TECHNO TALK

Logic Gates

2012-10-05T01:22:00.003-07:00

Logic gates are the basis of digital electronics. A logic gate is an idealized or physical device which performs a logical operation on one or more logic inputs and produces a single logic output. A logic gate is an electronic circuit which makes logical decisions. An ideal logic gate is the one that has zero rise time and unlimited fan-out. Diodes or transistors acting as electronic switches,implement logic gates. Electromagnetic relays, fluidic logic, pneumatic logic, optics, molecules and mechanical elements can also be used to implement logic gates. Logic circuits include multiplexers, registers, arithmetic logic units and computer memory. Microprocessors contain more than 100 million logic gates. Gates are made from field-effect transistors. Compound logic gates AND-OR-Invert (AOI) and OR-AND-Invert (OAI) are constructed from MOSFETs (metal–oxide–semiconductor field-effect transistors) and hence they are simpler and efficient. Transistors or relays, vacuum tubes are used to create functionally complete logic systems. The output of one gate can only drive a finite number of inputs to other gates, a number called the 'fanout limit'. Elementary logic gates have commonly two sets of symbols used for them. They are defined in ANSI/IEEE Std 91-1984 and its supplement ANSI/IEEE Std 91a-1991. The NOT gate is commonly called an inverter. The circle on the symbol is called a bubble, and is used in logic diagrams to indicate a logic negation between the external logic state and the internal logic state (1 to 0 or vice versa). In the 1980s, schematics were the predominant method to design both circuit boards and custom ICs known as gate arrays.

Consider different kinds of gates:

AND Gate
OR Gate
NOT Gate
BUF Gate
NAND Gate
NOR Gate
XOR Gate
XNOR Gate

Truth Table for AND gate

INPUT		OUTPUT
A	B	A AND B
0	0	0
0	1	0
1	0	0
1	1	1

Truth Table for OR gate

INPUT		OUTPUT
A	B	A OR B
0	0	0
0	1	1
1	0	1
1	1	1

Truth Table for NOT gate

INPUT	OUTPUT
A	NOT A
0	1
1	0

Truth Table for NAND gate

INPUT		OUTPUT
A	B	A NAND B
0	0	1
0	1	1
1	0	1
1	1	0

Truth Table for NOR gate

INPUT		OUTPUT
A	B	A NOR B
0	0	1
0	1	0
1	0	0
1	1	0

Truth Table for XOR gate

INPUT		OUTPUT
A	B	A XOR B
0	0	0
0	1	1
1	0	1
1	1	0

Truth Table for NXOR gate

INPUT		OUTPUT
A	B	A XNOR B
0	0	1
0	1	0
1	0	0
1	1	1

Logic Gates AND, OR, NOT

Logic Gates NAND, NOR, XOR, XNOR

Frequency Domain and Fourier Transform

2012-10-04T01:30:00.001-07:00

Frequency domain analysis is also called spectrum analysis or spectral analysis. Fourier transform is used to convert signals from time or space domain to the frequency domain. Signal information is converted to a magnitude and phase component of each frequency. The Fourier transform is converted to the magnitude of each frequency component squared, forming a power spectrum. This power spectrum is studied to determine which frequencies are present in the input signal and which are missing. The phase information can also be obtained from the Fourier transform. The cepstrum is a commonly used frequency domain transformation which converts a signal to the frequency domain through Fourier transform. It takes the Fourier transform (FT) of the logarithm of the estimated spectrum of a signal. The name cepstrum is devised by reversing the first four letters of the word spectrum. A very important property of the cepstral domain is that the convolution of two signals can be expressed as the addition of their cepstra.

x₁* x₂→ x’₁+ x’₂

Range of Values of Digital Quantities

2012-10-04T01:10:00.002-07:00

To be able to process analog quantities digitally, they have to be converted into digital values.

1 Bit =>	2¹ states	=	2 values
2 Bits =>	2²	=	4 values
3 Bits =>	2³	=	8 values
4 Bits =>	2⁴	=	16 values
8 Bits =>	2⁸	=	256 values
12 Bits =>	2¹²	=	4096 values
16 Bits =>	2¹⁶	=	65536 values
20 Bits =>	2²⁰	=	1048576 values

Transmission of Digital Signals

2012-10-03T22:45:00.000-07:00

Digital data can be transmitted between one or several devices or communication participants by two ways, either parallel or serial transmission.

Bit-parallel transmission
Bit-serial transmission

Parallel data transmission

Serial data transmission

All bits of a piece of information are transmitted at the same time, with parallel transmission, through an appropriate number of signal lines. Due to it's high installation costs they are only acceptable for short distances. The transmission of one byte requires a minimum of nine lines, 8 of which are bits and one is reference potential. This method is presently used for device busses. This application requires high transmission rates over short distances, and without conversion methods. Serial transmission is a good solution for long distances. Only one signal line in serial transmission method transmits the bits, one after the other. The transmission of information takes more time. The installation effort and the costs are considerably reduced because all the information is generated and processed in bit-parallel mode. The transmitter converts the data from parallel to serial, and the receiver reconverts it from serial to parallel. This is performed by specially operated shift registers, integrated in communication modules.

Signal Level of Transistor-Transistor/Low-power Schottky

2012-10-03T22:21:00.001-07:00

Consider the signal-to-noise ratio results from the difference between the transmitting and the receiving level. Using the binary information representation, the signal-to-noise ratio can be adjusted to the environmental conditions within broad limits .

Signal level of a TTL-LS circuit
LOW level
Guaranteed transmitter level	max. 0.5 volt
Guaranteed receiver level	max. 0.8 volt
Static signal-to-noise ratio	0.3 volt
HIGH level
Guaranteed transmitter level	min. 2.7 volt
Guaranteed receiver level	min. 2.0 volt
Static signal-to-noise ratio	0.7 volt

Digital Encoding of Information

2012-10-03T22:03:00.001-07:00

Data and messages can be processed digitally, by encoding them into binary digits. Each piece of information must be converted into a binary unit using an unambiguous code scheme. This process is also called data encoding. Effective data processing is only possible if cooperating computers and programs all use the same codes. Analog information is highly liable to interference and errors are caused by even the smallest disturbance signals, but digitally encoded information will only be distorted when the disturbance signal is larger than the signal-to-noise ratio of the digital level used.

Digital encoding has the following advantages:

High interference immunity
Easy data storage
Flexible processing
Various transmission options

Texts	Hallo	ASCII	48 61 6C 6C 6F
Signed integer	-1181	(16 bits)	FF8A
Floating point	1.375	(32 bits)	3FB00000
Any state	blue, yellow, red,	Fixed Representation Scheme	01, 02, 03,

Bits and Bytes In Hexadecimal Notation

2012-10-03T21:43:00.001-07:00

Digital technology groups 8 bits together to form a byte. It does not very often operate with the smallest possible digital quantity.

Since 8 bits is 1 byte, therefore 8, 16 or 32 bit units are termed accordingly 1, 2 or 4 byte units. When it comes to larger range of values, like 2-byte variable: 01101001 00001101, the binary system with its 0s and 1s soon becomes unclear. So inorder to achieve clarity, hexadecimal system can be used. In this numbering system, each character can assume 16 different values: 0 to 9 and A to F.

Binary and hexadecimal representation of a 4-bit unit

	Hexadecimal	Binary
	0	0000
	1	0001
	2	0010
	3	0011
	4	0100
	5	0101
	6	0110
	7	0111
	8	1000
	9	1001
	A	1010
	B	1011
	C	1100
	D	1101
	E	1110
	F	1111

Quantization Error Caused by A/D Conversion

2012-10-03T21:29:00.003-07:00

Compared to an analog signal, a binary signal which represents only two states contains very little information. If a quantitiy to be represented digitally requires a wider range of values, it must be described by several bits.Analog quantities are processed digitally, when are converted into digital values first. An analog quantity can assume an infinite number of intermediate values while a digital quantity can only assume a limited number of values, therefore when analog signals are converted into discretized digital signals, quantization errors occur. Increasing the number of bits used for digital representation and the sampling rate of the analog signal reduces quantization errors. The complexity of data processing and transmission is increased with an increasing number of bits. The range of values must be adapted to the particular task, while choosing a binary representation that is not too extensive, in order to keep the loss of information during conversion as low as possible.

Quantization error caused by reduced discretization
and sampling rate

Determining the quantization error for displacement measurement:
Analog measuring range --- 0 to 30 cm
Range of values of an 8-bit unit --- 256
Quantization error --- (30/256) cm = 1.2 mm
Range of values of a 12-bit unit --- 4096
Quantization error --- (30/4096) cm = 0.073 mm

Digital Signal

2012-10-03T21:09:00.001-07:00

Digital Signal is a signal which can only take discrete levels. A digitized analog signal or an arbitrary bit stream are digital signals. A signal generated by a modem, is in the first case considered as a digital signal, and in the second case as converted to an analog signal. A waveform that switches between two voltage levels representing the two states of a Boolean value (0 and 1) is referred to as a digital signal. The clock signal is a special digital signal that is used to synchronize digital circuits. The mathematical manipulation of an information signal to modify or improve it is called Digital signal processing. Digital signal transmission has many advantages over analog signal transmission. Applications of digital technology include the continuously growing number of PCs, the communication network ISDN and the increasing use of digital control stations (Direct Digital Control: DDC).

Network Topologies

2012-10-03T03:05:00.000-07:00

There are different layouts of computer networks. The topological structure of a network, either physical or logical is known as network topology.

Network topologies are basically divided into the following:

Physical topologies
Logical topologies

Physical topology is referred to the way a network's different components, devices cables are placed or installed. Logical topology refers to the data flows within a network, regardless of its physical design. Logical topologies are often closely associated with Media Access Control methods and protocols.

There are eight basic physical layouts of networks:

Point-to-point
Bus
Star
Ring or circular
Mesh
Tree
Hybrid
Daisy chain

Electronic Mail (E-mail)

2012-10-02T02:57:00.001-07:00

There are electronic mail systems with which you are all familiar by now. They allow you to send mails and files of data of all kinds from your computers to any other computer with an electronic mail address and a modem. An electronic mail is much more advanced and better to use than the ordinary mail and the telephone. In an e-mail a message can be sent anywhere in the world for free, without having to leave your desk. The same message can be sent to many people at the same time. The message is delivered really very fast, almost at the same moment. It is very easy to send a reply to an e-mail as soon as it is received, using a Reply button. Video, sound and graphics can be sent using an e-mail.

Intranet

2012-10-02T02:41:00.001-07:00

An Intranet is a network for any individual private or government company, it is run along the lines of the World Wide Web. The intranet makes it possible to share documents, databases and applications among many computers in the same company. Intranets have revolutionized the way organizations share information internally, just as the Internet will revolutionize the way businesses communicate with external suppliers, customers and consultants. There are software that let you implement Intranets in your company. A Microsoft Office suite allows to surf Word and Excel documents, reading them in a local Web site in a much similar way, that a web page designer would have designed them. An intranet uses Internet Protocol technology to share information, operational systems, or computing services within an organization.

World Wide Web / WWW

2012-10-02T02:33:00.002-07:00

The World Wide Web or simply known as the Web is a collection of pages stored on computers throughout the world, and joined by hypertext links where a hypertext link is something which enables you to click on a word or graphic, and be taken automatically to the related Web page. World Wide Web or the WWW is the fastest-growing part of the Internet. It became popular due to the Web-browsing software such as Internet Explorer. Yahoo, AOL, MSN and many other companies provide online information services. There are so many banks operating online and also many universities provide their long distance learning online anywhere in the world. Online is a term used for any active communication over the world wide web.

Data Communication/Networks

2012-10-02T02:27:00.002-07:00

Today, data communications and networking are the fastest growing technologies in the world. Professions that make use of technologies are increasing rapidly. A network can be described as a collection of entities wanting to share and have a conversation or the exchange of messages,information or data through physical sources. It can also be defined as resources or facilities that make the conversation possible. Internet is the largest wide area network in the world. It is not a single network, but a collection of thousands of computer networks throughout the world. These are either LAN (Local Area Network), covering an office block or University campus, or a WAN (Wide Area Network) connecting computers over a wide geographical area,
even over several countries.

Differential and Single-ended Signals

2012-10-02T02:06:00.002-07:00

Two complementary paths carrying copies of the same signal in equal and opposite polarity (relative to ground) are called Differential signals.

Differential Device Output

In Single-ended operation there is only one path plus ground. It is a rather common architecture.

Single-Ended Device Output

Signal Formats

2012-10-02T01:38:00.004-07:00

The most common signal formats are as follows:

Non-Return-to-Zero (NRZ)
Delayed Non-Return-to-Zero (DNRZ)
Return-to-Zero (RZ)
Return-to-One (R1)

For NRZ the waveform switches to a “1” and stays at that value until the next cycle boundary, when a valid bit occurs in the cycle. For DNRZ Similar to NRZ, the waveform switches to a “1” after a specified delay time, when a valid bit occurs in the cycle. For RZ the waveform switches to a “1,” then back to a “0” within the same cycle, when a valid bit occurs in the cycle. R1 assumes the cycle begins with a “1”, then switches to a “0” when the bit is valid, then switches back to a “1” before the cycle ends.

Frequency Sweep

2012-10-02T01:30:00.000-07:00

A swept sine wave, a wave that changes in frequency over a period of time is used to measure the frequency characteristics of an electronic device . The frequency change occurs linearly. It is either in Hz per seconds or logarithmically in Octaves per second. Advanced sweep generators support sweep sequences with selectable start frequency, hold frequency, stop frequency and associated times. A trigger signal is synchronously provided by the signal generator to the sweep for controlling an oscilloscope which measures the output response of the device.

Complex Waves

2012-10-02T01:23:00.000-07:00

Complex waves include:

Analog modulated, digitally modulated, pulse-width
modulated, and quadrature modulated signals
Digital patterns and formats
Pseudo-random bit and word streams

Quadrature Modulation

In Signal Modulation waves the amplitude, phase and/or frequency variations embed lower-frequency information into a carrier signal of higher frequency. It gives signals in the form of either speech, data or video. In Analog Modulation the signal varies the carrier’s amplitude and/or frequency. At the receiving end, demodulating circuits interpret the amplitude and/or frequency variations, and extract the content from the carrier. Phase modulation modulates the phase rather than the frequency of the carrier waveform to embed the content. Digital modulation is based on two states which allow the signal to express binary data. In amplitude-shift keying (ASK), the digital modulating signal causes the output frequency to switch between two amplitudes; in frequency-shift keying (FSK), the carrier switches between two frequencies (its center frequency and an offset frequency); and in phase-shift keying (PSK), the carrier switches between two phase settings. In PSK, a “0” is imparted by sending a signal of the same phase as the previous signal, while a “1” bit is represented by sending a signal of the opposite phase. Pulse-width modulation (PWM) is another common digital format; it is often used in digital audio systems. It is applicable to pulse waveforms only. With PWM, the modulating signal causes the active pulse width (duty cycle, explained earlier) of the pulse to vary. Quadrature (IQ) modulation technology is used for building digital wireless communications networks. An in-phase (I) waveform and a quadrature-phase (Q) waveform that is delayed by exactly 90 degrees relative to the “I” waveform are modulated to produce four states of information. An in-phase (I) waveform and a quadrature-phase (Q) waveform are combined and transmitted over one channel, then separated and demodulated at the receiving end. The IQ format delivers far more information than other forms of analog and digital modulation because it increases the effective bandwidth of the system. A digital pattern consists of multiple synchronized pulse streams. It makes up words of 8, 12, 16, or more bits wide data. The digital pattern generator, specializes in delivering words of data to digital buses and processors via parallel outputs. Digital computers have the inability to produce truly random numbers, therefore Pseudo-random bit streams (PRBS) and pseudo-random word streams (PRWS) are used. Digital video signals can have jagged lines on surfaces that should be smooth. Controlled amount of noise is added to hide these jagged lines from the eye without losing the original information. Serializers or multiplexers are tested using PRWS.

Logic Signal Sources

2012-10-01T04:06:00.001-07:00

Types of Logic Signal Sources

Pulse Pattern Generator (PPG)
Data Timing Generator (DTG)

Logic sources are classified into pulse pattern generators and data timing generators. Pulse pattern generators drive a stream of square waves or pulses at very high frequencies from a small number of outputs. the high frequency and fast rise time capabilities of an advanced pulse generator make it an ideal tool to test high-speed digital equipment. The data timing generator generates volumes of binary information. The data timing generator is also called a pattern generator or data generator. It produces the streams of 1s and 0s needed to test computer buses, microprocessor IC devices, and other digital elements. The DTG can be used early in the product development cycle to substitute for system components that are not yet available.

Signal Generator Types

2012-10-01T03:52:00.000-07:00

Signal Generators are broadly divided into the following:

Analog and Mixed Signal Generators
- Arbitrary Generators
  - Arbitrary/Function Generator (AFG)
  - Arbitrary Waveform Generator (AWG)

Logic Signal Sources (Pulse or pattern generators)

Each of these types has unique strengths that may make it more or less suitable for specific applications. The arbitrary/function generator (AFG) offers fewer waveform variations than its AWG equivalent, but with excellent stability and fast response to frequency changes. Arbitrary generators answer almost any kind of signal generation needs. In the past, AFGs created their output signals using analog oscillators and signal conditioning. Now they use Direct Digital Synthesis (DDS) techniques to determine the rate at which samples are clocked out of their memory. The typical AFG has several standard waveforms stored in a preprogrammed part of its memory. In general, sine and square waves are the most widely used for many test applications.

Most AFGs offer some subset of the following familiar wave shapes:

Sine
Square
Triangle
Sweep
Pulse
Ramp
Modulation
Haversine

The arbitrary waveform generator (AWG) can produce any waveform you can imagine. Whether it is an RF signal to test a GSM or CDMA based telephone handset or a data stream for disk drive characterization. An arbitrary waveform generator (AWG) delivers waveforms based on stored digital data describing the constantly changing voltage levels of an AC signal. though the curve makes their spacing appear to vary. In an AWG, the sampled values are stored in binary form in a fast Random Access Memory (RAM). Some AWGs include separate digital outputs. These outputs fall into two categories: marker outputs and parallel data outputs.

Basic Waves

2012-10-01T01:26:00.000-07:00

Following are the Basic types of waves:

Sine waves
Square and rectangular waves
Sawtooth and triangle waves
Step and pulse shapes
Complex waves

Sine waves are the most commonly known wave shape. Most AC power sources produce sine waves. The sine wave is the result of a basic mathematical function. Graphing a sine curve through 360 degrees will produce a definitive sine wave image. The power switches at homes deliver power in the form of sine waves. In classrooms, while teaching about waves, teachers usually give examples of sine waves and use them for demonstration. Square and rectangular waves are at the heart of all digital electronics. A square wave is a voltage that switches between two fixed voltage levels at equal intervals, used for testing amplifiers. A rectangular wave has switching characteristics similar to those of a square wave, except that its high and low time intervals are not of equal length. Sawtooth and triangle waves look very much like the geometric shapes they are named for. The triangle wave has a symmetrical rise and fall times while the sawtooth ramps up slowly and evenly to a peak in each cycle, then falls off quickly.They are used to control other voltages in systems. A step wave shows a sudden change in voltage, as if a power switch had been turned on. The pulse is related to the rectangular wave.It is produced by switching up and then down, or down and then up, between two fixed voltage levels. A pulse may represent one bit of information traveling through a computer. A collection of pulses traveling together creates a pulse train. Complex waveforms may include elements of
sines, squares, steps, and pulses. In real life, waves rarely look like the examples in the graphics that we see here.

Pulse Width

2012-10-01T00:55:00.001-07:00

Pulse width is the time that elapses between the leading and trailing edges of a pulse.

Leading in the above definition means, the positive-going or the negative going edges of a pulse. The events in a given cycle occur in the order described in the definition above. The positive-going edge is the leading edge, while the negative-going edge is the trailing edge. A pulse’s high and low (on/off) time interval is known as duty cycle.

Phase

2012-10-01T00:41:00.002-07:00

Inorder to understand Phase, consider a sine wave. The voltage level of sine waves is related to circular motion. One cycle of a sine wave travels through 360 degrees. Phase shift (also known as delay), describes the difference in timing between two signals. Phase is usually expressed in degrees but a time value may be more appropriate in some circumstances. The phase angle of a sine wave shows how much time it has passed. Two waveforms can have similar frequency and amplitude but they may differ in phase. Two waves may be similar in other ways, but the Phase shift describes the time difference or the delay in the waves.

Phase Shift or Delay

Waveform

2012-10-01T00:30:00.002-07:00

According to an English dictionary a waveform is a usually graphic representation of the shape of a wave that indicates its characteristics (as frequency and amplitude).

A waveform is a representation of how alternating current (AC) varies with time, e.g., sine wave. The sine wave represents energy entirely concentrated at a single frequency. An ideal, unmodulated wireless signal has a sine waveform, with a frequency usually measured in megahertz (MHz) or gigahertz (GHz).

A wave is a pattern of varying quantitative values that repeats over a certain interval of time. They are a periodically repeating phenomena. Signal generators produce electrical (voltage) waves that repeat in a controllable manner. A full repetition of a wave is called a cycle. Waveform graphically represents the activity of the wave and any change in it overtime. Some of the characteristics of waveforms are Amplitude, Frequency, and Phase. Amplitude of a wave measures the strength of the wave from the lowest point that a wave hits to the highest point. In other words it is the maximum disturbance (of a wave) from its undisturbed position. Frequency is the rate at which waveform cycles occur while phase is the time placement of a cycle relative to a reference waveform or point in time.

Signal Generation Techniques

2012-10-01T00:09:00.002-07:00

Signal Generator can be used to create waveforms in many different ways, depending upon the information available about the DUT and its input requirements; whether there is a need to add distortion or error signals, and other variables.

Following are the three ways to develop waveforms,

Create
Replicate
Generate

Creating brand new signals for testing and circuit stimulus, synthesizing a signal captured from an oscilloscope or logic analyzer, and ideal or stressed reference signals for industry standards with specific tolerances .