Technological Mandalas

Technological Mandala, the work by Leonardo Ulian. A complex symetry pattern made from electronic components and microchips. It shows contrast between hard cold tech objects in a warm spiritual Hinduism symbol. I personally think it looks like beautiful lace.

Technological Mandala No.2, 1912

Electronic components, microchip, wood frame, 120x120 cm

 images from leonardoulian

Describe the main energy transformations that take place in a nuclear power station

Power plants that depend on atomic energy don't operate that differently from a typical coal-burning power plant. Both heat water into pressurized steam, which drives a turbine generator. Where the two plants are dissimilar is in the method which is used to heat the water into steam. While a coal-burning power plant burns fossil fuels, nuclear plants depend on the heat that occurs during nuclear fission, when one atom splits into two (see sections 8.4.1 and 8.4.2).
The splitting of a single U-235 atom releases approximately 200 MeV (million electron volts). This may not seem like much, however, a pound of highly-enriched uranium is equal to one million gallons of gasoline. This shows the superior efficiency that nuclear power-production has in comparison to fossil-fuels.
To turn the energy produced through nuclear fission into electrical energy, the energy must be controlled so that it can be effectively and safely used to heat water into steam.
Enriched uranium is typically formed into inch-long (2.5-cm-long) pellets, each with approximately the same diameter as a dime. The pellets are then arranged into long rods, which are then gathered into large bundles. The bundles are submerged in water inside a pressure vessel. The water acts as a coolant, and without it, the uranium would eventually overheat and melt.


The uranium bundle acts as an extremely high-energy source of heat. It heats the water and turns it to steam. The steam drives a turbine, which spins a generator to produce power. The diagram above shows the step-by-step process which occurs within a nuclear power plant. Once the water has been heated by the enriched uranium metal, the energy transfers that take place are identical to that within a coal-burning power plant.

Energy Transfers:
- Water is heated by heat energy created through nuclear fission
- Energy is lost to surroundings
- Steam turns a turbine (heat energy transformed into kinetic energy)
- Energy is lost to friction
- Turbine powers a generator
- Energy is lost to friction
- Energy is transformed into electrical energy

Logic Gates

Introduction

Logic gates serve as the building blocks to digital logic circuits using combinational logic. We're going to consider the following gates: NOT gates (also called inverters), AND gates, OR gates, NAND gates, NOR gates, XOR gates, and XNOR gates. We'll also discuss the concept of gate deltay.

NOT gates

NOT gates or inverters have a single bit input and a single bit of output. This is a diagram of a NOT gate. It is a triangle with a circle on the right. The circle indicates "negation".
The truth table defines the behavior of this gate.

x	z
0	1
1	0

where x is the input and z is the output.

AND₂ gates

AND₂ gates have two bits of input and a single bit of output. The subscript, 2, indicates how many inputs this AND gate has. For example, AND₃ gates have 3 inputs. The output of AND₂ gate is 1 only if both inputs are 1. Otherwise, the output is 0.
The truth table defines the behavior of this gate.

x1	x0	z
0	0	0
0	1	0
1	0	0
1	1	1

The function implmented by AND₂ gates has interesting properties:

• The function is symmetric. Thus, x * y == y * x. This can be verified by using truth tables. We use * to represent AND₂.
• The function is associative. Thus, (x * y) * z == x * (y * z). This can be verified by using truth tables.

Because of these properties, it's easy to define AND_n, which is an n-input AND gate. AND_n(x₁, x₂,...,x_n) = x₁ * x₂ * ... * x_n That is, an AND gate with n-inputs is the AND of all the bits. This is not ambiguous because the AND function is associative (all parenthesization of this expression are equivalent).

OR₂ gates

OR₂ gates have two bits of input and a single bit of output. The subscript, 2, indicates how many inputs this OR gate has. For example, OR₃ gates have 3 inputs. The output of OR₂ gate is 0 only if both inputs are 0. Otherwise, the output is 1.
The truth table defines the behavior of this gate.

x1	x0	z
0	0	0
0	1	1
1	0	1
1	1	1

The function implemented by OR₂ gates has interesting properties:

• The function is symmetric. Thus, x + y == y + x. This can be verified by using truth tables. We use "+" to represent OR₂
• The function is associative. Thus, (x + y) + z == x + (y + z). This can be verified by using truth tables.

Because of these properties, it's easy to define OR_n, which is an n-input OR gate. OR_n(x₁, x₂,...,x_n) = x₁ + x₂ + ... + x_n That is, an AND gate with n-inputs is the AND of all the bits. This is not ambiguous because the AND function is associative (all parenthesization of this expression are equivalent).

NAND₂ gates

NAND₂ gates have two bits of input and a single bit of output. The subscript, 2, indicates how many inputs this NAND gate has. For example, NAND₃ gates have 3 inputs. NAND_k gates is define unusually. Since NAND₂ is not associative, the definition is based on AND₂.
In particular
NAND_k(x₁, x₂,...,x_n) = NOT( AND_k(x₁, x₂,...,x_n) ) Thus, NAND_k is the negation of AND_k.
The truth table defines the behavior of this gate. It's the negation of AND₂.

x1	x0	z
0	0	1
0	1	1
1	0	1
1	1	0

The function implemented by NAND₂ gates has interesting properties:

• The function is symmetric. Thus, x NAND y == y NAND x. This can be verified by using truth tables.
• The function is not associative. This can be verified by using truth tables.

Because of these properties, NAND_k is defined from AND_k, and not built from NAND₂ gates.

NOR₂ gates

OR₂ gates have two bits of input and a single bit of output. The subscript, 2, indicates how many inputs this OR gate has. For example, NOR₃ gates have 3 inputs. The output of NOR₂ gate is the negation of OR₂.
The truth table defines the behavior of this gate.

x1	x0	z
0	0	1
0	1	0
1	0	0
1	1	0

The function implmented by NOR₂ gates has interesting properties:

• The function is symmetric. Thus, x NOR y == y NOR x. This can be verified by using truth tables.
• The function is not associative. This can be verified by using truth tables.

Because of these properties, NOR_k is defined from OR_k, and not built from NOR₂ gates.

XOR₂ gates

XOR₂ gates have two bits of input and a single bit of output. The output of XOR₂ gate is 1 only if the inputs have opposite values. That is, when one input has value 0, and the other has value 1.. Otherwise, the output is 0.
This is called exclusive-or. The definition of OR₂ is inclusive-or, where the output is 1 if either input is 1, or if both inputs are 1.
XOR₂ can be defined using AND₂, OR₂, and NOT.
x XOR y == ( x AND (NOT y) ) OR ( (NOT x) AND y ) == x\y + y\x
Here's a diagram of the XOR₂ gate.

If you look carefully at the drawing of the gate, there is a second arc behind the first one near the inputs. Since this second arc is hard to see, it's usually a good idea to write the word "XOR" inside the gate.
The truth table defines the behavior of this gate.

x1	x0	z
0	0	0
0	1	1
1	0	1
1	1	0

The function implmented by XOR₂ gates has interesting properties:

• The function is symmetric. Thus, x (+) y == y (+) x. This can be verified by using truth tables. (We use (+) to denote logical XOR--ideally, we'd draw it with a + sign inside a circle, but HTML doesn't seem to have a symbol for this).
• The function is associative. Thus, [ x (+) y ] (+) z == x (+) [ y (+) z ]. This can be verified by using truth tables.

Because of these properties, it's easy to define XOR_n, which is an n-input XOR gate. XOR_n(x₁, x₂,...,x_n) = x₁ (+) x₂ (+) ... (+) x_n That is, an XOR gate with n-inputs is the XOR of all the bits. This is not ambiguous because the XOR function is associative (all parenthesization of this expression are equivalent).

XNOR₂ gates

XNOR₂ gates have two bits of input and a single bit of output. The output of XNOR₂ gate is the negation of XOR₂ and has 1 when both inputs are the same.
If you look carefully at the drawing of the gate, there is a second arc behind the first one near the inputs. Since this second arc is hard to see, it's usually a good idea to write the word "XNOR" inside the gate.
The truth table defines the behavior of this gate.

x1	x0	z
0	0	0
0	1	1
1	0	1
1	1	0

The function implmented by XNOR₂ gates has interesting properties:

• The function is symmetric. Thus, x XNOR y == y XNOR x. This can be verified by using truth tables.
• The function is associative. Thus, (x XNOR y) XNOR z == x XNOR (y XNOR z). This can be verified by using truth tables.

Because of these properties, it's easy to define XNOR_n, which is an n-input XNOR gate. XNOR_n(x₁, x₂,...,x_n) = x₁ XNOR x₂ XNOR ... XNOR x_n That is, an XNOR gate with n-inputs is the XNOR of all the bits. This is not ambiguous because the XNOR function is associative (all parenthesization of this expression are equivalent).
(Error-checkers! You may wish to verify this, and email me if this is incorrect!).

Building Blocks

We can use logic gates to build circuits. While we've described 6 gates, you can do with only three gates to build all possible circuits: AND₂, OR₂, and NOT. In fact, you don't even need all three gates. It can be done in two kinds of gates of less. We'll explain in a future section. These circuits can implement any truth table.

Valid Combinational Circuits

The inverse is not true. Not every circuit that is built from gates corresponds to a truth table. In particular, you must observe the following rules if it's to correspond to a truth table.

• The output of a gate may only be attached to the input of another gate. (Think of this as a directed edge from output to input).
• There must be no cycles in the circuit. Treat the circuit like a directed graph with directed edges defined in the previous item.
• Although the output of a gate may be attached to more than one input, an input may not have two different outputs attached to it (this would create conflicting input signals).
• Each input of a gate must come from either the output of another gate or a source. A source is a source that generates either a 0 or 1.

Gate Delay

Real gates have delay. In other words, if you change the value of the inputs, say from 0 and 0 to 0 and 1, then the output takes some small amount of time before it changes. This delay is called gate delay. This delay is due to the fact that information can travel at most, the speed of light, and in reality, the time it takes to do the computation is not infinitely quick.
This delay limits how fast the inputs can change and yet the output have meaningful values. It also allows certain kinds of circuits to be created that don't follow the rules from the previous section. In particular, flip flops (to be discussed later) can be generated from gates that use cycles.

Why Subscripts?

Most books don't distinguish between an AND₂ gate and a AND₃ gate. They claim an AND gate is an AND gate, regardless of the number of inputs. While this is true, I subscript it because an AND₂ and an AND₃ do not have the same truth table. In particular, an AND₂ truth table has 4 rows while an AND₃ has 8. While the two truth tables are related, they still define different functions.
Thus, I make the distinction by subscripting the number of inputs.

Summary

Logic gates are the building blocks of combinational logic circuits. You can buy logic gates from electronic hobby places. These gates are primarily for hobbyists. Each chip usually has about 4 logic gates. Real computers don't use these kinds of gates, because they take far too much space. With VLSI technology, you can cram millions of gates onto a wafer no bigger that your thumbnail.
The behavior of logic gates can be described by truth tables. However, because these gates are "physical", they have some properties not expressed in truth tables. In particular, gate delay describes the amount of time it takes for the output to change when the input changes. This time is not zero, thus, one must wait a short amount of time for the output to take effect.
We'll discuss how to build circuits from these gates in a later set of notes.

Direct-Current Motor Principles

FIGURE. Magnetic lines of force flow from the north pole to the south pole.

DC motors use the interaction of magnetic fields to convert the electrical energy into mechanical energy. Magnetic lines of force flow from the north pole to the south pole of a magnet. If a current-carrying conductor is placed within the magnetic field, two fields will be present. On the left side of the conductor, the lines of force are in the same direction. This will concentrate the flux density of the lines of force on the left side. This will produce a strong magnetic field because the two fields will reinforce each other. The lines of force oppose each other on the right side of the conductor. This results in a weaker magnetic field. The conductor will tend to move from the strong field to the weak field. This principle is used to convert electrical energy into mechanical energy in a starter motor by electromagnetism.

FIGURE. Interaction of two magnetic fields.

FIGURE. Conductor movement in a magnetic field.

A simple electromagnet-style starter motor is shown. The inside windings are called the armature. The armature is the moveable component of the motor that consists of a conductor wound around a laminated iron core. It is used to create a magnetic field. The armature rotates within the stationary outside windings, called the field coils, which has windings coiled around pole shoes. Field coils are heavy copper wire wrapped around an iron core to form an electromagnet. Pole shoes are made of high-magnetic permeability material to help concentrate and direct the lines of force in the field assembly.

FIGURE. Simple electromagnetic motor.

When current is applied to the field coils and the armature, both produce magnetic flux lines. The direction of the windings will place the left pole at a south polarity and the right side at a north polarity. Hie lines of force move from north to south in the field. In the armature, the flux lines circle in one direction on one side of the loop and in the opposite direction on the other side. Current will now set up a magnetic field around the loop of wire, which will interact with the north and south fields and put a turning force on the loop. This force will cause the loop to turn in the direction of the weaker field. However, the armature is limited in how far it is able to turn. When the armature is halfway between the shoe poles, the fields balance one another. The point at which the fields are balanced is referred to as the static neutral point.

FIGURE. Field coil wound around a pole shoe.

FIGURE. Rotation of the conductor is in the direction of the weaker field.

For the armature to continue rotating, the current flow in the loop must be reversed. To accomplish this, a split-ring commutator is in contact with the ends of the armature loops. The commutator is a series of conducting segments located around one end of the armature. Current enters and exits the armature through a set of brushes that slide over the commutator’s sections. Brushes are electrically conductive sliding contacts, usually made of copper and carbon. As the brushes pass over one section of the commutator to another, the current flow in the armature is reversed. The position of the magnetic fields are the same. However, the direction of current flow through the loop has been reversed. This will continue until the current flow is turned off.

FIGURE. Starter armature.

FIGURE. Starter and solenoid components.

Armature

FIGURE. Lamination construction of a typical motor armature.

The armature is constructed with a laminated core made of several thin iron stampings that are placed next to each other. Laminated construction is used because, in a solid iron core, the magnetic fields would generate eddy currents. These are counter voltages induced in a core. They cause heat to build up in the core and waste energy. By using laminated construction, eddy currents in the core are minimized.
The slots on the outside diameter of the laminations hold the armature windings. The windings loop around the core and are connected to the commutator. Each commutator segment is insulated from the adjacent segments. A typical armature can have more than 30 commutator segments.
A steel shaft is fitted into the center hole of the core laminations. The commutator is insulated from the shaft.

FIGURE. Lap winding diagram.

Two basic winding patterns are used in the armature: lap winding and wave winding. In the lap winding, the two ends of the winding are connected to adjacent commutator segments. In this pattern, the wires passing under a pole field have their current flowing in the same direction.

FIGURE. Wave-wound armature.

In the wave-winding pattern, each end of the winding connects to commutator segments that are 90 or 180 degrees apart. In this pattern design, some windings will have no current flow at certain positions of armature rotation. This occurs because the segment ends of the winding loop are in contact with brushes that have the same polarity. The wave-winding pattern is the most commonly used due to its lower resistance.

Field Coils

The field coils are electromagnets constructed of wire ribbons or coils wound around a pole shoe. The pole shoes are constructed of heavy iron. The field coils are attached to the inside of the starter housing. Most starter motors use four field coils. The iron pole shoes and the iron starter housing work together to increase and concentrate the field strength of the field coils.

FIGURE. Field coils mounted to the inside of starter housing.

When current flows through the field coils, strong stationary electromagnetic fields are created. The fields have a north and south magnetic polarity based on the direction the windings are wound around the pole shoes. The polarity of the field coils alternate to produce opposing magnetic fields.

FIGURE. Magnetic fields in a 4-pole starter motor.

In any DC motor, there are three methods of connecting the field coils to the armature: in series, in Darallel (shunt), and a comDound connection that uses both series and shunt coils.

Principle of Alternator

Principle :

    A.C. generators or alternators (as they are usually called) operate on the same fundamental principles of electromagnetic induction as D.C. generators.

    Alternating voltage may be generated by rotating a coil in the magnetic field or by rotating a magnetic field within a stationary coil. The value of the voltage generated depends on-

                     the number of turns in the coil.

                     strength of the field.

                     the speed at which the coil or magnetic field rotates.