Category: electronic Measuring Instruments

Signal Generators Signal generator is an electronic equipment that provides standard test signals like sine wave, square wave, triangular wave and etc. It is also called an oscillator, since it produces periodic signals. The signal generator, which produces the periodic signal having a frequency of Audio Frequency (AF) range is called AF signal generator. the range of audio frequencies is 20Hz to 20KHz. AF Sine and Square Wave Generator The AF signal generator, which generates either sine wave or square wave in the range of audio frequencies based on the requirement is called AF Sine and Square wave generator. Its block diagramis shown in below figure. The above block diagram consists of mainly two paths. Those are upper path and lower path. Upper path is used to produce AF sine wave and the lower path is used to produce AF square wave. Wien bridge oscillator will produce a sine wave in the range of audio frequencies. Based on the requirement, we can connect the output of Wien bridge oscillator to either upper path or lower path by a switch. The upper path consists of the blocks like sine wave amplifier and attenuator. If the switch is used to connect the output of Wien bridge oscillator to upper path, it will produce a desired AF sine wave at the output of upper path. The lower path consists of the following blocks: square wave shaper, square wave amplifier, and attenuator. The square wave shaper converts the sine wave into a square wave. If the switch is used to connect the output of Wien bridge oscillator to lower path, then it will produce a desired AF square wave at the output of lower path. In this way, the block diagram that we considered can be used to produce either AF sine wave or AF square wave based on the requirement. Function Generator Function generator is a signal generator, which generates three or more periodic waves. Consider the following block diagram of a Function generator, which will produce periodic waves like triangular wave, square wave and sine wave. There are two current sources, namely upper current source and lower current source in above block diagram. These two current sources are regulated by the frequency-controlled voltage. Triangular Wave Integrator present in the above block diagram, gets constant current alternately from upper and lower current sources for equal amount of time repeatedly. So, the integrator will produce two types of output for the same time repeatedly − The output voltage of an integrator increases linearly with respect to time for the period during which integrator gets current from upper current source. The output voltage of an integrator decreases linearly with respect to time for the period during which integrator gets current from lower current source. In this way, the integrator present in above block diagram will produce a triangular wave. Square Wave & Sine Wave The output of integrator, i.e. the triangular wave is applied as an input to two other blocks as shown in above block diagram in order to get the square wave and sine wave respectively. Let us discuss about these two one by one. Square Wave The triangular wave has positive slope and negative slope alternately for equal amount of time repeatedly. So, the voltage comparator multi vibrator present in above block diagram will produce the following two types of output for equal amount of time repeatedly. One type of constant (higher) voltage at the output of voltage comparator multi vibrator for the period during which the voltage comparator multi vibrator gets the positive slope of the triangular wave. Another type of constant (lower) voltage at the output of voltage comparator multi vibrator for the period during which the voltage comparator multi vibrator gets the negative slope of the triangular wave. The voltage comparator multi vibrator present in above block diagram will produce a square wave. If the amplitude of the square wave that is produced at the output of voltage comparator multi vibrator is not sufficient, then it can be amplified to the required value by using a square wave amplifier. Sine Wave The sine wave shaping circuit will produce a sine wave output from the triangular input wave. Basically, this circuit consists of a diode resistance network. If the amplitude of the sine wave produced at the output of sine wave shaping circuit is insufficient, then it can be amplified to the required value by using sine wave amplifier. Learning working make money

CRO Probes We can connect any test circuit to an oscilloscope through a probe. As CRO is a basic oscilloscope, the probe which is connected to it is also called CRO probe. We should select the probe in such a way that it should not create any loading issues with the test circuit. So that we can analyze the test circuit with the signals properly on CRO screen. CRO probes should have the following characteristics. High impedance High bandwidth The block diagram of CRO probe is shown in below figure. As shown in the figure, CRO probe mainly consists of three blocks. Those are probe head, co-axial cable and termination circuit. Co-axial cable simply connects the probe head and termination circuit. Types of CRO Probes CRO probes can be classified into the following two types. Passive Probes Active Probes Now, let us discuss about these two types of probes one by one. Passive Probes If the probe head consists of passive elements, then it is called passive probe. The circuit diagram of passive probe is shown in below figure. As shown in the figure, the probe head consists of a parallel combination of resistor, $R_{1}$ and a variable capacitor, $C_{1}$. Similarly, the termination circuit consists of a parallel combination of resistor, $R_{2}$ and capacitor, $C_{2}$. The above circuit diagram is modified in the form of bridge circuit and it is shown in below figure. We can balance the bridge, by adjusting the value of variable capacitor, $c_{1}$. We will discuss the concept of bridges in the following chapters. For the time being, consider the following balancing condition of AC bridge. $$Z_{1}Z_{4}=Z_{2}Z_{3}$$ Substitute, the impedances $Z_{1},Z_{2}, Z_{3}$ and $Z_{4}$ as $R_{1},frac{1}{jomega C_{1}}, R_{2}$ and $frac{1}{jomega C_{2}}$ respectively in above equation. $$R_{1}left ( frac{1}{j omega C_{2}} right )=left ( frac{1}{j omega C_{1}} right )R_{2}$$ $Rightarrow R_{1} C_{1}=R_{2} C_{2}$Equation 1 By voltage division principle, we will get the voltage across resistor, $R_{2}$ as $$V_{0}=V_{i}left ( frac{R_{2}}{R_{1}+R_{2}} right )$$ attenuation factor is the ratio of input voltage, $V_{i}$ and output voltage, $V_{0}$. So, from above equation we will get the attenuation factor, $alpha$ as $$alpha = frac{V_{i}}{V_{0}}=frac{R_{1}+R_{2}}{R_{2}}$$ $Rightarrow alpha = 1+frac{R_{1}}{R_{2}}$ $Rightarrow alpha-1 = frac{R_{1}}{R_{2}}$ $Rightarrow R_{1}= left ( alpha-1 right )R_{2}$Equation 2 From Equation 2, we can conclude that the value of $R_{1}$ is greater than or equal to the value of 𝑅2 for integer values of$:alpha > 1$. Substitute Equation 2 in Equation 1. $$left ( alpha-1 right )R_{2}C_{1}=R_{2}C_{2}$$ $Rightarrow left ( alpha-1 right )C_{1} =C_{2}$ $Rightarrow C_{1}=frac{C_{2}}{left ( alpha-1 right )}$Equation 3 From Equation 3, we can conclude that the value of $C_{1}$ is less than or equal to the value of $C_{2}$ for integer values of $alpha >1$ Example Let us find the values of $R_{1}$ and $C_{1}$ of a probe having an attenuation factor,$alpha$ as 10. Assume, $R_{2}=1 M Omega$ and $C_{2}=18pF$. Step1 − We will get the value of $R_{1}$ by substituting the values of $alpha$ and $R_{2}$ in Equation 2. $$ R_{1}=left ( 10-1 right )times 1 times 10^{6}$$ $$Rightarrow R_{1}=9 times 10^{6}$$ $$Rightarrow R_{1}=9 MOmega$$ Step 2 − We will get the value of $C_{1}$ by substituting the values of $alpha$ and $C_{2}$ in Equation 3. $$C_{1}=frac{18times10^{-12}}{left ( 10-1 right )}$$ $$Rightarrow C_{1}=2 times 10^{-12}$$ $$Rightarrow C_{1}=2 pF$$ Therefore, the values of $R_{1}$ and $C_{1}$ of a probe will be $9MOmega$ and $2pF$ respectively for the given specifications. Active Probes If the probe head consists of active electronic components, then it is called active probe. The block diagram of active probe is shown in below figure. As shown in the figure, the probe head consists of a FET source follower in cascade with BJT emitter follower. The FET source follower provides high input impedance and low output impedance. Whereas, the purpose of BJT emitter follower is that it avoids or eliminates the impedance mismatching. The other two parts, such as co-axial cable and termination circuit remain same in both active and passive probes. Learning working make money

Special Purpose Oscilloscopes In previous chapter, we had discussed about Cathode Ray Oscilloscope (CRO), which is a basic oscilloscope. We will get special purpose oscilloscopes just by including few additional blocks to the basic oscilloscope based on the requirement. Following are the special purpose oscilloscopes. Dual Beam Oscilloscope Dual Trace Oscilloscope Digital Storage Oscilloscope Now, let us discuss about these special purpose oscilloscopes one by one. Dual Beam Oscilloscope The Oscilloscope, which displays two voltage waveforms is called Dual Beam Oscilloscope. Its block diagram is shown in below figure. As shown in above figure, the CRT of Dual Beam Oscilloscope consists of two sets of vertical deflection plates and one set of horizontal deflection plates. The combination of the following blocks together is called a channel. Pre-Amplifier & Attenuator Delay Line Vertical Amplifier A set of Vertical Deflection Plates There are two channels in Dual Beam Oscilloscope. So, we can apply the two signals, namely A & B as input of channel A & Channel B respectively. We can choose any one of these four signals as trigger input to the trigger circuit by using a switch. Those are input signals A & B, External signal (Ext) and Line input. This oscilloscope will produce two vertically deflected beams, since there are two pairs of vertical deflection plates. In this oscilloscope, the blocks which are useful for deflecting the beam in horizontal direction is common for both the input signals. Finally, this oscilloscope will produce the two input signals simultaneously on the screen of CRT. Dual Trace Oscilloscope The Oscilloscope, which produces two traces on its screen is called Dual Trace Oscilloscope. Its block diagram is shown in below figure. As shown in above figure, the CRT of Dual Trace Oscilloscope consists of a set of vertical deflection plates and another set of horizontal deflection plates. channel consists of four blocks, i.e. pre-Amplifier & attenuator, delay line, vertical amplifier and vertical deflection plates. In above block diagram, the first two blocks are separately present in both channels. The last two blocks are common to both the channels. Hence, with the help of electronic switch we can connect the delay line output of a specific channel to vertical amplifier. We can choose any one of these four signals as trigger input to the trigger circuit by using a switch. Those are input signals A & B, External signal (Ext) and Line input. This oscilloscope uses same electron beam for deflecting the input signals A & B in vertical direction by using an electronic switch, and produces two traces. the blocks that deflect the beam horizontally is common for both the input signals. Digital Storage Oscilloscope The oscilloscope, which stores the waveform digitally is known as digital storage oscilloscope. The block diagram of (digital) storage oscilloscope is below − Additional blocks required for digital data storage are added to a basic oscilloscope to make it convert it into a Digital Storage Oscilloscope. The blocks that are required for storing of digital data are lies between the pre-amplifier & attenuator and vertical amplifier in Digital Storage Oscilloscope. Those are Sample and Hold circuit, Analog to Digital Converter (ADC), Memory & Digital to Analog Converter. Control logic controls the first three blocks by sending various control signals. The blocks like control logic and Digital to Analog Converter are present between the trigger circuit and horizontal amplifier in Digital Storage Oscilloscope. The Digital Storage Oscilloscope stores the data in digital before it displays the waveform on the screen. Whereas, the basic oscilloscope doesn’t have this feature. Learning working make money

Wave Analyzers The electronic instrument used to analyze waves is called wave analyzer. It is also called signal analyzer, since the terms signal and wave can be interchangeably used frequently. We can represent the periodic signal as sum of the following two terms. DC component Series of sinusoidal harmonics So, analyzation of a periodic signal is analyzation of the harmonics components presents in it. Basic Wave Analyzer Basic wave analyzer mainly consists of three blocks − the primary detector, full wave rectifier, and PMMC galvanometer. The block diagram of basic wave analyzer is shown in below figure − The function of each block present in basic wave analyzer is mentioned below. Primary Detector − It consists of an LC circuit. We can adjust the values of inductor, L and capacitor, C in such a way that it allows only the desired harmonic frequency component that is to be measured. Full Wave Rectifier − It converts the AC input into a DC output. PMMC Galvanometer − It shows the peak value of the signal, which is obtained at the output of Full wave rectifier. We will get the corresponding circuit diagram, just by replacing each block with the respective component(s) in above block diagram of basic wave analyzer. So, the circuit diagram of basic wave analyzer will look like as shown in the following figure − This basic wave analyzer can be used for analyzing each and every harmonic frequency component of a periodic signal. Types of Wave Analyzers Wave analyzers can be classified into the following two types. Frequency Selective Wave Analyzer Superheterodyne Wave Analyzer Now, let us discuss about these two wave analyzers one by one. Frequency Selective Wave Analyzer The wave analyzer, used for analyzing the signals are of AF range is called frequency selective wave analyzer. The block diagram of frequency selective wave analyzer is shown in below figure. Frequency selective wave analyzer consists a set of blocks. The function of each block is mentioned below. Input Attenuator − The AF signal, which is to be analyzed is applied to input attenuator. If the signal amplitude is too large, then it can be attenuated by input attenuator. Driver Amplifier − It amplifies the received signal whenever necessary. High Q-filter − It is used to select the desired frequency and reject unwanted frequencies. It consists of two RC sections and two filter amplifiers & all these are cascaded with each other. We can vary the capacitance values for changing the range of frequencies in powers of 10. Similarly, we can vary the resistance values in order to change the frequency within a selected range. Meter Range Attenuator − It gets the selected AF signal as an input & produces an attenuated output, whenever required. Output Amplifier − It amplifies the selected AF signal if necessary. Output Buffer − It is used to provide the selected AF signal to output devices. Meter Circuit − It displays the reading of selected AF signal. We can choose the meter reading in volt range or decibel range. Superheterodyne Wave Analyzer The wave analyzer, used to analyze the signals of RF range is called superheterodyne wave analyzer. The following figure shows the block diagram of superheterodyne wave analyzer. The working of superheterodyne wave analyzer is mentioned below. The RF signal, which is to be analyzed is applied to the input attenuator. If the signal amplitude is too large, then it can be attenuated by input attenuator. Untuned amplifier amplifies the RF signal whenever necessary and it is applied to first mixer. The frequency ranges of RF signal & output of Local oscillator are 0-18 MHz & 30-48 MHz respectively. So, first mixer produces an output, which has frequency of 30 MHz. This is the difference of frequencies of the two signals that are applied to it. IF amplifier amplifies the Intermediate Frequency (IF) signal, i.e. the output of first mixer. The amplified IF signal is applied to second mixer. The frequencies of amplified IF signal & output of Crystal oscillator are same and equal to 30MHz. So, the second mixer produces an output, which has frequency of 0 Hz. This is the difference of frequencies of the two signals that are applied to it. The cut off frequency of Active Low Pass Filter (LPF) is chosen as 1500 Hz. Hence, this filter allows the output signal of second mixer. Meter Circuit displays the reading of RF signal. We can choose the meter reading in volt range or decibel range. So, we can choose a particular wave analyzer based on the frequency range of the signal that is to be analyzed. Learning working make money

AC Voltmeters The instrument, which is used to measure the AC voltage across any two points of electric circuit is called AC voltmeter. If the AC voltmeter consists of rectifier, then it is said to be rectifier based AC voltmeter. The DC voltmeter measures only DC voltages. If we want to use it for measuring AC voltages, then we have to follow these two steps. Step1 − Convert the AC voltage signal into a DC voltage signal by using a rectifier. Step2 − Measure the DC or average value of the rectifier’s output signal. We get Rectifier based AC voltmeter, just by including the rectifier circuit to the basic DC voltmeter. This chapter deals about rectifier based AC voltmeters. Types of Rectifier based AC Voltmeters Following are the two types of rectifier based AC voltmeters. AC voltmeter using Half Wave Rectifier AC voltmeter using Full Wave Rectifier Now, let us discuss about these two AC voltmeters one by one. AC Voltmeter using Half Wave Rectifier If a Half wave rectifier is connected ahead of DC voltmeter, then that entire combination together is called AC voltmeter using Half wave rectifier. The block diagram of AC voltmeter using Half wave rectifier is shown in below figure. The above block diagram consists of two blocks: half wave rectifier and DC voltmeter. We will get the corresponding circuit diagram, just by replacing each block with the respective component(s) in above block diagram. So, the circuit diagram of AC voltmeter using Half wave rectifier will look like as shown in below figure. The rms value of sinusoidal (AC) input voltage signal is $$V_{rms}=frac{V_{m}}{sqrt{2}}$$ $$Rightarrow V_{m}=sqrt{2} V_{rms}$$ $$Rightarrow V_{m}=1.414 V_{rms}$$ Where, $V_{m}$ is the maximum value of sinusoidal (AC) input voltage signal. The DC or average value of the Half wave rectifier’s output signal is $$V_{dc}=frac{V_{m}}{pi}$$ Substitute, the value of $V_{m}$ in above equation. $$V_{dc}= frac{1.414 V_{rms}}{pi}$$ $$V_{dc}= 0.45 V_{rms}$$ Therefore, the AC voltmeter produces an output voltage, which is equal to 0.45 times the rms value of the sinusoidal (AC) input voltage signal AC Voltmeter using Full Wave Rectifier If a Full wave rectifier is connected ahead of DC voltmeter, then that entire combination together is called AC voltmeter using Full wave rectifier. The block diagram of AC voltmeter using Full wave rectifier is shown in below figure The above block diagram consists of two blocks: full wave rectifier and DC voltmeter. We will get the corresponding circuit diagram just by replacing each block with the respective component(s) in above block diagram. So, the circuit diagram of AC voltmeter using Full wave rectifier will look like as shown in below figure. The rms value of sinusoidal (AC) input voltage signal is $$V_{rms}=frac{V_{m}}{sqrt{2}}$$ $$Rightarrow V_{m}=sqrt{2} :V_{rms}$$ $$Rightarrow V_{m}= 1.414 V_{rms}$$ Where, $V_{m}$ is the maximum value of sinusoidal (AC) input voltage signal. The DC or average value of the Full wave rectifier’s output signal is $$V_{dc}=frac{2V_{m}}{pi}$$ Substitute, the value of $V_{m}$ in above equation $$V_{dc}=frac{2times 1.414 :V_{rms}}{pi}$$ $$V_{dc}=0.9 :V_{rms}$$ Therefore, the AC voltmeter produces an output voltage, which is equal to 0.9 times the rms value of the sinusoidal (AC) input voltage signal. Learning working make money

Other AC Voltmeters In previous chapter, we discussed about rectifier based AC voltmeters. This chapter covers the following two types of AC voltmeters. Peak responding AC voltmeter True RMS responding AC voltmeter Now, let us discuss about these two types of AC voltmeters one by one. Peak Responding AC Voltmeter As the name suggests, the peak responding AC voltmeter responds to peak values of AC voltage signal. That means, this voltmeter measures peak values of AC voltages. The circuit diagram of peak responding AC voltmeter is shown below − The above circuit consists of a diode, capacitor, DC amplifier and PMMC galvanometer. The diode present in the above circuit is used for rectification purpose. So, the diode converts AC voltage signal into a DC voltage signal. The capacitor charges to the peak value of this DC voltage signal. During positive half cycle of AC voltage signal, the diode conducts and the capacitor charges to the peak value of AC voltage signal. When the value of AC voltage signal is less than this value, the diode will be reverse biased. Thus, the capacitor will discharge through resistor of DC amplifier till the next positive half cycle of AC voltage signal. When the value of AC voltage signal is greater than the capacitor voltage, the diode conducts and the process will be repeated. We should select the component values in such a way that the capacitor charges fast and discharges slowly. As a result, the meter always responds to this capacitor voltage, i.e. the peak value of AC voltage. True RMS Responding AC Voltmeter As the name suggests, the true RMS responding AC voltmeter responds to the true RMS values of AC voltage signal. This voltmeter measures RMS values of AC voltages. The circuit diagram of true RMS responding AC voltmeter is shown in below figure. The above circuit consists of an AC amplifier, two thermocouples, DC amplifier and PMMC galvanometer. AC amplifier amplifies the AC voltage signal. Two thermocouples that are used in above circuit are a measuring thermocouple and a balancing thermocouple. Measuring thermocouple produces an output voltage, which is proportional to RMS value of the AC voltage signal. Any thermocouple converts a square of input quantity into a normal quantity. This means there exists a non-linear relationship between the output and input of a thermocouple. The effect of non-linear behavior of a thermocouple can be neglected by using another thermocouple in the feedback circuit. The thermocouple that is used for this purpose in above circuit is known as balancing thermocouple. The two thermocouples, namely measuring thermocouple and balancing thermocouple together form a bride at the input of DC amplifier. As a result, the meter always responds to the true RMS value of AC voltage signal. Learning working make money

MultiMeter In previous chapters, we discussed about voltmeters, ammeters and ohmmeters. These measuring instruments are used to measure voltage, current and resistance respectively. That means, we have separate measuring instruments for measuring voltage, current and resistance. Suppose, if a single measuring instrument can be used to measure the quantities such as voltage, current & resistance one at a time, then it is said to be multimeter. It has got the name multimeter, since it can measure multiple electrical quantities one at a time. Measurements by using Multimeter Multimeter is an instrument used to measure DC & AC voltages, DC & AC currents and resistances of several ranges. It is also called Electronic Multimeter or Voltage Ohm Meter (VOM). DC voltage Measurement The part of the circuit diagram of Multimeter, which can be used to measure DC voltage is shown in below figure. The above circuit looks like a multi range DC voltmeter. The combination of a resistor in series with PMMC galvanometer is a DC voltmeter. So, it can be used to measure DC voltages up to certain value. We can increase the range of DC voltages that can be measured with the same DC voltmeter by increasing the resistance value. the equivalent resistance value increases, when we connect the resistors are in series. In above circuit, we can measure the DC voltages up to 2.5V by using the combination of resistor, $R_{5}$ in series with PMMC galvanometer. By connecting a resistor, $R_{4}$ in series with the previous circuit, we can measure the DC voltages up to 10V. In this way, we can increase the range of DC voltages, simply by connecting a resistor in series with the previous (earlier) circuit. We can measure the DC voltage across any two points of an electric circuit, by connecting the switch, S to the desired voltage range. DC Current Measurement The part of the circuit diagram of Multimeter, which can be used to measure DC current is shown in below figure. The above circuit looks like a multi range DC ammeter. the combination of a resistor in parallel with PMMC galvanometer is a DC ammeter. So, it can be used to measure DC currents up to certain value. We can get different ranges of DC currents measured with the same DC ammeter by placing the resistors in parallel with previous resistor. In above circuit, the resistor, $R_{1}$ is connected in series with the PMMC galvanometer in order to prevent the meter gets damaged due to large current. We can measure the DC current that is flowing through any two points of an electric circuit, by connecting the switch, S to the desired current range AC voltage Measurement The part of the circuit diagram of Multimeter, which can be used to measure AC voltage is shown in below figure. The above circuit looks like a multi range AC voltmeter. We know that, we will get AC voltmeter just by placing rectifier in series (cascade) with DC voltmeter. The above circuit was created just by placing the diodes combination and resistor, $R_{6}$ in between resistor, $R_{5}$ and PMMC galvanometer. We can measure the AC voltage across any two points of an electric circuit, by connecting the switch, S to the desired voltage range. Resistance Measurement The part of the circuit diagram of Multimeter, which can be used to measure resistance is shown in below figure. We have to do the following two tasks before taking any measurement. Short circuit the instrument Vary the zero adjust control until the meter shows full scale current. That means, meter indicates zero resistance value. Now, the above circuit behaves as shunt ohmmeter and has the scale multiplication of 1, i.e. 100. We can also consider higher order powers of 10 as the scale multiplications for measuring high resistances. Learning working make money

DC Voltmeters DC voltmeter is a measuring instrument, which is used to measure the DC voltage across any two points of electric circuit. If we place a resistor in series with the Permanent Magnet Moving Coil (PMMC) galvanometer, then the entire combination together acts as DC voltmeter. The series resistance, which is used in DC voltmeter is also called series multiplier resistance or simply, multiplier. It basically limits the amount of current that flows through galvanometer in order to prevent the meter current from exceeding the full scale deflection value. The circuit diagram of DC voltmeter is shown in below figure. We have to place this DC voltmeter across the two points of an electric circuit, where the DC voltage is to be measured. Apply KVL around the loop of above circuit. $V-I_{m}R_{se}-I_{m}R_{m}=0$ (Equation 1) $$Rightarrow V-I_{m}R_{m}=I_{m}R_{se}$$ $$Rightarrow R_{se}=frac{V-I_{m}R_{m}}{I_{m}}$$ $Rightarrow R_{se}=frac{V}{I_{m}}-R_{m}$ (Equation 2) Where, $R_{se}$ is the series multiplier resistance $V$ is the full range DC voltage that is to be measured $I_{m}$ is the full scale deflection current $R_{m}$ is the internal resistance of galvanometer The ratio of full range DC voltage that is to be measured, $V$ and the DC voltage drop across the galvanometer, $V_{m}$ is known as multiplying factor, m. Mathematically, it can be represented as $m=frac{V}{V_{m}}$ (Equation 3) From Equation 1, we will get the following equation for full range DC voltage that is to be measured, $V$. $V=I_{m}R_{se}+I_{m}R_{m}$ (Equation 4) The DC voltage drop across the galvanometer, $V_{m}$ is the product of full scale deflection current, $I_{m}$ and internal resistance of galvanometer, $R_{m}$. Mathematically, it can be written as $V_{m}=I_{m}R_{m}$ (Equation 5) Substitute, Equation 4 and Equation 5 in Equation 3. $$m=frac{I_{m}R_{se}+I_{m}R_{m}}{I_{m}R_{m}}$$ $Rightarrow m=frac{R_{se}}{R_{m}}+1$ $Rightarrow m-1=frac{R_{se}}{R_{m}}$ $R_{se}=R_{m}left (m-1 right )$(Equation 6) We can find the value of series multiplier resistance by using either Equation 2 or Equation 6 based on the available data. Multi Range DC Voltmeter In previous section, we had discussed DC voltmeter, which is obtained by placing a multiplier resistor in series with the PMMC galvanometer. This DC voltmeter can be used to measure a particular range of DC voltages. If we want to use the DC voltmeter for measuring the DC voltages of multiple ranges, then we have to use multiple parallel multiplier resistors instead of single multiplier resistor and this entire combination of resistors is in series with the PMMC galvanometer. The circuit diagram of multi range DC voltmeter is shown in below figure. We have to place this multi range DC voltmeter across the two points of an electric circuit, where the DC voltage of required range is to be measured. We can choose the desired range of voltages by connecting the switch s to the respective multiplier resistor. Let, $m_{1},m_{2}, m_{2} $ and $m_{4}$ are the multiplying factors of DC voltmeter when we consider the full range DC voltages to be measured as, $V_{1} , V_{2}, V_{3}$ and $V_{4}$ respectively. Following are the formulae corresponding to each multiplying factor. $$m_{1}=frac{V_{1}}{V_{m}}$$ $$m_{2}=frac{V_{2}}{V_{m}}$$ $$m_{3}=frac{V_{3}}{V_{m}}$$ $$m_{4}=frac{V_{4}}{V_{m}}$$ In above circuit, there are four series multiplier resistors, $R_{se1}, R_{se2}, R_{se3}$ and $R_{se4}$. Following are the formulae corresponding to these four resistors. $$R_{se1}=R_{m}left (m_{1}-1 right )$$ $$R_{se2}=R_{m}left (m_{2}-1 right )$$ $$R_{se3}=R_{m}left (m_{3}-1 right )$$ $$R_{se4}=R_{m}left (m_{4}-1 right )$$ So, we can find the resistance values of each series multiplier resistor by using above formulae. Learning working make money

Electronic Measuring Instruments The instruments used to measure any quantity are known as measuring instruments. If the instruments can measure the basic electrical quantities, such as voltage and current are known as basic measuring instruments. Types of Basic Measuring Instruments We can classify the basic measuring instruments into the following two types. Voltmeters Ammeters Let us discuss about these two basic measuring instruments briefly. Voltmeters As the name suggests, voltmeter is a measuring instrument which measures the voltage across any two points of an electric circuit. The units of voltage are volt and the measuring instrument is meter. Hence, the word “voltmeter” is obtained by combining the two words “volt” and “meter”. We can classify the voltmeters into the following two types based on the type of voltage that it can measure. DC Voltmeters AC Voltmeters DC Voltmeter As the name suggests, DC voltmeter measures the DC voltage across any two points of an electric circuit. A practical DC voltmeter is shown in below figure. The DC voltmeter shown in the figure is a $(0-10)V$ DC voltmeter. Hence, it can be used to measure the DC voltages from zero volts to 10 volts AC Voltmeter As the name suggests, AC voltmeter measures the AC voltage across any two points of an electric circuit. A practical AC voltmeter is shown in below figure. The AC voltmeter shown in above figure is a $(0-250)V$ AC voltmeter. Hence, it can be used to measure the AC voltages from zero volts to 250 volts Ammeters As the name suggests, ammeter is a measuring instrument which measures the current flowing through any two points of an electric circuit. The unit of current is ampere and the measuring instrument is meter. The word “ammeter” is obtained by combining “am” of ampere with “meter”. We can classify the ammeters into the following two types based on the type of current that it can measure. DC Ammeters AC Ammeters DC Ammeter As the name suggests, DC ammeter measures the DC current that flows through any two points of an electric circuit. A practical DC ammeter is shown in figure. The DC ammeter shown in above figure is a $(0-50)A$ DC ammeter. Hence, it can be used to measure the DC currents from zero Amperes to 50 Amperes AC Ammeter As the name suggests, AC ammeter measures the AC current that flows through any two points of an electric circuit. A practical AC ammeter is shown in below figure. The AC ammeter shown in above figure is a $(0-100)A$ AC ammeter. Hence, it can be used to measure the AC currents from zero Amperes to 100 Amperes. We will discuss about various voltmeters and ammeters in detail in the following few chapters Learning working make money

Performance Characteristics The characteristics of measurement instruments which are helpful to know the performance of instrument and help in measuring any quantity or parameter, are known as Performance Characteristics. Types of Performance Characteristics Performance characteristics of instruments can be classified into the following two types. Static Characteristics Dynamic Characteristics Now, let us discuss about these two types of characteristics one by one. Static Characteristics The characteristics of quantities or parameters measuring instruments that do not vary with respect to time are called static characteristics. Sometimes, these quantities or parameters may vary slowly with respect to time. Following are the list of static characteristics. Accuracy Precision Sensitivity Resolution Static Error Now, let us discuss about these static characteristics one by one. Accuracy The algebraic difference between the indicated value of an instrument, $A_{i}$ and the true value, $A_{t}$ is known as accuracy. Mathematically, it can be represented as − $$Accuracy = A_{i}- A_{t}$$ The term, accuracy signifies how much the indicated value of an instrument, $A_{i}$ is closer to the true value, $A_{t}$. Static Error The difference between the true value, $A_{t}$ of the quantity that does not vary with respect to time and the indicated value of an instrument, $A_{i}$ is known as static error, $e_{s}$. Mathematically, it can be represented as − $$e_{s}= A_{t}- A_{i}$$ The term, static error signifies the inaccuracy of the instrument. If the static error is represented in terms of percentage, then it is called percentage of static error. Mathematically, it can be represented as − $$% e_{s}=frac{e_{s}}{A_{t}}times 100$$ Substitute, the value of $e_{s}$ in the right hand side of above equation − $$% e_{s}=frac{A_{t}- A_{i}}{A_{t}}times 100$$ Where, $% e_{s}$ is the percentage of static error. Precision If an instrument indicates the same value repeatedly when it is used to measure the same quantity under same circumstances for any number of times, then we can say that the instrument has high precision. Sensitivity The ratio of change in output, $Delta A_{out}$ of an instrument for a given change in the input, $Delta A_{in}$ that is to be measured is called sensitivity, S. Mathematically it can be represented as − $$S=frac{Delta A_{out}}{Delta A_{in}}$$ The term sensitivity signifies the smallest change in the measurable input that is required for an instrument to respond. If the calibration curve is linear, then the sensitivity of the instrument will be a constant and it is equal to slope of the calibration curve. If the calibration curve is non-linear, then the sensitivity of the instrument will not be a constant and it will vary with respect to the input. Resolution If the output of an instrument will change only when there is a specific increment of the input, then that increment of the input is called Resolution. That means, the instrument is capable of measuring the input effectively, when there is a resolution of the input. Dynamic Characteristics The characteristics of the instruments, which are used to measure the quantities or parameters that vary very quickly with respect to time are called dynamic characteristics. Following are the list of dynamic characteristics. Speed of Response Dynamic Error Fidelity Lag Now, let us discuss about these dynamic characteristics one by one. Speed of Response The speed at which the instrument responds whenever there is any change in the quantity to be measured is called speed of response. It indicates how fast the instrument is. Lag The amount of delay present in the response of an instrument whenever there is a change in the quantity to be measured is called measuring lag. It is also simply called lag. Dynamic Error The difference between the true value, $A_{t}$ of the quantity that varies with respect to time and the indicated value of an instrument, $A_{i}$ is known as dynamic error, $e_{d}$. Fidelity The degree to which an instrument indicates changes in the measured quantity without any dynamic error is known as Fidelity Learning working make money