Electronics Measurements and Instrumentation eBook & Notes - Download as PDF File .pdf), Text File .txt) or read online. Electrical and Electronics. Measurements and Instrumentation. Prithwiraj Purkait. Professor. Department of Electrical Engineering and. Dean, School of. Electronic Measurement & Instrumentation - Kindle edition by R S Sedha. Download it once and read it on your Kindle device, PC, phones or tablets.
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Electronic Instrumentation and Measurement - Kindle edition by Rohit Khurana. Download it once and read it on your Kindle device, PC, phones or tablets. photocopying or storing in any medium by electronic means and whether Choosing appropriate measuring instruments. 9. 2 INSTRUMENT. Text book Electronic Instrumentation and Measurements David A bell 2nd edition .pdf. Wajeeh Rehman. Loading Preview. Sorry, preview is currently unavailable.
The values of R1and R3 are known, and R2 and C1 are both adjustable. The unknown values are those of L1 and R4. Like other bridge circuits, the measuring ability of a Hay Bridge depends on 'balancing' the circuit. Balancing the circuit in Figure 1 means adjusting R2 and C1 until the current through the ammeter between points A and B becomes zero.
This happens when the voltages at points A and B are equal. Substituting R4, one comes up with the following equation: A Wien bridge oscillator is a type of electronic oscillator that generates sine waves. It can generate a large range of frequencies. The circuit is based on an electrical network originally developed by Max Wien in The bridge comprises four resistors and two capacitors.
It can also be viewed as a positive feedback system combined with a bandpass filter. Wien did. The modern circuit is derived from William Hewlett's Stanford University master's degree thesis. Hewlett, along with David Packard co-founded Hewlett-Packard.
Their first product was the HP A, a precision sine wave oscillator based on the Wien bridge. The A was one of the first instruments to produce such low distortion. Amplitude stabilization: The key to Hewlett's low distortion oscillator is effective amplitude stabilization.
The amplitude of electronic oscillators tends to increase until clipping or other gain limitation is reached. This leads to high harmonic distortion, which is often undesirable.
Hewlett used an incandescent bulb as a positive temperature coefficient PTC thermistor in the oscillator feedback path to limit the gain. The resistance of light bulbs and similar heating elements increases as their temperature increases. If the oscillation frequency is significantly higher than the thermal time constant of the heating element, the radiated power is proportional to the oscillator power.
Since heating elements are close to black body radiators, they follow the Stefan-Boltzmann law. The radiated power is proportional to T4, so resistance increases at a greater rate than amplitude. If the gain is inversely proportional to the oscillation amplitude, the oscillator gain stage reaches a steady state and operates as a near ideal class A amplifier, achieving very low distortion at the frequency of interest.
At lower frequencies the time period of the oscillator approaches the thermal time constant of the thermistor element and the output distortion starts to rise significantly. Light bulbs have their disadvantages when used as gain control elements in Wien bridge oscillators, most notably a very high sensitivity to vibration due to the bulb's microphonic nature amplitude modulating the oscillator output, and a limitation in high frequency response due to the inductive nature of the coiled filament.
Modern Wien bridge oscillators have used other nonlinear elements, such as diodes, thermistors, field effect transistors, or photocells for amplitude stabilization in place of light bulbs. Distortion as low. This is due to the low damping factor and long time constant of the crude control loop, and disturbances cause the output amplitude to exhibit a decaying sinusoidal response. This can be used as a rough figure of merit, as the greater the amplitude bounce after a disturbance, the lower the output distortion under steady state conditions.
Input admittance analysis If a voltage source is applied directly to the input of an ideal amplifier with feedback, the input current will be:. Where vin is the input voltage, vout is the output voltage, and Zf is the feedback impedance.
If the voltage gain of the amplifier is defined as:. If Av is greater than 1, the input admittance is a negative resistance in parallel with an inductance. The inductance is:. If a capacitor with the same value of C is placed in parallel with the input, the circuit has a natural resonance at:. If the net resistance is negative, amplitude will grow until clipping occurs. Similarly, if the net resistance is positive, oscillation amplitude will decay. Notice that increasing the gain makes the net resistance more negative, which increases amplitude.
If gain is reduced to exactly 3 when a suitable amplitude is reached, stable, low distortion oscillations will result. Amplitude stabilization circuits typically increase gain until a suitable output amplitude is reached. As long as R, C, and the amplifier are linear, distortion will be minimal.
Important Questions: What are the functional elements of an instrument? What is meant by accuracy of an instrument? Define international standard for ohm? What is primary sensing element? What is calibration? What are primary standards? Where are they used? When are static characteristics important? What is standard? What are the different types of standards?
Define static error. Distinguish reproducibility and repeatability. Distinguish between direct and indirect methods of measurements. With one example explain Instrumental Errors. Name some static and dynamic characteristics. State the difference between accuracy and precision of a measurement.
What are primary and secondary measurements? What are the functions of instruments and measurement systems? What is an error? How it is classified? Classify the standards of measurement? Define standard deviation and average deviation. What are the sources of error? Define resolution. What is threshold? Define zero drift. Write short notes on systematic errors. What are random errors? PART B 1. Describe the functional elements of an instrument with its block diagram.
And illustrate them with pressure gauge, pressure thermometer and DArsonval galvanometer. Draw the various blocks and explain their functions. Discuss in detail the various static and dynamic characteristics of a measuring system. Cathode-Ray Oscilloscope: The cathode-ray oscilloscope CRO is a common laboratory instrument that provides accurate time and aplitude measurements of voltage signals over a wide range of frequencies.
Its reliability, stability, and ease of operation make it suitable as a general purpose laboratory instrument. The heart of the CRO is a cathode-ray tube shown schematically in Fig. The cathode ray is a beam of electrons which are emitted by the heated cathode negative electrode and accelerated toward the fluorescent screen.
The assembly of the cathode, intensity grid, focus grid, and accelerating anode positive electrode is called an electron gun. Its purpose is to generate the electron beam and control its intensity and focus. Between the electron gun and the fluorescent screen are two pair of metal plates - one oriented to provide horizontal deflection of the beam and one pair oriented ot give vertical deflection to the beam.
These plates are thus referred to as the horizontal and vertical deflection plates. The combination of these two deflections allows the beam to reach any portion of the fluorescent screen. Wherever the electron beam hits the screen, the phosphor is excited and light is emitted from that point. This coversion of electron energy into light allows us to write with points or lines of light on an otherwise darkened screen.
The signal applied to the verical plates is thus displayed on the screen as a function of time. The horizontal axis serves as a uniform time scale. The linear deflection or sweep of the beam horizontally is accomplished by use of a sweep generator that is incorporated in the oscilloscope circuitry. The voltage output of such a generator is that of a sawtooth wave as shown in Fig. Application of one cycle of this voltage difference, which increases linearly with time, to the horizontal plates causes the.
When the voltage suddenly falls to zero, as at points a b c , etc The horizontal deflection of the beam is repeated periodically, the frequency of this periodicity is adjustable by external controls. To obtain steady traces on the tube face, an internal number of cycles of the unknown signal that is applied to the vertical plates must be associated with each cycle of the sweep generator. Thus, with such a matching of synchronization of the two deflections, the pattern on the tube face repeats itself and hence appears to remain stationary.
The persistance of vision in the human eye and of the glow of the fluorescent screen aids in producing a stationary pattern. In addition, the electron beam is cut off blanked during flyback so that the retrace sweep is not observed.
CRO Operation: A simplified block diagram of a typical oscilloscope is shown in Fig. In general, the instrument is operated in the following manner. The signal to be displayed is amplified by the vertical amplifier and applied to the verical deflection plates of the CRT.
A portion of the signal in the vertical amplifier is applied to the sweep trigger as a triggering signal. The sweep trigger then generates a pulse coincident with a selected point in the cycle of the triggering signal.
This pulse turns on the sweep generator, initiating the sawtooth wave form. The sawtooth wave is amplified by the horizontal amplifier and applied to the horizontal deflection plates. Usually, additional provisions signal are made for appliying an external triggering signal or utilizing the 60 Hz line for triggering.
Also the sweep generator may be bypassed and an external signal applied directly to the horizontal amplifier. CRO Controls: The controls available on most oscilloscopes provide a wide range of operating conditions and thus make the instrument especially versatile.
Since many of these controls are common to most oscilloscopes a brief description of them follows. Turns instrument on and controls illumination of the graticule. Focus the spot or trace on the screen.
Regulates the brightness of the spot or trace. Controls vertical positioning of oscilloscope display. Selects the sensitivity of the vertical amplifier in calibrated steps. Variable Sensitivity: Provides a continuous range of sensitivities between the calibrated steps. Normally the sensitivity is calibrated only when the variable knob is in the fully clockwise position. Selects desired coupling ac or dc for incoming signal applied to vertical amplifier, or grounds the amplifier input.
Selecting dc couples the input directly to the amplifier; selecting ac send the signal through a capacitor before going to the amplifier thus blocking any constant component. Selects desired sweep rate from calibrated steps or admits external signal to horizontal amplifier.
Provides continuously variable sweep rates. Calibrated position is fully clockwise. Controls horizontal position of trace on screen. Horizontal Variable: Controls the attenuation reduction of signal applied to horizontal aplifier through Ext. Selects whether triggering occurs at a specific dc or ac level.
Selects the source of the triggering signal. LINE - 60 cycle triger Level: Selects the voltage point on the triggering signal at which sweep is triggered. It also allows automatic auto triggering of allows sweep to run free free run. A pair of jacks for connecting the signal under study to the Y or vertical amplifier.
The lower jack is grounded to the case. Horizontal Input: A pair of jacks for connecting an external signal to the horizontal amplifier. The lower terminal is graounted to the case of the oscilloscope.
External Tigger Input: Input connector for external trigger signal. Provides amplitude calibrated square waves of 25 and millivolts for use in calibrating the gain of the amplifiers. Sensitivity is variable. Range of sweep is variable. Operating Instructions: Before plugging the oscilloscope into a wall receptacle, set the controls as follows: Plug line cord into a standard ac wall recepticle nominally V.
Turn power on. Do not advance the Intensity Control. Allow the scope to warm up for approximately two minutes, then turn the Intensity Control until the beam is visible on the screen. Set the signal generator to a frequency of cycles per second. Connect the output from the gererator to the vertical input of the oscilloscope.
Establish a steady trace of this input signal on the scope. Adjust play with all of the scope and signal generator controls until you become familiar with the functionof each. The purpose fo such "playing" is to allow the student to become so familiar with the oscilloscope that it becomes an aid tool in making measurements in other experiments and not as a formidable obstacle.
If the vertical gain is set too low, it may not be possible to obtain a steady trace. Measurements of Voltage: Consider the circuit in Fig. The signal generator is used to produce a hertz sine wave.
The AC voltmeter and the leads to the verticle input of the oscilloscope are connected across the generator's output. The trace represents a plot of voltage vs. To determine the size of the voltage signal appearing at the output of terminals of the signal generator, an AC Alternating Current voltmeter is connected in parallel across these terminals Fig. The AC voltmeter is designed to read the dc "effective value" of the voltage. The peak or maximum voltage seen on the scope face Fig.
Agreement is expected between the voltage reading of the multimeter and that of the oscilloscope. In this position, the trace is no longer calibrated so that you can not just read the size of the signal by counting the number of divisions and multiplying by the scale factor.
However, you can figure out what the new calibration is an use it as long as the variable control remains unchanged. The mathematical prescription given for RMS signals is valid only for sinusoidal signals.
The meter will not indicate the correct voltage when used to measure non-sinusoidal signals. Frequency Measurements: When the horizontal sweep voltage is applied, voltage measurements can still be taken from the vertical deflection.
Moreover, the signal is displayed as a function of time. If the time base i. Frequencies can then be determined as reciprocal of the periods. Set the oscillator to Hz. Display the signal on the CRO and measure the period of the oscillations. Use the horizontal distance between two points such as C to D in Fig. Set the horizontal gain so that only one complete wave form is displayed. Then reset the horizontal until 5 waves are seen. Keep the time base control in a calibrated position.
Measure the distance and hence time for 5 complete cycles and calculate the frequency from this measurement. Compare you result with the value determined above. Repeat your measurements for other frequencies of Hz, 5 kHz, 50 kHz as set on the signal generator. Lissajous Figures: These stationary patterns are known as Lissajous figures and can be used for comparison measurement of frequencies. Use two oscillators to generate some simple Lissajous figures like those shown in Fig.
You will find it difficult to maintain the Lissajous figures in a fixed configuration because the two oscillators are not phase and frequency locked. Their frequencies and phase drift slowly causing the two different signals to change slightly with respect to each other. Testing what you have learned: Your instructor will provide you with a small oscillator circuit. Examine the input to the circuit and output of the circuit using your oscilloscope.
Measure such quantities as the voltage and frequence of the signals. Specify if they are sinusoidal or of some other wave character. If square wave, measure the frequency of the wave. Also, for square waves, measure the on time when the voltage is high and off time when it is low. Q meter: For many years, the Q meter has been an essential piece of equipment for laboratories engaged in the testing of radio frequency circuits.
In modem laboratories, the Q meter has been largely replaced by more exotic and more expensive impedance measuring devices and today, it is difficult to find a manufacturer who still makes a Q meter. For the radio amateur, the Q meter is still a very useful piece of test equipment and the writer has given some thought to how a simple Q meter could be made for the radio shack.
For those who are unfamiliar with this type of instrument, a few introductory notes on the definition of Q and the measurement of Q, are included. The Q factor or quality factor of an inductance is commonly expressed as the ratio of its series reactance to its series resistance.
We can also express the Q factor of a capacitance as the ratio of its series reactance to its series resistance although capacitors are generally specified by the D or dissipation factor which is the reciprocal of Q. A tuned circuit, at resonance, is considered to have a Q factor. In this case, Q is equal to the ratio of either the inductive reactance, or the capacitive reactance, to the total series loss resistance in the tuned circuit. The greater the loss resistance and the lower the Q, the greater the power lost on each cycle of oscillation in the tuned circuit and hence the greater the power needed to maintain oscillation.
Another way to derive Q is as follows: Sometimes we talk of loaded Q such as in transmitter tank circuits and, in this case, resistance for calculation of Q is the unloaded tuned circuit series resistance plus the additional loss resistance reflected in series into the circuit from its coupled load.
There are other ways of expressing Q factor. It can be expressed approximately as the ratio of equivalent shunt resistance to either the inductive or the capacitive reactance. Series loss resistance can be converted to an equivalent shunt resistance using the following formula: To measure Q factor, Q meters make use of this principle. A basic Q meter is shown in Figure 1. Terminals are provided to connect the inductance Lx to be measured and this is resonated by a variable tuning capacitor C.
Terminals are also provided to add capacitance Cx , if required. The tuned circuit is excited from a tunable signal source which develops voltage across a resistor in series with the tuned circuit. The resistor must have a resistance small compared to the loss resistance of the components to be measured so that its value can be ignored.
A resistance of a mere fraction of an ohm is necessary. Metering is provided to measure the AC injection voltage across the series resistor and the AC output voltage across the terminals of the tuning capacitor. The output measurement must be a high input impedance circuit to prevent loading of the tuned circuit by the metering circuit. Q factor is calculated as the ratio of. In practice, the signal source level is generally set for a calibrate point on the meter which measures injected voltage and Q is directly read from calibration on the meter which measures output voltage.
Some of the uses of Q Meter: The Q meter can be used for many purposes. As the name implies, it can measure Q and is generally used to check the Q factor of inductors. As the internal tuning capacitor has an air dielectric its loss resistance is negligible compared to that of any inductor and hence the Q measured is that of the inductor. The value of Q varies considerable with different types of inductors used over different ranges of frequency.
Miniature commercial inductors, such as the Siemens B types or the Lenox-Fugal Nanored types, made on ferrite cores and operated at frequencies up to 1 MHz, have typical Q factors in the region of 50 to Air wound inductors with spaced turns, such as found in transmitter tank circuits and operating at frequencies above 10 MHz, can be expected to have Q factors of around to Some inductors have Q factors as low as five or 10 at some frequencies and such inductors are generally unsuitable for use in selective circuits or in sharp filters.
The Q meter is very useful to check these out. The tuning capacitor C of the Q meter has a calibrated dial marked in pico-farads so that, in conjunction with the calibration of the oscillator source, the value of inductance Lx can be derived. Providing the capacitor to be tested is smaller than the tuning range of the internal tuning capacitor, the test sample can be easily measured.
Firstly, the capacitor sample is resonated with a selected inductor by adjusting the source frequency and using the tuning capacitor set to a low value on its calibrated scale.
The sample is then disconnected and using the same frequency as before, the tuning capacitor is reset to again obtain resonance. The difference in tuning capacitor calibration read for the two tests is equal to the capacitance of the sample. Larger values of capacitance can be read by changing frequency to obtain resonance on the second test and manipulating the resonance formula.
A poorly chosen inductor is not the only cause of low Q in a tuned circuit as some types of capacitor also have high loss resistance which lowers the Q. Small ceramic capacitors are often used in tuned circuits and many of these have high loss resistance, varying considerably in samples often taken from the same batch.
If ceramic capacitors must be used where high Q is required, it is wise to select them for low loss resistance and the Q meter can be used for this purpose.
To do this, an inductor having a high Q, of at least , is used to resonate the circuit, first with the tuning capacitor C on its own and then with individual test sample capacitors in parallel. A drastic loss in the value of Q, when the sample is added, soon shows up which capacitor should not be used. Direct measurement of Q in an inductor, as discussed in previous paragraphs. Inductors also have distributed. High distributed capacitance is common in large value inductors having closely wound turns or having multiple layers.
Actual Q can be calculated from Qe, as read, from the following: Two methods of measuring distributed capacitance are described in the "Boonton Q Meter Handbook".
The simplest of these is said to be accurate for distributed capacitance above 10 pF and this method is described as follows: With the tuning capacitor C set to value C1 say 50 pF , resonate with the sample inductor by adjusting the signal source frequency.
Set the signal source to half the original frequency and re-resonate by adjusting C to a new value of capacitance C2. Calculate distributed capacitance as follows: State the principle of digital voltmeter. Give the importance of iron loss measurement. List two instruments for measurement of frequency. Write the function of instrument transformer. Brief the principle of digital phase meter. Write any two advantages and disadvantages of digital voltmeter.
Explain the purpose of Schmitt trigger in digital frequency meter. Which torque is absent in energy meter? What are the errors that take place in moving iron instrument? Explain the principle of analog type electrical instruments. How a PMMC meter can be used as voltmeter and ammeter? What is loading effect? State the basic principle of moving iron instrument.
Why an ammeter should have a low resistance? Define the sensitivity of a moving coil meter.
What is the use of Multimeter? Write its advantages and disadvantages. Voltmeter has high resistance, why it is connected in series? What is an energy meter? Mention some advantages and disadvantages of energy meter.
What is meant by creep adjustment in three phase energy meter? List some advantages and disadvantages of electrodynamic instrument. List the advantages of electronic voltmeter. What is a magnetic measurements and what are the tests performed for magnetic measurements? Mention the advantages and disadvantages of flux meter. What are the methods used to determine B-H Curve?
What are the errors in instrument transformers? What is frequency meter and classify it? What is phase meter and what are its type? Discuss why it is necessary to carry out frequency domain analysis of measurement systems? What are the two plots obtained when the frequency response of a system is carried out? Explain the function of three phase wattmeter and energy meter.
A function generator is a device which produces simple repetitive waveforms. Such devices contain an electronic oscillator, a circuit that is capable of creating a repetitive waveform.
Modern devices may use digital signal processing to synthesize waveforms, followed by a digital to analog converter, or DAC, to produce an analog output.
The most common waveform is a sine wave, but sawtooth, step pulse , square, and triangular waveform oscillators are commonly available as are arbitrary waveform generators AWGs. Function generators are typically used in simple electronics repair and design; where they are used to stimulate a circuit under test. A device such as an oscilloscope is then used to measure the circuit's output.
Function generators vary in the number of outputs they feature, frequency range, frequency accuracy and stability, and several other parameters. A function generator is a piece of electronic test equipment or software used to generate electrical waveforms. These waveforms can be either repetitive or single-shot, in which case some kind of triggering source is required internal or external.
Function Generators are used in development, testing and repair of electronic equipment, e. Explanation Analog function generators usually generate a triangle waveform as the basis for all of its other outputs. The triangle is generated by repeatedly charging and discharging a capacitor from a constant current source. This produces a linearly ascending or descending voltage ramp. As the output voltage reaches upper and lower limits, the charging and discharging is reversed using a comparator, producing the linear triangle wave.
By varying the current and the size of the capacitor, different frequencies may be obtained.
Sawtooth waves can be produced by charging the capacitor slowly, using a current, but using a diode over the current source to discharge quickly - the polarity of the diode changes the polarity of the resulting sawtooth, i. Most function generators also contain a non-linear diode shaping circuit that can convert the triangle wave into a reasonably accurate sine wave.
It does so by rounding off the hard corners of the triangle wave in a process similar to clipping in audio systems.
A typical function generator can provide frequencies up to 20 MHz. RF generators for higher frequencies are not function generators in the strict sense since typically produce pure or modulated sine signals only. Function generators, like most signal generators, may also contain an attenuator, various means of modulating the output waveform, and often the ability to automatically and repetitively "sweep" the frequency of the output waveform by means of a voltage-.
This capability makes it very easy to evaluate the frequency response of a given electronic circuit. Some function generators can also generate white or pink noise. Arbitrary waveform generators use DDS to generate any waveform that can be described by a table of amplitudes.
Signal generator: A signal generator, also known variously as function generator, pitch generator, arbitrary waveform generator, digital pattern generator or frequency generator is an electronic device that generates repeating or non-repeating electronic signals in either the analog or digital domains.
They are generally used in designing, testing, troubleshooting, and repairing electronic or electroacoustic devices; though they often have artistic uses as well. There are many different types of signal generators, with different purposes and applications and at varying levels of expense ; in general, no device is suitable for all possible applications.
Traditionally, signal generators have been embedded hardware units, but since the age of multimedia-PCs, flexible, programmable software tone generators have also been available.
Basic Sweep Generator A basic system for the sweep generator is shown in figure 1. A low-frequency sawtooth wave is generated from some form of oscillator or waveform generator. The instantaneous voltage of the sawtooth wave controls the frequency of an RF oscillator with its centre frequency set at the centre frequency of the device under test filter or IF channel etc.
Over a single sweep of frequency, RF output voltage from the device, as a function of time, is a plot of the filter response.
By rectifying and RF filtering in a simple AM detector, the output is converted to a DC voltage varying as a function of time and this voltage is applied to the vertical input of the CRO. To achieve this for a range of frequencies, it is easiest to sweep a single frequency say 1MHz and heterodyne this to the test frequency required. The system developed is shown. A 1MHz oscillator is frequency modulated by the output of a sawtooth generator operating at 33 Hz.
The modulated output is beat with an external signal generator set to provide the difference frequency centered at the center frequency of the filter or IF circuit under test. By synchronising the CRO sweep circuit to the 33 Hz sweep generator, a plot of test circuit response is displayed in terms of amplitude verses frequency. It calculates the total distortion introduced by all the harmonics of the fundamental frequency wave. In most cases THD is the amount required to be calculated, rather than distortion caused by individual harmonics.
This type of analysis is very important in systems e. Block Diagram of a THD Analyzer This is a specific type of THD analyzer, in which basically the fundamental frequency of the input wave is suppressed so as to remove it from the spectra of the meters used for distortion measurement, and the total gain of all the harmonics is calculated, thus obtaining the total distortion caused by the harmonics.
This basic construction consists of three main sections: Input section with impedance matcher, a rejection amplifier section and an output metering circuit. Notice the feedback from the bridge amplifier to the pre-amp section, that enables the rejection circuit to work more accurately. The applied input wave is impedance matched with the rejection circuit with the help of an attenuator and an impedance matcher. This signal is then applied to a pre-amplifier which raises the signal level to a desired value.
The following section consists of a Wien bridge. The bridge is tuned to the fundamental frequency by frequency control and it is balanced for zero output by adjusting the bridge controls, thus giving a notch in the frequency response of the rejection section.
After the Wien Bridge, a bridge amplifier follows that simply amplifies low harmonic voltage levels to measurable higher levels. This filtered output is then applied to a meter amplifier which can be an instrumentation amplifier.
Thus the total voltage obtained at the meter output shows the amount of distortion present in the wave due to harmonics of fundamental.
A spectrum analyzer or spectral analyzer is a device used to examine the spectral composition of some electrical, acoustic, or optical waveform. It may also measure the power spectrum. There are analog and digital spectrum analyzers: An analog spectrum analyzer uses either a variable band-pass filter whose midfrequency is automatically tuned shifted, swept through the range of frequencies of which the spectrum is to be measured or a superheterodyne receiver where the local oscillator is swept through a range of frequencies.
A digital spectrum analyzer computes the discrete Fourier transform DFT , a mathematical process that transforms a waveform into the components of its frequency spectrum. Some spectrum analyzers such as "real-time spectrum analyzers" use a hybrid technique where the incoming signal is first down-converted to a lower frequency using superheterodyne techniques and then analyzed using fast fourier transformation FFT techniques. Typical functionality: Allows one to fix the window of frequencies to visualize and center the display on a chosen frequency.
Controls the position and function of markers and indicates the value of power. Several spectrum analyzers have a "Marker Delta" function that can be used to measure Signal to Noise Ratio or Bandwidth. The spectrum analyzer captures the measure on having displaced a filter of small bandwidth along the window of frequencies. Amplitude The maximum value of a signal at a point is called amplitude. A spectrum analyzer that implements amplitude analysis is called a Pulse height analyzer.
Manages parameters of measurement. It stores the maximum values in each frequency and a solved measurement to compare it. Usually, a spectrum analyzer displays a power spectrum over a given frequency range, changing the display as the properties of the signal change. There is a trade-off between how quickly the display can be updated and the frequency resolution, which is for.
With an analog spectrum analyzer, it is dependent on the bandwidth setting of the bandpass filter. Choosing a wider bandpass filter will improve the signal-to-noise ratio at the expense of a decreased frequency resolution. With Fourier transform analysis in a digital spectrum analyzer, it is necessary to sample the input signal with a sampling frequency s that is at least twice the highest frequency that is present in the signal, due to the Nyquist limit. This can place considerable demands on the required analog-to-digital converter and processing power for the Fourier transform.
Often, one is only interested in a narrow frequency range, for example between 88 and MHz, which would require at least a sampling frequency of MHz, not counting the low-pass anti-aliasing filter. In such cases, it can be more economic to first use a superheterodyne receiver to transform the signal to a lower range, such as 8 to 28 MHz, and then sample the signal at 56 MHz. This is how an analog-digitalhybrid spectrum analyzer works.
For use with very weak signals, a pre-amplifier can be used, although harmonic and intermodulation distortion may lead to the creation of new frequency components that were not present in the original signal.
A new method, without using a high local oscillator LO that usually produces a high-frequency signal close to the signal is used on the latest analyzer generation like Aaronias Spectran series. The analog signal is converted into a digital code proportionate to the magnitude of the signal.
Voltages from picovolts to megavolts are measurable, though the scale usually graduates in millivolts, volts, or kilovolts. Frequencies between zero and several megahertz may also be measured. Common laboratory and commercial applications involve electromechanical machinery with a current flowing through wires and circuits.
Often, a digital voltmeter is used to monitor a unit, such as a generator. Portable or handheld devices, such as the digital multimeter DMM , for example, may combine several functions into one instrument measuring voltage, current, and resistance.
This is the preferred tool of an electrician. Many DVMs integrate outputs for monitoring, controlling, transmitting, and printing of data. Advanced systems are often connected to computers, allowing for automation, optimization of processes, and prevention of malfunctions and critical failure safeties. Chemical plants can convert measurements to voltage, and control and monitor temperature, pressure, level, or flow. Medical equipment, such as x-ray machines, may use a digital voltmeter to make sure the voltage of the equipment is in the proper range.
Draw Maxwells AC bridge and give the balance equation interms of resistance. Explain any two technical parameters to be consider in grounding. Give some applications of Wheatstones bridge. What is a potentiometer? List the applications of dc and ac potentiometer. Differentiate the principle of dc potentiometer and ac potentiometer. What is meant by transformer ratio bridge 2 8. What are the features of ratio transformer?
List its applications. What is meant by electromagnetic interference? List the sources of electromagnetic interference. What are the ways of minimizing the electromagnetic interference? Define electromagnetic compatibility. EMC 2 What are the main causes of group loop currents? What are the limitations of single point grounding method? What is the necessity of grounding and state is advantages.
What is meant by ground loop? How it is created? What are the sources of errors in bridge measurement? Define standardization. Give the relationship between the bridge balance equation of DC bridge and AC bridge 2 What does a bridge circuit consists of?
Explain voltage sensitive self balancing bridge, and derive the bridge sensitivity of voltage sensitive bridge with fundamentals. The reverse operation is performed by a digital-to-analog converter DAC. Typically, an ADC is an electronic device that converts an input analog voltage or current to a digital number proportional to the magnitude of the voltage or current.
However, some non-electronic or only partially electronic devices, such as rotary encoders, can also be considered ADCs. The digital output may use different coding schemes. Typically the digital output will be a two's complement binary number that is proportional to the input, but there are other possibilities. An encoder, for example, might output a Gray code. An ADC might be used to make an isolated measurement. ADCs are also used to quantize time-varying signals by turning them into a sequence of digital samples.
The result is quantized in both time and value. An 8-level ADC mid-tread coding scheme.
As in figure 2 but with equal half-LSB intervals at the highest and lowest codes. Note that LSB is now slightly larger than in figures 1 and 2.
The resolution of the converter indicates the number of discrete values it can produce over the range of analog values. The values are usually stored electronically in binary form, so the resolution is usually expressed in bits. In consequence, the number of discrete values available, or "levels", is usually a power of two. The values can represent the ranges from 0 to i.
Resolution can also be defined electrically, and expressed in volts. The minimum change in voltage required to guarantee a change in the output code level is called the LSB least significant bit, since this is the voltage represented by a change in the LSB. The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of discrete voltage intervals:.
N is the number of voltage intervals, EFSR is the full scale voltage range, given by,. Normally, the number of voltage intervals is given by,. M is the ADC's resolution in bits. That is, one voltage interval is assigned per code level. However, figure 3 shows a situation where.
Some examples: The largest code represents a range of 1. The other N 2 codes are all equal in width and represent the ADC voltage resolution Q calculated above. Doing this centers the code on an input voltage that represents the M th division of the input voltage range.
This practice is called "mid-tread" operation. This type of ADC can be modeled mathematically as:. The exception to this convention seems to be the Microchip PIC processor, where all M steps are equal width, as shown in figure 1. This practice is called "Mid-Rise with Offset" operation. In practice, the useful resolution of a converter is limited by the best signal-to-noise ratio SNR that can be achieved for a digitized signal. Linear ADCs Most ADCs are of a type known as linear The term linear as used here means that the range of the input values that map to each output value has a linear relationship with the output value, i.
Here b is typically 0 or 0. Non-linear ADCs If the probability density function of a signal being digitized is uniform, then the signal-tonoise ratio relative to the quantization noise is the best possible. Because this is often not the case, it is usual to pass the signal through its cumulative distribution function CDF before the quantization.
This is good because the regions that are more important get quantized with a better resolution. In the dequantization process, the inverse CDF is needed. This is the same principle behind the companders used in some tape-recorders and other communication systems, and is related to entropy maximization. For example, a voice signal has a Laplacian distribution. This means that the region around the lowest levels, near 0, carries more information than the regions with higher amplitudes.
Because of this, logarithmic ADCs are very common in voice communication systems to increase the dynamic range of the representable values while retaining fine-granular fidelity in the low-amplitude region. An eight-bit A-law or the -law logarithmic ADC covers the wide dynamic range and has a high resolution in the critical low-amplitude region, that would otherwise require a bit linear ADC. Accuracy An ADC has several sources of errors. Quantization error and assuming the ADC is intended to be linear non-linearity is intrinsic to any analog-to-digital conversion.
There is also a so-called aperture error which is due to a clock jitter and is revealed when digitizing a time-variant signal not a constant value. These errors are measured in a unit called the LSB, which is an abbreviation for least significant bit.
Quantization error Quantization error is due to the finite resolution of the ADC, and is an unavoidable imperfection in all types of ADC.
The magnitude of the quantization error at the sampling instant is between zero and half of one LSB. In the general case, the original signal is much larger than one LSB. When this happens, the quantization error is not correlated with the signal, and has a uniform distribution.
Its RMS value is the standard deviation of this distribution, given by. In the eight-bit ADC example, this represents 0. At lower levels the quantizing error becomes dependent of the input signal, resulting in distortion. In order to make the quantizing error independent of the input signal, noise with an amplitude of 2 least significant bits is added to the signal. This slightly reduces signal to noise ratio, but, ideally, completely eliminates the distortion. It is known as dither.
All ADCs suffer from non-linearity errors caused by their physical imperfections, causing their output to deviate from a linear function or some other function, in the case of a deliberately non-linear ADC of their input. These errors can sometimes be mitigated by calibration, or prevented by testing. These non-linearities reduce the dynamic range of the signals that can be digitized by the ADC, also reducing the effective resolution of the ADC.
Aperture error: Provided that the actual sampling time uncertainty due to the clock jitter is t, the error caused by this phenomenon can be estimated as. The error is zero for DC, small at low frequencies, but significant when high frequencies have high amplitudes. This effect can be ignored if it is drowned out by the quantizing error. Jitter requirements can be calculated using the following formula: ADC input frequency resolution 1 Hz This table shows, for example, that it is not worth using a precise bit ADC for sound recording if there is not an ultra low jitter clock.
One should consider taking this phenomenon into account before choosing an ADC. Clock jitter is caused by phase noise. The input frequency in this case, 22 kHz , not the ADC clock frequency, is the determining factor with respect to jitter performance. The analog signal is continuous in time and it is necessary to convert this to a flow of digital values.
It is therefore required to define the rate at which new digital values are sampled from the analog signal. The rate of new values is called the sampling rate or sampling frequency of the converter.
A continuously varying bandlimited signal can be sampled that is, the signal values at intervals of time T, the sampling time, are measured and stored and then the original signal can be exactly reproduced from the discrete-time values by an interpolation formula.
The accuracy is limited by quantization error. However, this faithful reproduction is only possible if the sampling rate is higher than twice the highest frequency of the signal. This is essentially what is embodied in the Shannon-Nyquist sampling theorem. Since a practical ADC cannot make an instantaneous conversion, the input value must necessarily be held constant during the time that the converter performs a conversion called the conversion time.
An input circuit called a sample and hold performs this taskin most cases by using a capacitor to store the analog voltage at the input, and using an electronic switch or gate to disconnect the capacitor from the input. Many ADC integrated circuits include the sample and hold subsystem internally. All ADCs work by sampling their input at discrete intervals of time. Their output is therefore an incomplete picture of the behaviour of the input.
There is no way of knowing, by looking at the output, what the input was doing between one sampling instant and the next. If the input is known to be changing slowly compared to the sampling rate, then it can be assumed that the value of the signal between two sample instants was somewhere.
If, however, the input signal is changing rapidly compared to the sample rate, then this assumption is not valid. If the digital values produced by the ADC are, at some later stage in the system, converted back to analog values by a digital to analog converter or DAC, it is desirable that the output of the DAC be a faithful representation of the original signal. If the input signal is changing much faster than the sample rate, then this will not be the case, and spurious signals called aliases will be produced at the output of the DAC.
The frequency of the aliased signal is the difference between the signal frequency and the sampling rate. For example, a 2 kHz sine wave being sampled at 1. This problem is called aliasing. To avoid aliasing, the input to an ADC must be low-pass filtered to remove frequencies above half the sampling rate. This filter is called an anti-aliasing filter, and is essential for a practical ADC system that is applied to analog signals with higher frequency content.
Although aliasing in most systems is unwanted, it should also be noted that it can be exploited to provide simultaneous down-mixing of a band-limited high frequency signal see undersampling and frequency mixer. In A-to-D converters, performance can usually be improved using dither. This is a very small amount of random noise white noise which is added to the input before conversion. Its amplitude is set to be twice the value of the least significant bit.
Its effect is to cause the state of the LSB to randomly oscillate between 0 and 1 in the presence of very low levels of input, rather than sticking at a fixed value. Rather than the signal simply getting cut off altogether at this low level which is only being quantized to a resolution of 1 bit , it extends the effective range of signals that the A-to-D converter can convert, at the expense of a slight increase in noise - effectively the quantization error is diffused across a series of noise values which is far less objectionable than a hard cutoff.
The result is an accurate representation of the signal over time. A suitable filter at the output of the system can thus recover this small signal variation. An audio signal of very low level with respect to the bit depth of the ADC sampled without dither sounds extremely distorted and unpleasant. Without dither the low level may cause the least significant bit to "stick" at 0 or 1. Passive electronic components - 8. Passive filters - 9.
PN diodes - Bipolar transistors - Fieldeffect transistors - Operational amplifiers - Frequency-selective transfer functions with operational amplifiers - Non-linear signal processing with operational amplifiers - Electronic switching circuits - Signal generation - Modulation - Digital-to-analogue and analogue-to-digital conversion - Digital electronics - Measurement instruments - Measurement errors - Appendix - Answers to exercises - Index Download table of contents and more here Download file for readers of this book: eanswers.
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