#### Semiconductor memories, Physics tutorial

Introduction:

The benefit of digital systems over analogue systems is their skill to store information for short and long periods that makes them versatile. Digital computer has minimum amount of memory with the help of which it is capable to manipulate information or data as preferred. It also has memory that makes it able to store this information as long as we desire and make it available to us whenever we wish. The registers are very high-speed memory elements and are utilized widely in internal operation of digital computer. With advent of integrated circuit technology and its further advancement in LSI (Large Scale Integration) and VLSI (Very Large Scale Integration), a large number of registers can be attained on single chip. Cost of such semiconductor devices is also decreasing. Though, cost of these devices per bit of storage is very high, that forbids their use as mass storage devices. The computer has internal memory that is constantly in communication with central processing unit of computer as the program of instructions is being executed. Program and any other information or data utilized by program are also stored in internal memory. Mass storage memory devices are external to computer and are able to store millions of bits even without needing any electrical power. Mass storage memory is usually very slow compared to internal memory and information stored is one which is not presently needed by computer. It is supplied to computer only when needed. Mass storage memory devices are floppies, magnetic tapes and disks, etc. Cost of per bit storage of such devices is much less compared to internal memory.

Capacity of Memory:

Capacity of memory is a term utilized to express how many bits can be stored in the specific memory device or in complete memory system. For instance, consider we have a memory that can store 2048 eight-bit words. This memory can store 2048 x 8 = 16384 bits and we say that memory can store 16384 bits. Another way to express this capacity is as 2048 x 8. This type of expression of memory signifies that there are 2048 words and size of word is 8 bits. Number of words in memory is usually multiple of 1024. Figure of 1024 = 210 is usually represented as 'IK'. Therefore memory capacity of 2048x 8 is also expressed as 2Kx 8. Therefore, 4Mx 8 memory has a capacity of 4,194,304x 8 or alternatively of 33,554,432 bits.

Random-Access Memory (RAM):

Random-Access Memory (RAM) is also called as read-write memory. It is the group of registers that have their unique addresses, and using the suitable address the stored word on memory location can be read and new contents, if desired, can be written on location. Actual physical location of the stored word in RAM doesn't make any difference as access time (that is speed of memory device that is time needed to carry out read operation) is same for any address in memory. Semiconductor RAMs are volatile, as when electrical power is turned off stored data is lost.

While working with the computer when user is giving instructions or doing some calculations using program, it is the RAM which is being continuously utilized to read stored information and write new information. You might have heard term being utilized that particular computer has 1 or 4 MB (Mega Byte) RAM or so.

General Memory Operation:

Despite the fact that internal operation of each kind of memory is different, general memory operation remains the same for all. Every memory system will have terminals for data input, data output, address input, selecting read or write operation and for enabling or disabling memory operation.

In the general memory operation, first the address of memory location is selected where read or write operation is to be done. Decide whether you wish to carry out read or write operation. If you want to write, then carry out write operation and supply data to memory. If you wish to read, and then perform read operation and hold output data coming from the memory. If you want that the memory must respond to address and read/write operation, then enable memory and if you don't wish memory to respond then disable memory.

To demonstrate aforementioned operations consider 16 x 4 memory device shown. As word size is 4 bit, it has four data input lines and four output data lines. It will also have four address lines as the given memory device has 16 memory locations that can be stated by 4-bit addresses.

It has one read/ write command terminal; it will read if kept at 1 and write if at 0. It has one enable/ disable terminal. If this terminal is kept at 1, it enables memory and it disables if kept at 0. A virtual arrangement of memory cells into 4-bit words is shown along with their address.

Read-Only Memory (ROM) is the broad class of semiconductor memories that are designed for those types of applications where only read operation is needed. These memories hold data permanently. In general, no new data can be written on ROM but it can be read. Data to be stored permanently in ROM is selected and built in by manufacturer at time of 1C fabrication. Though, there are some varieties of ROM in which data can be entered electrically once only. Process of entering data is called as programming or burning ROM. Such ROMs are known as PROMs (Programmable-ROM). In some other ROMs data stored can be erased and ROM can be reprogrammed. Such ROMs are known as EPROMs (Erasable-PROM).

All ROMs are nonvolatile i.e. they keep storing data even when electrical power is removed. It has four address lines, eight terminals for data output and one terminal known as chip select (CS) that enables or disables memory. To read data, say, at location with address 1010, we have to apply A3A2A1A0 = 1010 to address inputs and then select chip select so as to enable the memory. Data output terminals will show actual word stored in that location.

A/D and D/A converters:

Digital systems or computers carry out all their functions and internal operations by using digital circuits that need digital inputs. The digital quantity will have value either 0 or 1, while the analogue quantity can take any value over continuous range of values and its exact value is important. Most physical variables are analogue in nature, like temperature, pressure, light intensity, audio signals, position, speed, etc.

Thus, it is necessary to put the analogue quantity to be analyzed using digital system first in digital form. Analogue-to-digital (A/D or ADC) converter is digital circuit that converts analogue quantity in digital form comprising of number of bits which represents value of analogue input. This circuit is utilized as interface between digital system or computer and analogue system of input stage. Output of digital system is digital and has to be converted back in analogue quantity. Digital-to-analogue (D/A or DAC) converter serves this function and its output is proportional analogue voltage or current corresponding to analogue quantity. This is utilized as interface between digital system or computer and analogue system of the output stage.

Digital-to-Analogue Converter:

We are first treating Digital-to-Analogue Converter (DAC) as Analogue-to-Digital Converter (ADC) needs use of DAC. Circuit for DAC takes BCD or binary input and converts it to voltage or current that is proportional to digital value. Digital input is usually derived from output register of digital system that can theoretically be of any number of bits. Generally, registers utilized are 8-bit registers. For purpose of an illustration, consider that digital output from digital system is of four bits. Thus, we need a DAC which can convert 4-bit digital output to proportional analogue value.

Block diagram of such a DAC has four binary input lines representing A3A2A1A0 and one output line representing corresponding proportional analogue quantity. Each 4-bit input has unique proportional output voltage. There are 24 = 16 states that binary input can contain. Let us say that each input specifies decimal number. Let us designate 1V output equivalent to decimal number 1, 2V as number 2, and so on.

The output voltage could be twice the binary number or any multiple. We can, thus, write

Analogue output = k x digital input where k is proportionality factor, a constant for given DAC.

Value of k in given example is 1V, thus out V is 1V times the digital input. For 01102 = 610, we get out V = 1 V x 6 = 6 V

Analogue Output:

DAC output is technically not the analogue quantity. It can have only specific values. In above example, it can contain values only from 0 to 15 in steps of 1, that is 1, 2, 3, ..., 15. Thus, strictly speaking it is digital. By increasing number of input bits, number of possible output values can be increased and difference between successive values decreased. Therefore output can be made more or less analogue. For time being we can only say that DAC output is pseudo analogue.

Resolution (Step Size): Resolution is smallest change which can occur in analogue output because of a change in digital input. Resolution is also called as step size. In said example, voltage rises in step of 1 V and goes up from 0 to 15 in 15 steps.

It can simply be observed that there are 16 levels from 0 to 15V, but there are just 15 jumps. That is, number of steps between 0 and 16 is 15. Number of steps in general can be computed as

Number of steps = 2n - 1.

Resolution or step size is really constant k in equation. Percentage resolution is stated as

%resolution = (step size/full scale) x 100

DAC circuit:

There are numerous methods and circuits for digital to analogue conversion that need not be known. The basic DAC circuit is attained using op-amp as summing amplifier. 4-bit DAC circuit is shown. Input resistors are binary weighted, that is, they are in ratio of 1 : 2 : 4 : 8.

Output voltage of this circuit is provided as

Vout = -(VA3 + 1/2.VA2 + 1/4.VA1 + 1/8.VA0)

Negative sign signifies that it is inverting amplifier. Digital input bits can be either 0 or 1, thus VA3, VA2, VA1, V A0. VA0 will have values either 0 or 5V. Thus, out V for 0001 or LSB would be one-eighth of 5V, i.e. 0.625V. And this is the step size of this converter. Sixteen levels of the out V are shown

Analogue-to-Digital Converter:

Circuit of counter type (or digital ramp) Analogue-to-Digital Converter (ADC) is shown below. It comprises of op amp as comparator, a DAC, counter and a 3-input AND gate.

Functioning of this kind of ADC is as follows:

Apply start pulse that is making START input equal to 1. This resets counter to 0 output. With 1 at START input, AND gate is inhibited that doesn't permit CLK from passing through AND gate. Counter output is input to DAC. With counter reset, DAC output ax V = 0. VA is analogue input to be converted in its digital equivalent. As Vax< VA, op amp comparator output EOC is HIGH, i.e., 1. When start pulse returns to 0, AND gate permits CLK to pass through and CLK reaches counter that begins counting. As counter advances, DAC output V ax advances step by step as shown in the figure. When Vax reaches step that exceeds VA, EOC goes low, i.e., 0, disabling AND gate. Thus, CLK can't pass through and counter stops advancing further. Conversion of analogue input in its digital equivalent is complete. Contents of counter are digital representative of VA. Counter holds output until next start pulse to initiate the new conversion is supplied.

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