CHAPTER 6 DIGITAL INSTRUMENTS - PDF Free Download

CHAPTER 6 DIGITAL INSTRUMENTS 1

LECTURE CONTENTS 6.1 Logic Gates 6.2 Digital Instruments 6.3 Analog to Digital Converter 6.4 Electronic Counter 6.6 Digital Multimeters 2

6.1 Logic Gates 3

AND Gate The AND operation is the basic Boolean Operation. The truth table in Figure 6.1 shows what happen when two logic inputs A and B combined using the AND operation to produce output x. The table shows that x is a logic 1 only when both A and B are at the logic level 1. For any case where one of the inputs is 0, the output is 0. The Boolean expression for the AND operation is X = A.B 4

A B AND GATE (a) x=ab Figure 6.1: AND Gate AND A B x=ab 0 0 0 0 1 0 1 1 0 1 0 1 (b) 5

OR Gate The OR operation is also the basic Boolean Operation. The truth table in Figure 6.2 shows what happen when two logic inputs A and B are combined using OR operation to produce the output x. The table shows that x is logic 1 for every combination of input levels where one or more input are 1. The only case where x is 0 is when both inputs are 0. The Boolean expression for the OR operation is X = A + B 6

A B OR GATE (a) x=ab OR A B x=a+b 0 0 0 0 1 1 1 1 0 1 1 1 (b) Figure 6.2: OR Gate 7

NOT Gate The NOT operation is unlike the OR and AND operations in that it can be performed on a single input variable. For example, if the variable A is subjected to the NOT operation, the result x can be expressed as x A 8

A NOT Gate x=a NOT A x=a 0 0 1 0 (a) (b) Figure 6.3 : NOT Gate 9

NOR and NAND gates Two other types of logic gates, NOR gates and NAND gates are used extensively in digital circuitry. These gates actually combine the basic operations AND, OR and NOT, which make it relatively easy to describe them using the Boolean algebra operations learned previously. 10

NOR gate The symbol for two input NOR gate is shown in Figure 6.4. It is the same as the OR gate symbol except that it has a small circle on the output. The small circle represents the inversion operation. Thus, the NOR gate operates like an OR gate followed by an INVERTER, so that the circuits is Figure 6.4 are equivalent, and the output expression for the NOR gate is x A B 11

A B A B OR GATE (a) x=a+b x=a+b OR A B A+B 0 0 0 0 1 1 1 1 0 1 1 1 (b) NOR A+B 1 0 0 0 Figure 6.4: NOR Gate 12

NAND Gate The symbol for a two input NAND gate is shown in Figure 6.5. It is the same as the AND gate symbol except for the small circle on its output. Once again this small circle denotes the inversion operation. Thus the NAND operates like an AND gate followed by the inverter, so that the circuits of Figure 6.5 are equivalent, and the output expression for the NAND gate is x AB 13

A B A B OR GATE x=ab x=ab AND A B A+B 0 0 0 0 1 0 1 1 0 1 0 1 NAND A+B 1 1 1 0 (a) (b) Figure 6.5: NAND Gate 14

6.2 Digital Instruments 15

Digital Instruments Digital instruments offer several very attractive advantages over analog instruments including 1) greater speed, 2) increased accuracy and resolution, 3) reduction in user errors and 4) the ability to provide automatic measurement in system applications. 16

Digital instruments versus digital readout instruments A digital readout instrument is one in which the measuring circuitry is of analog design while only the indicating device is of digital design - no more accurate than the same analog instrument with analog readout. A digital instrument is one in which the circuitry required to obtain a measurement is of digital design - unambiguous and can be read more 17 quickly.

Digital Display Analog to Digital Converter Digital Display Analog Input Signal Conditioning Analog Circuitry Digital Logic Circuitry Digital Readout Instrument Signal Conditioning Analog to Digital Converter Analog Input Digital Instrument Figure 6.6: Block Diagram of Digital Instrument and Digital Readout Instrument 18

Comparison of digital and analog meters Digital instruments use logic circuits and techniques to carry out measurements or to process data. Digital instruments may be viewed as an arrangement of logic gates that change states at very high speeds in the process of making a measurement. Because of the rapidly expanding use of digital techniques in measuring instruments, a comparison of factors affecting error in measurement when using analog and digital instruments is made. 19

Comparison of digital and analog meters 1. Readability digital meter easy to read. 2. Accuracy digital meter more accurate. 3. Resolution digital meter provide more resolution. 4. Sample Speed more faster to get stable reading. 5. Digits displayed and overranging allow the user to read beyond full scale. 20

6.3 Analog to Digital Converter 21

Analog to Digital Converter Digital instruments, particularly digital multimeters are used to measure analog parameter, therefore it is necessary to convert the analog signal to an equivalent digital signal. The three conversion techniques generally used are 1) single-slope, 2) dual-slope and 3) voltage-tofrequency conversion. Most of the laboratory-quality digital multimeters use dual-slope conversion 22

Single-slope converter Low cost instruments. To make a linear conversion of unknown voltage to time. Conversion to time is chosen because a digital counting circuit be used to display the time in digital format. 23

V C R t V C Constant Voltage Source C V C (a) R Constant Current Source C t V C (b) Figure 6.7: Voltage time relationship for a charging capacitor 24

Single-slope converter use an operational amplifier integrator circuit. C t 1 t 2 t 3 t 4 t 5 t 6 t 7 V in R V in - + V O 0 t (a) 0 t V 0 (b) Figure 6.8: Op amp Integrator and Associated Waveform: (a) Schematic, (b) Input Squarewave to Output with Linear Voltage Time Relationship 25

Single-slope converter S Driver Main Gate Control 1 C S Digital Readout V in R 2 - + Integrator Comparator 3 4 5 Binary Counter S Open S Closed 1 VX Clock V X 1 (a) 0 2 0 3 Figure 6.9: Circuit and Timing Diagram for a Single Slope A to D Converter 0 0 (b) 26 4 5

Single-slope converter It can measure voltages of only one polarity. Additional circuitry is required for overrange conditions. The circuit is susceptible to oscillator frequency shift. The circuit is susceptible to drift in the constant current source. Accuracy depends on the stability of the capacitor. Accuracy depends on the stability of the different voltage that trips the comparator. The converter is very susceptible to noise on the analog voltage. 27

Dual-slope A/D Converter Overcome most of the limitations of single-slope converters in particular, improved long term accuracy. Also uses a capacitor charged by a constant current source to provide a voltage to time conversion. This charge/discharge cycle tends to reduce significantly the long term drift and stability problems associated with single-slope converter. 28

Dual-slope A/D Converter Logic Control CIrcuit S 2 C V ref B A V in S 1 R - + Integrator - - + Counter V i Clock Figure 6.10: Basic Dual- Slope A/D Converter 29

Dual-slope A/D Converter When switch S1 at the position A, the integrator is connected to the input and the voltage of the output integrator is; V A 1/( RC) V dt With S1 in position B, the reference voltage Vref is connected to the input of the integrator, which cause the integrator capacitor C to discharge at the constant rate. During the period of discharge from t 2 to t 3 the voltage VA at the output of the comparator is given by; V A 1/( RC) i V ref dt 30

Dual-slope A/D Converter Integrator Output t 1 t 2 t 3 Comparator Output Figure 6.11: Integrator and Comparator Output Waveform for the Circuit in Figure 6.10 31

Dual-slope A/D Converter When the output of the integrator reaches zero at t 3, the comparator changes states setting its output low which disables the counter. The count registered by the counter at this time is directly proportional to the ratio of the input voltage to the reference voltage. This proportional relationship can be developed mathematically; V A 1/( RC) V dt i If the capacitor charges linearly, can be written as, V A V i ( T / RC) V ( t t )/( RC) i 2 1 32

Dual-slope A/D Converter If the capacitor discharge at a linear rate then equation (6.2) can be expressed as; V A V ref ( T / RC) V ( t t )/( RC) ref 3 2 Since the right sides of the both equation (6.4) and (6.5) are equal to VA they can be set equal to each other. Thus V Hence, ( i 2 t t )/( RC) V ( t t )/( RC) 2 1 ref 3 t t ( t t ) V i / V 3 2 2 1 ref 33

Example 6.1 An integrator contains 100kΩ resistor and a 1μF capacitor. If the voltage applied to the integrator input is 1V, what voltage will be present at the output of the integrator after 1 sec? Solution Using equation (6.4), compute the integrator output as V V A A V i ( t 2 t 1 ) /( RC) 5 1 0 sec/ 1 10 1 F V 1V 10 34

Example 6.2 If the reference voltage applied to the integrator at time t 2 in Example 1 is 5V in amplitude, what is the time interval form t 2 to t 3? Solution Using equation (6.7), the time interval can be computed as t 3 t 2 ( t 2 t 1 ) V i / V ref t 3 t 2 1sec 1V / 5V 0.2 sec 35

Voltage to Frequency Converters A voltage to frequency converters converts an input voltage to a periodic waveform whose frequency is directly proportional to the input voltage. Voltage to frequency converter is very linear, wide range and voltage controller oscillator (VCO). The basic concept of voltage to frequency conversion is demonstrated in Figure 6.12. The output signal from the VCO is applied to one input of a two AND gate. The second input to the AND gate is identical to the VCO output. If there is linear relationship between the VCO input voltage and output frequency, the AND gate output can be applied to a digital counter to provide an indication of the VCO input voltage. 36

Voltage to Frequency Converters V i VCO Gating Pulses To digital counter Gate Pulse Generator Figure 6.12: Block Diagram of a Basic Voltage to Frequency Converter 37

Example 6.3 The relationship between the input voltage V i and the output frequency f for the VCO in figure 7 is given as V i = f /50 If 530 pulses are passes by the AND gate during a 0.1 sec gating pulse, what is the amplitude of V i? Solution The VCO output frequency is f = pulse/gate duration = 530 pulses/0.1 sec = 5300 Hz the voltage is, V i = f/50 = 106 V 38

Voltage to Frequency Converters The basic circuit of Figure 6.12 has limited usefulness primarily because of the nonlinearly of the VCO. The block diagram show in Figure 6.13 is more useful voltage to frequency converter. This basic circuit consists of an integrator, a voltage comparator, a pulse generator and voltage reference source. When the unknown voltage is applied to the integrator, its output voltage begins to increase at a rate proportional to the magnitude of the input voltage. When the amplitude of the voltage of the integrator exceeds to the amplitude of the reference voltage the comparator output change states. 39

Voltage to Frequency Converters This voltage change at the output of the comparator causes a pulse out of the pulse generator and will discharge the integrator capacitor and resets the comparator, after which a new ramp is initiated. A short duration pulse appears at the comparator output which appears at the frequency that is proportional at the input signal level. The number of pulses per-unit of time can be counted with a digital counter, thereby completing the analog to digital conversion. 40

Voltage to Frequency Converters C Dc Volts In R + - Comparator - - + To Counter R Reference Voltage Pulse Generator Figure 6.13: Voltage to Frequency Converter that Uses an Integrator 41

Voltage to Frequency Converters The primary advantages and limitations of the voltage to frequency converter are as follows; Advantages, 1) Good 50Hz noise rejection without noise filters, which would reduce sampling period. 2) Circuit is easily adapted to a digital counter. 3) Circuit requires no special overranging circuit. Limitations, Accuracy is limited by, 1) stability of the integrating time constant. 2) Stability and accuracy of the comparator switching point. 3) Stability and accuracy of the reference voltage source. 42

6.4 Electronic Counter 43

Electronic Counter Most of the commercial electronic counters are capable of performing the following measurement, totalize, frequency, period, ratio, time interval and averaging. Several mode of electronic counters, a) Totalizing mode b) Frequency mode c) Period Mode d) Ratio Mode e) Time interval mode f) Averaging Mode 44

a) Totalizing mode In the totalizing mode, input pulses are totalized (counted) by the decade counting units as long as switch S1 is closed (see Figure 6.14). If the pulse count exceeds the capability of the decade counters, the overflow indicator is activated and the counter starts counting again from zero. If the overflow indicator is on the indicated count is ignored since it is 45 incorrect.

a) Totalizing mode Input Signal Gate Pulse Generator VCO AND Gate S 1 E Figure 6.14: Block Diagram of the Totaling Mode of an Electronic Counter 46

b) Frequency mode If the time interval in which pulses are being totalized is accurately controlled, the counter is operating in the frequency mode. Accurate control of time interval is achieved by applying a rectangular pulse of known duration to the AND gate in Figure 6.14 in place of the dc voltage source. This technique is referred to as gating the counter. A block diagram of the electronic counter operating in the frequency mode is shown in Figure 6.15. commercial electronic counters use a more stable clock than an astable multivibrator. 47

b) Frequency mode Gate Pulse 1μs AND Gate Decade Counter Digital Readout 10μs 100μs 1ms 10ms 1s 100ms Clock (Astable MV) f= 1MHz 1/10 1/10 1/10 1/10 1/10 1/10 Decade Dividers Figure 6.15: Block Diagram of the Frequency Mode of an Electronic Counter 48

c) Period Mode Measurement of period can easily be accomplished by using the input signal as a gating pulse and count the clock pulse as shown in Figure 6.16. The period of the input signal is determined from the number of pulses of known frequency or known time duration, which are stored in the counter during one cycle of the input signal. 49

c) Period Mode T Flip Flop T Decade Counter Digital Readout AND Gate Clock f= 1 MHz Figure 6.16: Block Diagram of the Period Mode of an Electronic Counter 50

d) Ratio Mode The ratio mode of operation simply displays the numerical value of the ratio of the frequency of two signals. The lower frequency signal is used in place of the click to provide a gate pulse. The number of cycles of the higher frequency signal, which are stored in the decade counter during the presence of the externally generated gate pulse, is read directly as the ratio of the frequencies. A basic circuit for the ratio mode of operation is shown in Figure 6.17. 51

d) Ratio Mode Input A Input B EXT AND Gate Decade Counter Digital Readout INT Clock Figure 6.17: Block Diagram of the Ratio Mode of an Electronic Counter 52

e) Time interval mode The time interval mode operation provides a measurement of elapsed time between two events. The measurement can be accomplished using circuit of Figure 6.18. as can been seen in the circuit, the gate is controlled by two independent inputs which are the START input which open the gate and STOP input which close the gate. During the time interval between the START signal and STOP signal, clock pulses accumulate in the register thus providing an indication of the time interval between the start and completion of an event. 53

e) Time interval mode START STOP Decade Counter Digital Readout AND Gate Decade Dividers Clock Figure 6.18: Block Diagram of the Time Interval Mode of an Electronic Counter 54

f) Averaging Mode It is sometimes desirable when making measurements of frequency, period, or time interval to obtain average measurements over several cycles, periods or time intervals to increase accuracy and resolution. This is often referred to a simple period averaging. 55

Averaging The primary source of measurement error for an electronic counter are generally categorize as ± count error Time base error Trigger error Systematic error 57

6.7 Digital Multimeters 58

Digital Multimeters A basic digital multimeter (DMM) is made up of several types of analog to digital converters, including the three types described and circuitry for counting. Figure 6.19 shows a block diagram of a basic digital multimeter. 59

DCV ACV S 1B DCMA OHMS Attenuator DCV ACV A/D Converter S 1C OHMS DCMA Compensated Attenuator Rectifier Decade Counter DCV Test Probes S 1A ACV OHMS DCMA Current to Voltage Converter Digital Readout Constant Current Source Figure 6.19: Block Diagram of a Basic Digital Multimeter 60

GAME OVER 62