AND Gate

The AND gate performs logical multiplication, commonly known as AND function. The AND gate has two or more inputs and single output. The output of AND gate is HIGH only when all its inputs are HIGH (i.e. even if one input is LOW, Output will be LOW). If X and Y are two inputs, then output F can be represented mathematically as F = X.Y, Here dot (.) denotes the AND operation. Truth table and symbol of the AND gate is shown in the figure above.

Truth Table For AND gate

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

AND Gate using Diodes We use the same logic levels, but the diodes are reversed and the resistor is set to pull the output voltage up to a logic 1 state. For this example, +V = +5 volts, although other voltages can just as easily be used. Now, if both inputs are unconnected or if they are both at logic 1, output Z will be at logic 1. If either input is grounded (logic 0), that diode will conduct and will pull the output down to logic 0 as well. Both inputs must be logic 1 in order for the output to be logic 1, so this circuit performs the logical AND function.

AND Gate using Transistors

A simple 2-input logic AND gate can be constructed using transistor switches connected together as shown below with the inputs connected directly to the transistor bases.

Types of AND IC's

TTL Logic Types	CMOS Logic Types
74LS08 Quad 2-input	CD4081 Quad 2-input
74LS11 Triple 3-input	CD4073 Triple 3-input
74LS21 Dual 4-input	CD4082 Dual 4-input

Application of AND Gate

• Garden Floodlight System

• subsystem diagram

This will be discussed in detail later

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Logic Blocks in Digital Basics

Depending upon how these "switches" and "inverters" are arranged in integrated circuits we are able to obtain "logic blocks" to perform various tasks. In figure 2 we look at some of the most basic logic blocks. In the first set of switches A, B, and C they are arranged in "series" so that for the input to reach the output all the switches must be closed. This may be considered an "AND-GATE".

In the second set of switches A, B, and C they are arranged in "parallel" so that for any input to reach the output any one of the switches may be closed. This may be considered an "OR-GATE".

These are considered the basic building blocks in digital logic. If we added "inverters" to either of those blocks, called "gates", then we achieve a "NAND-GATE" and a "NOR-GATE" respectively.

Here in figure 3 we examine the digital basics in schematic form. Now here we have depicted four major logic blocks AND-GATE, NAND-GATE, OR-GATE and NOR-GATE plus the inverter. Firstly the "1's" and the "0's" or otherwise known as the "ones" and "zeros". A "1" is a HIGH voltage (usually the voltage supply) and the "0" is no voltage or ground potential. Other people prefer designating "H" and "L" for high and low instead of the "1's" and the "0's". Stick with which system you feel most comfortable. Several interesting points emerge here. Of interest to the next section on binary numbers is the pattern of all the inputs for each logic block. Not only are they identical but, for only two inputs A and B there are four possible output situations which are called "states". These are digital basics. There actually can be many numbers of inputs. An eight input NAND-GATE is a common and quite useful digital logic block. Next of particular interest is if you study them very carefully, that for the very identical inputs, each of these logic blocks gives us a totally different output result. Compare them. Finally for the same inputs the NOR-GATE outputs are the direct opposite to the AND-GATE outputs while the OR-GATE outputs are the direct opposite to the NAND-GATE outputs.

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Digital Electronics Basic Principle

Digital circuits work on the basis of a transistor being used as a switch. Consider a light switch, a transistor can be considered almost the same and in some circuits transistors are used to control large amounts of power with very little input power being used. Look at figure 1 below. Here are two crude transistor switch circuits. In the first circuit if there is no voltage applied to the base of Q1 then it is not switched "on" and accordingly the + 5V passing through the 10K load resistor from our + 5V supply appears at both the collector of the transistor and also at output 1. If we apply + 5V to the base of Q1 then because it is greater than 0.7 V than the grounded emitter, Q1 will switch on just like a light switch causing the + 5V from our supply to drop entirely across the 10K load resistor. This load could also be replaced by a small light bulb, relay or LED in conjunction with a resistor of suitable value. In any event the bulb or led would light or the relay would close. The basic principle in digital basics is that we have just created an "electronic switch" where the positive voltage on the base produces zero voltage at the output and zero voltage on the input produces the + 5V on the output. The output is always the opposite to the input and in digital basics terms this is called an "inverter" a very important property. Now looking at Q2 and Q3 to the right of the schematic we simply have two inverters chained one after the other. Here if you think it through the final output 2 from Q3 will always follow the input given to Q2. This in digital basics is your basic transistor switch.

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Forward and reverse bias in pn junctions

We now consider a p-n diode with an applied bias voltage, Va. A forward bias corresponds to applying a positive voltage to the anode (the p-type region) relative to the cathode (the n-type region). A reverse bias corresponds to a negative voltage applied to the cathode. Both bias modes are illustrated with Figure below. The applied voltage is proportional to the difference between the Fermi energy in the n-type and p-type quasi-neutral regions. As a negative voltage is applied, the potential across the semiconductor increases and so does the depletion layer width. As a positive voltage is applied, the potential across the semiconductor decreases and with it the depletion layer width. The total potential across the semiconductor equals the built-in potential minus the applied voltage,

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The built-in potential

The built-in potential in a semiconductor equals the potential across the depletion region in thermal equilibrium. Since thermal equilibrium implies that the Fermi energy is constant throughout the p-n diode, the built-in potential equals the difference between the Fermi energies, EFn and EFp, divided by the electronic charge. It also equals the sum of the bulk potentials of each region, fn and fp, since the bulk potential quantifies the distance between the Fermi energy and the intrinsic energy. This yields the following expression for the built-in potential.

Example 2

An abrupt silicon p-n junction consists of a p-type region containing 2 x 10^16 cm-3 acceptors and an n-type region containing also 10^16 cm-3 acceptors in addition to 10^17 cm-3 donors. 1. Calculate the thermal equilibrium density of electrons and holes in the p-type region as well as both densities in the n-type region. 2. Calculate the built-in potential of the p-n junction 3. Calculate the built-in potential of the p-n junction at 400 K..

Solution

where the instrinsic carrier density at 400 K was obtained from example1 1. The thermal equilibrium densities are: In the p-type region: p = Na = 2 x 10^16 cm-3 n = ni^2/p = 10^20/2 x 10^16 = 5 x 103 cm-3 In the n-type region n = Nd - Na = 9 x 10^16 cm-3 p = ni2/n = 10^20/(1 x 10^16) = 1.11 x 10^3 cm-3 2 The built-in potential is obtained from: 3.Similarly, the built-in potential at 400 K equals:

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Thermal equilibrium for pn junctions

To reach thermal equilibrium, electrons/holes close to the metallurgical junction diffuse across the junction into the p-type/n-type region where hardly any electrons/holes are present. This process leaves the ionized donors (acceptors) behind, creating a region around the junction, which is depleted of mobile carriers. We call this region the depletion region, extending from x = -x_p to x = x_n. The charge due to the ionized donors and acceptors causes an electric field, which in turn causes a drift of carriers in the opposite direction. The diffusion of carriers continues until the drift current balances the diffusion current, thereby reaching thermal equilibrium as indicated by a constant Fermi energy. This situation is shown in Figure below While in thermal equilibrium no external voltage is applied between the n-type and p-type material, there is an internal potential, fi, which is caused by the workfunction difference between the n-type and p-type semiconductors. This potential equals the built-in potential, which will be further discussed in the next section

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