Instrumentation and MeasurementsDr. Mohammad Kilani Analog Electrical Devices and Voltage Dividing Circuits
Electric Signal in Measuring Instruments Electric signal measurement and conditioning. Common components in a large variety of Instruments Sensor Variable Conversion Element Signal Processor Presentation / Recording Unit Measured Variable Signal Transmission Output Use of Measurement at Remote Location
Advantages of Electrical signal forms over Non-Electrical Forms • Many detecting elements provide an output in the form of varying resistance, capacitance or inductance, voltage or current. Compared to mechanical, pneumatic or hydraulic forms, electric signal forms provide the following advantages:: • Fast transient response. Inertia effect are negligible compared with hydraulic and pneumatic systems. • Light weight and low power consumption in the measuring instrument • Possibility of obtaining large amplification for the signal, with good linearity. • Lower hysteresis effect. Hysteresis is present in mechanical devices due to friction, backlash, and windup effects. • Availability a multitude of proven analog and digital signal conditioning circuits for filtering, compensation, error-rejection, recording and other signal processing operations.
Galvanometer Instruments • A galvanometer is an analog device that produces a deflection proportional to the current in passing in its coil. It utilizes the principle that a current-carrying conductor placed in a magnetic field is acted upon by a force that is proportional to the current passing through the conductor • This force can be used as a measure of the flow of current in a conductor by moving a pointer on a display.
Galvanometer Instruments:Force on a straight current conductor placed on magnetic field • Consider a straight length lof a conductor through which a current I flows. The force on this conductor due to a magnetic field strength B is: • The vector k is a unit vector along the direction of the current flow, and the force F and the magnetic field B are also vector quantities.
Galvanometer Instruments: Force on a Current Loop in a Magnetic Field • A current loop in a magnetic field experiences a torque if the loop is not aligned with the magnetic field. The torque is given by • where • N Number of turns in the loop • I: current • A: cross-sectional area defined by the perimeter of the current loop • B: Magnitude of magnetic field strength • α angle between the normal cross-sectional area of the current loop and the magnetic field
Galvanometer Instruments: Analog DC Current Measurement • One approach to utilizing the previous equation in current measurement is in the D’Arsonval arrangement. In this arrangement, the uniform radial magnetic field and torsional spring result in a steady angular deflection of the coil that corresponds to the coil current. • The coil and fixed permanent magnet are arranged in the normal direction to the current loop. The problem with this arrangement is that the deflection is nonlinear with the current. (torque proportional to sin α) The torque becomes zero when α = 0 irrespective of the amount of current in the coil.
Galvanometer Instruments: Analog DC Current Measurement • To produce a deflection proportional to the current, the coil is usually wrapped around cylindrical iron core with the two poles form circular arcs around the core. The presence of the iron core causes the magnetic field lines to direct themselves radially toward the center of the core. • As the field lines act in the radial direction, they always act normal to the inwards and outwards current paths irrespective over the range of motion. The angle α is always 90⁰ and • where • r radius of the cylindrical iron core • l: length of the cylindrical core
Galvanometer Instruments: Analog DC Current Measurement • In a typical ammeter the deflection of the pointer indicates the magnitude of the current flow. The range of current that can be measured is determined by selection of the combination of shunt resistor and the internal resistance of the meter movement. • The shunt resistor provides a bypass for current flow, reducing the current that flows through the movement. A break switch prevents current overload through the meter coil.
Galvanometer Instruments: Analog DC Current Measurement • A galvanometer is a highly sensitive D’Arsonval movement device calibrated about zero current; the indicator can deflect to the plus or minus direction. • The pointer can be used to adjust a circuit to a zero current state. This mode of operation is called the null mode. The highest sensitivity of commercial galvanometers is about 0.1 µA/division.
Galvanometer Instruments: Analog DC Voltage and Resistance Measurement • DC voltage can be measured through a D’Arsonval configuration placed in series with a resistor. The arrangement is basically a current measuring device, but can be calibrated in terms of voltage by using an appropriate known fixed resistor and through Ohm’s law relating it to the measured current. • The same device can be used to measure resistance if instead if an appropriate fixed known DC voltage is applied at the input. Pointer movement can, in this case be calibrated to reflect resistance.
Galvanometer Instruments: Analog DC Voltage and Resistance Measurement • Practical analog ohmmeters use circuits employing a D’Arsonval mechanism with shunt resistors for measuring a wide range of resistance while limiting the flow of current through the meter movement. • The lower limit on the measured resistance is determined by the upper limit of current flow through it. A practical limit to the maximum current flow through a resistance is imposed by the ability of the resistance element to dissipate the power generated by the flow of current (Joule heating). At a too high current, the sensor resistance may melt.
Galvanometer Instruments: Analog DC Voltage and Resistance Measurement • This basic circuit is employed in the construction of analog voltage dials and volt-ohmmeters (VOMs), which were commonly used for the measurement of current, voltage, and resistance.
Galvanometer Instruments: Analog AC Current and Voltage Measurement • Deflection meters can be employed for measuring AC current by the uses of diodes to form a rectifier that converts the AC current into a DC current. This current then can be measured with a calibrated D’Arsonval movement meter. • An electrodynamometer is basically a D’Arsonval movement modified for use with AC current by replacing the permanent magnet with an electromagnet in series with the current coil. These AC meters have upper limits on the frequency of the alternating current that they can effectively measure; most common instruments are calibrated for use with standard line frequency.
Galvanometer Instruments: Analog AC Current and Voltage Measurement • The waveform output of the rectifier must be considered if a steady meter reading is to be obtained. • An AC meter indicates a true rms value for a simple periodic signal only, but a true rms AC voltmeter performs the signal integration required to accurately determine the rms value in a signal-conditioning stage and indicates true signal rms regardless of waveform
Galvanometer Instruments: Errors in D’Arsonval Movement • Errors in the D’Arsonval movement include hysteresis and repeatability errors due to mechanical friction in the pointer-bearing movement, and linearity errors in the spring that provides the restoring force for equilibrium. • Also, in developing a torque, the D’Arsonval movement must extract energy from the current flowing through it. This draining of energy from the signal being measured changes the measured signal. Such an effect is called a loading error. • This is a consequence of all instruments that operate in deflection mode.
Dynamic Response of a Galvanometer A galvanometer consists of N turns of a conductor wound about a core of length l and radius r that is situated perpendicular to a magnetic field of uniform flux density B. A DC current passes through the conductor due to an applied potential, Ei(t). The output of the device is the rotation of the core and pointer, u. Develop a lumped parameter model relating pointer rotation and current.
Dynamic Response of a Galvanometer Applying Newton’s 2nd law on the iron core we have The rotation of the current carrying coil in the magnetic field generates an opposing electromotive force Em, given by: Applying Kirchhoff’s law to the resulting circuit gives,
Dynamic Response of a Galvanometer The equations are coupled. The current due to potential E produces torque T that moves the pointer. This motion develops an opposing potential Em.
Dynamic Response of a Galvanometer Using Laplace
Dynamic Response of a Galvanometer Using Laplace
Dynamic Response of a Galvanometer HW 2: Analyze the dynamic response of a galvanometer to step input and harmonic input. Discuss the effect of system parameters on the stability, settling time, overshoot and other pertinent dynamic characteristics. Use system analysis tools including: 1. Routh’s stability criterion 2. Root-locus plots 3. Bode diagrams 4. Polar plots 5. Log-Magnitude-vs.-Phase plots 6. Nyquist stability analysis Verify the results of your analysis with computer simulations (e.g. simulink), or video recorded experiments.
The Oscilloscope • The oscilloscope is a practical graphical display device which provides an analog representation of a measured signal. It is used to measure and to visually display voltage magnitude versus time for dynamic signals over a wide range of frequencies with a signal frequency extending into the megahertz or gigahertz range. • The oscilloscope provides a visual output of signal magnitude, frequency, distortion, and a delineation of the DC and AC components. The visual image provides a direct means to detect the superposition of noise and interference on a measured signal, something non visual metering devices cannot do.
The Oscilloscope • In addition to signal versus time, a typical unit can also display two or more signals X(t) and Y(t), perform addition and subtraction of signals, and display amplitude versus amplitude (XY) plots and other features. • Some digital oscilloscopes have significant internal storage so as to mimic a data-logging signal recorder. Others have internal fast Fourier transform (FFT) circuitry to provide for direct spectral analysis of a signal.
The Oscilloscope • In the cathode ray oscilloscope, the cathode tube operates as a time-based voltage transducer. A beam of electrons emitted by a heated cathode are guided vertically and horizontally by pairs of plates to control the location of the impact of the electron beam on the screen • The output of the oscilloscope is a signal trace created by the impact of the electrons on a phosphorescent coating on the screen.
The Oscilloscope • Input voltages result in vertical deflections of the beam, and produce a trace of the voltage variations versus time (horizontal or x axis) on the screen. • The vertical plates are excited by the electrical field to be measured. The horizontal sweep frequency can be varied over a wide range, and the operation of the oscilloscope is such that high-frequency waveforms can be resolved.
Resistance Measurement Circuits Rm G kRt 0≤k ≤1 Vs
The Simple Current-Sensitive Circuit Rm • Many sensing element produce their output in the form of varying resistance. The element may be a sliding contact, a thermistor, a piezoresistive element or other, where the resistance varies between zero and a maximum value, Rt. • The simple current-sensitive circuit may be used to determine the resistance of a varying resistance element through measurement of current magnitude. • Rm represents the resistance of the remaining parts of the circuit, including the meter resistance and the internal resistance of the voltage source. The current is related to kRt through Ohm’s law. G io kRt 0≤k ≤1 Vs
The Simple Current-Sensitive Circuit • The maximum current flow, imax = Vs/Rm takes place when the resistance of the sensing element is zero. The current ratio,io/imax may be written as: • The output (current ratio) is nonlinear with the input (resistance change). The sensitivity is small for small values of Rt/Rm . Greater sensitivity may be obtained for larger values of Rt/Rm but it drops rapidly as the resistance approaches its upper limit (k approaches 1). • Careful control of the driving voltage is also necessary if calibration relationship between current and resistance is to be maintained. Rm G kRt 0≤k ≤1 Vs Rt / Rm = 0.5 1 io/imax 2 4 10 k
Voltage Dividing Circuits Vs R2 R1 Vo
The Resistive Voltage Divider • A resistive voltage divider is obtained from a set of resistors connected in series to divide a voltage source. • The voltage across each resistor may be calculated by multiplying the value of the current flowing through the circuit by the resistance of the resistor considered. Vs R2 R1 Vo
The Ballast Circuit • The ballast circuit is simply a voltage divider with one of the resistors representing the resistive sensing element. The voltage across that resistor changes as its resistance varies with the input to be measured. A voltage sensitive device is placed across that resistance which can be calibrated to indicated the input of interest. • Assuming a high-impedance meter, the relationship between the output ratio (Vo/Vs) to the input ratio (R/Rt) can be found from Ohm’s law Vs Rt Rb Voltage Indicator Vo
The Ballast Circuit • The relationship between the output ratio (Vo/Vs) and the input ratio (R/Rt) is nonlinear and a percentage variation in the supply voltage results in a greater variation in the output than does a similar percentage change in k. Voltage regulation must be strictly controlled for successful operation. Vs Rt Rb Voltage Indicator Vo Rt/Rb = 4 2 Vo/Vs 1 0.5 k
The Sliding Contact Resistive Voltage Divider • A sliding contact voltage divider is a resistive voltage divider whereby the resistance ratio is adjusted with a movable contact. • A voltage Vs is applied across the two ends A and B of a resistance element , RAB, and the output voltage Vo is measured between the point of contact C of the sliding element and the end A of the resistance element. • The output voltage from the divider is controlled by the position of the slider, taking the range 0 ≤ Vo ≤ Vs. as the resistance ratio is adjusted from zero to 1 with a movable contact. Vs L C B A x Vo
The Null Type Resistive Potentiometer • The null type potentiometer uses the sliding contact voltage divider to measure DC voltage. It balances an unknown input voltage against a known internal voltage until both sides are equal. The voltage to be measured, Vm, is applied at the divider’s output, and a current-sensing device, such as a galvanometer, is used to detect current flow on the output branch. • The output voltage of the divider VAC is adjusted by moving the sliding contact A; any current flow through the galvanometer, G, would be a result of an imbalance between the measured voltage, Vm, and VAC. The value of Vm is determined from knowledge of VAC. Vs L C B A x G Vm
The Null Type Resistive Potentiometer • A null balance, corresponding to zero current flow through G, occurs only when Vm = VAC. • With a known and constant supply voltage Vs , VAC is related to the position of the slider, which can be calibrated to indicate Vm. • Potentiometers have been supplanted by digital voltmeters, which are deflection mode devices but have very high input impedances so as to keep loading errors small, even at low-level voltages. Vs L C B A x G Vm
The Deflection Type Resistive Potentiometer • The resistive potentiometer is commonly used as a displacement-measuring device. • Assuming high galvanometer impendence, a linear relationship exists between the output voltage Vo and the distance x, for uniform resistivity for RAB Resistance change (ΔR) Displacement (x) Voltage change (Δv) Vs L C B A x G Vo
The Resistive Potentiometer: Loading Error Loading error occurs when the resistance RL is finite. It can be estimated by calculating the voltage across RL for finite values of RL/RAB . Noting that RAC = kRAB and RBC = (1-k)RAB The total resistance seen by the source Vs is: The current through RBCis thus The voltage across RL is Vs L C B A x G RL
The Resistive Potentiometer: Loading Error Comparing the values of Vo for finite and infinite values of RL/RAB , the error in Vo for a finite RL/RABis: The percentage error is thus: Vs L C B A RL/RAB = 1 x 2 G 5 10 RL
The Resistive Potentiometer: Loading Error The error ratio may alternatively be defined as the ratio of the error to the full scale output, Vs, in this case, Vs L RL/RAB = 1 C B A x 2 G 5 10 RL
Direct Voltage Dividing Circuits for Measurement of Variable Resistance • A voltage divider may be used to measure the small changes in resistance from variable resistance detectors such as RTDs, strain gauges and photoresistive elements. • These detectors show only a small change in their resistance in response to the detected input. For example, the resistance of metal strain gauges may vary only be 1 x 10-4 in use. The smallness of resistance change has important consequences on the performance of the voltage dividing circuit. Vs R1 R0 Vo
Direct Voltage Dividing Circuits for Measurement of Variable Resistance : Sensitivity • Suppose that a voltage divider is formed from a detector of an initial resistance R0 and a second resistance with R = R0. The initial output is: • Assuming no change in the supply voltage during measurement, dVs = 0, Vo → Vo + Δ Vo Vs R1 R0 → R0 + ΔR
Direct Voltage Dividing Circuits for Measurement of Variable Resistance : Sensitivity • The sensitivity of the potentiometer increases with Vs , so = r/(1+r2) and with 1/Ro. Practical considerations place an upper limit on Vs . Ro can not be made too small as δRo is related to the value of Ro . The ratio r = R1 / Ro, can be chosen to maximize so = r/(1+r2) Vo → Vo + Δ Vo Vs R1 R0 → R0 + ΔR
Direct Voltage Dividing Circuits for Measurement of Variable Resistance : Sensitivity • The sensitivity coefficient so is maximum when r = R1 / Ro = 1. The maximum value of so occurs when r = R1 / Ro = 1, and its value is 1/4. Thus R0 is usually chosen to be equal to R1, and the sensitivity is Vo → Vo + Δ Vo Vs R1 R0 → R0 + ΔR
Example: Strain Gauge in Ballast Circuit Configuration • A strain gauge with a nominal resistance R0= 120 Ω is used in a ballast circuit designed to produce maximum sensitivity. The maximum expected change in the resistance of the gauge when maximum load is applied is ΔR = 240 x 10-6Ω . • What is the percentage change in the measured voltage when maximum load is applied. • What is the percentage change in the measured voltage due to a 0.1 % drift in the supply voltage Vs Vo → Vo + Δ Vo Vs R0 R0 → R0 + ΔR
Example: Strain Gauge in Ballast Circuit Configuration • Solution: percentage change in the measured voltage when maximum load is applied. For a ballast circuit with maximum sensitivity, we have Vo → Vo + Δ Vo R0= 120 Ω ΔR = 240 x 10-6Ω Maximum sensitivity configuration Δ Vo / Vo ? Vs R0 R0 → R0 + ΔR • A meter with a resolution of better than one part in a millionth is needed in order to see any change in Vo . This excludes most common voltmeters, which may resolve to only 0.01%, (10-4)
Example: Strain Gauge in Ballast Circuit Configuration • Solution: percentage change in the measured voltage due to a 0.1 % drift in the supply voltage Vs • The percentage change in the measured voltage due to a 0.1 % the drift in Vs is 0.1 % which is a 1000 times greater than the strain induced change in voltage, 0.0001% Vo → Vo + Δ Vo R0= 120 Ω ΔR = 240 x 10-6Ω Maximum sensitivity configuration Δ Vo / Vo ? Vs R0 R0 → R0 + ΔR
Voltage Dividing Circuits for Measurements of Variable Resistance Detectors • A solution to the voltage divider problems may be obtained by a circuit having an output voltage proportional to ΔVo itself, without the large offset voltage, Vo . This can be done by introducing another voltage divider with fixed resistors Ro, which has a midpoint voltage Vo . We now measure the difference between the midpoint voltages of the two dividers as the output voltage of the circuit • This eliminates the problem of caused by the offset voltage Vo . • The arrangement of two voltage dividers is in fact identical to the Wheatstone bridge circuit to be discussed next. R0 R0 Vs B A Vout R0 R0