this for every point surrounding a charge we know what would happen if we put a test charge at any location.

This map of what would happen at any point we call a field map. It is a map of the electric field due to a charge. It tells us how large the force on a test charge would be and in what direction the force would be.

Our map consists of the lines that tell us how the test charge would move if it were placed there.

Test Charge
This is the key to mapping out an electric field. The equation for the force between two electric charges has been shown earlier and is:

If we want to map the field for Q1 then we need to know exactly what would happen if we put Q2 at every point around Q1. But this obviously depends on the value of Q2. This is a time when we need to agree on a convention. What should Q2 be when we make the map? By convention we choose Q2 = + 1C.

This means that if we want to work out the effects on any other charge we only have to multiply the result for the test charge by the magnitude of the new charge.

The electric field strength is then just the force per unit of charge and has the same magnitude and direction as the force on our test charge but has different units:

The electric field is the force per unit of charge and hence has units of newtons per coulomb [N/C].

So to get the force the electric field exerts we use:

Notice we are just multiplying the electric field magnitude by the magnitude of the charge it is acting on.

What do field maps look like?
The maps depend very much on the charge or charges that the map is being made for. We will start off with the simplest possible case. Take a single positive charge with no other charges around it. First, we will look at what effects it would have on a test charge at a number of points.

Positive Charge Acting on Test Charge
At each point we calculate the force on a test charge, q, and represent this force by a vector.

We can see that at every point the positive test charge, q, would experience a force pushing it away from the charge, Q. This is because both charges are positive and so they repel. Also notice that at points further away the vectors are shorter. That is because the force is smaller if you are further away.

If the charge were negative we would have the following result.

Negative Charge Acting on Test Charge

Notice that it is almost identical to the positive charge case. This is important - the arrows are the same length because the magnitude of the charge is the same and so is the magnitude of the test charge. Thus the magnitude of the force is the same. The arrows point in the opposite direction because the charges now have opposite sign and so the test charge is attracted to the charge.

Now, to make things simpler, we draw continuous lines showing the path that the test charge would travel. This means we don't have to work out the magnitude of the force at many different points.

Electric Field Map due to a Positive Charge

Some important points to remember about electric fields:

 * There is an electric field at every point in space surrounding a charge.
 * Field lines are merely a representation - they are not real. When we draw them, we just pick convenient places to indicate the field in space.
 * Field lines always start at a right-angle (90o) to the charged object causing the field.
 * Field lines never cross!

Combined Charge Distributions
We look at the field of a positive charge and a negative charge placed next to each other. The net resulting field would be the addition of the fields from each of the charges. To start off with let us sketch the field maps for each of the charges as though it were in isolation.

Electric Field of Negative and Positive Charge in Isolation

Notice that a test charge starting off directly between the two would be pushed away from the positive charge and pulled towards the negative charge in a straight line. The path it would follow would be a straight line between the charges.

Now let's consider a test charge starting off a bit higher than directly between the charges. If it starts closer to the positive charge the force it feels from the positive charge is greater, but the negative charge does attract it, so it would move away from the positive charge with a tiny force attracting it towards the negative charge. As it gets further from the positive charge the force from the negative and positive charges change and they are equal in magnitude at equal distances from the charges. After that point the negative charge starts to exert a stronger force on the test charge. This means that the test charge moves towards the negative charge with only a small force away from the positive charge.

Now we can fill in the other lines quite easily using the same ideas. The resulting field map is:

Two Like Charges I: The Positive Case
For the case of two positive charges things look a little different. We can't just turn the arrows around the way we did before. In this case the test charge is repelled by both charges. This tells us that a test charge will never cross half way because the force of repulsion from both charges will be equal in magnitude.

The field directly between the charges cancels out in the middle. The force has equal magnitude and opposite direction. Interesting things happen when we look at test charges that are not on a line directly between the two.

We know that a charge the same distance below the middle will experience a force along a reflected line, because the problem is symmetric (i.e. if we flipped vertically it would look the same). This is also true in the horizontal direction. So we use this fact to easily draw in the next four lines.

Working through a number of possible starting points for the test charge we can show the electric field map to be:

Two Like Charges II: The Negative Case
We can use the fact that the direction of the force is reversed for a test charge if you change the sign of the charge that is influencing it. If we change to the case where both charges are negative we get the following result:

Parallel plates
One very important example of electric fields which is used extensively is the electric field between two charged parallel plates. In this situation the electric field is constant. This is used for many practical purposes and later we will explain how Millikan used it to measure the charge on the electron.

Field Map for Oppositely Charged Parallel Plates

This means that the force that a would feel at any point between the plates would be identical in magnitude and direction. The fields on the edges exhibit fringe effects, i.e. they bulge outwards. This is because a test charge placed here would feel the effects of charges only on one side (either left or right depending on which side it is placed). Test charges placed in the middle experience the effects of charges on both sides so they balance the components in the horizontal direction. This isn't the case on the edges.

What about the Strength of the Electric Field?
When we started making field maps we drew arrows to indicate the strength of the field and the direction. When we moved to lines you might have asked "Did we forget about the field strength?". We did not. Consider the case for a single positive charge again:

Notice that as you move further away from the charge the field lines become more spread out. In field map diagrams the closer field lines are together the stronger the field. This brings us to an interesting case. What is the electric field like if the object that is charged has an irregular shape.


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FHSST Physics/Electrostatics/Electrical Potential

= Electrical Potential =

Work Done and Energy Transfer in a Field
When a charged particle moves in an electric field work is done and energy transfers take place. This is exactly analogous to the case when a mass moves in a gravitational field such as that set up by any massive object.

Gravitational Case
A mass held at a height h above the ground has gravitational potential energy since, if released, it will fall under the action of the gravitational field. Once released, in the absence of friction, only the force of gravity acts on the mass and the mass accelerates in the direction of the force (towards the Earth's centre).

In this way, work is done by the field. When the mass falls a distance h (from point A to B), the work done is,

$$\begin{matrix}W &=& Fs\\&=& mgh\end{matrix}$$

In falling, the mass loses gravitational potential energy and gains kinetic energy.

Energy is conserved!

The work done by the field is equal to the energy transferred,

$$\begin{matrix}W = \mathrm{Gain\ in\ }E_k = \mathrm{Loss\ in\ }E_p\qquad\mathrm{(a\ falling\ mass)}\end{matrix}$$

Electrical Case
A charge in an electric field has electrical potential energy since, if released, it will move under the action of the electric field. When released, in the absence of friction, only the electric force acts on the charge and the charge accelerates in the direction of the force (for positive charges the force and acceleration are in the direction of the electric field, while negative charges experience a force and acceleration in the opposite direction to the electric field.) Consider a positive charge +Q placed in the uniform electric field between oppositely charged parallel plates.

The positive charge will be repelled by the positive plate and attracted by the negative plate (i.e. it will move in the direction of the electric field lines). In this way, work is done by the field. In moving the charge a distance s in the electric field, the work done is,

$$\begin{matrix}W &=& Fs\\&=& QEs\qquad\mathrm{since\ }E={F\over Q}.\end{matrix}$$

In the process of moving, the charge loses electrical potential energy and gains kinetic energy. The work done by the field is equal to the energy transferred,

$$\begin{matrix}W &=& \mathrm{Gain\ in\ }E_k = \mathrm{Loss\ in\ }E_p\qquad\mathrm{(charge\ moving\ under\ the\ influence\ of\ an\ electric\ field)}\end{matrix}$$

Gravitational Case
In order to return the mass m in Figure 12.1 to its original position (i.e. lift it a distance h from B back to A) we have to apply a force mg to balance the force of gravity. An amount of work mgh is done by the lifter. In the process, the mass gains gravitational potential energy,

$$\begin{matrix}mgh &=& \mathrm{Gain\ in\ }E_p\qquad\mathrm{(lifting\ a\ mass)}\end{matrix}$$

Electrical Case
In order to return the charge in Figure 12.2 to its original position (i.e. from B back to A) we have to exert a force QE on the charge to balance the force exerted on it by the electric field. An amount of work QEs is done by us. In the process, the charge gains electrical potential energy,

$$\begin{matrix}QEs &=& \mathrm{Gain\ in\ }E_p\qquad\mathrm{(charge\ moved\ against\ an\ electric\ field)}\end{matrix}$$

In summary, '''when an object moves under the influence of a field, the field does work and potential energy is transferred into kinetic energy. Potential energy is lost, while kinetic energy is gained. When an object is moved against a field we have to do work and the object gains potential energy.'''

Worked Example 62 Work done and energy transfers in a field
Question: A charge of +5nC is moved a distance of 4 cm against a uniform electric field of magnitude $$2\times10^{12}\mathrm{N.C^{-1}}$$ from A to B.

(a) Calculate the work done in moving the charge from A to B. (b) The charge is now released and returns to A. Calculate the kinetic energy of the charge at A.

Answer: (a) Step 1 :

We are given the values of the charge, the field and the distance the charge must move. All are in the correct units.

Step 2 :

Since the charge is positive we have to do work to move it from A to B (since this is against the field). This work is given by,

$$\begin{matrix}W &=& QEs\\&=& (5\times10^{-9})(2\times10^{12})(0.04)\\&=& 400\ \mathrm{J}\end{matrix}$$

(b)

Step 3 :

When released the charge moves under the influence of the electric field and returns to A. Work is now done by the field and the work done is equal to the kinetic energy gained,

$$\begin{matrix}\mathrm{Gain\ in\ }E_k &=& QEs\\&=& (5\times10^{-9})(2\times10^{12})(0.04)\\&=& 400\ \mathrm{J}\end{matrix}$$

Since the charge started at rest, the gain in kinetic energy is the final kinetic energy,

$$\begin{matrix}E_k^{\mathrm{at\ A}} &=& 400\ \mathrm{J}\end{matrix}$$

Electrical Potential Difference
Consider a positive test charge + Q placed at A in the electric field of another positive point charge.

The test charge moves towards B under the influence of the electric field of the other charge. In the process the test charge loses electrical potential energy and gains kinetic energy. Thus, at A, the test charge has more potential energy than at B - A is said to have a higher electrical potential than B. The potential energy of a charge at a point in a field is defined as the work required to move that charge from infinity to that point.

The potential difference between two points in an electric field is defined as the work required to move a unit positive test charge from the point of lower potential to that of higher potential. If an amount of work W is required to move a charge Q from one point to another, then the potential difference between the two points is given by,

$$\begin{matrix}V &=&{W\over Q}\qquad \mathrm{unit:J.C^{-1}\ or\ V\ (the\ volt)}\end{matrix}$$

From this equation it follows that one volt is the potential difference between two points in an electric field if one joule of work is done in moving one coulomb of charge from the one point to the other.

Worked Example 63 Potential difference
Question: A positively charged object Q is placed as shown in the sketch. The potential difference between two points A and B is $$4\times10^{-4}\ \mathrm{V}$$

(a) Calculate the change in electrical potential energy of a +2nC charge when it moves from A to B. (b) Which point, A or B, is at the higher electrical potential? Explain. (c) If this charge were replaced with another of charge -2nC, in what way would its change in energy be affected?

Answer: (a) The electrical potential energy of the positive charge decreases as it moves from A to B since it is moving in the direction of the electric field produced by the object Q. This loss in potential energy is equal to the work done by the field,

$$\begin{matrix}\mathrm{Loss\ in\ Electrical\ Potential\ Energy} &=& W\\&=&VQ\qquad \mathrm{(Since\ }V={W\over Q})\\&=& (4\times10^{-4})(2\times10^{-9})\\&=& 8\times10^{-13}\ \mathrm{J}\end{matrix}$$

(b) Point A is at the higher electrical potential since work is required by us to move a positive test charge from B to A. (c) If the charge is replaced by one of negative charge, the electrical potential energy of the charge will increase in moving from A to B (in this case we would have to do work on the charge).

As an example consider the electric field between two oppositely charged parallel plates a distance d apart maintained at a potential difference V.

This electric field is uniform so that a charge placed anywhere between the plates will experience the same force. Consider a positive test charge Q placed at point O just off the surface of the negative plate. In order to move it towards the positive plate we have to apply a force QE. The work done in moving the charge from the negative to the positive plate is,

$$\begin{matrix}W &=& Fs \\&=& QEd,\end{matrix}$$

but from the definition of electrical potential,

$$\begin{matrix}W &=& VQ.\end{matrix}$$

Equating these two expressions for the work done,

$$\begin{matrix}QEd &=& VQ,\end{matrix}$$

and so, rearranging,

$$\begin{matrix}E &=& {V\over d}.\qquad \end{matrix}$$

Worked Example 64 Parallel plates
Question: Two charged parallel plates are at a distance of 180 mm from each other. The potential difference between them is $$3600\ \mathrm{V}$$ as shown in the diagram.

(a) If a small oil drop of negligible mass, carrying a charge of $$+6.8\times10^{-9}\ \mathrm{C}$$, is placed between the plates at point X, calculate the magnitude and direction of the electrostatic force exerted on the droplet.

(b) If the droplet is now moved to point Y, would the force exerted on it be bigger, smaller or the same as in (a)?

Answer: (a)

Step 1 :

First find the electric field strength between the plates,

$$\begin{matrix}E &=& {V \over d}\\&=& {3600\over 0.180}\\&=& 20000\ \mathrm{N.C^{-1}\ from\ the\ positive\ to\ the\ negative\ plate}\end{matrix}$$

Step 2 :

Now the force exerted on the charge at X is,

$$\begin{matrix}F &=& QE\\&=& (6.8\times10^{-9})(20000)\\&=& 1.36\times10^{-4}\ \mathrm{down}\end{matrix}$$

(b)

Step 3 :

The same. Since the electric field strength is uniform, the force exerted on a charge is the same at all points between the plates.

Millikan's Oil-drop Experiment
Robert Millikan measured the charge on an electron by studying the motion of charged oil drops between oppositely charged parallel plates.

Consider one such negative drop between the plates in Figure 12.3. Since this drop is negative, the electric field exerts an upward force on the drop. In addition to this upward force, gravity exerts a downward force on the drop. Millikan adjusted the electric field strength between the plates by varying the potential difference applied across the plates. In this way, Millikan was able to bring the drops to rest. *EDIT* Millikan's experiment was meant to have the drops fall at a constant rate. At this constant rate the force of the earth on the drop and the force of the field on the drop are equal *End EDIT*

$$\begin{matrix}F_{\mathrm{up}} &=& F_{\mathrm{down}}\\QE &=& mg\end{matrix}$$

Since $$E={V \over d}$$

$$\begin{matrix}Q{V \over d} &=& mg,\\\end{matrix}$$

and, therefore,

$$\begin{matrix}Q &=& {mgd\over V}\end{matrix}$$

Millikan found that all drops had charges which were multiples of $$1.6\times10^{-19}\ \mathrm{C}$$. Since objects become charged by gaining or losing electrons, the charge on an electron must be $$-1.6\times10^{-19}\ \mathrm{C}$$. The magnitude of the electron's charge is denoted by e,

$$\begin{matrix}e &=& 1.6\times10^{-19}\ \mathrm{C}\end{matrix}$$

Worked Example 65 Charge
Question: A metal sphere carries a charge of $$+3.2\times10^{-8}\ \mathrm{C}$$. How many electrons did it have to lose to attain its charge?

Answer: Since the sphere is positive it lost electrons in the process of charging (when an object loses negative charges it is left positive). In fact, it lost,

$$\begin{matrix}{3.2\times10^{-8}\over 1.6\times10^{-19}}&=& 2\times10^{11}\ \mathrm{electrons}\end{matrix}$$

Worked Example 66 Millikan oil-drop experiment
Question: In a Millikan-type experiment a positively charged oil drop is placed between two horizontal plates, 20 mm apart, as shown.

The potential difference across the plates is 4000V. The drop has a mass of $$1.2\times10^{-14}$$ and a charge of $$8\times10^{-19}$$. (a) Draw the electric field pattern between the two plates. (b) Calculate:

 * 1) the electric field intensity between the two plates.
 * 2) the magnitude of the gravitational force acting on the drop.
 * 3) the magnitude of the Coulomb force acting on the drop.

(c) The drop is observed through a microscope. What will the drop be seen to do? Explain. (d) Without any further calculations, give two methods that could be used to make the drop remain in a fixed position.

Answer: (a)

(b) 1.

$$\begin{matrix}E &=& {V \over d}\\&=& {4000 \over 0.02}\\&=& 2\times 10^5\ \mathrm{V.m^{-1}\ up}\\\end{matrix}$$

2.

$$\begin{matrix}F_{\mathrm{grav}} &=& mg\\&=& (1.2\times10^{-14})(10)\\&=& 1.2\times 10^{-13}\mathrm{N}\end{matrix}$$

3.

$$\begin{matrix}F_{\mathrm{Coulomb}} &=& QE \\&=& (8\times10^{-19})(s\times10^5)\\&=& 1.6\times10^{-13}\mathrm{N}\end{matrix}$$

(c) Since $$F_{up}>F_{down}$$, the drop accelerates upwards.

(d) The Coulomb force can be decreased by decreasing the electric field strength between the plates. Since $$E={V\over d}$$, this can be done either by increasing d or decreasing V.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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FHSST Physics/Electrostatics/Summary

= Important Equations and Quantities =

title: FHSST Physics/Electrostatics/Summary


text:
FHSST Physics/Electronics

= Electronics =

title: FHSST Physics/Electronics


text: Template:FHSST Physics/Electronics

title: Template:FHSST Physics/Electronics


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FHSST Physics/Electronics/Capacitive and Inductive Circuits

A capacitor
A capacitor is simply two conductors separated by a dielectric (insulator). A capacitor (historically known as a "condenser") is a device that stores energy in an electric field.

The most common kind of capacitor has two parallel plates with a (fairly) uniform electric field between the plates.

A battery can be used to fill one end of the capacitor with electrons and drain electrons from the other end of the capacitor. This is known as charging. Charging a capacitor creates a charge imbalance between the two plates and creates a voltage that stops the capacitor from charging. When capacitors are connected to a battery, current flows only until the capacitor becomes charged to the same voltage as the battery. When the capacitor is charged to the same voltage as the battery, current stops flowing—the capacitor acts like an open circuit. It is as if the capacitor gained infinite resistance.

If we pull a capacitor out of the circuit, it retains the voltage to which it was charged. (In real capacitors, the excess electrons on one plate slowly leak over to the other plate. But the higher the quality of the capacitor, the closer it acts like an "ideal capacitor". An "ideal capacitor" would hold that charge forever. )

Just as the capacitor charges it can be discharged.

An inductor
If we are going to talk of inductive circuits we need a definition of a inductor.

An inductor is simply a coil of wire (or some other conductive material). An inductor is a device which stores energy in a magnetic field.

An inductor only resists changes in current. An ideal inductor does not offer any resistance to direct current, except when the current is switched on and off, in which case it makes the change more gradual. However, all real-world inductors are constructed from material with finite electrical resistance, which opposes even direct current.

Whenever current flows, it creates a magnetic field proportional to the current. (In other words, whenever electrons move, they create a magnetic field—proportional to both how many electrons there are, and how fast their average speed is). Coiling the wire concentrates that field inside the coil.

A changing magnetic field always induces a voltage in any wire.

When we apply a voltage source to the inductor—for example, when we energize the field winding of an electric fan by plugging it in—the current will flow through the coil, creating a magnetic field.

As more and more current flows, the magnetic field also increases proportionally. The changing magnetic field creates a "back-emf" (the voltage across the coil). That same wire, when straightened out, would act like a short circuit—but when formed into a coil, much less current goes through it.

If we applied a constant DC voltage to this coil, the current would keep increasing more and more, until something failed.

As you know, the voltage supplied by the wall socket isn't DC. It returns to zero then increases in the opposite direction many times a second.

When the voltage returns to zero, the current through the inductor stays constant—the constant current causes a constant magnetic field, the constant magnetic field causes zero "back-emf". When the supply voltage reverses direction, the current through the coil decreases, causing the magnetic field to decrease. Because the magnetic field is decreasing, it induces a "back-emf" voltage across the inductor in the opposite direction than when the magnetic field was increasing. (Something interesting happens after the magnetic field decreases all the way to zero, but we don't have time to talk about that).

To summarize, at first, the current through the coil goes from + to -, just like a resistor or a charging capacitor. But just after the voltage reverses, the current continues going in the same direction, which is now - to +. This makes inductors unlike any other component known to mankind. We say that "in an inductor, the voltage leads the current" or ELI.

Normally inductors are made of copper wire, but not always (Example: aluminum wire, or spiral pattern etched on circuit board). The material around and within the coil affects its properties common types are air-core (only a coil of wire), iron-core, and ferrite core. Iron and ferrite types are more efficient because they conduct the magnetic field much better than air. Ferrite is more efficient than iron because stray electricity cannot flow through it.

Some inductors have more than a core, which is just a rod the coil is formed about. Some are formed like transformers, using two E-shaped pieces facing each other, the wires wound about the central leg of the E's. The E's are made of laminated iron/steel or ferrite.

Important qualities of an inductor:

There are several important properties for an inductor.

 * Current carrying capacity is determined by wire thickness.
 * Q, or quality, is determined by the uniformity of the windings, as well as the core material and how thoroughly it surrounds the coil.
 * Last but not least, the inductance of the coil.

The inductance is determined by several factors.

 * coil shape: short and squat is best
 * core material
 * windings: winding in opposite directions will cancel out the inductance effect, and you will have only a resistor.

A comparison of capacitors and inductors

 * In capacitors, current leads voltage.
 * In inductors, voltage leads current.

I remember this by saying "ELI the ICE man".

See:
 * Electronics/Inductors
 * Electronics/Inductor Construction
 * Electronics/LR
 * Electronics/Impedance
 * Electrodynamics
 * w:Inductor


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FHSST Physics/Electronics/Filters and Signal Tuning

= Filters and Signal Tuning =

Author's Note: I think this relies on an understanding of second order ODEs and thats beyond the scope of the maths syllabus - we can put something high level but there is no way they'll understand it properly - surely we should teach as little phenomonology as possible - the waves chapter has a ton of it already


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FHSST Physics/Electronics/Active Circuit Elements

= active circuit elements, diode, LED and field effect transistor, operational amplifier =

Diode
A diode functions as the electronic version of a one-way valve. By restricting the direction of movement of charge carriers, it allows an electric current to flow in one direction, but blocks it in the opposite direction. It is a one-way street for current.

Diode behavior is analogous to the behavior of a hydraulic device called a check valve. A check valve allows fluid flow through it in one direction only:

Check valves are essentially pressure-operated devices: they open and allow flow if the pressure across them is of the correct "polarity" to open the gate (in the analogy shown, greater fluid pressure on the right than on the left). If the pressure is of the opposite "polarity," the pressure difference across the check valve will close and hold the gate so that no flow occurs.

Like check valves, diodes are essentially "pressure-" operated (voltage-operated) devices. The essential difference between forward-bias and reverse-bias is the polarity of the voltage dropped across the diode. Let's take a closer look at the simple battery-diode-lamp circuit shown earlier, this time investigating voltage drops across the various components:

When the diode is forward-biased and conducting current, there is a small voltage dropped across it, leaving most of the battery voltage dropped across the lamp. When the battery's polarity is reversed and the diode becomes reverse-biased, it drops all of the battery's voltage and leaves none for the lamp. If we consider the diode to be a sort of self-actuating switch (closed in the forward-bias mode and open in the reverse-bias mode), this behavior makes sense. The most substantial difference here is that the diode drops a lot more voltage when conducting than the average mechanical switch (0.7 volts versus tens of millivolts).

This forward-bias voltage drop exhibited by the diode is due to the action of the depletion region formed by the P-N junction under the influence of an applied voltage. When there is no voltage applied across a semiconductor diode, a thin depletion region exists around the region of the P-N junction, preventing current through it. The depletion region is for the most part devoid of available charge carriers and so acts as an insulator:

LED
A light-emitting diode (LED) is a semiconductor device that emits light when charge flows in the correct direction through it. If you apply a voltage to force current to flow in the direction the LED allows it will light up.

This notation of having two small arrows pointing away from the device is common to the schematic symbols of all light-emitting semiconductor devices. Conversely, if a device is light-activated (meaning that incoming light stimulates it), then the symbol will have two small arrows pointing toward it. It is interesting to note, though, that LEDs are capable of acting as light-sensing devices: they will generate a small voltage when exposed to light, much like a solar cell on a small scale. This property can be gainfully applied in a variety of light-sensing circuits.

The color depends on the semiconducting material used to construct the LED, and can be in the near-ultraviolet, visible or infrared part of the electromagnetic spectrum.

Physical function
Because LEDs are made of different chemical substances than normal rectifying diodes, their forward voltage drops will be different. Typically, LEDs have much larger forward voltage drops than rectifying diodes, anywhere from about 1.6 volts to over 3 volts, depending on the color. Typical operating current for a standard-sized LED is around 20 mA. When operating an LED from a DC voltage source greater than the LED's forward voltage, a series-connected "dropping" resistor must be included to prevent full source voltage from damaging the LED. Consider this example circuit:

With the LED dropping 1.6 volts, there will be 4.4 volts dropped across the resistor. Sizing the resistor for an LED current of 20 mA is as simple as taking its voltage drop (4.4 volts) and dividing by circuit current (20 mA), in accordance with Ohm's Law (R = E/I). This gives us a figure of 220 Ω. Calculating power dissipation for this resistor, we take its voltage drop and multiply by its current (P=IE), and end up with 88 mW, well within the rating of a 1/8 watt resistor. Higher battery voltages will require larger-value dropping resistors, and possibly higher-power rating resistors as well. Consider this example for a supply voltage of 24 volts:

Here, the dropping resistor must be increased to a size of 1.12 kΩ in order to drop 22.4 volts at 20 mA so that the LED still receives only 1.6 volts. This also makes for a higher resistor power dissipation: 448 mW, nearly one-half a watt of power! Obviously, a resistor rated for 1/8 watt power dissipation or even 1/4 watt dissipation will overheat if used here.

Dropping resistor values need not be precise for LED circuits. Suppose we were to use a 1 kΩ resistor instead of a 1.12 kΩ resistor in the circuit shown above. The result would be a slightly greater circuit current and LED voltage drop, resulting in a brighter light from the LED and slightly reduced service life. A dropping resistor with too much resistance (say, 1.5 kΩ instead of 1.12 kΩ) will result in less circuit current, less LED voltage, and a dimmer light. LEDs are quite tolerant of variation in applied power, so you need not strive for perfection in sizing the dropping resistor.

Also because of their unique chemical makeup, LEDs have much, much lower peak-inverse voltage (PIV) ratings than ordinary rectifying diodes. A typical LED might only be rated at 5 volts in reverse-bias mode. Therefore, when using alternating current to power an LED, you should connect a protective rectifying diode in series with the LED to prevent reverse breakdown every other half-cycle:

Light emission
The wavelength of the light emitted, and therefore its color, depends on the materials forming the pn junction. A normal diode, typically made of silicon or germanium, emits invisible far-infrared light (so it can't be seen), but the materials used for an LED have emit light corresponding to near-infrared, visible or near-ultraviolet frequencies.

Considerations in use
Unlike incandescent light bulbs, which can operate with either AC or DC, LEDs require a DC supply of the correct electrical polarity. When the voltage across the pn junction is in the correct direction, a significant current flows and the device is said to be forward biased. The voltage across the LED in this case is fixed for a given LED and is proportional to the energy of the emitted photons. If the voltage is of the wrong polarity, the device is said to be reverse biased, very little current flows, and no light is emitted.

Because the voltage versus current characteristics of an LED are much like any diode, they can be destroyed by connecting them to a voltage source much higher than their turn on voltage.

The voltage drop across a forward biased LED increases as the amount of light emitted increases because of the optical power being radiated. One consequence is that LEDs of the same type can be readily operated in parallel. The turn-on voltage of an LED is a function of the color, a higher forward drop is associated with emitting higher energy (bluer) photons. The reverse voltage that most LEDs can sustain without damage is usually only a few volts. Some LED units contain two diodes, one in each direction and each a different color (typically red and green), allowing two-color operation or a range of colors to be created by altering the percentage of time the voltage is in each polarity.

LED materials
LED development began with infrared and red devices made with gallium arsenide. Advances in materials science have made possible the production of devices with ever shorter wavelengths, producing light in a variety of colors.

Conventional LEDs are made from a variety of inorganic minerals, producing the following colors:

 * aluminium gallium arsenide (AlGaAs): red and infrared
 * gallium arsenide/phosphide (GaAsP): red, orange-red, orange, and yellow
 * gallium nitride (GaN): green, pure green (or emerald green), and blue
 * gallium phosphide (GaP): red, yellow and green
 * zinc selenide (ZnSe): blue
 * indium gallium nitride (InGaN): bluish-green and blue
 * silicon carbide (SiC): blue
 * diamond (C): ultraviolet
 * silicon (Si) - under development

Note to self: The above list is taken from public sources, but at least one LED given as blue does not produce blue light. (There is a good chance that almost none do, because of the higher frequency of blue.) This is a common problem in daily life due to the majority of mankind being ignorant of colour theory and conflating blue with light blue with cyan, the latter often called "sky blue". A cyan LED may be distinguished from a blue LED in that adding a yellow phosphor to the output makes green, rather than white light. And often aqua is called blue-green when in actuality the latter is cyan, and light cyan-green would be aqua. What adds to the confusion is that cyan LEDs are enclosed in blue plastic. A great amount of work is needed to dispel these intuitive myths of colour mixing before accurate descriptions of physical phenomena and their production can happen. - This needs to be sorted out

Blue and white LEDs and Other colors
Commercially viable blue LEDs based invented by Shuji Nakamura while working in Japan at Nichia Corporation in 1993 and became widely available in the late 1990s. They can be added to existing red and green LEDs to produce white light.

Most "white" LEDs in production today use a 450 nm & 470 nm blue GaN (gallium nitride) LED covered by a yellowish phosphor coating usually made of cerium doped yttrium aluminium garnet (YAG:Ce) crystals which have been powdered and bound in a type of viscous adhesive. The LED chip emits blue light, part of which is converted to yellow by the YAG:Ce. The single crystal form of YAG:Ce is actually considered a scintillator rather than a phosphor. Since yellow light stimulates the red and green receptors of the eye, the resulting mix of blue and yellow light gives the appearance of white.

The newest method used to produce white light LEDs uses no phosphors at all and is based on homoepitaxially grown zinc selenide (ZnSe) on a ZnSe substrate which simultaneously emits blue light from its active region and yellow light from the substrate.

Other colors
Recent color developments include pink and purple. They consist of one or two phosphor layers over a blue LED chip. The first phosphor layer of a pink LED is a yellow glowing one, and the second phosphor layer is either red or orange glowing. Purple LEDs are blue LEDs with an orange glowing phosphor over the chip. Some pink LEDs have run into issues. For example, some are blue LEDs painted with fluorescent paint or fingernail polish that can wear off, and some are white LEDs with a pink phosphor or dye that unfortunately fades after a short tme.

Ultraviolet, blue, pure green, white, pink and purple LEDs are relatively expensive compared to the more common reds, oranges, greens, yellows and infrareds and are thus less commonly used in commercial applications.

The semiconducting chip is encased in a solid plastic lens, which is much tougher than the glass envelope of a traditional light bulb or tube. The plastic may be colored, but this is only for cosmetic reasons and does not affect the color of the light emitted.

Operational parameters and efficiency
Most typical LEDs are designed to operate with no more than 30-60 milliwatts of electrical power. It is projected that by 2005, 10-watt units will be available. These devices will produce about as much light as a common 50-watt incandescent bulb, and will facilitate use of LEDs for general illumination needs.

Organic light-emitting diodes (OLEDs)
If the emissive layer material of an LED is an organic compound, it is known as an Organic Light Emitting Diode (OLED). To function as a semiconductor, the organic emissive material must have conjugated pi bonds. The emissive material can be a small organic molecule in a crystalline phase, or a polymer. Polymer materials can be flexible such LEDs are known as PLEDs or FLEDs.

Compared with regular LEDs, OLEDs are lighter and polymer LEDs can have the added benefit of being flexible. Some possible future applications of OLEDs could be:

 * Light sources
 * Wall decorations
 * Luminous cloth
 * Computer screens
 * Televisions

LED applications
Here is a list of known applications for LEDs, some of which are further elaborated upon in the following text:

 * in general, commonly used as information indicators in various types of embedded systems (many of which are listed below)
 * thin, lightweight message displays, e.g. in public information signs (at airports and railway stations, among other places)
 * status indicators, e.g. on/off lights on professional instruments and consumers audio/video equipment
 * infrared LEDs in remote controls (for TVs, VCRs, etc.)
 * clusters in traffic signals, replacing ordinary bulbs behind colored glass
 * car indicator lights and bicycle lighting also for pedestrians to be seen by car traffic
 * calculator and measurement instrument displays (seven segment displays), although now mostly replaced by LCDs
 * red or yellow LEDs are used in indicator and [alpha]numeric displays in environments where night vision must be retained: aircraft cockpits, submarine and ship bridges, astronomy observatories, and in the field, e.g. night time animal watching and military field use
 * red or yellow LEDs are also used in photographic darkrooms, for providing lighting which does not lead to unwanted exposure of the film
 * illumination, e.g. flashlights (a.k.a. torches, UK), and backlights for LCD screens
 * signaling/emergency beacons and strobes
 * movement sensors, e.g. in mechanical and optical computer mice and trackballs
 * in LED printers, e.g. high-end color printers

LEDs offer benefits in terms of maintenance and safety.

 * The typical working lifetime of a device, including the bulb, is ten years, which is much longer than the lifetimes of most other light sources.
 * LEDs fail by dimming over time, rather than the abrupt burn-out of incandescent bulbs.
 * LEDs give off less heat than incandescent light bulbs and are less fragile than fluorescent lamps.
 * Since an individual device is smaller than a centimetre in length, LED-based light sources used for illumination and outdoor signals are built using clusters of tens of devices.

Because they are monochromatic, LED lights have great power advantages over white lights where a specific color is required. Unlike the white lights, the LED does not need a filter that absorbs most of the emitted white light. Colored fluorescent lights are made, but they are not widely available. LED lights are inherently colored, and are available in a wide range of colors. One of the most recently introduced colors is the emerald green (bluish green, about 500 nm) that meets the legal requirements for traffic signals and navigation lights.

There are applications that specifically require light that does not contain any blue component. Examples are photographic darkroom safe lights, illumination in laboratories where certain photo-sensitive chemicals are used, and situations where dark adaptation (night vision) must be preserved, such as cockpit and bridge illumination, observatories, etc. Yellow LED lights are a good choice to meet these special requirements because the human eye is more sensitive to yellow light.

Transistor
The transistor is a solid state semiconductor device used for amplification and switching, and has three terminals. The transistor itself does not amplify current though, which is a common misconception, but a small current or voltage applied to one terminal controls the current through the other two, hence the term transistor a voltage- or current-controlled resistor. It is the key component in all modern electronics. In digital circuits, transistors are used as very fast electrical switches, and arrangements of transistors can function as logic gates, RAM-type memory and other devices. In analog circuits, transistors are essentially used as amplifiers.

Transistor was also the common name in the sixties for a transistor radio, a pocket-sized portable radio that utilized transistors (rather than vacuum tubes) as its active electronics. This is still one of the dictionary definitions of transistor.

The only functional difference between a PNP transistor and an NPN transistor is the proper biasing (polarity) of the junctions when operating. For any given state of operation, the current directions and voltage polarities for each type of transistor are exactly opposite each other.

Bipolar transistors work as current-controlled current regulators. In other words, they restrict the amount of current that can go through them according to a smaller, controlling current. The main current that is controlled goes from collector to emitter, or from emitter to collector, depending on the type of transistor it is (PNP or NPN, respectively). The small current that controls the main current goes from base to emitter, or from emitter to base, once again depending on the type of transistor it is (PNP or NPN, respectively). According to the confusing standards of semiconductor symbology, the arrow always points against the direction of electron flow:

Bipolar transistors are called bipolar because the main flow of electrons through them takes place in two types of semiconductor material: P and N, as the main current goes from emitter to collector (or vice versa). In other words, two types of charge carriers - electrons and holes - comprise this main current through the transistor.

As you can see, the controlling current and the controlled current always mesh together through the emitter wire, and their electrons always flow against the direction of the transistor's arrow. This is the first and foremost rule in the use of transistors: all currents must be going in the proper directions for the device to work as a current regulator. The small, controlling current is usually referred to simply as the base current because it is the only current that goes through the base wire of the transistor. Conversely, the large, controlled current is referred to as the collector current because it is the only current that goes through the collector wire. The emitter current is the sum of the base and collector currents, in compliance with Kirchhoff's Current Law.

If there is no current through the base of the transistor, it shuts off like an open switch and prevents current through the collector. If there is a base current, then the transistor turns on like a closed switch and allows a proportional amount of current through the collector. Collector current is primarily limited by the base current, regardless of the amount of voltage available to push it. The next section will explore in more detail the use of bipolar transistors as switching elements.

Importance
The transistor is considered by many to be one of the greatest discoveries or inventions in modern history, ranking with banking and the printing press. Key to the importance of the transistor in modern society is its ability to be produced in huge numbers using simple techniques, resulting in vanishingly small prices. Computer "chips" consist of millions of transistors and sell for rands, with per-transistor costs in the thousandths-of-cents.

The low cost has meant that the transistor has become an almost universal tool for non-mechanical tasks. Whereas a common device, say a refrigerator, would have used a mechanical device for control, today it is often less expensive to simply use a few million transistors and the appropriate computer program to carry out the same task through "brute force". Today transistors have replaced almost all electromechanical devices, most simple feedback systems, and appear in huge numbers in everything from computers to cars.

Hand-in-hand with low cost has been the increasing move to "digitizing" all information. With transistorized computers offering the ability to quickly find (and sort) digital information, more and more effort was put into making all information digital. Today almost all media in modern society is delivered in digital form, converted and presented by computers. Common "analog" forms of information such as television or newspapers spend the vast majority of their time as digital information, being converted to analog only for a small portion of the time.

The transistor as a switch
Because a transistor's collector current is proportionally limited by its base current, it can be used as a sort of current-controlled switch. A relatively small flow of electrons sent through the base of the transistor has the ability to exert control over a much larger flow of electrons through the collector. Suppose we had a lamp that we wanted to turn on and off by means of a switch. Such a circuit would be extremely simple:

For the sake of illustration, let's insert a transistor in place of the switch to show how it can control the flow of electrons through the lamp. Remember that the controlled current through a transistor must go between collector and emitter. Since it's the current through the lamp that we want to control, we must position the collector and emitter of our transistor where the two contacts of the switch are now. We must also make sure that the lamp's current will move against the direction of the emitter arrow symbol to ensure that the transistor's junction bias will be correct:

In this example I happened to choose an NPN transistor. A PNP transistor could also have been chosen for the job, and its application would look like this:

The choice between NPN and PNP is really arbitrary. All that matters is that the proper current directions are maintained for the sake of correct junction biasing (electron flow going against the transistor symbol's arrow).

Going back to the NPN transistor in our example circuit, we are faced with the need to add something more so that we can have base current. Without a connection to the base wire of the transistor, base current will be zero, and the transistor cannot turn on, resulting in a lamp that is always off. Remember that for an NPN transistor, base current must consist of electrons flowing from emitter to base (against the emitter arrow symbol, just like the lamp current). Perhaps the simplest thing to do would be to connect a switch between the base and collector wires of the transistor like this:

If the switch is open, the base wire of the transistor will be left "floating" (not connected to anything) and there will be no current through it. In this state, the transistor is said to be cutoff. If the switch is closed, however, electrons will be able to flow from the emitter through to the base of the transistor, through the switch and up to the left side of the lamp, back to the positive side of the battery. This base current will enable a much larger flow of electrons from the emitter through to the collector, thus lighting up the lamp. In this state of maximum circuit current, the transistor is said to be saturated.

Of course, it may seem pointless to use a transistor in this capacity to control the lamp. After all, we're still using a switch in the circuit, aren't we? If we're still using a switch to control the lamp - if only indirectly - then what's the point of having a transistor to control the current? Why not just go back to our original circuit and use the switch directly to control the lamp current?

There are a couple of points to be made here, actually. First is the fact that when used in this manner, the switch contacts need only handle what little base current is necessary to turn the transistor on, while the transistor itself handles the majority of the lamp's current. This may be an important advantage if the switch has a low current rating: a small switch may be used to control a relatively high-current load. Perhaps more importantly, though, is the fact that the current-controlling behavior of the transistor enables us to use something completely different to turn the lamp on or off. Consider this example, where a solar cell is used to control the transistor, which in turn controls the lamp:

Or, we could use a thermocouple to provide the necessary base current to turn the transistor on:

Even a microphone of sufficient voltage and current output could be used to turn the transistor on, provided its output is rectified from AC to DC so that the emitter-base PN junction within the transistor will always be forward-biased:

The point should be quite apparent by now: any sufficient source of DC current may be used to turn the transistor on, and that source of current need only be a fraction of the amount of current needed to energize the lamp. Here we see the transistor functioning not only as a switch, but as a true amplifier: using a relatively low-power signal to control a relatively large amount of power. Please note that the actual power for lighting up the lamp comes from the battery to the right of the schematic. It is not as though the small signal current from the solar cell, thermocouple, or microphone is being magically transformed into a greater amount of power. Rather, those small power sources are simply controlling the battery's power to light up the lamp.

Field-Effect Transistor (FET)
Note: Schematic can be found under GFDL on wikipedia

The schematic symbols for p- and n-channel MOSFETs. The symbols to the right include an extra terminal for the transistor body (allowing for a seldom-used channel bias) whereas in those to the left the body is implicitly connected to the source.

The most common variety of field-effect transistors, the enhancement-mode MOSFET (metal-oxide semiconductor field-effect transistor) consists of a unipolar conduction channel and a metal gate separated from the main conduction channel by a thin layer of (SiO2) glass. This is why an alternative name for the FET is 'unipolar transistor.' When a potential difference (of the proper polarity) is impressed across gate and source, charge carriers are introduced to the channel, making it conductive. The amount of this current can be modulated, or (nearly) completely turned off, by varying the gate potential.

Because the gate is insulated, no DC current flows to or from the gate electrode. This lack of a gate current and the ability of the MOSFET to act like a switch, allows particularly efficient digital circuits to be created, with very low power consumption at low frequencies. The power consumption increases markedly with frequency, because the capacitive loading of the FET control terminal takes more energy to slew at higher frequencies, in direct proportion to the frequency. Hence, MOSFETs have become the dominant technology used in computing hardware such as microprocessors and memory devices such as RAM. Bipolar transistors are more rugged and hence more useful for low-impedance loads and inductively reactive (e.g. motor) loads.

Power MOSFETs become less conductive with increasing temperature and can therefore be applied in shunt, to increase current capacity, unlike the bipolar transistor, which has a negative temperature coefficient of resistance, and is therefore prone to thermal runaway. The downside of this is that, while the power FET can protect itself from overheating by diminishing the current through it, high temperatures need to be avoided by using a larger heat sink than for an equivalent bipolar device. Macroscopic FET power transistors are actually composed of many little transistors. They are stacked (on-chip) to increase breakdown potential and paralleled to reduce Ron, i.e. allowing for more current, bussing the gates to provide a single control (gate) terminal.

The depletion mode FET is a little different. It uses a back-biased diode for the control terminal, which presents a capacitive load to the driving circuit in normal operation. With the gate tied to the source, a DFET is fully on. Changing the potential of a DFET (pulling an N-channel gate downward, for example) will turn it off, i.e. 'deplete' the channel (drain-source) of charge carriers. MOSFETs, formerly called IGFETs (for Insulated Gate Field-Effect Transistor) can be depletion-mode, enhancement-mode, or mixed-mode, but are almost always enhancement mode in modern commercial practice. This means that, with the source and gate tied together (thus equipotential) the channel will be off (high impedance or non-conducting). The n-channel device (reverse for P-channel), like in the DFET, is turned on by raising the potential of the gate. Typically, the gate on a MOSFET will withstand +-20V, relative to the source terminal. If one were to raise the gate potential of an n-channel device without limiting the current to a few milliamps, one would destroy the gate diode, like any other small diode. Why do we typically think of n-channel devices as the default? In silicon devices, the ones that use majority carriers that are electrons, rather than holes, are slightly faster and can carry more current than their P-type counterparts. The same is true in GaAs devices.

The FET is simpler in concept than the bipolar transistor and can be constructed from a wide range of materials.

The most common use of MOSFET transistors today is the CMOS (complementary metallic oxide semiconductor) integrated circuit which is the basis for most digital electronic devices. These use a totem-pole arrangement where one transistor (either the pull-up or the pull-down) is on while the other is off. Hence, there is no DC drain, except during the transition from one state to the other, which is very short. As mentioned, the gates are capacitive, and the charging and discharging of the gates each time a transistor switches states is the primary cause of power drain.

The C in CMOS stands for 'complementary.' The pull-up is a P-channel device (using holes for the mobile carrier of charge) and the pull-down is N-channel (electron carriers). This allows busing of the control terminals, but limits the speed of the circuit to that of the slower P device (in silicon devices). The bipolar solutions to push-pull include 'cascode' using a current source for the load. Circuits that utilize both unipolar and bipolar transistors are called Bi-Fet. A recent development is called 'vertical P.' Formerly, BiFet chip users had to settle for relatively poor (horizontal) P-type FET devices. This is no longer the case and allows for quieter and faster analog circuits.

A clever variant of the FET is the dual-gate device. This allows for two opportunities to turn the device off, as opposed to the dual-base (bipolar) transistor which presents two opportunities to turn the device on.

FETs can switch signals of either polarity, if their amplitude is significantly less than the gate swing, as the devices (especially the parasitic diode-free DFET) are basically symmetrical. This means that FETs are the most suitable type for analog multiplexing. With this concept, one can construct a solid-state mixing board, for example.

The power MOSFET has a 'parasitic diode' (back-biased) normally shunting the conduction channel that has half the current capacity of the conduction channel. Sometimes this is useful in driving dual-coil magnetic circuits (for spike protection), but in other cases it causes problems.

The high impedance of the FET gate makes it rather vulnerable to electrostatic damage, though this is not usually a problem after the device has been installed.

A more recent device for power control is the insulated-gate bipolar transistor, or IGBT. This has a control structure akin to a MOSFET coupled with a bipolar-like main conduction channel. These have become quite popular.


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FHSST Physics/Electronics/Logical Gates

= Electronic Logic Gates =

The simplest form of electronic logic is diode logic (DL). This allows AND and OR gates to be built, but not inverters, and so is an incomplete form of logic. To built a complete logic system, valves or transistors can be used. The simplest family of logic gates using bipolar transistors is called resistor-transistor logic, or RTL. Unlike diode logic gates, RTL gates can be cascaded indefinitely to produce more complex logic functions. These gates were used in early integrated circuits. For higher speed, the resistors used in RTL were replaced by diodes, leading to diode-transistor logic, or DTL. It was then discovered that one transistor could do the job of two diodes in the space of one diode, so transistor-transistor logic, or TTL, was created. In some types of chip, to reduce size and power consumption still further, the bipolar transistors were replaced with complementary field-effect transistors (MOSFETs), resulting in complementary metal-oxide-semiconductor (CMOS) logic.

For small-scale logic, designers now use prefabricated logic gates from families of devices such as the TTL 7400 series invented by Texas Instruments and the CMOS 4000 series invented by RCA, and their more recent descendants. These devices usually contain transistors with multiple emitters, used to implement the AND function, which are not available as separate components. Increasingly, these fixed-function logic gates are being replaced by programmable logic devices, which allow designers to pack a huge number of mixed logic gates into a single integrated circuit.

Electronic logic gates differ significantly from their relay-and-switch equivalents. They are much faster, consume much less power, and are much smaller (all by a factor of a million or more in most cases). Also, there is a fundamental structural difference. The switch circuit creates a continuous metallic path for current to flow (in either direction) between its input and its output. The semiconductor logic gate, on the other hand, acts as a high-gain voltage amplifier, which sinks a tiny current at its input and produces a low-impedance voltage at its output. It is not possible for current to flow between the output and the input of a semiconductor logic gate.

Another important advantage of standardised semiconductor logic gates, such as the 7400 and 4000 families, is that they are cascadable. This means that the output of one gate can be wired to the inputs of one or several other gates, and so on ad infinitum, enabling the construction of circuits of arbitrary complexity without requiring the designer to understand the internal workings of the gates.

In practice, the output of one gate can only drive a finite number of inputs to other gates, a number called the 'fanout limit', but this limit is rarely reached in the newer CMOS logic circuits, as compared to TTL circuits. Also, there is always a delay, called the 'propagation delay', from a change an input of a gate to the corresponding change in its output. When gates are cascaded, the total propagation delay is approximately the sum of the individual delays, an effect which can become a problem in high-speed circuits.

The US symbol for an AND gate is: AND symbol and the IEC symbol is AND symbol.

The US circuit symbol for an OR gate is: OR symbol and the IEC symbol is: OR symbol.

The US circuit symbol for a NOT gate is: NOT symbol and the IEC symbol is: NOT symbol.

In electronics a NOT gate is more commonly called an inverter. The circle on the symbol is called a bubble, and is generally used in circuit diagrams to indicate an inverted input or output.

The US circuit symbol for a NAND gate is: NAND symbol and the IEC symbol is: NAND symbol.

The US circuit symbol for a NOR gate is: NOR symbol and the IEC symbol is: NOR symbol.

In practice, the cheapest gate to manufacture is usually the NAND gate. Additionally, Charles Peirce showed that NAND gates alone (as well as NOR gates alone) can be used to reproduce all the other logic gates.

Two more gates are the exclusive-OR or XOR function and its inverse, exclusive-NOR or XNOR. Exclusive-OR is true only when exactly one of its inputs is true. In practice, these gates are built from combinations of simpler logic gates.

The US circuit symbol for an XOR gate is: XOR symbol and the IEC symbol is: XOR symbol

title: FHSST Physics/Electronics/Logical Gates


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FHSST Physics/Electronics/Counting Circuits

= Counting circuits =

An arithmetic and logical unit (ALU) adder provides the basic functionality of arithmetic operations within a computer, and is a significant component of the arithmetic and logical unit. Adders are composed of half adders and full adders, which add two-bit binary pairs, and ripple carry adders and carry look ahead adders which do addition operations to a series of binary numbers.

Note: Pictures on wikipedia under GFDL

Half Adder
A half adder is a logical circuit that performs an addition operation on two binary digits. The half adder produces a sum and a carry value which are both binary digits.

Sum(s) = A xor B Cot(c) = A and B

Following is the logic table for a half adder:

Full adder
A full adder is a logical circuit that performs an addition operation on three binary digits. The full adder produces a sum and carry value, which are both binary digits.

Sum = (A xor B) xor Cin

Cot = (A nand B) nand (Cin nand (A xor B))


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FHSST Physics/Modern Physics

= Modern Physics = "Modern Physics" concerns areas of Physics which have only recently begun to be explored. Such areas include quantum physics and the exploration of particles. By "recently" here we mean since about the beginning of the 20th century, like modern art, so most of the things that will be covered here are really already well verified and understood.

title: FHSST Physics/Modern Physics


text: Template:FHSST Physics/Modern Physics

title: Template:FHSST Physics/Modern Physics


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FHSST Physics/Modern Physics/Quantum Introduction

= Introduction to the idea of a quantum =

Imagine that a beam of light is actually made up of little "packets" or "bundles" of energy, called quanta.

It's like looking at a crowd of people from above. At first, it seems as though they are one huge patch, without any spaces between them. You would never suspect that they were people. But as you move closer, you slowly begin to see that they are individuals, and when you get even closer, you may even recognize a few. Light seems like a continuous wave at first, but when we zoom in at the subatomic level, we notice that a beam of light actually consists of little "packets" of energy, or quanta. (You will not be able to tell the particles of light apart though because they are of the same energy, and thus identical. The fact that they can't be distinguished has to do with how a laser works.)

The only thing which differentiates one quantum from another is the energy contained in individual quanta (or "packets"). The "packets" are assigned a particular energy, depending on the frequency (or to put it simply: the colour) of the light wave. Quanta of Violet coloured light have the maximum energy and that of Red have the minimum energy.

This idea introduces the concept of the quantum (particle) nature of light, which is demonstrated by the photoelectric effect. When a metal surface is illuminated with light, electrons can be emitted from the surface. This is known as the photoelectric effect. It was explained by the theoretical physicist Albert Einstein.


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FHSST Physics/Modern Physics/Wave-particle Duality

= The wave-particle duality =

Looking at things we can see with our eyes, it seems that wave and particle behavior belong to distinct types of object, but as science reached the atomic and subatomic levels it gradually appeared that each of these is really a property shared by everything. We start by talking about light, but the same concepts apply to everything else, at the atomic scale of size and momentum.

The wave nature of light is demonstrated by diffraction, interference, and polarization of light and the particle nature oflight is demonstrated by the photoelectric effect. So light has both wave-like and particle-like properties, but only shows one or the other, depending on the kind of experiment we perform. A wave-type experiment shows the wave nature, and a particle-type experiment shows particle nature.

How do we know light acts like a wave?

Demonstrating that light has wave properties: imagine dropping a pebble in water - you see circular waves stretching out in ever widening circles. Now imagine placing a barrier (for example a card or piece of wood) in the path of the wave - but a barrier with a slot cut in it. What you would see is the wave hit that barrier and its slot - and a second wave would emendate from the other side of the slot (these would be semicircular waves). This is easy to see at home - try it in a bath of water - well, light waves do the same thing. However, now imagine having not one slot in the barrier, but two. What you would see then is the initial wave hit the barrier - and two semicircular waves emendate from the other side - one from the other side of each slot. The key point is that these two semicircular waves would crash into each other at some point - they would 'interfere' with each other. Where their respective waves were both 'high' they would add up and you would get a peak. Similarly where their respective waves were both low they would add up (you would get an even deeper trough), but where they were in opposite states (one high, one low) they would cancel each other out. If you could stand on the shore with your eye at water level what you would see is a series of peaks and gaps - a sort of stripped imaged. This is exactly what we see when we place a detector (for example a piece of photographic film) on the other side of the two slots when you pass a light wave light through the two slots. You see the stripped pattern where the peaks have left an image (light had fallen on the photo paper) and the gaps (where light had not fallen on the paper) - indicating that 'interference' had taken place - and that indicates that light must be behaving like a wave.

Actually you see a hint of this in supermarkets, when they scan the bar codes with lasers. Ordinary light is a mixture of wavelengths, so that the diffraction patterns of different wavelengths cover each other up. The light from a laser is all the same wavelength, so the random diffraction patterns are visible as speckles.

Now, we consider light to behave not as a wave, but as particles. But what do we call a 'particle' of light?

Photon : A photon is a quantum (energy packet) of light.

Imagine a sheet of metal. On the surface, there are electrons that can be set free. If a photon comes along and strikes the surface of the metal, then it will give its entire energy packet to one electron. This means that the electron now has some energy, and it may escape (leave the surface) if this energy Ek (kinetic energy) is greater than the minimum energy required to free an electron Emin.

Now, suppose the electron needs 5eV of kinetic energy to escape. And suppose this little photon has just 2eV of energy in its energy packet. Then the electron will not leave the surface of the metal. But suppose the photon has 8eV of energy. This means that the electron will emerge with 3eV of kinetic energy.

Note that this does not mean the photon can give 5eV of energy to one electron and 3eV to another. A photon will give all of its energy to just one electron.

The minimum amount of energy needed for an electron to escape (electrons do not normally leave a metal whenever they please), is called the work function of the metal. In our example, the work function is 5eV. The work function has a different value for each metal: 4.70eV for copper and 2.28eV for sodium. It is worth mentioning that the best conductors tend to be those with the smallest work functions. (For Advanced Readers: Work Function actually represents the energy required to overcome the negative potential energy of the electron which is caused by the electrostatic attraction acting on the electron by the nucleus)

The frequency of the radiation is directly related to the energy of the photon. It is important because if the frequency (and hence the energy) of the photon is below a certain threshold value, no electrons will be emitted. Even if the intensity of the light is increased, and the light is allowed to fall on the surface for a long period of time, if the frequency of the radiation is below the threshold frequency, electrons will not be emitted.

The energy of the photon is calculated using the formula: E = hν   (where h = 6.57 X 10^-34 J-s is Planck's constant, and ν is the frequency of the radiation).

The kinetic energy of an electron that escapes from the metal is equal to the energy of the photon minus the work function, Φ, i.e.

Ek = (hν) - Φ

The electrons emerge with a range of velocities from zero up to a maximum Vmax. The maximum kinetic energy, (1/2)m(Vmax)^2, depends (linearly) on the frequency of the radiation, and is independent of its intensity.

For incident radiation of a given frequency, the number of electrons emitted per unit time is proportional to the intensity of the radiation.

Electron emission takes place from the instant the light shines on the surface, i.e. there is no detectable time delay.

What are the uses of the photoelectric effect?

The most common use of photoelectric effect is in solar cells. Light energy from the sun is used to excite electrons out of metal surfaces which can then be made to flow in a circuit (i.e., replace a conventional cell!). The current obtained depends on the intensity (or simply: the brightness) of the light.

For this (and other work), Einstein received the Nobel Prize (Physics) in 1921 ("...for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.").


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FHSST Physics/Atomic Nucleus

= Inside atomic nucleus =

Amazingly enough, the human mind that is contained inside a couple of liters of human's brain, is able to deal with extremely large as well as extremely small objects such as the whole universe and its smallest building blocks. So, what are these building blocks? As we already know, the universe consists of galaxies, which consist of stars with planets moving around. The planets are made of molecules, which are bound groups (chemical compounds) of atoms.

There are more than stars in the universe. Currently, scientists know over 12 million chemical compounds i.e. 12 million different molecules. All this variety of molecules is made of only a hundred of different atoms. For those who believe in beauty and harmony of nature, this number is still too large. They would expect to have just few different things from which all other substances are made. In this chapter, we are going to find out what these elementary things are.

title: FHSST Physics/Atomic Nucleus


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title: Template:FHSST Physics/Atomic Nucleus


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FHSST Physics/Atomic Nucleus/Composition

= What the atom is made of =

The Greek word $$\alpha\tau o\mu o\nu$$ (atom) means indivisible. The discovery of the fact that an atom is actually a complex system and can be broken in pieces was the most important step and pivoting point in the development of modern physics.

It was discovered (by Rutherford in 1911) that an atom consists of a positively charged nucleus and negative electrons moving around it. At first, people tried to visualize an atom as a microscopic analog of our solar system where planets move around the sun. This naive planetary model assumes that in the world of very small objects the Newton laws of classical mechanics are valid. This, however, is not the case.

The microscopic world is governed by quantum mechanics which does not have such notion as trajectory. Instead, it describes the dynamics of particles in terms of quantum states that are characterized by probability distributions of various observable quantities.

For example, an electron in the atom is not moving along a certain trajectory but rather along all imaginable trajectories with different probabilities. If we were trying to catch this electron, after many such attempts we would discover that the electron can be found anywhere around the nucleus, even very close to and very far from it. However, the probabilities of finding the electron at different distances from the nucleus would be different. What is amazing: the most probable distance corresponds to the classical trajectory!

You can visualize the electron inside an atom as moving around the nucleus chaotically and extremely fast so that for our mental eyes it forms a cloud. In some places this cloud is more dense while in other places more thin. The density of the cloud corresponds to the probability of finding the electron in a particular place. Space distribution of this density (probability) is what we can calculate using quantum mechanics. Results of such calculation for hydrogen atom are shown in Fig. 15.1. As was mentioned above, the most probable distance (maximum of the curve) coincides with the Bohr radius.

Quantum mechanical equation for any bound system (like an atom) can have solutions only at a discrete set of energies E_1, E_2, E_3 \dots$$ $$, etc. There are simply no solutions for the energies $$E$$ in between these values, such as, for instance, $$E_1 < E < E_2$$. This is why a bound system of microscopic particles cannot have an arbitrary energy and can only be in one of the quantum states. Each of such states has certain energy and certain space configuration, i.e. distribution of the probability. A bound quantum system can make transitions from one quantum state to another either spontaneously or as a result of interaction with other systems. The energy conservation law is one of the most fundamental and is valid in quantum world as well as in classical world. This means that any transition between the states with energies $$E_i$$ and $$E_j$$ is accompanied with either emission or absorption of the energy $$\Delta E=|E_i-E_j|$$. This is how an atom emits light.

An electron is a very light particle. Its mass is negligible as compared to the total mass of the atom. For example, in the lightest of all atoms, hydrogen, the electron constitutes only 0.054% of the atomic mass. In the silicon atoms that are the main component of the rocks around us, all 14 electrons make up only 0.027% of the mass. Thus, when holding a heavy rock in your hand, you actually feel the collective weight of all the nuclei that are inside it.


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FHSST Physics/Atomic Nucleus/Nucleus

= Nucleus =

Is the nucleus a solid body? Is it an elementary building block of nature?! Although it is very small, a nucleus consists of something even smaller.

Proton
The only way to do experiments with such small objects as atoms and nuclei, is to collide them with each other and watch what happens. Perhaps you think that this is a barbaric way, like colliding a Mercedes and Toyota in order to learn what is under their bonnets. But with microscopic particles nothing else can be done.

In the early 1920s Rutherford and other physicists made many experiments, changing one element into another by striking them with energetic helium nuclei. They noticed that all the time hydrogen nuclei were emitted in the process. It was apparent that the hydrogen nucleus played a fundamental role in nuclear structure and was a constituent part of all other nuclei. By the late 1920's physicists were regularly referring to hydrogen nucleus as proton. The term proton seems to have been coined by Rutherford, and first appears in print in 1920.

Neutron
Thus it was established that atomic nuclei consist of protons. The number of protons in a nucleus is such that makes up its positive charge. This number, therefore, coincides with the atomic number of the element in the Mendeleev's Periodic table.

This sounded nice and logical, but serious questions remained. Indeed, how can positively charged protons stay together in a nucleus? Repelling each other by electric force, they should fly away in different directions. Who keeps them together?

Furthermore, the proton mass is not enough to account for the nuclear masses. For example, if the protons were the only particles in the nucleus, then a helium nucleus (atomic number 2) would have two protons and therefore only twice the mass of hydrogen. However, it actually is four times heavier than hydrogen. This suggests that it must be something else inside nuclei in addition to protons.

These additional particles that kind of glue the protons and make up the nuclear mass, apparently, are electrically neutral. They were therefore called neutrons. Rutherford predicted the existence of the neutron in 1920. Twelve years later, in 1932, his assistant James Chadwick found it and measured its mass, which turned out to be almost the same but slightly larger than that of the proton.

Isotopes
Thus, in the early 1930s it was finally proved that atomic nucleus consists of two types of particles, the protons and neutrons. The protons are positively charged while the neutrons are electrically neutral. The proton charge is exactly equal but opposite to that of the electron. The masses of proton and neutron are almost the same, approximately 1836 and 1839 electron masses, respectively.

Apart from the electric charge, the proton and neutron have almost the same properties. This is why there is a common name for them: nucleon. Both the proton and neutron are nucleons, like a man and a woman are both humans. In physics literature, the proton is denoted by letter $$p$$ and the neutron by $$n$$. Sometimes, when the difference between them is unimportant, it is used the letter $$N$$ meaning nucleon (in the same sense as using the word person instead of man or woman).

Chemical properties of an element are determined by the charge of its atomic nucleus, i.e. by the number of protons. This number is called the atomic number and is denoted by letter $$Z$$. The mass of an atom depends on how many nucleons its nucleus contains. The number of nucleons, i.e. total number of protons and neutrons, is called the atomic mass number and is denoted by letter $$A$$.

Standard nuclear notation shows the chemical symbol, the mass number and the atomic number of the isotope.

For example, the iron nucleus (26-th place in the Mendeleev's periodic table of the elements) with 26 protons and 30 neutrons is denoted as $${}^{56}_{26}{\rm Fe}\ $$, where the total nuclear charge is $$Z=26$$ and the mass number $$A=56$$. The number of neutrons is simply the difference $$N=A-Z$$(here, it is used the same letter $$N$$, as for nucleon, but this should not cause any confusion). Chemical symbol is inseparably linked with $$Z$$. This is why the lower index is sometimes omitted and you may encounter the simplified notation like $${}^{56}{\rm Fe}$$.

If we add or remove a few neutrons from a nucleus, the chemical properties of the atom remain the same because its charge is the same. This means that such atom should remain in the same place of the Periodic table. In Greek, same place reads $$\acute{\iota}\sigma o\varsigma$$ $$\tau \acute{o}\pi o\varsigma$$ (isos topos). The nuclei, having the same number of protons, but different number of neutrons, are called therefore isotopes.

Different isotopes of a given element have the same atomic number $$Z$$, but different mass numbers $$A$$ since they have different numbers of neutrons $$N$$. Chemical properties of different isotopes of an element are identical, but they will often have great differences in nuclear stability. For stable isotopes of the light elements, the number of neutrons will be almost equal to the number of protons, but for heavier elements, the number of neutrons is always greater than $$Z$$ and the neutron excess tends to grow when $$Z$$ increases. This is because neutrons are kind of glue that keeps repelling protons together. The greater the repelling charge, the more glue you need.

title: FHSST Physics/Atomic Nucleus/Nucleus


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FHSST Physics/Atomic Nucleus/Nuclear Force

= Nuclear force =

Since atomic nuclei are very stable, the protons and neutrons must be kept inside them by some force and this force must be rather strong. What is this force? All of modern particle physics was discovered in the effort to understand this force!

Trying to answer this question, at the beginning of the twentieth century, physicists found that all they knew before, was inadequate to explain how the nucleus held together in spite of the electrostatic repulsion of the protons pushing it apart. They knew only gravitational and electromagnetic forces. It was clear that the forces holding nucleons were not electromagnetic. Indeed, the protons, being positively charged, repel each other and all nuclei would decay in a split of a second if some other forces would not hold them together. On the other hand, it was also clear that they were not gravitational, which would be too weak for the task.

The simple conclusion was that nucleons are able to attract each other by yet unknown nuclear forces, which are stronger than the electromagnetic ones. Further studies proved that this hypothesis was correct.

Nuclear force has rather unusual properties. Firstly, it is charge independent. This means that in all pairs $$nn$$, $$pp$$, and $$np$$ nuclear forces are the same.

Secondly, at distances of about $$10^{-15}$$ meter, the nuclear force is attractive and very strong, roughly 100 times stronger than electromagnetic repulsion.

Thirdly, the nuclear force is of a very short range. If the nucleons move away from each other for more than few fermi (1 fermi = 1 fm [femtometer] = $$10^{-15}$$ meter) the nuclear attraction practically disappears. Therefore the nuclear force looks like a strong man with very short arms.


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FHSST Physics/Atomic Nucleus/Binding Energy and Nuclear Masses

Binding energy and nuclear masses
When a system of particles is bound, you have to spend certain energy to disintegrate it, i.e. to separate the particles. The easiest way to do it is to strike the system with a moving particle that carries kinetic energy, like we can destroy a glass bottle with a bullet or a stone. If our bullet-particle moves too slow (i.e. does not have enough kinetic energy) it cannot disintegrate the system. On the other hand, if its kinetic energy is too high, the system is not only disintegrated but the separated particles acquire some kinetic energy, i.e. move away with some speed. There is an intermediate value of the energy which is just enough to destroy the system without giving its fragments any speed. This minimal energy needed to break up a bound system is called binding energy of this system. It is usually denoted by letter $$B$$.

Nuclear energy units
The standart unit of energy, the joule, is too large to measure the energies associated with individual nuclei. This is why in nuclear physics it is more convenient to use a much smaller unit called megaelectronvolt (MeV). This is the amount of energy that an electron acquires after passing between two charged plates with the potential difference (voltage) of one million volts. Sounds very huge, isn't it? But look at this relation $1\,{\rm MeV}=1.602\times10^{-19}\,{\rm J}$ and think again. In the units of MeV, most of the energies in nuclear world can be expressed by values with only few digits before decimal point and without ten to the power of something. For example, the binding energy of proton and neutron (which is the simplest nuclear system and is called deuteron) is $B_{pn}=2.225\,{\rm MeV}\ .$ The simplicity of the numbers is not the only advantage of using the unit MeV. Another, more important advantage, comes from the fact that most of experiments in nuclear physics are collision experiments, where particles are accelerated by electric field and collide with other particles. From the above value of $$B_{pn}$$, for instance, we immediately know that in order to break up deuterons, we need to bombard them with a flux of electrons accelerated through a voltage not less than 2.225 million volts. No calculation is needed! On the other hand, if we know that a charged particle (with a unit charge) passes through a voltage, say, 5 million volts, we can, without any calculation, say that it acquires the energy of 5 MeV. It is very convenient. Isn't it?

Mass defect
Comparing the masses of atomic nuclei with the masses of the nucleons that constitute them, we encounter a surprising fact: Total mass of the nucleons is greater than mass of the nucleus! For example, for the deuteron we have

$m_d < m_p + m_n\ ,$

where $$m_d$$ $$m_p$$, and $$m_n$$ are the masses of deuteron, proton and neutron, respectively. The difference is rather small, $(m_p+m_n)-m_d= 3.968\times10^{-30}\,{\rm kg}\ ,$ but on the nuclear scale is noticeable since the mass of proton, for example, $m_p=1672.623\times10^{-30}\,{\rm kg}$ is also very small. This phenomenon is called 'mass defect'. Where the mass disappears to, when nucleons are bound? To answer this question, we notice that the energy of a bound state is lower than the energy of free particles. Indeed, to liberate them from a bound complex, we have to give them some energy. Thinking in the opposite direction, we conclude that, when forming a bound state, the particles have to get rid of the energy excess, which is exactly equal to the binding energy. This is observed experimentally: When a proton captures a neutron to form a deuteron, the excess energy of 2.225MeV is emitted via electromagnetic radiation. A logical conclusion from the above comes by itself: When proton and neutron are bounding, some part of their mass disappears together with the energy that is carried away by the radiation. And in the opposite process, when we break up the deutron, we give it the energy, some part of which makes up the lost masses Albert Einstein came to the idea of the equivalence between the mass and energy long before any experimental evidences were found. In his theory of relativity, he showed that total energy $$E$$ of a moving body with mass $$m$$ is

where $$v$$ is its velocity and $$c$$ the speed of light. Applying this equation to a non-moving body ($$v=0$$), we conclude that it possesses the rest energy

simply because it has mass. As you will see, this very formula is the basis for making nuclear bombs and nuclear power stations!

All the development of physics and chemistry, preceding the theory of relativity, was based on the assumption that the mass and energy of a closed system are conserving in all possible processes and they are conserved separately. In reality, it turned out that the conserving quantity is the mass-energy, $E_{\rm kin}+E_{\rm pot}+E_{\rm rad}+mc^2={\rm const}\ ,$ i.e. the sum of kinetic energy, potential energy, the energy of radiation, and the mass of the system. In chemical reactions the fraction of the mass that is transformed into other forms of energy (and vice versa), is so small that it is not detectable even in most precise measurements. In nuclear processes, however, the energy release is very often millions times higher and therefore is observable. You should not think that mutual transformations of mass and energy are the features of only nuclear and atomic processes. If you break up a piece of rubber or chewing gum, for example, in two parts, then the sum of masses of these parts will be slightly larger than the mass of the whole piece. Of course we will not be able to detect this mass defect with our scales. But we can calculate it, using the Einstein formula (15.1). For this, we would need to measure somehow the mechanical work W used to break up the whole piece (i.e. the amount of energy supplied to it). This can be done by measuring the force and displacement in the breaking process. Then, according to Eq. (15.2), the mass defect is $\Delta m=\frac{W}{c^2}$ To estimate possible effect, let us assume that we need to stretch a piece of rubber in 10 cm before it breaks, and the average force needed for this is 10N (approximately 1 kg). Then $W=10\,{\rm N}\times 0.1\,{\rm m}=1\,{\rm J} $, and hence $\Delta m=\frac{1\,{\rm J}}{(299792458\,{\rm m/s})^2}\approx1.1\times10^{-17}\,{\rm kg}$.|undefined This is very small value for measuring with a scale, but huge as compared to typical masses of atoms and nuclei.

Nuclear masses
Apparently, an individual nucleus cannot be put on a scale to measure its mass. Then how can nuclear masses be measured? This is done with the help of the devices called mass spectrometers. In them, a flux of identical nuclei, accelerated to a certain energy, is directed to a screen where it makes a visible mark. Before striking the screen, this flux passes through magnetic field, which is perpendicular to velocity of the nuclei. As a result, the flux is deflected to certain angle. The greater the mass, the smaller is the angle (because of inertia). Thus, measuring the displacement of the mark from the center of the screen, we can find the deflection angle and then calculate the mass. Since mass and energy are equivalent, in nuclear physics it is customary to measure masses of all particles in the units of energy, namely, in MeV. Examples of masses of subatomic particles are given in Table 15.1

The values given in this table, are the energies to which the nuclear masses are equivalent via the Einstein formula 15.1.

There are several advantages of using the units of MeV to measure particle masses. First of all, like with nuclear energies, we avoid handling very small numbers that involve ten to the power of something. For example, if we were measuring masses in kg, the electron mass would be $$m_e=9.1093897 \times 10^{-31}$$ kg. When masses are given in the equivalent energy units, it is very easy to calculate the mass defect. Indeed, adding the masses of proton and neutron, given in the second and third rows of Table 15.1, and subtracting the mass of $${}^2_1$$H, we obtain the binding energy 2.225MeV of the deuteron without further ado. One more advantage comes from particle physics. In collisions of very fast moving particles new particles (like electrons) can be created from vacuum, i.e. kinetic energy is directly transformed into mass. If the mass is expressed in the energy units, we know how much energy is needed to create this or that particle, without calculations.