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Signal Conditioning Circuits :Power Supplies คณะวิศวกรรมศาสตร์ มหาวิทยลัยธรรมศาสตร์ Measurement and Instrumentation Electronic measurement system Power supply Transducer Conditioning circuits Amplifier Data processor For engineering analysis - Graphs or Tables Controller Process control Recorder Command generator Power Supplies Some transducers need the power supply in order to convert the sensed information from the sensor into the electrical signal. Power supply Transducer Signal Conditioning Power supplies for instruments 1. Battery supplies 2. Line voltage supplies Battery supplies widely used and inexpensive voltage declines after used voltage regulating circuit required Voltage regulating circuits Ebatt. Eo Simple voltage regulator Output voltage = Zener voltage Zener diode is a type of diode that permits current not only in the forward direction like a normal diode, but also in the reverse direction if the voltage is larger than the breakdown voltage known as "Zener voltage” (Breakdown voltage) P N Line voltage supplies take the (high) voltage from a wall outlet and lower its into the desired (low) voltage. The (low) alternating voltage is converted to direct voltage and is then regulated. 220Vac Power line 220 Vac at 50 Hz Transformer Low voltage Vac Rectifier Unregulated Vdc Regulator Regulated Vdc Transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors – The transformer’s coils. Vs Vp = Ns Step-up transformer Np Step-down transformer Ns Np Ns Np > 1 < 1 Rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which is in only one direction Vdc = Vav = 2Vp/ Vrms = Vp/2 Voltage regulator is an electrical regulator designed to automatically maintain a constant voltage level Three pin 12 V DC voltage regulator IC. Signal Conditioning Circuits :Bridge Circuits คณะวิศวกรรมศาสตร์ มหาวิทยลัยธรรมศาสตร์ Measurement and Instrumentation Bridge circuits have been devised for measuring capacitance, inductance, and most often for measuring resistance. A purely resistance bridge, called a “Wheatstone bridge”, provides a means for accurately measuring resistance, and for detecting small changes in resistance. Galvanometer Bridge’s analysis The basic arrangement for a bridge circuit is shown in the figure below. A dc voltage is applied as an input across nodes A to D, and the bridge forms a parallel circuit arrangement between these two nodes. The currents flowing through the resistors R1 to R4 are I1 to I4 , respectively. Under the condition that the current flow through the galvanometer, Ig = 0, the bridge is in a balanced condition. For a balanced bridge: R2 R4 = R1 R3 If the resistor R1 is a transducer, a change in resistance, associated with a change in some physical variable, causes an unbalance of the bridge. Bridge’s analysis 1. Null Method R1 is the resistance of the transducer R2 is the resistance of the adjustable resistor Ig = 0 R1 Principle: If the resistance R1 varies with changes in the measured variable, one of the other arms of the bridge can be adjusted to null the circuit and determine resistance. 1. Null Method The resistance R2 must be calibrated such that the adjustments directly indicate the value of R1 M Transducer R1 (unknown) Wheatstone bridge Null Method R2 (known) Advantages: 1. no need to know the input voltage. 2. current detector required (Galvanometer) to detect Ig Disadvantages: 1. sensitivity depending on the galvanometer 2. uncertainty in the measured resistance depending on the input voltage Uncertainty, uR 1/Ei Bridge’s analysis 2. Deflection Method R1 is the resistance of a transducer R1 Principle: a voltage measuring device is used to measure the voltage unbalance in the bridge (the voltage drop from B to C) as a n indication of the change in resistance. 1 1 3 2 3 4 2. Deflection Method M Transducer R Eo Wheatstone bridge Deflection Method For identical resistors, R1 = R2 = R3 = R4 = R R1 EEo Under balanced conditions (Ig = 0), Eo = 0 In an unbalanced condition, / 4 2 / Advantage: can be used to measure time-varying signals, but the voltage measuring device must have the frequency response not less than that of the sensor. Disadvantage: 1. high capability of the galvanometer required. 2. known and regulated input voltage required. In case of the low impedance galvanometer, Rg / 4 / 4 1 / Example 1 Null method A certain temperature sensor experiences a change in electrical resistance with temperature according to the equation 1 where R R0 T = sensor resistance [] = sensor resistance at the ref. temperature T0 [] = measuring temperature [°C] = constant = 0.00395 °C-1 Given: 1) R3 = R4 = 500 2) R0 = 100 at T0 = 0°C Determine the value of R2 that would balance the bridge at 0 °C Solution R1 Under balanced condition, R2 = R1 (R4 /R3 ) = R1 R3 = R4 = 200 160 140 R2 120 100 80 60 0 20 40 60 Temperature [C] 80 100 Example 2 Deflection method Consider a deflection bridge, which initially has all arms of the bridge equal to 100 ohms, with the temperature sensor described in Example 1. The input voltage to the bridge is 10V. If the temperature of R1 is changed such that the bridge output is 0.569 V, what is the temperature of the sensor? How much current flows through the sensor and how much power must it dissipate? Solution At deflection state, Eo = 0.569 V A change in the resistance of the sensor can be obtained from / 4 2 / We obtain R ohms Therefore, the temperature of the sensor is 1 0 100 0 25.67 1 0.00395 100 1 0.00395 65 By Kirchoff’s law, the current flowing through R1 is given by 1 1 1 2 44.3 The power dissipated from the sensor is 1 2 1 1 0.25 0 0 Solution R1 Under balanced condition, R EEo R 0 R / 0 / 4 2 1 0.00395 0 1.0 Ei = 10 V E0 [V] 0.8 0.6 0.4 0.2 0.0 0 20 40 60 Temperature [C] 80 100 Types of Wheatstone’s bridges Quarter bridge Types of Wheatstone’s bridges Half bridge Benefits - Compensation of interference effects, especially temperature effects - Increase of the static sensitivity Types of Wheatstone’s bridges Full bridge Benefits - Compensation of interference effects, especially temperature effects - Increase of the static sensitivity 3-wire circuit analysis Initially, If R1 RK R4 where R1 R2 R3 R4 R R2 RK R3 R1 0 then vo 1 R1 vs 4 R RK vo 0 Signal Conditioning Circuits :Amplifiers คณะวิศวกรรมศาสตร์ มหาวิทยลัยธรรมศาสตร์ Measurement and Instrumentation Amplifiers Is a device that scales the magnitude of an analog input signal according to the relation Vo = G x Vi Input voltage, Vi where G = Gain Output voltage, Vo Supply voltage, Vs 1 1 0.8 0.8 0.6 vi 0.6 vo 0.4 0.2 0.4 0.2 0 0 2 4 6 t 8 10 0 0 2 4 6 t 8 10 Types of amplifier 1. Single-ended amplifiers are amplifiers which amplify a single input signal. Both input and output signal voltages are referenced a common connection in the circuit called ground. (used for potentiometer circuits) 2. Differential amplifiers are amplifiers which amplify two input signals. All voltages are referenced to the circuit's ground point. (used for bridge circuits) Vs Vs G Vi G Vo Vo = G x Vi Single-ended amplifiers Vi,1 Vo Vi,2 Vo = G (Vi,1- Vi,2) Differential amplifiers Operational Amplifiers (op-amp) An “op-amp” is a high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. Characteristics of op-amps 1. High internal gain G = 105 to 106 2. High input impedance Zi > 107 3. Low output impedance Zo < 100 4. two input ports, a noninverting and an inverting input, and one output port Non-inverting terminal (+5V) Inverting terminal (-5V) Vo = G (Vnon-inv - Vinv) Summing amp. Non-inverting amp. Inverting amp. Differentiator Integrator Voltage Follower Inverting Amplifier: Circuit analysis Rf Rf R1 Vi if i1 A ia Vo Va Ra Sum of currents at Node A 1 1 1 Output voltage of the inverting amplifier ≅ 1 Non-inverting Amplifier: ≅1 Summing Amplifier: Voltage follower: ≅ 1 ,1 ,2 ,3 1 2 3 1 *** Differentiator: Integrator: 1 1 1 0 Signal Conditioning Circuits :Filters คณะวิศวกรรมศาสตร์ มหาวิทยลัยธรรมศาสตร์ Measurement and Instrumentation Filters In many instrumentation applications, the (dynamic) signal from the transducer is combined with noise or some other parasitic signal. These undesired signals can be eliminated with a filter that is designed to attenuate the noise signals but transmit the transducer signal without distortion. Two filters that utilize passive components and are commonly employed in signal conditioning include (1) High-pass RC filter and (2) Low-pass RC filter C R R C RC filter circuits Filters High-pass filter Unfiltered signal with low frequency variation and high frequency noise Filtered signal High-pass filter employed to remove low frequency variation Low-pass filter Low-pass filter employed to remove high frequency noise High-pass RC filters High-pass filter permits only frequencies above the cutoff frequency to pass. Consider a summation of voltage drops around the loop 0 If | | and High pass 0 The output voltage Vo is Passband 2 1 | | where 2 ~0 1 if Stopband Low-pass filters Low-pass filter permits only frequencies below the cutoff frequency to pass while blocking the passage of frequency information above the cut off frequency. The output voltage is 1 2 1 | | Passband where 1 ~0 ถ ้า Stopband Cut-off frequency is defined as the frequency at which the ratio of the amplitudes of the output to the input has a magnitude of 0.02 (2% error). For examples, (1) Hi-pass filter C = 5/RC fC = 5/(2RC) C = 0.203/RC fC = 0.203/(2RC) |Vo|/|Vi| = CRC/[1+(CRC)2]1/2 = 0.02 (2) Lo-pass filter |Vo|/|Vi| = 1/[1+(CRC)2]1/2 = 0.02 Active filters Operational amplifiers are employed to construct active filters where select frequencies can be attenuated and the signal amplified during the filtering process. R2 C2 R1 Vi R2 C1 741 + Vo Low-pass active filter 1 2 2 2 Vi R1 741 + Vo High-pass active filter 1 2 1 1 Signal Conditioning Circuits :Modulators and Demodulators คณะวิศวกรรมศาสตร์ มหาวิทยลัยธรรมศาสตร์ Measurement and Instrumentation Amplitude Modulators Amplitude modulation is a signal conditioning process in which the signal from a transducer is multiplied by a carrier signal of constant frequency and amplitude. Transducer signal (sinusoidal, transient, or random) sin x Carrier signal (sinusoidal, transient, or random) sin Modulated signal sin 2 sin cos cos In general, noise signals occur at 50-Hz 4000 50 3950 4050 Amplitude Modulators Advantages (1) Stability (2) Low power (3) Noise suppression Demodulation is the process that the transducer signal is separated from the carrier signal. Rectifier Filter Assignment #3 1. Shown that the output voltage of the summing amplifier be expressed by the equation ,1 ,2 ,3 1 2 3 2. Consider the Wheatstone bridge. Suppose R3 = R4 = 200 R2 = variable calibrated resistor, and R1 = transducer resistance = 40x + 100 a) When x = 0, what is the value of R2 required to balance the bridge? b) If the bridge is operated in a balanced condition in order to measure x, determine the relationship between R2 and x. Fundamental of Sampling, Data Acquisition and Digital Devices คณะวิศวกรรมศาสตร์ มหาวิทยลัยธรรมศาสตร์ Measurement and Instrumentation Sampling concepts Conversion of analog signals to digital code is extremely important in any instrument system that involves digital processing of the analog output signals from the signal conditioners. Discrete Signal Continuous Signal “discrete time series” Discrete time series Suppose the transducer signal is measured repeatedly at successive sample time increments t 1, 2, 3, … , total sample period sample rate Sample rate fs = 1/t [Hz] The sample rate has a significant effect on perception and reconstruction of the continuous analog signal in the time domain fm = 10 Hz (sine wave analog signal) fs = 100 Hz fs > 2 fm t < 1/(2 fm ) *** s = sampling m = measuring fs = 27 Hz fs = 12 Hz Alias Frequencies When the sample rate is less than 2fm , the higher frequency content of the analog signal will take on the false identity of a lower frequency in the resulting discrete series. A false frequency is called an “alias frequency”. sample rate 12 Hz Original signal 10 Hz Interpreted signal 2 Hz Folding Diagram is the diagram that is used to find the alias frequency. Example 1.67 f = 10 Hz [f/fN]y-axis= 10/6 = 1.67 fN = 6 Hz [f/fN]x-axis = 0.33 Hz falias = 0.33 x fN = 2 Hz 0.33 Nyquist frequency and Anti-Aliasing Nyquist frequency is the highest frequency that can be coded at a given sampling rate in order to be able to fully reconstruct the signal, fN = 0.5 fs Anti-aliasing is a process that remove signal content at and above Nyquist frequency by use of a low-pass filter prior to sampling and use an appropriate sample rate for the signal Signal = Signal [f < fN ] + Signal [f > fN ] Anti-aliasing filter Example Consider a complex periodic signal in the form 10 sin 50 0.5 sin 150 1.2 sin 250 15 10 ym 5 10 sin () y(t) 0.5 sin() 1.2 sin() 0 0 20 40 60 80 ‐5 ‐10 ‐15 t 100 120 140 Example (cont.) If the signal is sampled at 100 Hz fN = 0.5 fs = 0.5 x 100 Hz = 50 Hz Observe all frequency content in the sampled signal 10 sin 50 f1 = 25 Hz 0.5 sin 150 f2 = 75 Hz 1.2 sin 250 f3 = 125 Hz fN < fm Alias frequency Example (Cont.) Sampled signal 10 sin 50 0.5 sin 50 1.2 sin 50 Alias frequency = 25 Hz 15 10 ys 5 ym y(t) 10 sin () 0 0 20 40 60 80 ‐5 ‐10 ‐15 t 100 120 140 Example (cont.) Use a low-pass filter with the cut-off frequency > 50 Hz 10 sin 50 15 ym yA = 10sin() 10 y(t) 5 0 0 20 40 60 80 ‐5 ‐10 ‐15 t 100 120 140 Amplitude Ambiguity The sampling signal can be completely reconstructed from a discrete time series, if (1) Total sample period remains an integer multiple of the fundamental period, T1 mT1 = N t (2) Sample rate meets the sampling criterion. fs > 2 fm Note: N = 2M: M = # of sample points (8-bit) Example 10cos 2 100 f = (Nt)-1 = fs/N = 39 Hz Amplitude = 10 Fundamental period T1 =1/ 100 s (a) m = N t / T 1 = 2.56 amplitude leakage (b) m = N t / T 1 = 10.24 amplitude leakage (c) m = N t / T 1 No leakage Amplitude spectra = 8 Selecting sample rate and data number For an exact discrete representation in both frequency and amplitude of analog signal, both the number of data points and the sample rate should be chosen based on the following criteria: (1) fs > 5 fm (2) long total sample periods (large N) and (3) use of anti-alias filter. Data-Acquisition System (DAS) is the portion of a measurement system that quantifies and stores data. A typical signal flow scheme is shown in the following diagram. Data-Acquisition System components A/D converter Signal flow scheme for an automated data-acquisition system Signal Conditioning: Filters and Amplification Filters 1. Analog filters are used to control the frequency content of the signal being sampled. Example: Anti-alias filter 2. Digital filters, which are software-based algorithms, are effective for signal analysis after sampling Example: moving-averaging scheme (for removing noise) ∗ ⋯ 1 1 ⋯ / 2 1 Signal Conditioning: Filters and Amplification Amplifiers All DASs are input range limited; that is, there is a minimum value and a maximum value of signal. Some transducer signals will need amplification or attenuation prior to conversion. Most DASs contain on-board instrumentation amplifiers. Voltage divider for signal attenuation 0-50 V signal 0-10 V A/D converter R1 = 40 k R2 = 10 k Signal Conditioning: Filters and Amplification Shunt circuits An A/D converter requires a voltage signal at its input. It is straightforward to convert current signals into voltage signals using a shunt resistor. In general, the standard current signal has a range of 4 – 20 mA Using a shunt resistor = 250 the current signal would be converted into the voltage signal 1–5V Signal Conditioning: Filters and Amplification Multiplexer When multiple input signal lines are connected by a common throughout line to a single A/D converter, a multiplexer is used to switch between connections, one at a time. A/D Converters convert the analog signals into the digital signals with conversion rates typically up to the 1 kHz – 10 MHz range . The input resolution, Q which depends on the number of bits of the converter, is given by 2 Example A12 bit A/D converter with input signal range of 0-10V. The resolution where EFSR = Full scale voltage range M = resolution in bits Q = 10/212 = 2.44 mV The amplifier permits signal conditioning with gains from G = 0.5 to 1000 The minimum detectable voltage when set at maximum gain is 3-bits resolution Q = 2.44 mV / 1000 = 2.44 V Analog signal input connections Single-ended connection Suitable only when all of the analog signals can be made relative to the common ground point. Differential-ended connection Allow the voltage difference between two distinct input signals to be measured Example + V signal O - Vi Strain gage (Rg) , S = 2.5V/ A signal from the strain gage with the sensitivity = 2.5V/is connected to DAS which has the 12-bit A/D converter, an input range of ± 5V, and sample rate of 1000 Hz. For an expected measurement range of 1-500 , specify appropriate G for amplifier, filter type and cut-off frequency. Amplifier Resolution = 10/212 = 2.44 mV Signal Range = (1 - 500 ) x 2.5 V/ = 2.5 V – 1.25 mV G = 1000: Amplified Signal = (2.5V – 1.25 mV) x 1000 = 2.5 mV – 1.25 V G = 3000: Amplified Signal = (2.5V – 1.25 mV) x 3000 = 7.5 mV – 3.75 V Filter f Sample rate, s = 1000 Hz f Nyquist frequency , N = 1000/2 = 500 Hz *** Low-pass filter with a cut-off frequency = 500 Hz required *** Differential-ended connections required Final Examination on OCT 8, 2011 (1300-1600) Closed books and closed notes Non-programmable calculators are permitted Electronic dictionaries are not permitted 7 questions (10 marks each) Data Logger คืออุปกรณ์อิเล็คทรอนิคส์ซงึ่ ทําหน้ าที่บนั ทึกและจัดเก็บข้ อมูลที่ตรวจวัด จากเครื่ องมือวัดหรื อเซนเซอร์ ตา่ งๆ ปั จจุบนั Data logger ใช้ พื ้นฐาน ของระบบประมวลผลแบบดิ จิ ต อล ส่ ว นประกอบที่ สํ า คั ญ คื อ ไมโครโปรเซสเซอร์ หน่วยความจํา และเซนเซอร์ สามารถแบ่งออกได้ เป็ น 2 ลักษณะคือ - General purpose types - Specific devices ข้ อ ดี 1. ทํางานด้ วยตัวเอง (Stand-alone) 2. เคลื่อนย้ ายง่าย (Portable) 3. บันทึกข้ อมูล 24 ชัว่ โมง 4. สามารถใช้ กบั DC power http://www.dataq.com/images/products/data-logger/gl200_500w.jpg ตัวอย่าง Data logger ตัวอย่าง ข ้อมูลจําเพาะ Data logger ตัวอย่าง ข ้อมูลจําเพาะ Data logger (ต่อ) Grounds, Shielding, and connecting wires การเชื่อมต่อสายสัญญาณในอุปกรณ์อิเล็กทรอนิคส์อาจเป็ นสาเหตุของการเกิด สัญญาณรบกวน (noise) ในระบบ สัญญาณรบกวนจะมีผลมากในสัญญาณที่มีกําลังตํ่า (< 100 mv) วิธป ี ้ องกันสัญญาณรบกวน ้ สุ ่ ด 1. ใช ้สายสัญญาณให ้สันที 2. ไม่ให ้สายสัญญาณอยูใ่ กล ้แหล่งสัญญาณรบกวน 3. ใช ้ชีล (shield) ป้ องกันและต่อสายลงดิน (ground) 4. บิดสายเป็ นเกลียว Ground and Ground loop Ground คือจุดอ้ างอิงในวงจรไฟฟ้าใช้ ในการเปรี ยบเทียบแรงดันไฟฟ้า โดยทัว่ ไป Ground จะเป็ นเส้ นทางเดินของกระแสลงสูพ ่ ื ้นดิน ( earth ground) ซึง่ มีคา่ แรงดันไฟฟ้า เท่ากับศูนย์ Ground potential อาจมีคา่ ต่างกันขึ ้นกับจุดเชื่อมต่อ (เช่น อุปกรณ์ อาคาร และพื ้นดิน) สายดินที่ความยาวมากๆ อาจเป็ นทําหน้ าที่เหมือนกับ เสาอากาศ (Antennae) Ground Symbols Signal ground Chassis ground Earth ground Ground loop Ground loop เป็ นสาเหตุมาจากการเชื่อมต่อ ground ของหลายวงจรเข้ ารวมกัน โดย Ground potential ของวงจรที่ตอ่ ร่วมกันมีคา่ ไม่เท่ากัน ผลต่างของศักย์ไฟฟ้าที่เกิดใน Ground loop ส่งผลให้ เกิดการไหลของกระแสใน สายสัญญาณ นําไปสูส่ ญ ั ญาณรบกวนในระบบ Signal current Ground current วิธีป้องกัน ground loop มีการต่อสายดินเพียง 1 จุด (single-point ground) ติดตัง้ Isolation transformer ( 1:1 power transformer AC signal ผ่านได้ เท่านัน) ้ ใช้ Shield ป้องกันสัญญาณรบกวนหากสัญญาณส่งมีกําลังตํ่า ่ ถก การต่อ Shield ป้ องกันทีไม่ ู ต ้อง ่ กต ้อง การต่อ Shield ป้ องกันทีถู ่ ้านสายส่งสัญญาณด ้านเดียว) (ต่อสาย ground ของShield ป้ องกันทีปลายด