Lecture Notes: EEEC6430312 Measurements And Instrumentation - Instrumentation
Download as PPTX, PDF0 likes200 views
This document discusses thermistors and the Wheatstone bridge circuit. It begins by explaining that thermistors are temperature dependent resistors used for temperature sensing. It then discusses the Steinhart-Hart equation used to relate resistance and temperature for NTC thermistors. Finally, it explains how the Wheatstone bridge circuit can be used to measure unknown resistances by balancing the bridge.
Lecture Notes: EEEC6430312 Measurements And Instrumentation - Instrumentation
- 1. EEEC6430312 MEASUREMENTS AND INSTRUMENTATION FACULTY OF ENGINEERING AND COMPUTER TECHNOLOGY BENG (HONS) IN ELECTRICALAND ELECTRONIC ENGINEERING Ravandran Muttiah BEng (Hons) MSc MIET Instrumentation
- 2. Thermistors are non-linear temperature dependent resistors with a high resistance temperature coefficient. They are advanced ceramics where the repeatable electrical characteristics of the molecular structure allow them to be used as solid-state, resistive temperature sensors. This molecular structure is obtained by mixing metal oxides together in varying proportions to create a material with the proper resistivity. Two types of Thermistors are available: Negative Temperature Coefficient (NTC), resistance decreases with increasing temperature and Positive Temperature Coefficient (PTC), resistance increases with increasing temperature. In practice only NTC Thermistors are used for temperature measurement. PTC Thermistors are primarily used for relative temperature detection. In this class we will use an NTC thermistor. The temperature versus resistance data of our thermistor is shown on the table and figure below. Thermoelectric Transducer 1
- 3. 2 Resistance Multiplier 10 K Temperature (℃) Rt/R25 Nominal 0 3.363000 5 2.599000 10 2.024000 15 1.589000 20 1.256000 25 1.000000 30 0.801300 35 0.646100 40 0.524100 45 0.427600 50 0.350700 55 0.289400 60 0.240000 65 0.200100 70 0.167700 75 0.141200 80 0.119400 85 0.101400 90 0.086520 95 0.074090 100 0.063700 Figure 1 NTC Thermistor Temperature (Celcius) Resistance (Ω)
- 4. For convenience we would like derive a mathematical expression which describes the behavior of the device. The Steinhart and Hart equation is an empirical expression that has been determined to be the best mathematical expression for resistance temperature relationship of NTC thermistors. The most common form of this equation is: 1 𝑇 = 𝑎 + 𝑏 ln 𝑅 + 𝑐 ln 𝑅 3 (1) Where T is in Kelvin and R in Ω. The coefficients a, b and c are constants which in principle are determined by measuring the thermistor resistance at three different temperatures T1, T2, and T3 and then solving the resulting three equations for a, b, and c. 1 𝑇1 = 𝑎 + 𝑏 ln 𝑅1 + 𝑐 ln 𝑅1 3 1 𝑇2 = 𝑎 + 𝑏 ln 𝑅2 + 𝑐 ln 𝑅2 3 1 𝑇3 = 𝑎 + 𝑏 ln 𝑅3 + 𝑐 ln 𝑅3 3 3
- 5. The parameters a, b and c for the thermistors provided with the lab kit in the temperature range between 0 − 50 ℃ are: 𝑎 = 1.1869 × 10−3 𝑏 = 2.2790 × 10−4 𝑐 = 8.7000 × 10−8 The Steinhart and Hart equation may be used in two ways. (i) If resistance is known, the temperature may be determined from equation 1. (ii) If temperature is known the resistance is determined from equation 2. 𝑅 = exp 𝛽 − 𝛼 2 1 3 − 𝛽 + 𝛼 2 1 3 (2) where, 𝛼 = 𝑎− 1 𝑇 𝑐 and 𝛽 = 𝑏 3𝑐 + 𝛼2 4 4
- 6. The non-linear resistance versus temperature behavior of the thermistor is the main disadvantage of these devices. However, with the availability of low cost microcontroller systems the non-linear behavior can be handled in software by simply evaluating the Steinhart and Hart equation at the desired point. The sensitivity of the thermistor, d𝑅 d𝑇 , varies with temperature. For our thermistor the sensitivity as a function of temperature is shown on the following figure. Note that the thermistor sensitivity decreases with increasing temperature. This is the primary reason for the small temperature measuring range of thermistors. Notice however that in temperature range of interest to biological and most environmental applications the sensitivity is greater than 100 Ω ℃ which results in the design of sensitive and robust systems. 5
- 7. 6 Figure 2 Temperature (Celcius) NTC Thermistor Sensitivity d𝑅 d𝑇 ( Ω ℃ )
- 8. Electronic Transducer 7 Figure 3 Earth Ground AC Return 240 V AC Plug Heater Elements Toaster Adjustment, Moves Magnet w.r.t. Heater Element Magnet On Spring Solenoid
- 9. 8 The Function Of Electronic Transducer For a certain design when a toaster is engaged a magnetic material is placed in contact with an electromagnet. The magnetic contact to the solenoid is made of a material whose magnetism is a function of temperature. Indeed the temperature at which the material loses its magnetisation (labeled the Curie temperature Tc) is in the order to 100 ℃. When the temperature is less than Tc the magnet maintains its magnetism, however when T > Tc, then the magnetism is lost and the switch opens. Pushing down on the toaster engages the switch. The control for browning the toast, simply moves the magnetic switch closer or further away from the heating elements. Notice that the AC plug has two grounds. The Earth ground is for user protection and typically is connected to the chassis of the toaster. The AC return completes the circuit and allows current to flow. The Earth and AC return should never be connected together. In two prong AC plugs the Earth ground is missing.
- 10. 9 𝑉 s 𝐼Total 𝐼2 𝐼1 𝑅4 𝑅3 𝑅2 𝑅1 Figure 4: Wheatstone bridge. Wheatstone Bridge The Wheatstone bridge was originally developed by Charles Wheatstone to measure unknown resistance values and as a means of calibrating measuring instruments, voltmeters, ammeters, etc, by the use of a long resistive slide wire. 𝑉C − 𝑉D 𝑉out A B D C + −
- 11. 10 Although today digital multimeters provide the simplest way to measure a resistance. The Wheatstone bridge can still be used to measure very low values of resistances down in the milli-Ohms range. The Wheatstone bridge (or resistance bridge) circuit can be used in a number of applications and today, with modern operational amplifiers we can use the Wheatstone bridge circuit to interface various transducers and sensors to these amplifier circuits. The Wheatstone bridge circuit is nothing more than two simple series-parallel arrangements of resistances connected between a voltage supply terminal and ground producing zero voltage difference between the two parallel branches when balanced. A Wheatstone bridge circuit has two input terminals and two output terminals consisting of four resistors configured in a diamond-like arrangement as shown. This is typical of how the Wheatstone bridge is drawn.
- 12. 11 When balanced, the Wheatstone bridge can be analysed simply as two series strings in parallel. In our tutorial about resistors in series, we can see that each resistor within the series chain produces an 𝐼𝑅 drop, or voltage drop across itself as a consequence of the current flowing through it as defined by Ohms Law. Consider the series circuit in figure 5. Figure 5 12 V 𝐼 A B 𝑉𝑅1 𝑉𝑅2 𝑅1 𝑅2 10 Ω 20 Ω C
- 13. 12 As the two resistors are in series, the same current, 𝐼 flows through both of them. Therefore the current flowing through these two resistors in series is given as, 𝑉 𝑅T. 𝐼 = 𝑉 𝑅 = 12 V 10 Ω + 20 Ω = 0.4 A The voltage at point C, which is also the voltage drop across the lower resistor, 𝑅2 is calculated as, 𝑉𝑅2 = 𝐼 × 𝑅2 = 0.4 A × 20 Ω = 8 V Then we can see that the source voltage 𝑉S is divided among the two series resistors in direct proportion to their resistances as 𝑉𝑅1 = 4 V and 𝑉𝑅2 = 8 V. This is the principle of voltage division, producing what is commonly called a potential divider circuit or voltage divider network.
- 14. 13 Now if we add another series resistor circuit using the same resistor values in parallel with the first we would have the circuit as in figure 6. As the second series circuit has the same resistive values of the first, the voltage at point D, which is also the voltage drop across resistor, 𝑅4 will be the same at 8 V, with respect to zero (battery negative), as the voltage is common and the two resistive networks are the same. Figure 6 12 V 𝐼 A B 𝑅1 𝑅2 10 Ω 20 Ω C D 𝑅4 20 Ω 10 Ω 𝑅3 𝐼2 𝐼1
- 15. 14 But something else equally as important is that the voltage difference between point C and point D will be zero volts as both points are at the same value of 8 V as, C = D = 8 V, then the voltage difference is 0 V. When this happens, both sides of the parallel bridge network are said to be balanced because the voltage at point C is the same value as the voltage at point D with their difference being zero. Now let’s consider what would happen if we reversed the position of the two resistors, 𝑅3 and 𝑅4 in the second parallel branch with respect to 𝑅1 and 𝑅2. Figure 7 12 V 𝐼 A B 𝑅1 𝑅2 10 Ω 20 Ω C = 8 V 𝑅4 10 Ω 20 Ω 𝑅3 𝐼2 𝐼1 D = 4 V
- 16. 15 With resistors, 𝑅3 and 𝑅4 reversed, the same current flows through the series combination and the voltage at point D, which is also the voltage drop across resistor, 𝑅4 will be, 𝑉𝑅4 = 0.4 A × 10 Ω = 4 V Now with 𝑉R4 having 4 volts dropped across it, the voltage difference between points C and D will be 4 volts as: C = 8 V volts and D = 4 V. Then the difference this time is, 8 − 4 = 4 V. The result of swapping the two resistors is that both sides or “arms” of the parallel network are different as they produce different voltage drops. When this happens the parallel network is said to be unbalanced as the voltage at point C is at a different value to the voltage at point D. Then we can see that the resistance ratio of these two parallel arms, ACB and ADB, results in a voltage difference between 0 V (balanced) and the maximum supply voltage (unbalanced), and this is the basic principal of the Wheatstone Bridge Circuit.
- 17. 16 So we can see that a Wheatstone bridge circuit can be used to compare an unknown resistance 𝑅X with others of a known value, for example, 𝑅1 and 𝑅2, have fixed values, and 𝑅3 could be variable. If we connected a voltmeter, ammeter or classically a galvanometer between points C and D, and then varied resistor, 𝑅3 until the meters read zero, would result in the two arms being balanced and the value of 𝑅X, (substituting 𝑅4) known as shown in figure 8. Figure 8: Wheatstone bridge circuit. 12 V 𝐼2 𝐼1 𝑅X 𝑅3 𝑅2 𝑅1 𝑉out = 𝑉C − 𝑉D A B D C + − V
- 18. 17 By replacing 𝑅4 above with a resistance of known or unknown value in the sensing arm of the Wheatstone bridge corresponding to 𝑅X and adjusting the opposing resistor, 𝑅3 to “balance” the bridge network, will result in a zero voltage output. Then we can see that balance occurs when: 𝑅1 𝑅2 = 𝑅3 𝑅X = 1 (Balanced) The Wheatstone bridge equation required to give the value of the unknown resistance, 𝑅X at balance is given as, 𝑉out = 𝑉C − 𝑉D = 𝑉𝑅2 − 𝑉𝑅4 = 0 𝑅C = 𝑅2 𝑅1 + 𝑅2 and 𝑅D = 𝑅4 𝑅3 + 𝑅4 At Balance, 𝑅C = 𝑅D ∴ 𝑅2 𝑅1 + 𝑅2 = 𝑅4 𝑅3 + 𝑅4
- 19. 18 ∴ 𝑅2 𝑅3 + 𝑅4 = 𝑅4 𝑅1 + 𝑅2 𝑅2𝑅3 + 𝑅2𝑅4 = 𝑅1𝑅4 + 𝑅2𝑅4 ∴ 𝑅4 = 𝑅2𝑅3 𝑅1 = 𝑅X Where resistors, 𝑅1 and 𝑅2 are known or preset values.
- 20. 19 Example 1: The following unbalanced Wheatstone bridge is constructed. Calculate the output voltage across points C and D and the value of resistor 𝑅4 required to balance the bridge circuit. Figure 9 100 V 𝑅1 80 Ω 𝑉out A B D C 𝑅3 480 Ω 𝑅2 120 Ω 𝑅4 160 Ω
- 21. 20 For the first series arm, ACB 𝑉C = 𝑅2 𝑅1 + 𝑅2 × 𝑉S 𝑉C = 120 Ω 80 Ω + 120 Ω × 100 = 60 V For the second series arm, ADB 𝑉D = 𝑅4 𝑅3 + 𝑅4 × 𝑉S 𝑉D = 160 Ω 480 Ω + 160 Ω × 100 = 25 V The voltage across points C-D is given as, 𝑉out = 𝑉C − 𝑉D ∴ 𝑉out= 60 − 25 = 35 V
- 22. 21 The value of resistor, R4 required to balance the bridge is given as, 𝑅4 = 𝑅2𝑅3 𝑅1 = 120 Ω × 480 Ω 80 Ω = 720 Ω We have seen above that the Wheatstone bridge has two input terminals (A- B) and two output terminals (C-D). When the bridge is balanced, the voltage across the output terminals is 0 V. When the bridge is unbalanced, however, the output voltage may be either positive or negative depending upon the direction of unbalance.
- 23. 22 Wheatstone Bridge Light Detector Balanced bridge circuits find many useful electronics applications such as being used to measure changes in light intensity, pressure or strain. The types of resistive sensors that can be used within a wheatstone bridge circuit include: photoresistive sensors (LDR’s), positional sensors (potentiometers), piezoresistive sensors (strain gauges) and temperature sensors (thermistor’s), etc. There are many wheatstone bridge applications for sensing a whole range of mechanical and electrical quantities, but one very simple wheatstone bridge application is in the measurement of light by using a photoresistive device. One of the resistors within the bridge network is replaced by a Light Dependent Resistor (LDR).
- 24. 23 An LDR, also known as a Cadmium Sulphide (Cds) photocell, is a passive resistive sensor which converts changes in visible light levels into a change in resistance and hence a voltage. Light dependent resistors can be used for monitoring and measuring the level of light intensity, or whether a light source is ON or OFF. A typical CdS cell such as the ORP12 light dependent resistor typically has a resistance of about 1 MΩ in dark or dim light, about 900 Ω at a light intensity of 100 Lux (typical of a well lit room), down to about 30 Ω in bright sunlight. Then as the light intensity increases the resistance reduces. By connecting a light dependant resistor to the Wheatstone bridge circuit above, we can monitor and measure any changes in the light levels as shown in figure 10.
- 25. 24 Figure 10: Wheatstone bridge light detector. R A Op- Amp 741 Relay LDR ORP 12 𝑅4 10 KΩ 𝑅5 1 KΩ 𝑅3 10 KΩ 𝑉𝑅1 LDR at Nominal Light Levels Out 2N2222 +12 V D C 𝑉D B A 𝐷1 TR1 − +
- 26. 25 The LDR photocell is connected into the Wheatstone bridge circuit as shown to produce a light sensitive switch that activates when the light level being sensed goes above or below the pre-set value determined by 𝑉R1. In this example 𝑉R1 either a 22 KΩ or 47 KΩ potentiometer. The op-amp is connected as a voltage comparator with the reference voltage 𝑉D applied to the inverting pin. In this example, as both 𝑅3 and 𝑅4 are of the same 10 KΩ value, the reference voltage set at point D will therefore be equal to half of 𝑉 cc. That is 𝑉cc 2 . The potentiometer, 𝑉R1 sets the trip point voltage 𝑉C, applied to the non- inverting input and is set to the required nominal light level. The relay turns “ON” when the voltage at point C is less than the voltage at point D.
- 27. 26 Adjusting 𝑉R1 sets the voltage at point C to balance the bridge circuit at the required light level or intensity. The LDR can be any cadmium sulphide device that has a high impedance at low light levels and a low impedance at high light levels. Note that the circuit can be used to act as a “light-activated” switching circuit or a “dark-activated” switching circuit simply by transposing the LDR and 𝑅3 positions within the design. The Wheatstone bridge has many uses in electronic circuits other than comparing an unknown resistance with a known resistance. When used with operational amplifier, the Wheatstone bridge circuit can be used to measure and amplify small changes in resistance, 𝑅X due, for example, to changes in light intensity as we have seen above.
- 28. 27 But the bridge circuit is also suitable for measuring the resistance change of other changing quantities, so by replacing the above photo-resistive LDR light sensor for a thermistor, pressure sensor, strain gauge, and other such transducers, as well as swapping the positions of the LDR and 𝑉R1, we can use them in a variety of other Wheatstone bridge applications. Also more than one resistive sensor can be used within the four arms (or branches) of the bridge formed by the resistors 𝑅1 to 𝑅4 to produce “full- bridge”, “half-bridge” or “quarter-bridge circuit arrangements providing thermal compensation or automatic balancing of the Wheatstone bridge.
- 29. 28 Wien Bridge Oscillator One of the simplest sine wave oscillators which uses a RC network in place of the conventional LC tuned tank circuit to produce a sinusoidal output waveform, is called a Wien bridge oscillator. The Wien bridge oscillator is so called because the circuit is based on a frequency-selective form of the Wheatstone bridge circuit. The Wien bridge oscillator is a two-stage RC coupled amplifier circuit that has good stability at its resonant frequency, low distortion and is very easy to tune making it a popular circuit as an audio frequency oscillator but the phase shift of the output signal is considerably different from the phase shift RC oscillator. The Wien bridge oscillator uses a feedback circuit consisting of a series RC circuit connected with a parallel RC of the same component values producing a phase delay or phase advance circuit depending upon the frequency. At the resonant frequency 𝑓r the phase shift is 0°. Consider the circuit shown in figure 11.
- 30. 29 Figure 11: Wien bridge. Wien bridge oscillator frequency, 𝑓r = 1 2π𝑅𝐶 Where: 𝑓r is the resonant frequency in Hz R is the resistance in Ω C is the capacitance in Farads 𝑅1 𝐶1 𝑅2 𝐶2 𝑅1 = 𝑅2 𝐶1 = 𝐶2 High Pass Filter Stage Low Pass Filter Stage 𝑉in 𝑉out
- 31. 30 We know that the magnitude of the output voltage, 𝑉out from the RC network is at its maximum value and equal to one third 1 3 of the input voltage, 𝑉in to allow for oscillations to occur. But why one third and not some other value. In order to understand why the output from the RC circuit above needs to be one-third, that is 0.333 × 𝑉in , we have to consider the complex impedance 𝑍 = 𝑅 ± j𝑋 of the two connected RC circuits. We know that the real part of the complex impedance is the resistance, 𝑅 while the imaginary part is the reactance, 𝑋. As we are dealing with capacitors here, the reactance part will be capacitive reactance, 𝑋c.
- 32. 31 The RC Network If we redraw the above RC network as shown, we can clearly see that it consists of two RC circuits connected together with the output taken from their junction. Resistor 𝑅1 and capacitor 𝐶1 form the top series network, while resistor 𝑅2 and capacitor 𝐶2 form the bottom parallel network. Therefore the total impedance of the series combination 𝑅1𝐶1 we can call, 𝑍S and the total impedance of the parallel combination 𝑅2𝐶2 we can call, 𝑍P. As 𝑍S and 𝑍P are effectively connected together in series across the input, 𝑉IN, they form a voltage divider network with the output taken from across 𝑍P as shown in figure 12.
- 33. 32 Lets assume then that the component values of 𝑅1 and 𝑅2 are the same at 12 KΩ, capacitors 𝐶1 and 𝐶2 are the same at 3.9 nF and the supply frequency, 𝑓 is 3.4 KHz. Figure 12 𝑅2 𝐶2 𝐶1 𝑅1 𝑉IN 𝑉OUT 𝑍S 𝑍P
- 34. 33 Series Circuit The total impedance of the series combination with resistor, 𝑅1 and capacitor, 𝐶1 is simply, 𝑅 = 12 KΩ, but 𝑋C = 1 2π𝑓𝐶 ∴ 𝑋C = 1 2π × 3.4 KHz × 3.9 nF = 12 KΩ 𝑍S = 𝑅2 + 𝑋C 2 = 120002 + 120002 = 17 KΩ We now know that with a supply frequency of 3.4 KHz the reactance of the capacitor is the same as the resistance of the resistor at 12 KΩ. This then gives us an upper series impedance 𝑍S of 17 KΩ. For the lower parallel impedance 𝑍P, as the two components are in parallel, we have to treat this differently because the impedance of the parallel circuit is influenced by this parallel combination.
- 35. 34 Parallel Circuit The total impedance of the lower parallel combination with resistor, 𝑅1 and capacitor, 𝐶2 is given as, 𝑅 = 12 KΩ, and 𝑋C = 12 KΩ 1 𝑍 = 1 𝑅 + 1 𝑋C = 1 12000 + 1 12000 ∴ 𝑍 = 6 KΩ At the supply frequency of 3.4 KHz, the combined resistance and reactance of the RC parallel circuit becomes 6 KΩ and their parallel impedance is therefore calculated as, 𝑅 = 6 KΩ and 𝑋C = 6 KΩ (Parallel) 𝑍P = 𝑅2 + 𝑋C 2 = 60002 + 60002 ∴ 𝑍P = 8.5 KΩ
- 36. 35 So we now have the value and for the series impedance, 𝑍S = 17 KΩ and for the parallel impedance, 𝑍p = 8.5 KΩ. Therefore the output impedance, 𝑍OUT of the voltage divider network at the given frequency is, 𝑍OUT = 𝑍P 𝑍P + 𝑍S = 8.5 KΩ 8.5 KΩ + 17 KΩ = 0.333 Then at the oscillation frequency, the magnitude of the output voltage, 𝑉OUT will be equal to 𝑍OUT × 𝑉IN which as shown is equal to one third 1 3 of the input voltage, 𝑉IN and it is this frequency selective RC network which forms the basis of the Wien bridge oscillator circuit. If we now place this RC network across a non- inverting amplifier which has a gain of 1 + 𝑅1 𝑅2 , then the basic Wien bridge oscillator circuit is produced as shown in figure 13.
- 37. 36 Figure 13: Wien bridge oscillator. The output of the operational amplifier is fed back to both the inputs of the amplifier. One part of the feedback signal is connected to the inverting input terminal (negative feedback) via the resistor divider network of 𝑅1 and 𝑅2 which allows the amplifiers voltage gain to be adjusted within narrow limits. The other part is fed back to the non- inverting input terminal (positive feedback) via the RC Wien bridge network. + − A 𝑅 𝑅 𝐶 𝑅1 𝑅2 1 3 V 𝑉out Feedback 𝐶
- 38. 37 The RC network is connected in the positive feedback path of the amplifier and has zero phase shift a just one frequency. Then at the selected resonant frequency, 𝑓r the voltages applied to the inverting and non-inverting inputs will be equal and “in-phase” so the positive feedback will cancel out the negative feedback signal causing the circuit to oscillate. The voltage gain of the amplifier circuit MUST be equal too or greater than three “Gain = 3” for oscillations to start because as we have seen above, the input is 1 3 of the output. This value, Av ≥ 3 is set by the feedback resistor network, 𝑅1 and 𝑅2 and for a non-inverting amplifier this is given as the ratio 1 + 𝑅1 𝑅2 . Also, due to the open-loop gain limitations of operational amplifiers, frequencies above 1 MHz are unachievable without the use of special high frequency op-amps.
- 39. 38 Example 2: Determine the maximum and minimum frequency of oscillations of a Wien bridge oscillator circuit having a resistor of 10 KΩ and a variable capacitor of 1 nF to 1000 nF. The frequency of oscillations for a Wien bridge oscillator is given as, 𝑓r = 1 2π𝑅𝐶 Wien bridge oscillator lowest frequency, 𝑓min = 1 2π × 10 × 103 × 1000 × 10−9 = 15.9 Hz Wien bridge oscillator highest frequency, 𝑓max = 1 2π × 10 × 103 × 1 × 10−9 = 15.9 KHz
- 40. 39 Example 3: A Wien bridge oscillator circuit is required to generate a sinusoidal waveform of 5.2 KHz. Calculate the values of the frequency determining resistors 𝑅1 and 𝑅2 and the two capacitors 𝐶1 and 𝐶2 to produce the required frequency. Also, if the oscillator circuit is based around a non-inverting operational amplifier configuration, determine the minimum values for the gain resistors to produce the required oscillations. Finally draw the resulting oscillator circuit. 𝑓r = 1 2π𝑅𝐶 = 5.2 KHz
- 41. 40 The frequency of oscillations for the Wien bridge oscillator was given as 5.2 KHz. If resistors 𝑅1 = 𝑅2 and capacitors 𝐶1 = 𝐶2 and we assume a value for the feedback capacitors of 3.0 nF, then the corresponding value of the feedback resistors is calculated as, 𝑓r = 1 2π𝑅𝐶 𝑅 = 1 2π𝑓rC = 1 2π × 5.2 × 103 × 3 × 10−9 = 10.2 KΩ For sinusoidal oscillations to begin, the voltage gain of the Wien bridge circuit must be equal too or greater than 3, Av ≥ 3 . For a non-inverting op-amp configuration, this value is set by the feedback resistor network of 𝑅3 and 𝑅4 and is given as, 𝐴V = 𝑉OUT 𝑉IN = 1 + 𝑅3 𝑅4 = 3 or more
- 42. 41 If we choose a value for resistor 𝑅3 of say, 100 KΩ’s, then the value of resistor 𝑅4 is calculated as, 1 + 𝑅3 𝑅4 = 3 ∴ 𝑅4 = 𝑅3 3 − 1 = 𝑅3 2 = 1 2 𝑅3 if 𝑅3 = 100 KΩ then, 𝑅4 = 50 KΩ While a gain of 3 is the minimum value required to ensure oscillations, in reality a value a little higher than that is generally required. If we assume a gain value of 3.1 then resistor 𝑅4 is recalculated to give a value of 47 KΩ’s. This gives the final Wien bridge oscillator circuit as shown in figure 14.
- 43. 42 Figure 14: Wien bridge oscillator circuit of example 3. + − A 𝑅1 10.2 KΩ 𝐶1 3 nF 𝑅3 𝑅4 47 KΩ 𝑉out 5.2 KHz 100 KΩ 𝑅2 10.2 KΩ 𝐶2 3 nF
- 44. 43 Wien Bridge Oscillator Summary Then for oscillations to occur in a Wien bridge oscillator circuit the following conditions must apply. • With no input signal a Wien bridge oscillator produces continuous output oscillations. • The Wien bridge oscillator can produce a large range of frequencies. • The Voltage gain of the amplifier must be greater than 3. • The RC network can be used with a non-inverting amplifier. • The input resistance of the amplifier must be high compared to R so that the RC network is not overloaded and alter the required conditions. • The output resistance of the amplifier must be low so that the effect of external loading is minimised. • Some method of stabilizing the amplitude of the oscillations must be provided. If the voltage gain of the amplifier is too small the desired oscillation will decay and stop. If it is too large the output will saturate to the value of the supply rails and distort. • With amplitude stabilisation in the form of feedback diodes, oscillations from the Wien Bridge oscillator can continue indefinitely.
- 45. 44 Instrumentation Amplifier Example 4: For the differential amplifier circuit shown in figure 15. Derive the equation for: (a) The Voltage Gain. (b) The Common Mode Rejection Ratio (CMRR). Solution: The derivation of the equations are as follows: (a) The Voltage Gain is given by, 𝐴V = 𝑉out 𝑉in+−𝑉in− (b) Common Mode Rejection Ratio (CMRR) = Differentail Gain Common Gain
- 46. 45 𝑅1 𝑅2 𝑅1 𝑅2 𝑉in- 𝑉in + −𝑉 cc +𝑉 cc 𝑉out Figure 15: Differential amplifier.
- 47. 46 Example 5: The differential amplifier has a Common Mode Rejection Ratio (CMRR) of about 30,000. If we build a circuit with a differential gain of 1,000, find the common gain of the circuit. Solution: Common Gain = Differentail Gain CMRR = 1000 30000 = 1 30 = 0.03 Example 6: The design of an Instrumentation amplifier circuit using a buffers and differential amplifier is shown in figure 16.
- 48. 47 𝑅3 𝑅4 𝑅3 −𝑉 cc +𝑉 cc 𝑉out 𝑅2 𝑅4 𝑉in- 𝑉in + −𝑉 cc +𝑉 cc 𝑅2 −𝑉 cc +𝑉 cc −𝑉 cc 10 K 10 K 47 K 10 K 47 K Figure 16: Differential amplifier. Differential Amplifier Buffers 𝑅1 (No current flow) Offset CMRR = 10 log 1 + 2𝑅2 𝑅1 and Gain = 𝑅4 𝑅3 1 + 𝑅2 𝑅1
- 49. 48 Vector Voltmeter The vector voltmeter is basically a new type of amplitude and phase measuring device. It uses two samples to sample the two waves whose amplitudes and relative phase are to be measured. It measures the voltages at two different points in the circuit and also measures the phase difference between these voltages at these two points. In this voltmeter, two RF signals of same fundamental frequency (1 MHz to 1 GHz) are converted to two IF signals. The amplitudes, waveforms and the phase relations of IF signals are same as that of RF signals. Thus, the fundamental components of the RF signals. These fundamental components are filtered from the IF signals and are measured by a voltmeter and a phase meter. The block diagram of the vector voltmeter is shown in figure 17. The instrument consists of four sections: (i) Two RF to IF converters (ii) Automatic phase control circuit (iii) Phase meter circuit (iv) Voltmeter circuit
- 50. 49 Sampling Gate Sampling Gate Sampling Pulse Generator 20 KHz Reference Oscillator Automatic Phase Control Voltage Tuned Oscillator 20 KHz Tuned Amplifier Amplifier and Limiter +60° Phase Shifter Trigger Amplifier 20 KHz Tuned Amplifier Amplifier and Limiter -120° Phase Shifter Trigger Amplifier Constant Current Sourse Current Switch Bistable Multivibrator Meter Attenuator and Amplifier Phase Meter Voltmeter Phase Meter Circuit Channel “A” RF to IF Converter Channel “B” RF to IF Converter Voltmeter Circuit Automatic Phase Control Circuit “B” Probe RF Input 1 MHz - 1 GHz “A” Probe RF Input 1 MHz - 1 GHz CH A CH B Figure 17 ∅ 20 KHz 20 KHz 𝑉C 𝑉C 20 KHz ∅ 20 KHz ∅ 𝑉A 𝑉A 𝑉B 𝑉B 20 KHz 20 KHz
- 51. 50 The channel A and B ate the two RF to IF converters. The RF signals are applied to sampling gates. The sampling pulse generator controls the opening and closing of the gates. The RF to IF converters and phase control circuit section produce two 20 KHz sine waves with the same amplitudes and the same phase relationship as that of the same amplitude and the same phase relationship as that of the fundamental components of the RF signals applied to the channels A and B. The turned amplifier extracts the 20 KHz fundamental component from these sine waves. The pulse control unit generates the sampling pulses for both the RF to IF converters. The sampling pulse rate is controlled by voltage tuned oscillator for which the tuning voltage is supplied by the automatic phase control unit. This section locks the IF signal of channel A to a 20 KHz reference oscillator. Due to this, the section is also called phase locked section. The tuned amplifier passes only 20 KHz fundamental component of the IF signal of each channel. Thus the output of each tuned amplifier maintains the original phase relationship with respect to the signal in the other channel and also its correct amplitude relationship.
- 52. 51 These two filtered signals are then connected to the voltmeter circuit by a front panel switch marked channel A and channel B. The appropriate meter range is decided by the input attenuator. This attenuator is also a front panel control marked amplitude range. It is basically a d.c. voltmeter and it consists of input attenuator, feedback amplifier having fixed gain, the rectifier and filtering arrangement and a d.c. voltmeter corresponding to the channel A and channel B. To determine the phase difference, there exists a phase meter circuit. The signals from channel A and B are applied to the amplifier and the limiter circuit. Due to this the signals are amplified and limited i.e. clipped. This produces a square wave signal at the output of each amplifier and limiter circuit. These square waves are then applied to the phase shifting network. The circuit in upper part i.e. channel A shifts the phase of the square waves by + 60° while the circuit in lower part i.e. channel B shifts the phase by −120°. The phase shifts are achieved by using capacitive networks and inverting, non- inverting amplifiers. The shifted square wave signals are then applied to trigger amplifiers.
- 53. 52 These trigger amplifiers convert the square wave signals to the positive spikes with very fast rise times. These spikes are used to trigger the bistable multivibrator. The signal from channel A is connected to set input of the multivibrator while the signal from channel B is connected to the reset input of the multivibrator. Now of the phase shift between the two signals is zero then the trigger pulses are +60° − −120° i.e. 180° out of phase due to phase shift circuitry. Hence in such a case the bistable multivibrator produces a square waves which is symmetrical about zero Thus if there exists a phase shift between the two signals, the bistable multivibrator produces asymmetrical square wave. Such asymmetrical signal is used to control the current switch which is transistorised switch is during the negative portion of the square waves. This switch connects the constant current supply to the phase meter. When phase shift is 0°, then the current from constant source is so adjusted that the meter reading is 0°. Depending upon the asymmetric nature of the square waves, current by current source varies and causes the appropriate reading of the phase difference, on the meter.
- 54. 53 The main limitation of the meter is when the shift at the input side is 180° then the square wave produced by the bistabel multivibrator causes either zero current or maximum current as in such a case square waves no longer remains square but collapse into either positive or negative d.c. voltage. These maximum deviations from the center reading of 0° are marked on the meters as +180° and −180°. The phase range can be selected by a front panel switch that places a shunt across the phase meter and changes its sensitivity. Features Of Vector Voltmeter (i) The vector voltmeters cover a 1000 to 1 frequency range accomodating inputs from few microvolts upto about 1 V without input attenuation. Thus it gives broad frequency range. (ii) They allow voltage ratios to be measured over 70 to 80 dB range within a few lengths of a decibel. (iii) The phase to be measured to an accuracy of about 1°. (iv) Due to self locking feature, there is automatic tuning of the local oscillator in each frequency range. (v) Easy to operate, as simple as normal voltmeters.
- 55. 54 A TDR is an electronic instrument that uses time domain reflectometry to characterize and locate faults in metallic cables (for example, twisted pair wire or coaxial cable). It can also be used to locate discontinuities in a connector, printed circuit board, or any other electrical path. The equivalent device for optical fiber is an optical time- domain reflectometer. Time Domain Reflectometer (TDR)
- 56. 55 Signal Transmitted Through And Reflected From A Discontinuity Figure 18
- 57. 56 Generally, the reflections will have the same shape as the incident signal, but their sign and magnitude depend on the change in impedance level. If there is a step increase in the impedance, then the reflection will have the same sign as the incident signal, if there is a step decrease in impedance, the reflection will have the opposite sign. The magnitude of the reflection depends not only on the amount of the impedance change, but also upon the loss in the conductor. The reflections are measured at the output/input to the TDR and displayed or plotted as a function of time. Alternatively, the display can be read as a function of cable length because the speed of signal propagation is almost constant for a given transmission medium. Because of its sensitivity to impedance variations, a TDR may be used to verify cable impedance characteristics, splice and connector locations and associated losses, and estimate cable lengths. Reflection
- 58. 57 TDRs use different incident signals. Some TDRs transmit a pulse along the conductor; the resolution of such instruments is often the width of the pulse. Narrow pulses can offer good resolution, but they have high frequency signal components that are attenuated in long cables. The shape of the pulse is often a half cycle sinusoid. For longer cables, wider pulse widths are used. Fast rise time steps are also used. Instead of looking for the reflection of a complete pulse, the instrument is concerned with the rising edge, which can be very fast. A 1970s technology TDR used steps with a rise time of 25 ps. Still other TDRs transmit complex signals and detect reflections with correlation techniques. See spread-spectrum time-domain reflectometry. Incident Signal
- 59. 58 Usage Of TDR In a TDR-based level measurement device, the device generates an impulse that propagates down a thin waveguide (referred to as a probe) - typically a metal rod or a steel cable. When this impulse hits the surface of the medium to be measured, part of the impulse reflects back up the waveguide. The device determines the fluid level by measuring the time difference between when the impulse was sent and when the reflection returned. The sensors can output the analyzed level as a continuous analog signal or switch output signals. In TDR technology, the impulse velocity is primarily affected by the permittivity of the medium through which the pulse propagates, which can vary greatly by the moisture content and temperature of the medium. In many cases, this effect can be corrected without undue difficulty. In some cases, such as in boiling and/or high temperature environments, the correction can be difficult. In particular, determining the froth (foam) height and the collapsed liquid level in a frothy/boiling medium can be very difficult. TDR In Level Measurement
- 60. 59 The Dam Safety Interest Group of CEA Technologies, Inc. (CEATI), a consortium of electrical power organizations, has applied spread-spectrum time domain reflectometry to identify potential faults in concrete dam anchor cables. The key benefit of time domain reflectometry over other testing methods is the non-destructive method of these tests. TDR Used In Anchor Cable In Dam
- 61. 60 TDR Used In The Earth And Agricultural Sciences A TDR is used to determine moisture content in soil and porous media. Over the last two decades, substantial advances have been made measuring moisture in soil, grain, food stuff, and sediment. The key to TDR’s success is its ability to accurately determine the permittivity (dielectric constant) of a material from wave propagation, due to the strong relationship between the permittivity of a material and its water content, as demonstrated in the pioneering works of Hoekstra and Delaney (1974) and Topp et al. (1980). Recent reviews and reference work on the subject include, Topp and Reynolds (1998), Noborio (2001), Pettinellia et al. (2002), Topp and Ferr (2002), and Robinson et al. (2003). The TDR method is a transmission line technique, and determines apparent permittivity (Ka) from the travel time of an electromagnetic wave that propagates along a transmission line, usually two or more parallel metal rods embedded in soil or sediment. The probes are typically between 10 and 30 cm long and connected to the TDR via coaxial cable.
- 62. 61 Time domain reflectometry has also been utilized to monitor slope movement in a variety of geotechnical settings including highway cuts, rail beds, and open pit mines (Dowding and O'Connor, 1984, 2000a, 2000b; Kane and Beck, 1999). In stability monitoring applications using TDR, a coaxial cable is installed in a vertical borehole passing through the region of concern. The electrical impedance at any point along a coaxial cable changes with deformation of the insulator between the conductors. A brittle grout surrounds the cable to translate earth movement into an abrupt cable deformation that shows up as a detectable peak in the reflectance trace. Until recently, the technique was relatively insensitive to small slope movements and could not be automated because it relied on human detection of changes in the reflectance trace over time. Farrington and Sargand (2004) developed a simple signal processing technique using numerical derivatives to extract reliable indications of slope movement from the TDR data much earlier than by conventional interpretation. TDR In Geotechnical Usage
- 63. 62 Time domain reflectometry is used in semiconductor failure analysis as a non-destructive method for the location of defects in semiconductor device packages. The TDR provides an electrical signature of individual conductive traces in the device package, and is useful for determining the location of opens and shorts. TDR In Semiconductor Device Analysis
- 64. 63 TDR In Aviation Wiring Maintenance TDR, specifically spread-spectrum TDR is used on aviation wiring for both preventative maintenance and fault location. Spread spectrum TDR has the advantage of precisely locating the fault location within thousands of miles of aviation wiring. Additionally, this technology is worth considering for real time aviation monitoring, as spread spectrum TDR can be employed on live wires. This method has been shown to be useful to locating intermittent electrical faults.
- 65. 64 An OTDR is an optoelectronic instrument used to characterise an optical fiber. An OTDR is the optical equivalent of an electronic TDR. It injects a series of optical pulses into the fiber under test and extracts, from the same end of the fiber, light that is scattered (Rayleigh backscatter) or reflected back from points along the fiber. The scattered or reflected light that is gathered back is used to characterize the optical fiber. This is equivalent to the way that an electronic time-domain meter measures reflections caused by changes in the impedance of the cable under test. The strength of the return pulses is measured and integrated as a function of time, and plotted as a function of fiber length. Optical Time Domain Reflectometer (OTDR)
- 66. 65 Optoelectronics Optoelectronics is the study and application of electronic devices and systems that source, detect and control light, usually considered a sub- field of photonics. In this context, light often includes invisible forms of radiation such as gamma rays, X-rays, ultraviolet and infrared, in addition to visible light. Optoelectronic devices are electrical-to-optical or optical- to-electrical transducers, or instruments that use such devices in their operation. Electro-optics is often erroneously used as a synonym, but is a wider branch of physics that concerns all interactions between light and electric fields, whether or not they form part of an electronic device. Optoelectronics is based on the quantum mechanical effects of light on electronic materials, especially semiconductors, sometimes in the presence of electric fields.
- 67. 66 Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, which is visible to the human eye and is responsible for the sense of sight. Visible light is usually defined as having wavelengths in the range of 400 − 700 nm , between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths). This wavelength means a frequency range of roughly 430 − 750 THz. The main source of light on Earth is the Sun. Sunlight provides the energy that green plants use to create sugars mostly in the form of starches, which release energy into the living things that digest them. This process of photosynthesis provides virtually all the energy used by living things. Historically, another important source of light for humans has been fire, from ancient campfires to modern kerosene lamps. With the development of electric lights and power systems, electric lighting has effectively replaced firelight. Light
- 68. 67 Figure 18
- 69. 68 Reliability And Quality Of OTDR Equipment The reliability and quality of an OTDR is based on its accuracy, measurement range, ability to resolve and measure closely spaced events, measurement speed, and ability to perform satisfactorily under various environmental extremes and after various types of physical abuse. The instrument is also judged on the basis of its cost, features provided, size, weight, and ease of use. Some of the terms often used in specifying the quality of an OTDR are as follows: • Accuracy • Measurement Range • Instrument Resolution
- 70. 69 Defined as the correctness of the measurement i.e., the difference between the measured value and the true value of the event being measured. Accuracy Measurement Range Defined as the maximum attenuation that can be placed between the instrument and the event being measured, for which the instrument will still be able to measure the event within acceptable accuracy limits.
- 71. 70 Instrument resolution is a measure of how close two events can be spaced and still be recognized as two separate events. The duration of the measurement pulse and the data sampling interval create a resolution limitation for OTDRs. The shorter the pulse duration and the shorter the data sampling interval, the better the instrument resolution, but the shorter the measurement range. Resolution is also often limited when powerful reflections return to the OTDR and temporarily overload the detector. When this occurs, some time is required before the instrument can resolve a second fiber event. Some OTDR manufacturers use a “masking” procedure to improve resolution. The procedure shields or “masks” the detector from high-power fiber reflections, preventing detector overload and eliminating the need for detector recovery. Instrument Resolution
- 72. 71 This application note provides a summary description of the operation and capabilities of a Vector Network Analyser (VNA), including general considerations of front panel operation and measurement methods. Included in this note are discussions on the following topics: • System description; • General discussion about network analysers; • Basic measurements and how to make them; • Error correction; • General discussion on test sets. For detailed information regarding calibration techniques, accuracy considerations, or specific measurement applications, pleaser refer to additional manufacturer application notes and technical papers. Vector Network Analyser Introduction
- 73. 72 Anritsu VNAs measure the magnitude and phase characteristics of networks, amplifiers, components, cables, and antennas. They compare the incident signal that leaves the analyzer with either the signal that is transmitted through the test device or the signal that is reflected from its input. Figure 20 and figure 21 illustrate the types of measurements that the VNA performs. VNAs are self contained, fully integrated measurement systems that include an optional time domain capability. The system hardware consists of the following: • Analyser; • Precision components required for calibration and performance verification; • Optional use of synthesizers used as a second source; • Optional use of power meters for test port power leveling and calibration. General Description
- 74. 73 Transmission Measurements Figure 20 Device Under Test (DUT) Incident Transmitted • Gain (dB) • Insertion Loss (dB) • Insertion Phase (degrees) • Transmission Coefficients (S21) • Separations of Transmission Components (Real and Imaginary) • Electrical Length (m) • Electrical Delay (s) • Deviation from Linear Phase (degrees) • Group Delay (s)
- 75. 74 Reflection Measurements Figure 21 DUT Incident Reflected Termination • Return Loss (dB) • Reflection Coefficients (S11, S22) • Reflection Coefficients vs Time (Fourier Transform) • Impedance 𝑅 ± j𝑋 • Standing Wave Ratio (SWR)
- 76. 75 Source Module The VNA Internal System Module Perform The Following Functions This module provides the stimulus to the Device Under Test (DUT). The frequency ranges of both the source and the test set modules establish the frequency range of the system. The frequency stability of the source is an important factor in the accuracy (especially phase accuracy) of the network analyser. Hence, VNAs always phase lock the source to an internal crystal reference for a synthesized, step sweep mode of operation. VNAs avoid the use of unlocked, analog sweep modes because of the sacrifices in measurement stability, phase performance, and group delay accuracy.
- 77. 76 Test Set Module The test set module routes the stimulus signal to the DUT and samples the reflected and transmitted signals. The type of connector that is used is important, as is the “Auto Reversing” feature. Auto Reversing means that the stimulus signal is applied in both the forward and reverse directions. The direction is reversed automatically. This saves you from having to reverse the test device physically in order to measure all four Scattering parameters (S-parameters). It also increases accuracy by reducing connector repeatability errors. Frequency conversion to the IF range also occurs in the test set module.
- 78. 77 Analyser Module The analyser module receives and interprets the IF signal for phase and magnitude data. It then displays the results of this analysis on a high resolution display screen. This display can show all four S-parameters simultaneously as well as a variety of other forms of displayed information such as Group Delay, Time and Distance information, and complex impedance information. In addition to the installed display, you can also view the measurement results on an external monitor.
- 79. 78 We will begin this discussion with a subject familiar to most microwave test equipment users, scalar network analysis. After showing comparisons, we will proceed to the fundamentals of network analyzer terminology and techniques. This discussion serves as an introduction to topics that are presented in greater detail later in this section. This discussion will touch on new concepts that include the following: • Reference Delay; • S-parameters, what they are and how they are displayed; • Complex Impedance and Smith Charts. Network Analyser
- 80. 79 VNAs do everything that scalar analyzers do, plus they add the ability to measure the phase characteristics of microwave devices over a greater dynamic range and with more accuracy. If all a vector network analyzer added was the capability for measuring phase characteristics, its usefulness would be limited. While phase measurements are important in themselves, the availability of phase information provides the potential for many new features for complex measurements. These features include Smith Charts, Time Domain, and Group Delay. Phase information also allows greater accuracy through vector error correction of the measured signal. First, let us look at Scalar Network Analyzers (SNAs). SNAs measure microwave signals by converting them to a DC voltage using a diode detector as shown in figure 22. This DC voltage is proportional to the magnitude of the incoming signal. The detection process, however, ignores any information regarding the phase of the microwave signal. Also, a detector is a broadband detection device, which means that all frequencies (the fundamental, harmonic, sub harmonic, and spurious signals) are detected and simultaneously displayed as one signal. This, of course, adds significant error to both the absolute and relative measurements. Scalar Analyser Comparison
- 81. 80 In a VNA, information is extracted of both the magnitude and phase of a microwave signal. While there are different ways to perform the measurement, the method the VNA employs is to down convert the signal to a lower intermediate frequency (i.e. harmonic sampling). This signal can then be measured directly by a tuned receiver. The tuned receiver approach gives the system greater dynamic range due to the variable IF filter bandwidth control. The system is also much less sensitive to interfering signals, including harmonics. Figure 22 Microwave Signal Microwave Detector Detector Output Voltage Detector Output Voltage is Proportional to Signal Amplitude
- 82. 81 The VNA is a tuned receiver as shown in figure 23. The microwave signal is down converted into the passband of the IF. To measure the phase of this signal as it passes through the DUT, we must have a reference to compare. If the phase of a signal is 90°, it is 90° different from the reference signal as shown in figure 24. The vector network analyser would read this as −90°, since the test signal is delayed by 90° with respect to the reference signal. The phase reference can be obtained by splitting off a portion of the microwave signal before the measurement as shown in figure 25. The phase of the microwave signal after it has passed through the DUT is then compared with the reference signal. A network analyzer test set automatically samples the reference signal, so no external hardware is needed. VNA Basics
- 83. 82 VNA Is A Tuned Receiver Figure 23 Microwave Signal Intermediate Frequency (IF) Tunable Local Oscillator
- 84. 83 Signals With A 90 Degree Phase Difference Figure 24: Phase Measurement Reference Signal Test Signal Time
- 85. 84 Splitting The Microwave Signal Figure 25 Phase Detector DUT Microwave Source Reference Signal Splitter Test Signal
- 86. 85 Let us consider the case when the DUT is removed, and a length of transmission line is substituted as shown in figure 26. Note that the path length of the test signal is longer than that of the reference signal. Let us see how this affects our measurement. Assume that we are making a measurement at 1 GHz, and that the difference in path length between the two signals is exactly 1 wavelength. This means that test signal is lagging the reference signal by 360° as shown in figure 27. We cannot really tell the difference between one sine wave maxima and the next (they are all identical), so the network analyzer would measure a phase difference of 0°.
- 87. 86 Split Signal Where A Length Of The Line Replaces DUT Figure 26 Phase Detector Microwave Source Reference Signal Splitter Test Signal Longer Path Length
- 88. 87 Split Signal Where Path Length Differs By Exactly One Wavelength Figure 27 Phase Detector Microwave Source Reference Signal Splitter Test Signal Longer By One Wavelength Length 360°
- 89. 88 Now consider that we make this same measurement at 1.1 GHz. Since the frequency is higher by 10 percent, the wavelength of the signal is shorter by 10 percent. The test signal path length is now 0.1 wavelength longer than that of the reference signal as shown in figure 28. This test signal is, 1.1 × 360 = 396°. This is 36° different from the phase measurement at 1 GHz. The network analyser will display this phase difference as −36°. The test signal at 1.1 GHz is delayed by 36° more than the test signal at 1 GHz. You can see that if the measurement frequency is 1.2 GHz, then we will get a reading of −72°, −108° for 1.3 GHz, and so forth as shown in figure 29. An electrical delay occurs between the reference and test signals. For this delay, we will use the common industry term of reference delay. You also may hear it called phase delay. In older network analysers, the length of the reference path had to be constantly adjusted relative to the test path in order to make an appropriate measurement of phase versus frequency.
- 90. 89 Figure 28 Split Signal Where Path Length Is Longer Than One Wavelength Phase Detector Microwave Source Reference Signal Splitter Test Signal Same Path Length But Wavelength is Now Shorter 1.1 Wavelengths = 396°
- 91. 90 Figure 29 Electrical Delay Frequency in GHz Measured Phase 1.1 1.2 1.3 1.4 0° +90° +180° -90° -180°
- 92. 91 To measure phase on a DUT, we need to remove this phase change versus frequency due to changes in the electrical length. This will allow us to view the actual phase characteristics of the device, which may be much smaller than the phase change due to electrical length difference of the two paths. This can be accomplished in two ways. The most obvious way is to insert a length of line into the reference signal path to make both paths of equal length as shown in figure 30. With perfect transmission lines and a perfect splitter, we would then measure a constant phase as we change the frequency. The problem using this approach is that we must change the line length with each measurement setup.
- 93. 92 Figure 30 Split Signals Where Paths Are Of Equal Length Phase Detector Microwave Source Reference Signal Splitter Test Signal Both Line Lengths Now Equal
- 94. 93 Another approach is to handle the path length difference in software. Figure 31 displays the phase versus frequency of a device. This device has different effects on the output phase at different frequencies. Because of these differences, we do not have a perfectly linear phase response. We can easily detect this phase deviation by compensating for the linear phase. The size of the phase difference increases linearly with frequency, so we can modify the phase display to eliminate this delay. VNAs offer automatic reference delay compensation with the push of a button. Figure 32 shows the resultant measurement when we compensate path length. In a system application, you can usually correct for length differences, however, the residual phase characteristics are critical.
- 95. 94 Figure 31 Phase Difference Increases Linearly With Frequency Frequency in GHz Measured Phase 1.1 1.2 1.3 1.4 0° +90° +180° -90° -180° Subtract Linear Phase From Measured Phase
- 96. 95 Figure 32 Resultant Phase With Path Length Frequency in GHz Resultant Phase 1.1 1.2 1.3 1.4 0° +1° +2° -1° -2°
- 97. 96 Now let us consider measuring the DUT. Consider a two port device, that is a device with a connector on each end. What measurements would be of interest? First, we could measure the reflection characteristics at either end with the opposite end terminated into 50 Ω. If we designate one of the inputs as Port 1 of the device, then we have a reference port. We can then define the reflection characteristics from the reference end as forward reflection, and those from the other end as reverse reflection as shown in figure 33. Second, we can measure the forward and reverse transmission characteristics. However, instead of saying “forward,” “reverse,” “reflection,” and “transmission” all the time, we use a shorthand. That is all that S-parameters are, shorthand! The “S” stands for scattering. The second number is the device port that the signal is being injected into, while the first is the device port that the signal is leaving. S11, therefore, is the signal leaving port 1 relative to the signal injected into port 1. The four Scattering Parameters (S-Parameters) in figure 34 are: • S11 Forward Reflection; • S21 Forward Transmission; • S22 Reverse Reflection; • S12 Reverse Transmission. Network Analyser Measurement
- 98. 97 Figure 33 Forward And Reverse Measurement DUT S22 Reverse Reflection S11 Forward Reflection Port 1 Port 2
- 99. 98 Figure 34 S-Parameter DUT S22 Reverse Reflection S11 Forward Reflection Port 1 Port 2 S21 Forward Transmission S12 Reverse Transmission
- 100. 99 S-parameters can be displayed in many ways. An S-parameter consists of a magnitude and a phase. We can display the magnitude in dB, just like a scalar network analyzer. We often call this term log magnitude. Another method of magnitude display is to use Units instead of dB. When displaying magnitude in Units, the value of the reflected or transmitted signal will be between 0 and 1 relative to the reference. We can display phase as “linear phase” as shown in figure 35. As discussed earlier, we cannot tell the difference between one cycle and the next. Therefore, after going through 360°, we are back to where we began. We can display the measurement from −180 to +180°, which is a more common approach. This method keeps the display discontinuity removed from the important 0 degree area that is used as the phase reference.
- 101. 100 Figure 35 Linear Phase With Frequency Waveform Frequency Phase +180° -180° 0°
- 102. 101 Several methods are available to display all of the information on one trace. One method is a polar display as shown in figure 36. The radial parameter (distance from the center) is magnitude. The rotation around the circle is phase. We sometimes use polar displays to view transmission measurements, especially on cascaded devices (i.e. devices in series). The transmission result is the addition of the phase and the log magnitude (dB) information in the polar display of each device.
- 104. 103 One common method for measuring the reflection and transmission characteristics of any Device Under Test (DUT), in this case open, short, and matched loads, involves the using a network analyser. A network analyser allows convenient measurements of signal reflection and transmission in a variety of formats. It can measure signal delay, phase, and gain of the DUT. All of these measurements are made with respect to the source and terminal impedance of the network analyser. The default impedance of the Agilent network analyser is set at 50 Ω. The signal reflected from the DUT is usually measured as a ratio to the incident signal. It can be expressed as reflection coefficient or return loss. These measurements are described mathematically as, Reflection coefficient ≡ reflected power incident power = 𝐸refl 𝐸inc = 𝜌 (magnitude only) = Γ (Reflection magnitude and phase) Return loss (dB) = −20 log 𝜌 Standing Waves Ratio, 𝑆𝑊𝑅 = 1+ Γ 1− Γ Network Analysis
- 105. 104 Displaying the reflection measurement in polar form on the network analyser with a marker allows direct determination of the complex impedance of the DUT. The center of the circle represents a coefficient Γ of 0, a perfect match, no reflected signal. The outermost circumference of the scale represents a Γ of 1, 100 % reflection. The phase angle is directly read from the display. The magnitude and phase will be directly displayed in the marker data readout for any frequency. The amount of power reflected from a device is directly related to the impedances of the DUT and the measurement instrument. Γ=0 occurs when the DUT and the analyser have identical impedances. A short circuit has Γ=1∠180°. Every other value of Γ corresponds uniquely to complex device impedance. In terms of impedances, 𝑍o is the impedance of the measurement instrument, 𝑍DUT is the impedance of the DUT. To facilitate computations, the normalised (in this case normalised to 50 Ω) impedance is, 𝑍N = 𝑍DUT 𝑍o = 1 + Γ 1 − Γ
- 106. 105 Scattering parameters (S-parameters) are commonly used to characterise high frequency circuits. S-parameters basically are two-port characteristics of the DUT. Additionally, the behaviour of traveling waves is readily deduced from S-parameters. S-parameters can readily be found using the schematic of the test set up shown in figure 37. DUT 2-Port Network Figure 37: Two port network used for S-parameters measurements. 𝑍𝐿 + - 𝑍0 𝐸r2 𝐸i2 𝐸r1 𝐸i1
- 107. 106 Define new variables with respect to the characteristic impedance of the measurement instrument, 𝑎1 = 𝐸i1 𝑍o 𝑎2 = 𝐸i2 𝑍o 𝑏1 = 𝐸r1 𝑍o 𝑏2 = 𝐸r2 𝑍o S-parameters relates these four waves as follows: 𝑏1 = 𝑆11𝑎1 + 𝑆12𝑎2 𝑏2 = 𝑆21𝑎1 + 𝑆22𝑎2 For 𝑆11, the output port of the DUT is terminated, with 𝑍o = 50 Ω and the ratio of 𝑏1 to 𝑎1 is measured, 𝑆11 = 𝑏1 𝑎1 𝑎2=0
- 108. 107 Terminating the output port of the DUT with the impedance of the measurement instrument is equivalent to setting 𝑎2 = 0 since a traveling wave incident on this load will be totally absorbed. 𝑆11 is the input reflection coefficient of the DUT. The forward transmission through the DUT is the ratio of 𝑏2 to 𝑎1. This could either be the gain of the amplifier or the attenuation of a passive network, 𝑆21 = 𝑏2 𝑎1 𝑎2=0 By terminating the input side of the network, we set 𝑎1 = 0 and can then measure the output reflection coefficient, 𝑆22, and the reverse transmission coefficient, 𝑆12, defined as, 𝑆22 = 𝑏2 𝑎2 𝑎1=0 𝑆12 = 𝑏1 𝑎2 𝑎1=0 S-parameters are typically expressed as a magnitude and phase.
- 109. 108 Spectrum Analyser Introduction • A spectrum in the practical sense is a collection of sine waves, when combined properly produces the required time domain signal. • The frequency domain also has its measurement strengths. • The frequency domain is better for determining the harmonic content of a signal. A spectrum analyser is a device used to examine the spectral composition of some electrical, acoustic, or optical waveform. Mostly it finds application in measurement of power spectrum .
- 110. 109 Figure 38 Amplitude (Power) Time Domain Measurements Frequency Domain Measurements
- 111. 110 Figure 39
- 112. 111 Analog Spectrum Analyser An analog spectrum analyser uses either a variable bandpass filter whose mid-frequency 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. Figure 40
- 113. 112 Digital Spectrum Analyser A digital spectrum analyser computes the Fast Fourier Transform (FFT), a mathematical process that transforms a waveform into the components of its frequency spectrum Figure 41
- 114. 113 Spectrum Analysis • In various field operations involving signals there is need to ascertain the nature of the signal at several points. • Signal characteristics affect the parameters of operation of a system. • Spectrum analysis mostly involves study of the signal entering a system or that produced by it. • Spectrum analysers usually display raw, unprocessed signal information such as voltage, power, period, waveshape, sidebands and frequency. They can provide with a clear and precise window into the frequency spectrum.
- 115. 114 Fast Fourier Transform (FFT) Spectrum Analyser The Fourier analyser basically takes a time-domain signal, digitizes it using digital sampling, and then performs the mathematics required to convert it to the frequency domain, and display the resulting spectrum as shown in figure 42. Figure 42: Parallel filters measured simultaneously. 𝑓1 𝑓2 A 𝑓
- 116. 115 Swept Spectrum Analyser The most common type of spectrum analyser is the swept-tuned receiver. It is the most widely accepted, general-purpose tool for frequency-domain measurements. The technique most widely used is superheterodyne. 𝑓1 𝑓2 A 𝑓 Figure 43: Filter sweeps over range of interest.
- 117. 116 FFT Spectrum Analyser The Measurement System • The analyser is looking at the entire frequency range at the same time using parallel filters measuring simultaneously. • It is actually capturing the time domain information which contains all the frequency information in it. • With its real-time signal analysis capability, the Fourier analyser is able to capture periodic as well as random and transient events. • It also can provide significant speed improvement over the more traditional swept analyser and can measure phase as well as magnitude.
- 118. 117 Swept Spectrum Analyser • Very basically, these analysers "sweep" across the frequency range of interest, displaying all the frequency components present. • The swept-tuned analyser works just like the AM radio in your home except that on your radio, the dial controls the tuning and instead of a display, your radio has a speaker. • The swept receiver technique enables frequency domain measurements to be made over a large dynamic range and a wide frequency range. • It has significant contributions to frequency-domain signal analysis for numerous applications, including the manufacture and maintenance of microwave communications links, radar, telecommunications equipment, cable TV systems, and broadcast equipment; mobile communication systems; EMI diagnostic testing; component testing; and signal surveillance.
- 119. 118 Theory Of Operation Figure 44 RF Input Attenuator Input Signal Local Oscillator Crystal Reference Mixer IF Gain IF Filter Detector Log Amplifier Video Filter Sweep Generator CRT Display Pre Selector (Low Pass Filter)
- 120. 119 The major components in a spectrum analyser are: • RF input attenuator; • Mixer; • IF (Intermediate Frequency) gain; • IF filter; • Detector; • Video filter; • Local oscillator; • Sweep generator; • CRT display. Components In Spectrum Analyser
- 121. 120 Mixer Figure 45 RF IF LO 𝑓sig 𝑓LO 𝑓sig 𝑓LO − 𝑓sig 𝑓LO + 𝑓sig 𝑓LO
- 122. 121 • A mixer is a device that converts a signal from one frequency to another. • It is sometimes called a frequency-translation device. • A mixer is a non-linear device (frequencies are present at the output that were not present at the input). • The output of a mixer consists of the two original signals 𝑓Sig and 𝑓LO as well as the sum 𝑓LO + 𝑓Sig and difference 𝑓LO − 𝑓Sig frequencies of these two signals. • In a spectrum analyser, the difference frequency is actually the frequency of interest. The mixer has converted our RF input signal to an IF (Intermediate Frequency) signal that the analyser can now filter, amplify and detect for the purpose of displaying the signal on the screen.
- 124. 123 • The IF filter is a bandpass filter which is used as the “window” for detecting signals. • It's bandwidth is also called the Resolution Bandwidth (RBW) of the analyser and can be changed via the front panel of the analyser. • By giving a broad range of variable resolution bandwidth settings , the instrument can be optimized for the sweep and signal conditions, letting trade-off frequency selectivity (the ability to resolve signals), Signal-to-Noise Ratio (SNR), and measurement speed. • As RBW is narrowed, selectivity is improved (we are able to resolve the two input signals). This will also often improve SNR.
- 125. 124 Detector Figure 47 Amplitude ■ Positive detection: Largest value in bin displayed ● Negative detection: Smallest value in bin displayed ♦ Sample detection: Last value in bin displayed ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ● ● ● ● ● ● ● ● ● ♦ ♦ ● ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ Bins Detector
- 126. 125 • The analyser must convert the IF signal to a baseband or video signal so it can be viewed on the instrument's display. This is accomplished with an envelope detector which then deflects the CRT beam on the y- axis, or amplitude axis. • Many modern spectrum analysers have digital displays which first digitise the video signal with an analog-to-digital converter (ADC). • The positive-peak detector mode captures and displays the peak value of the signal over the duration of one trace element. • The negative-peak detector mode captures the minimum value of the signal for each bin.
- 128. 127 • The video filter is a low-pass filter that is located after the envelope detector and before the ADC. • This filter determines the bandwidth of the video amplifier, and is used to average or smooth the trace seen on the screen. • By changing the video bandwidth (VBW) setting, we can decrease the peak-to-peak variations of noise.
- 129. 128 Other Components Figure 49 Sweep Generator Frequency IF Gain CRT Display Local Oscillator RF Input Attenuator
- 130. 129 • The local oscillator is a Voltage Controlled Oscillator (VCO) which in effect tunes the analyser. • The sweep generator actually tunes the LO so that its frequency changes in proportion to the ramp voltage. • This also deflects the CRT beam horizontally across the screen from left to right, creating the frequency domain in the x-axis. • The RF input attenuator is a step attenuator located between the input connector and the first mixer. It is also called the RF attenuator. • This is used to adjust the level of the signal incident upon the first mixer. • This is important in order to prevent mixer gain compression and distortion due to high-level and/or broadband signals. • The IF gain is located after the mixer but before the IF, or RBW, filter. • This is used to adjust the vertical position of signals on the display without affecting the signal level at the input mixer. • When it changed, the value of the reference level is changed accordingly. • The IF gain will automatically be changed to compensate for input attenuator changes, so signals remain stationary on the CRT display, and the reference level is not changed. The Auxillaries
- 131. 130 How It All Work Together Figure 50 IF Filter Detector Input Mixer Local Oscillator CRT Display Sweep Generator 0 1 2 3 4 5 6 3.6 6.5 0 1 2 3 𝑓s Signal Range LO Range 3 4 5 6 3.6 6.5 𝑓LO GHz 0 1 2 3 A 𝑓 GHz GHz 𝑓LO − 𝑓s 𝑓s 𝑓LO 𝑓LO − 𝑓s 3.6 𝑓IF
- 132. 131 • First of all, the signal to be analyzed is connected to the input of the spectrum analyser. This input signal is then combined with the LO through the mixer, to convert or translate it to an intermediate frequency (IF). • These signals are then sent to the IF filter. • The output of this filter is detected, indicating the presence of a signal component at the analyser’s tuned frequency. The output voltage of the detector is used to drive the vertical axis (amplitude) of the analyser display. • The sweep generator provides synchronization between the horizontal axis of the display (frequency) and tuning of the LO. The resulting display shows amplitude versus frequency of spectral components of each incoming signal. • The horizontal arrows are intended to illustrate the "sweeping" of the analyser. Starting with LO at 3.6 GHz, the output of the mixer has four signals, one of which is at 3.6 GHz 𝑓LO .
- 133. 132 • IF filter is also at 3.6 GHz (it’s shape has been imposed onto the frequency graph for clarity). Therefore, we expect to see this signal on the display. At 0 Hz on the CRT, we do indeed see a signal - this is called “LO Feed through”. • Sweep generator moving to the right, causes the LO to sweep upward in frequency. As the LO sweeps, so two will three of the mixer output signals (the input signal is stationary). • As the LO Feed through moves out of the IF filter bandwidth, we see it taper off on the display. As soon as the difference frequency 𝑓LO − 𝑓S comes into the envelop of the IF filter, we start to see it. • When it is at the center (e.g. 3.6 GHz) we see the full amplitude of this signal on the display. • And, as it moves further to the right, it leaves the filter envelop, and no signal is seen on the display. • The signal is being swept through the fixed IF filter, and properly displayed on the analyser screen.
- 134. 133 Figure 51 Front Panel Operation Primary Functions (Frequency, Amplitude, Span) Softkeys Control Functions (RBW, Sweep Time, VBW) RF Input Numerical Keypad
- 135. References 134 (1) Chaniotakis and Cory, Introduction to Electronics, Signals and Measurement, Massachusetts Institute of Technology, 2006. (2) A. V. Bakshi and U. A. Bakshi, Electronic Measurements and Instrumentation, 2008. (3) Anritsu, Vector Network Analyser Primer, Application Note, 2009.