Analog to Digital Conversion (ADC)The process of converting an analog voltage into an equivalent digital signal is know as analog to digital (ADC) conversion. Although a pure analog system is capable of better accuracy than a digital system, its accuracy is rarely completely usable because it is presented in a form that cannot be read, recorded or interpreted to such high accuracy. This is why pure analog data are converted to digital form. Digital data, however are readily presented in numerical form, and are easily manipulated, processed, stored and recorded.A great variety of ADC has been made to satisfy a broad spectrum of requirements. In some applications the dominant parameters are the precision and stability of conversion, in others conversion speed is of greatest important. There are various type of analog to digital converters. Some of them are given as under:1. Counter type ADC2. Successive Approximation type ADCCounter Type ADCFigure 1 shows the block diagram of counter type ADC. As shown, it comprises on input voltage comparator a clock generator, a gate and n-bit counter.To begin with, the counter is reset to all 0's. Then a converted signal appears on the start-lie, the input gate is ENABLED and the clock pulses are allowed to the counter's clock input. The counter advances through its normal binary count sequence, the staircase waveform is generated at the output of the binary ladder constituting a DAC. This staircase waveform forms one of the inputs of the comparator whose other input is the analog input signal. Whenever the binary ladder output exceeds the analog input voltage, the comparator changes state, the gate is DISABLED and the counter stops. The counter output is then the required digital output corresponding to analog input signal.

The counter type ADC provides a very good method for digitizing to a high resolution. This method is much simpler than the simultaneous method for high resolution, but the conversion time required is longer. Since the counter always begins at zero and counts through its normal binary sequence , it may require as many as 2ncounts before conversion is complete. The average conversion time is 2n/ 2 or 2n-1counts, where n is the number of bits of the counter.Successive Approximation MethodSuccessive approximation ADC is much faster than the counter ADC. In an n-bit converter, the counter type ADC on an average would require 2n+1clock cycles for each conversion whereas successive approximation type conversion requires only n clock cycles,Figure 2 shows the bock diagram of successive approximate ADC, the operation is as follows.WorkingThe output from the DAC are programmed to be all initially low, then DAC is at zero count. The MSB output bit of digital to analog converter is caused to go high and the comparator is sensed for a state changed. If the change occurs the MSB output from the digital to analog converter is returned to low, as the digital to analog converter output voltage was greater than the input voltage, if no change occurs the MSB output is left high.

The next lower DAC output bit is caused to go high and the comparator is sensed for a state change. If a change occurs the bit is returned to low, as the new DAC output voltage was greater than the input voltage. This process of changing the next lower DAC output bit and sensing teh comparator for a change is continued through the LSB of the DAC.When the process is complete, the final DAC output states represent the digital equivalent of the step just below the actual input voltage magnitude. The whole requires a maximum of only 2npulses to complete the entire analog to digital conversion.SpecificationsThe major ADC specifications are resolution, accuracy and speed.ResolutionThe resolution for an ADC is defined as the change in analog input voltage for obtaining change in output by one bit. The resolution of ADC is given asResolution = ( E / (2n- 1) X 100%)AccuracyAccuracy is defined as the difference between the digital output values and the analog input values of the ADC.SpeedSpeed in converters is another important specification. In ADC converters speed is the time to perform one conversion.Digital to analog converterDigital to analog converter is used to convert digital quantity into analog quantity. DAC converter produces an output current of voltage proportional to digital quantity (binary word) applied to its input. Today microcomputers are widely used for industrial control. The output of the microcomputer is a digital quantity. In many applications the digital output of the microcomputer has to be converted into analog quantity which is used for the control of relay, small motor, actuator e.t.c. In communication system digital transmission is faster and convenient but the digital signals have to be converted back to analog signals at the receiving terminal. DAC converters are also used as a part of the circuitry of several ADC converters.There are several ways of making a digital to analog converter. Some of them are given as under.1. Binary weighted resistor DAC2. R-2R Ladder network3. Serial DAC converter4. BCD DAC5. Bipolar DACBinary weighted Resistor DACA binary weighted resistor ladder D/A converter is shown in figure 1.

It consists of the following four major components.1. n switches one for each bit applied to the input2. a weighted resistor ladder network, where the resistance are inversely proportional to the numerical significance of the corresponding binary digital3. a reference voltage Vrefand4. a summing amplifier that adds the current flowing in the resistive network to develop a signal that is proportional to the digital input.The behavior of the circuit may be analyzed easily by using "Millman'stheorem". It state that "the voltage appearing at any node in a resistive network is equal to the summation of the current entering the node (assuming the node voltage is zero) divided by the summation of the conductance connected to the mode".Mathematically we can write

Assume that the resistor R1, R2, R3....... Rnare binary weighted resistors, thusR1= RR2= 2RR3= 4R........................................Rn= (2n-1) R

A Resistor Ladder Network, can delivers a binary number say number of n bits.

Each bit controls a switch sithat is connected to Vref.when ai= 1 , then bit is ON, and whenai= 0, then bit is OFF.The reference voltage source VRis considered to have zero internal impedance. The resistor that are connected to the switches have value such as to make the current flow proportion to the binary weight of the respective input. But the resistor in the MSB position has the value R, the next has the value 2R etc. The resistor of the LSB have the value of(2n-1) R.The current flowing in the summing amplifier is

Multiplying and dividing by (2)n-1R

Above relation shows that output voltage of the D/A converter is proportional to a number represented by the switch that are connected to VRi.e. ai= 1Maximum current will flow when all aicoefficient are 1, i.e.

When all the bits of digital word have value of 1, then the output current of D/A converter is termed the full scale output current and is an important design parameter.On the other hand, if all switches are open i.e. all aicoefficients are zero, then the output voltage (current) is zero.The maximum output voltage Vo= -RiI depends on the feedback resistor Rf. As, the operational amplifier is operated in the negative feedback mode for the purpose of summing so that it performs as an excellent current to voltage converter.AdvantagesAs only one resistor is used per it in the resistor network, thus it is an economical D/A converter.Disadvantages / Limitations1. Resistors used in the network have a wide range of values, so it is very difficult to ensure the absolute accuracy and stability of all the resistors.2. It is very difficult to match the temperature coefficients of all the resistors. This factor is specially important in D/A converters operation over a wide temperature range.3. When n is so large, the resistance corresponding to LBS can assume a large value, which may be comparable with the input resistance of the amplifier. This leads to erroneous results.4. As the switches represent finite impedance that are connected in series with the weighted resistors and their magnitudes and variations have to be taken in to account in a D/A converter design.R-2R Ladder NetworkR-2R Ladder NetworkIn case of weighted resistor DAC requires a wide range of resistance values and switches for each bit position if high accuracy conversion is required. A digital to analog converter with an R-2R ladder network as shown in figure 2 eliminates these complications at the expense of an additional resistor for each bit.

The operation of R-2R ladder DAC is easily explained considering the weights of the different bits one at a time. This can be followed by superposition to construct analog output corresponding any digital input word. Let only the MSB is turned ON in the first case, and all other bits are OFF, a simplified equivalent circuit can be drawn as shown in figure 3.

Figure 3: Equivalent Circuit for R-2R ladder network, when MSB is ON and all other are OFFThe equivalent circuit with only switch Sn-2connected to the reference voltage is shown in figure 4.

By using principle of superposition all contributions are summed up and the resultant output isVo= VR[an-12n-1+ an-22n-2+ .............a12-(n-1)+ ao2-n]Vo= VR2-n[an-12n-1+ an-22n-2+ .............a12+1+ ao2o]

Note that aidepends on whether thithe switch is at 0 or at VR. Thus the output of the DAC is proportional to the sum of the weights represented by thoseeswitches that are connected to VRand the ratio of resistors in the R-2Rladder network.From this circuit, voltage at mode (n-1) is given byVn-1= VR(R/3R)(-3R) = VR/3As the input terminal of the operational amplifier is at virtual ground. If the feedback resistor Rffor the operational amplifier is taken as 3R, the corresponding output voltage du to the MSBalone isVo= (VR/ 3 ) ( -3R / 2R ) = - VR/ 2Let next switch Sn-2at VRwith all other switches at zero. Here, the current at node (n - 2) divide equally to the right and to the left resulting in a voltage at node (n - 2)Vn-2= VR/ 3This voltage is attenuated by a factor of 2 at node ( n - 1 ), asVn-1= Vn-2( R / 2R) = VR/ 6Output voltage due to node n-2 at the operational amplifier isVo= ( VR/ 6 ) ( -3R / 2R) = - VR/ 4Advantages1. Only two values of resistors are used; R and 2R.2. The actual value used for R is relatively less important as long as extremely large values, where stray capacitance enter the picture, are not employsonly ratio of resistor values is critical.3. R-2R ladder network are available in monolithic chips,. These are laser trimmed to be within 0.01% of the desired ratios.4. The staircase voltage is more likely to be monotonic as the effect of the MSBresistor is not many times grater than that for LSB resistor.

Operational Amplifier differentiator & Integrator

Operational Amplifier differentiatorThe operational amplifier is an amplifier which is directly coupled between the output and input, having a very high gain. It is used to perform a wide variety of mathematical operations like summation, subtraction, multiplication, differentiation and integration etc. in analogue computers.An operation amplifier can be used as a differentiator as shown in Fig. 1. This circuit produces an output voltage that is proportional to the time derivative input voltage. Hence this circuit is called differentiator.

Assuming that G is virtually ground. Since the current flowing in to the virtual ground is equal to current flowing out of it we can write.i1= if= i-1i_ = 0i1= if-=0i1= iffrom the definition of capacitance, thecharge on the capacitor isq = CVHence, output voltage V0is equal to a constant RC times the derivative of the input voltage Vi.Operational Amplifier IntegratorAn operational amplifier can also be used as a integrator by changing the position of R and C as shown in Fig. 2. this circuit produces an output voltage that is proportional to the time integral of the input voltage. Hence, this circuit is called an integrator.

Assuming that G is virtually ground. Since the current flowing in to the virtual ground is equal to the current flowing out of it we can write.i1+ if =i_i_= 0i1+ if= 0i1= if

Hence, output voltage V, is equal to a constant -1/RC times the integral of the input voltage Vi.

MEMORYOne of the most basic functions which a digital computer must perform is that of storing information. The stored information includes both the data to be processed and the instruction specifying the processing steps. The memory unit in a digital computer performs the storage function. It must provide means of access for the retrieval or readout, and alteration or write-in, of selected portions of the stored information. Therefore the memory unit must be able to retain, identify and retrieve digital information upon the appropriate commands.The memory can be classified as operation memory, inner memory and auxiliary memory. The operation memory is the fastest memory and it normally consist of flip flop register. The earlier versions used transistors but now SSI and MSI memories are available. The flip flops have high cost per stored bit and that is why these are not used for bulk storage. The inner memory or the main memory has moderate cost per stored bit. This memory is normallyof passive elements like ferrite cores. Semiconductor memories (MSI and LSI) are now being used as inner memories. The inner memory is supposed to be as fast as possible, because all the information processing is done through the main memory. Normally auxiliary memory or secondary memory is added to most of the computers. The main characteristics of this memory are low cost per bit of information stored. It has a high access time as compared to operation and inner memory. Magnetic tape and magnetic discs from this bulk storage memory.Types of MemoriesThe memories can be classified as:Static (stationary)Dynamic1. StaticA static storage device is one in which the information does not change positions: flip-flop, registers, magnetic-core registers or even punched cards or tape are examples of static devices.2. DynamicDynamic storage devices are devices in which information stored is continually changing position. Circulating register utilizing delay lines are examples of dynamic storage devices, as are magnetic drums, and magnetic disks. Dynamic storage provides the property of compressed time, which has an application in correlation receivers.The storage can be both temporary and permanent. Also access to the stored data falls into two classification:random access, the facility to go directly to the stored location to read the data; andsequential access, where the data are scanned in a predetermined manner and access to a particular storage location is obtained by waiting until the desired location is reached. A flip-flop register is an example of a random access storage device while a magnetic tape is an example of sequential access memory.Memory system in which the stored information is lost when the power is turned off, or in which it is lost with elapse of time are known as volatile memories. For example a memory made up of IC flip-flop is volatile as information is lost when power is turned off. A non-volatile memory holds the information even after the power is removed. Example are the magnetic core, magnetic drum, Ferro electric devices and film.Another way to subdivide memory unit is according to whether it is primary or auxiliary. Primary or internal storageforms an essential part of the memory unit. It performs the following three main functions in a digital computer.1. The temporary storage of numbers and instructions directed to and from the input-out.2. The storage of all data instructions required for the problem begin handled by the computer.3. Temporary storage of the intermediate results of any calculation.As in the case of computers, digital instruments have instructions or numbers stored in an arrangement of bistables or flip-flop, each capable of storing one bit of information.RAMIn read and write memory or random access memory (RAM), data can be stored (or written) into the memory as well as read out.ROMIn read only memory (ROM) , data are permanently stored by the manufacturer or user and data can only be read later, and the stored data are not changed when the circuit is switched off.EPROMEPROM or electrically programmed read only memory (or known as erasable programmableROM) allows a user with the required equipment later to change the stored data. In use, such memories only have data read from them.Now the size of the memory circuit is given in terms of the number of bits of data it can stored. Most instruments use the bits as a group or word of data. Figure 1 (a) shows general RAM with data input lines to the left and the write input below. When the latter goes HIGH, the data on the input lines, would set up an bits of the memory at the section specified by the address lines. The k address lines can specify 2ksuch sections, each of n-bits, so the total number of elements in the memory is 2kx n bits. For example, a memory of 256x8 bit size would deal with 8-bit data word, it would have eight address lines as 28= 256 and would be called a 2k memory chip.