# Electronic Instruments

www.getmyuni.com Electronic Instruments In this chapter the instruments to measure voltage, current, resistance, inductance, power, capacitance, etc are presented. The instruments which are basically Electro-mechanical Instruments use D’Arsonval meter which is shown in Fig. 1 Fig. 1 D’Arsonval meter Working of D’Arsonval meter A commonly used sensing mechanism used in DC ammeters, voltmeters, and ohm meters is a current-sensing device called a D'Arsonval meter movement. The D'Arsonval movement is a DC moving coil type movement in which an electromagnetic core is suspended between the poles of a permanent magnet. The current measured is directed through the coils of the electromagnet so that the magnetic field produced by the current opposes the field of the permanent magnet and causes rotation of the core. The core is restrained by springs so that the needle will deflect or move in proportion to the current intensity. The D'Arsonval movement is a DC device and can only measure DC current or AC current rectified to DC. Limitations of D’Arsonval meter • An amplifier is required for increasing the – Current sensitivity below 50µA – Voltage below 10mV • Power required greater than ½ µW – Drawn from the circuit under measurement – Varies with the voltage range The next few sections illustrate the modifications used for measuring AC current with a D’Arsonval meter. www.getmyuni.com Rectification for an Average Responding Voltmeter As shown in Fig. 2, the series-connected diode provides half-wave rectification and the average value of the half-wave voltage is developed across the resistor and is applied to the input terminals of the DC amplifier of an average responding meter. Fig.2 Half wave rectification Full-wave rectification can be obtained by the bridge circuit of Fig. 3, where the average value of the sine wave is applied to the amplifier and meter circuit. Fig. 3 Full wave Rectification Average-Responding AC voltmeters In these meters, the meter scale of an average responding meter is calibrated in terms of the rms value of a sine wave. As most of the wave-forms in electronics are sinusoidal, this is an entirely satisfactory solution and certainly much less expensive than a true rms-responding voltmeter. Nonsinusoidal waveforms, however, will cause this type of meter to read high or low, depending on the form factor of the waveform. www.getmyuni.com Peak Reading Voltmeter Fig. 4 These meters are used when required to measure the peak value of a waveform instead of the average value. As shown in Fig. 4 the rectifier diode charges the small Capacitor to the peak of the applied input voltage and the meter will indicate the peak voltage. In most cases, the meter scale of an average responding (DC) meter is calibrated in terms of both the rms and peak values of the sinusoidal input waveform. The rms value of a voltage wave that has equal positive and negative excursions is related to the average value by the form factor Form Factor • The form factor, is the ratio of the rms value to the average value of this waveform, • for a sinusoid it is expressed as www.getmyuni.com Form Factor of a Square Wave Since Erms = Eav , the calibrated meter scale (Erms = 1.11 Eav) reads high By a factor ksin e _ wave k square _ wave = 1.11 www.getmyuni.com Form Factor of a Sawtooth Wave The derivation of the voltage e, its rms value, etc is shown below. Since Erms = 1.155Eav, the calibrated meter scale (Erms = 1.11 Eav) reads low By a ksin e _ wave 1.11 factor = = 0.961 . k saw _ tooth _ wave 1.155 The effect of non-sinusoidal waveforms on ac voltmeter based on an average responding meter whose meter is calibrated in terms of form factor of a sinusoidal wave is presented above. As seen as any departure from a true sinusoidal wave causes a significant error in the measurement. www.getmyuni.com True RMS Meters As compared to the average and peak responding voltmeters the rmsresponding voltmeters present special circuit design problems. RMS implies that the input quantity (say voltage in voltmeter) has to be squared and then the square root of the average of the squared quantity is taken. These meters are used to provide accurate rms readings of complex waveforms i.e., non-sinusoidal waveforms having a crest factor of 10:1. Some of the applications are: – Measurements of electrical or acoustical noise – Low duty cycle pulse trains – Voltages of undetermined waveforms Problems with Waveforms having a DC Component Many waveforms have a DC component, which usually shows as the wave not being symmetrical above and below ground level. Determination of the rms level of such a waveform sometimes requires separate dc and ac measurements. First the DC level is measured on a DC voltmeter with the AC quantity filtered out. Then the AC rms level is measured on a capacitor-coupled AC voltmeter. The rms value of the original waveform is then determined as the square root of the sum of the squares of the two readings, The procedure above is not necessary with the true-rms instrument described next Features of a True RMS Responding Voltmeter • • • • Complex waveforms are accurately measured with a RMS Responding Voltmeter Heating power of the waveform is sensed Which is proportional to the square of the rms value of the waveform (P α V2rms R) The input to be measured is applied to a heater element. The temperature of the heater element R, which is proportional to the applied input rms value is measured using a thermo couple. www.getmyuni.com • • the output voltage from a thermocouple is directly proportional to the rms level of the current through its heater regardless of the current waveform. an input voltage (E1) with a nonsinusoidal waveform is amplified and applied to a fine heater wire the thermocouple attached to the heater element generates a DC voltage proportional to the rise in temperature of the hot junction Fig. 5 Block diagram of a true rms-reading voltmeter Working: The 2 thermocouples form part of a bridge in the input circuit of the DC amplifier. The input voltage is amplified and fed to the heating element of the thermocouple. The heat produced by the wire is sensed by the measuring thermocouple which produces a proportional DC voltage. This DC voltage upsets the bridge balance. The unbalance voltage is amplified by the DC amplifier and fed back to the heating element of the balancing thermocouple. Bridge balance is reestablished when the two thermocouples produce the same output voltages. At this point the DC current in the heating element of the feedback thermocouple is proportional to the AC current in the input thermocouple i.e., the DC is proportional to the rms value of the input AC signal. This DC value is indicated by the meter movement in the output circuit A frequent limitation of the usefulness of the rms responding voltmeter for measuring highly non-linear waveforms such as the pulse trains is the crest factor rating. A typical laboratory type rms responding voltmeter has a crest factor of 10/1. At 10% of full scale deflection it can go as high as 100/1. The crest factor of a waveform is the ratio of its peak value to its rms value. www.getmyuni.com The crest factor for a pure sine wave is 1.414, but non-sinusoidal waveforms can have much larger crest factors. The rms level of waveforms with a crest factor of 2 or 3 can be determined by most rms measuring instruments. Waveforms with higher crest factors are more difficult to measure. The maximum waveform crest factor is usually specified for all rms measuring instruments Disadvantages of a true rms-reading voltmeter The accuracy of this technique has been difficult to control because of the nonlinear behavior of the thermocouple which complicates the meter calibration, Thermal variations & Sluggish response of the thermocouple which are also susceptible to burnout also aggravate the problem. Thermal variations are reduced by installing the heater and the thermo couple in an evacuated glass bulb and by using fine wires of low thermal conductivity. Use of null balance techniques reduces the effect of non linear behavior. Generally the Nonlinear behavior of the measuring and feedback (balancing) thermocouples cancel each other. www.getmyuni.com Electronic Multimeters One of the most versatile general-purpose instruments capable of measuring dc and ac voltages as well as current and resistance is the solid-state electronic multimeter or VOM. Although circuit details will vary from one instrument to the next, an electronic multimeter generally contains the following elements: • Balanced-bridge dc amplifier and indicating meter • Input attenuator or RANGE switch, to limit the magnitude of the input voltage to the desired value • Rectifier section, to convert an ac input voltage to a proportional dc value • internal battery and additional circuitry, to provide the capability of resistance measurement • FUNCTION switch, to select the various measurement functions of the instrument In addition, the instrument generally has a built-in power supply for ac line operation and, in most cases, one or more batteries for operation as a portable test instrument. Fig.6 Balanced Bridge dc amplifier with input attenuator and indicating meter www.getmyuni.com Working of individual Components Balanced Bridge DC amplifier As shown in Fig. 6 the balanced-bridge dc amplifier uses FETs (BJTs can also be used). The two FETs should be well matched for current gain to ensure thermal stability of the circuit. The two FETs form the upper arms of a bridge circuit. Source resistors R I and R2 , together with ZERO adjust resistor R3 , form the lower bridge arms. The meter movement is connected between the source terminals of the FETs, representing two opposite corners of the bridge. Without an input signal, the gate terminals of the FETs are at ground potential and the transistors operate under identical quiescent conditions. In this case, the bridge is balanced and the meter indication is zero. However, small differences in the operating characteristics of the transistors, and slight tolerance differences in the various resistors, cause a certain amount of unbalance in the drain currents, and the meter shows a small deflection from zero. To return the meter to zero, the circuit is balanced by ZERO adjust control R3 for a true null indication. Output Indication When a positive voltage is applied to the gate of input transistor Q1, its drain current increases which causes the voltage at the source terminal to rise. The resulting unbalance between the Ql and Q2 source voltages is indicated by the meter movement, whose scale is calibrated to agree with the magnitude of the applied input voltage. Input Attenuator Or RANGE Switch Typical input voltage attenuator for a VOM is shown in Fig.7. The RANGE switch on the front of the panel of the VOM allows selection of the desired voltage range. The maximum voltage that can be applied to the gate of Q1 is determined by the operating range of FET (usually a few volts). The range of input voltages can easily be extended by an input attenuator or RANGE switch, as shown in Fig.7. The unknown dc input voltage is applied through a large resistor in the probe body to a resistive voltage divider. Thus, with the RANGE www.getmyuni.com switch in the 3-V position as shown, the voltage at the gate of the input FET is developed across 8 MΩ of the total resistance of 11.3 MΩ and the circuit is so arranged that the meter deflects full scale when 3 V is applied to the tip of the probe. With the RANGE switch in the 12-V position, the gate voltage is developed across 2 MΩ of the total divider resistance of 11.3 MΩ and an input voltage of 12 V is required to cause the same full-scale meter deflection. Fig. 7 www.getmyuni.com Resistance Ranges When the function switch of the multimeter is placed in the OHMS position, the unknown resistor is connected in series with an internal battery, and the meter simply measures the voltage drop across the unknown. A typical circuit is shown in Fig.8, where a separate divider network, used only for resistance measurements, provides for a number of different resistance ranges. When unknown resistor Rx is connected to the OHMS terminals of the multimeter, the 1.5-V battery supplies current through one of the range resistors and the unknown resistor to ground. Fig.8 Voltage drop Vx across Rx is applied to the input of the bridge amplifier and causes a deflection on the meter. Since the voltage drop across Rx is directly proportional to its resistance the meter scale can be calibrated in terms of resistance which in an Electronic multimeter is from left to right (vice versa for ordinary multimeter). i.e., High Rx => High Vx ( in ordinary multimeter High Rx => Low current I) www.getmyuni.com Digital Voltmeters Digital voltmeters are essentially analog-to-digital converters with digital displays to indicate the measured voltage. DVM displays measurements of ac or dc voltages as discrete numerals instead of a pointer deflection on a continuous scale. The development of ICs has lead to drastic reduction of the size, power requirements and cost of DVM. Hence DVMs can actively compete with conventional analog instruments, both in portability and price. CONSIDERATIONS IN CHOOSING AN ANALOG VOLTMETER The most appropriate instrument for a particular voltage measurement depends on the performance required in a given situation. Some important considerations are – – – – – Input Impedance Voltage Ranges Decibels Sensitivity Versus Bandwidth Battery Operation Typical Operating And Performance Characteristics of DVMs • Input range.. from ±1.000000 V to ±1,000.000 V, with automatic range selection and overload indication • Absolute accuracy.. as high as ±0.005 per cent of the reading • Stability.` short-term, 0.002 per cent of the reading for a 24-hr period; longterm, 0.008 per cent of the reading for a 6-month period • Resolution.. 1 part in 106 (1µ V can be read on the 1-V input range) • input characteristics.. input resistance typically 10 MΩ; input capacitance typically 40 pF • Calibration. internal calibration standard allows calibration independent of the measuring circuit; derived from stabilized reference source • Output signals. print command allows output to printer; BCD (binarycoded-decimal) output for digital processing or recording • Additional features may include additional circuitry to measure current, resistance, and voltage ratios. Other physical variables may be measured by using suitable transducers. www.getmyuni.com Classification of DVMs 1. Ramp-type DVM 2. Integrating DVM 3. Continuous-balance DVM 4. Successive-approximation DVM Ramp-type DVM Its Operating principle is based on the measurement of the time it takes for a linear ramp voltage to rise from 0 V to the level of the input voltage, or to decrease from the level of the input voltage to zero. This time interval is measured with an electronic time-interval counter, and the count is displayed as a number of digits on electronic indicating tubes. Fig. 9 Block diagram of a ramp-type digital voltmeter The working principle i.e., the Conversion from a voltage to a time interval is illustrated by the waveform in Fig. 10 www.getmyuni.com Fig.10 At the start of the measurement cycle, a ramp voltage is initiated; this voltage can be positive-going or negative-going. The negative-going ramp, (see Fig. 10) is continuously compared with the unknown input voltage. At the instant that the ramp voltage equals the unknown voltage, a coincidence circuit, or comparator, generates a pulse which opens a gate. The ramp voltage continues to decrease with time until it finally reaches 0 V (or ground potential) and a second comparator generates an output pulse which closes the gate. An oscillator generates clock pulses which are allowed to pass through the gate to a number of decade counting units (DCUs) which totalize the number of pulses passed through the gate. The decimal number, displayed by the indicator tubes associated with the DCUs, is a measure of the magnitude of the input voltage. The sample-rate multivibrator determines the rate at which the measurement cycles are initiated. The oscillation of this multivibrator can usually be adjusted by a front-panel control , marked rate , from a few cycles per second to as high 1,000 or more. The sample-rate circuit provides an initiating pulse for the ramp generator to start its next ramp voltage. At the same time, a reset pulse is generated which returns all the DCUs to their 0 state, removing the display momentarily from the indicator tubes. www.getmyuni.com Staircase-Ramp DVM It is a variation of the ramp-type DVM but is simpler in overall design, resulting in a moderately priced general-purpose instrument that can be used in the laboratory, on production test-stands, in repair shops, and at inspection stations. Stair case ramp DVM makes voltage measurements by comparing the input voltage to an internally generated staircase-ramp voltage. Fig. 11 It contains a 10-MΩ input attenuator, providing five input ranges from 100 mV to 1,000 V full scale. The dc amplifier with a fixed gain of 100, delivers 10 V to the comparator at any of the full-scale voltage settings of the input divider. The comparator senses coincidence between the amplified input voltage and the staircase-ramp voltage which is generated as the measurement proceeds through its cycle . A Clock (4.5 kHz oscillator) provides pulses to three DCUs in cascade. The units counter provides a carry pulse to the tens decade at every tenth input pulse. The tens decade counts the carry pulses from the units decade and provides its own carry pulse after it has counted ten carry pulses. This carry pulse is fed to the hundreds decade which provides a carry pulse to an overrange circuit. The over range circuit causes a front panel indicator to light up, warning the operator that the input capacity of the instrument has been exceeded. The operator should then switch to the next higher setting on the input attenuator. Each decade counter unit is connected to a digital-to-analog (D/A) converter. www.getmyuni.com The outputs of the D/A converters are connected in parallel and provide an output current proportional to the current count of the DCUs. The staircase amplifier converts the D/A current into a staircase voltage which is applied to the comparator. When the comparator senses coincidence of the input voltage and the staircase voltage, it provides a trigger pulse to stop the oscillator. The current content of the counter is then proportional to the magnitude of the input voltage. The sample rate is controlled by a simple relaxation oscillator. This oscillator triggers and resets the transfer amplifier at a rate of two samples per second. The transfer amplifier provides a pulse that transfers the information stored in the decade counters to the front panel display unit. The trailing edge of this pulse triggers the reset amplifier which sets the three decade counters to zero and initiates a new measurement cycle by starting the master oscillator or clock. The display circuits store each reading until a new reading is completed, eliminating any blinking or counting during the computation. The ramp type of A/D converter requires a precision ramp to achieve accuracy. Maintaining the quality of the ramp requires a precise, stable capacitor and resistor in the integrator. In addition, the offset voltages and currents of the operational amplifier used in the integrator are critical in the accurate ramp generator. One method of reducing the dependence of the accuracy of the conversion on the resistor, capacitor, and operational amplifier is to use a technique called the dual-slope converter. Dual-Slope Converter In the dual-slope technique, an integrator is used to integrate an accurate voltage reference for a fixed period of time. The same integrator is then used to integrate with the reverse slope, the input voltage, and the time required to return to the starting voltage is measured. The Order of integrations does not matter. Consider the integration of the unknown first as shown in Fig. 12 www.getmyuni.com Fig. 12 The output voltage Vout is given by Where t - elapsed time from when the integration began. The above Equation also assumes that the integrator capacitor started with no charge & thus the output of the integrator started at zero volts. If the integration were allowed to continue for a fixed period of time T1, the output voltage would be Notice that the integrator output has gone in the opposite polarity as the input. That is, a positive input voltage produces a negative integrator output. If a reference voltage Vref, were substituted for the input voltage Vx, as shown in Fig.13, the integrator would begin to ramp toward zero at a rate of Vref/ RC assuming that the Vref was of the opposite polarity as the unknown input voltage. The integrator for this situation does not start at zero but at an output voltage of V1, and the output voltage Vout is www.getmyuni.com Fig.13 Setting the output voltage of the integrator to zero and solving for Vx yields where Tx is the time required to ramp down from the output level of V1 to zero volts. Notice that the relationship between the reference voltage and the input voltage does not include R or C of the integrator but only the relationship between the two times. Because the relationship between the two times is a ratio, an accurate clock is not required but only that the clock used for the timing be stable enough that the frequency does not change appreciably from the up ramp to the down ramp. Fig. 14 www.getmyuni.com As the integrator responds to the average of the input, it is not necessary to provide a sample and hold, as changes in the input voltage will not cause significant errors. Although the integrator output will not be a linear ramp, the integration will represent the end value obtained by a voltage equal to the average of the unknown input voltage. Therefore, the dual-slope analog-to-digital conversion will produce a value equal to the average of the unknown input. The dual-slope type of A/D conversion is a very popular method for digital voltmeter applications. When compared to other types of ADC techniques, the dual-slope method is slow but is quite adequate for a digital voltmeter used for laboratory measurements. For data acquisition applications, where a number of measurements are required, faster techniques are recommended. Many refinements have been made to the technique and many large-scale-integration (LSI) chips are available to simplify the construction of DVMs. When a dual-slope A/D converter is used for a DVM the counters may be decade rather than binary and the segment and digit drivers may be contained in the chip. When the converter is to interface to a microprocessor, and many highperformance DVMs use microprocessors for data manipulation, the counters employed are binary. One significant enhancement made to the dual-slope converter is automatic zero correction. As with any analog system, amplifier offset voltages, offset currents, and bias currents can cause errors. In addition, in the dual-slope A/D converter, the leakage current of the capacitor can cause errors in the integration and consequentially, an error. These effects, in the dual-slope AID converter, will manifest themselves as a reading of the DVM when no input voltage is present. Fig.15 shows a method of counteracting these effects. www.getmyuni.com Fig.15 The input to the converter is grounded and a capacitor, the auto zero capacitor, is connected via an electronic switch to the output of the integrator. The feedback of the circuitry is such that the voltage at the integrator output is zero. This effectively places an equivalent offset voltage on the automatic zero capacitor so that there is no integration. When the conversion is made, this offset voltage is present to counteract the effects of the input circuitry offset voltages. This automatic zero function is performed before each conversion, so that changes in the offset voltages and currents will be compensated. Fig. 16 Block Diagram of complete dual-slope A/D converter www.getmyuni.com Successive-approximation DVM Fig. 17 A D/A converter is used to provide the estimates. The "equal to or greater than" or "less than" decision is made by a comparator. The D/A converter provides the estimate and is compared to the input signal. A special shift register called a successive-approximation register (SAR) is used to control the D/A converter and consequentially the estimates. At the beginning of the conversion all the outputs from the SAR are at logic zero. If the estimate is greater than the input, the comparator output is high and the first SAR output reverses state and the second output changes to a logic "one." If the comparator output is low, indicating that the estimate is lower than the input signal, the first output remains in the logic one state and the second output assumes the logic state one. This continues to all the states until the conversion is complete. www.getmyuni.com Q-Meter The Q meter is an instrument designed to measure some of the electrical properties of coils and capacitors. The operation of this useful laboratory instrument is based on the characteristics of a series-resonant circuit, i.e., that the voltage across the coil or the capacitor is equal to the applied voltage times the Q of the circuit. If a fixed voltage is applied to the circuit, a voltmeter across the capacitor can be calibrated to read Q directly. Fig. 18 Basic Q-Meter Circuit if E is maintained at a constant and known level, a voltmeter connected across the capacitor can be calibrated directly in terms of the circuit Q as Practical Q-meter Circuit Fig. 19 www.getmyuni.com The wide-range oscillator with a frequency range from 50 kHz to 50 MHz delivers current to a low-value shunt resistance RsH. The value of this shunt is very low, typically on the order of 0.02 Ω. It introduces almost no resistance into the oscillatory circuit and it therefore represents a voltage source of magnitude E with a very small (in most cases negligible) internal resistance. The voltage E across the shunt, corresponding to E in Fig.19, is measured with a thermocouple meter, marked “Multiply Q by”. The voltage across the variable capacitor, corresponding to EC in Fig.19 , is measured with an electronic voltmeter whose scale is calibrated directly in Q values. To make a measurement, the unknown coil is connected to the test terminals of the instrument, and the circuit is tuned to resonance either by setting the oscillator to a given frequency and varying the internal resonating capacitor or by presetting the capacitor to a desired value and adjusting the frequency of the oscillator. The Q reading on the output meter must be multiplied by the index setting of the "Multiply Q by" meter to obtain the actual Q value. The indicated Q (which is the resonant reading on the “Circuit Q" meter) is called the circuit Q because the losses of the resonating capacitor, voltmeter, and insertion resistor are all included in the measuring circuit. The effective Q of the measured coil will be somewhat greater than the indicated Q. This difference can generally be neglected except in certain cases where the resistance of the coil is relatively small in comparison with the value of the insertion resistor The inductance of the coil can be calculated from the known values of freq f and capacitance C as XL =XC & L = 1 / (2πf)2C Measurement Methods There are three methods for connecting unknown components to the test terminals of a Q meter: direct, series, and parallel. The type of component and its size determine the method of connection Direct connection Most coils can be connected directly across the test terminals, exactly as shown in the basic Q-circuit of Fig.19. The circuit is resonated by adjusting either the oscillator frequency or the resonating capacitor. The indicated Q is read directly from the www.getmyuni.com "Circuit Q" meter, modified by the setting of the "Multiply Q by" meter. When the "Multiply Q by" meter is set at the unity mark, the “Circuit Q" meter reads the correct value of Q directly. Series connection Low-impedance components, sub as low-value resistors, small coils, and large capacitors, are measured in series with the measuring circuit. Fig.20 shows the connections. The component to be measured here indicated by [Z], is placed in series with a stable work coil across the test terminals. (The work coil is usually supplied with the instrument) Fig.20 Q-meter measurement of a low-impedance component in series connection. Two measurements are made: In the first measurement the unknown is short-circuited by a small shorting strap and the circuit is resonated, establishing a reference condition. The values of the tuning capacitor (C1) and the indicated Q (Q1) are noted. In the second measurement the shorting strap is removed and the circuit is resonated, giving a new value for the tuning capacitor (C2) and a change in the Q value from Q1 to Q2 . www.getmyuni.com For the second measurement, the reactance of the unknown can be expressed in terms of the new value of the tuning capacitor (C2) and the in-circuit value of the inductor (L). This yields XS is inductive if C1 > C2 and capacitive if C1 < C2 The resistive component of the unknown impedance can be found in terms of reactance XS and the indicated values of circuit Q, since If Rs were purely resistive, in the tuning process C will not change, C1 = C2 If the unknown is a small inductor, the value of the inductance is found from Eq. and is Q of the coil is found as www.getmyuni.com Where Rs & Xs are If the unknown where a large capacitor, Xs is used to find Cs value as & its Q is as above Parallel connection High-impedance components, such as high-value resistors, certain inductors, and small capacitors are connected them in parallel with the measuring circuit. Fig.21 Circuit for Parallel Connection Before the unknown is connected, the circuit is resonated, by using a suitable work coil to establish reference values for Q and C (Q1 & C1 ). Next the component under test is connected to the circuit, the capacitor is readjusted for resonance, a new value for the tuning capacitance (C2) is obtained and a change in the value of circuit Q (∆Q) from Q1 to Q2. At the initial resonance condition, when the unknown is not yet connected into the circuit, the working coil (L) is tuned by the capacitor (C1). Therefore www.getmyuni.com When the unknown impedance is connected into the circuit and the capacitor is tuned for resonance, the reactance of the working coil (XL) equals the parallel reactances of the tuning capacitor (Xc2) & the unknown (Xp) If unknown is inductive, X P = ωLP and LP = 1 2 ω (C1 − C 2 ) If the unknown is capacitive, Xp = 1/ωCp and CP = C1 – C2 In a parallel resonant circuit the total resistance at resonance is equal to the product of the circuit Q and the reactance of the coil. Therefore The resistance (Rp) of the unknown impedance is found by using the conductances in the circuit • GT -- total conductance of the resonant circuit • Gp -- conductance of the unknown impedance • GL -- conductance of the working coil GT = GP + GL GP = GT – GL www.getmyuni.com Sources of Error Distributed capacitance measurement The most important factor affecting measurement accuracy is the distributed capacitance or self capacitance of the measuring circuit. The presence of distributed capacitance in a coil modifies the actual or effective Q and the inductance of the coil. At the frequency at which the self-capacitance and the inductance of the coil are resonant, the circuit exhibits a purely resistive impedance. This characteristic may be used for measuring the distributed capacitance as shown in Fig.22 . Fig.22 Working: make two measurements at different frequencies. The coil under test is connected directly to the test terminals of the Q meter, as shown in Fig.22. The tuning capacitor is set to a high value, preferably to its maximum position, and the circuit is resonated by adjusting the oscillator frequency. Resonance is indicated by maximum deflection on the "Circuit Q" meter. The values of the tuning capacitor ( C1) and the oscillator frequency (f1) are noted. The frequency is then increased to twice its original value = 2f1 and the circuit is returned by adjusting the resonating capacitor (C2). The resonant frequency of an LC circuit is given by At the initial resonance condition, the capacitance of the circuit equals C1 + Cd & the resonant frequency equals www.getmyuni.com After the oscillator and the tuning capacitor are adjusted, the capacitance of the circuit is C2 + Cd , and the resonant frequency equals Solving for the distributed capacitance

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