Chapter 2 Aspects of Technology

Transcription

1 Chapter 2 Aspects of Technology Now that we have covered some elements of physics in Chapter 1 we can continue with our survey of basic concepts by touching on a number of topics from analog electronics. We concentrate here on describing the large-scale technology of circuit elements, on how they are constructed. We review what is meant by an analog waveform, an analog filter, the transistor amplifier and the operational amplifier. We shall see how a transistor or an operational amplifier can be used as a gate, in preparation for our discussion of digital electronics in Chapter 3. Energy Sources The Chemical Cell The most common small-scale source of electrical energy is the chemical cell. Chemical cells are constructed from various materials, usually of two chemically dissimilar substances, called a cathode and an anode, separated by a liquid or a paste medium called electrolyte. The anode serves as a source of electrons which are driven by chemical action through the electrolyte to the cathode. Thus the anode takes on a positive potential, the cathode a negative potential. An example is the carbon-zinc type whose internal structure is drawn in Figure 2-1. intended. Cells are connected in series and in parallel to form batteries of 9 volts, 12 volts etc., capable of delivering various currents (Figure 2-2). Figure 2-2. At the top are shown common consumer type chemical cells of 1.5V. The batteries (bottom) of 6 and 9V consist of two or more cells connected in series or in parallel and encapsulated in a single convenient container. Figure 2-1. Internal structure of the carbon-zinc cell. A chemical cell is designed to produce an electromotive force (emf) of 1.5 volts and to have a size and a shape appropriate to the device for which it is Cells and batteries are designed to have a charge capacity expressed in ampere-hours (Ah) or milliamperehours (mah). Capacities for typical cell types are listed in Table 2-1. The larger the current drawn from a battery the shorter is its lifetime. Charge capacity is roughly related to the amount of chemical mass in the cell and therefore indirectly to the cell s volume. A cell for a digital watch or a hearing aid might be tiny whereas a battery in a nuclear submarine might be as large as an average refrigerator. Research is being 2-1

2 carried out in major corporations like Union Carbide, Sony and others to produce cells of ever-increasing capacity and lifetime. 1 Table 2-1. Charge Capacities of Some Cell Types. 2 Type Description Elements Capacity D Gen Purpose Carbon-Zn 1500 C Gen Purpose Carbon-Zn 700 AA General Carbon-Zn 300 AAA Heavy Duty Zn Chloride 120 Example Problem 2-1 Cell Lifetime Ordinary flashlights use D cells. A fresh D cell has a typical charge capacity of 1500 mah. If 25 ma are drawn from the cell continuously, how long in hours should the cell last? Solution: The number of milliampere-hours can be written I x t, where I is in ma and t is in hours. Thus t = 1500 ma-hours/25 ma = 60 hours. The D cell should be expected to last 60 hours. solar cell has a lifetime that, in principle, is infinite. The physics of the silicon solar cell is basically the physics of the PN junction diode that we have discussed in Chapter 1. We shall concentrate here on the practical uses of the cell as an alternative source of power and the practical details of its power output for various light and load conditions. Each silicon solar cell (Figure 2-3) can convert solar energy directly into electrical energy by a process called photovoltaic conversion. Essentially a large-area PN junction diode, the cell is made from two pieces of silicon fused together. One piece is doped so as to yield an excess of free electrons (N type) while the other is doped so as to yield a deficiency of free electrons or an excess of holes (P type). One layer of the cell is made thin enough to enable photons of light to penetrate to the junction and there to interact with free electrons. A free electron, in absorbing a photon, acquires enough energy to take part in electrical conduction. This means that the number of minority charge carriers in each semiconductor type increases holes in the P-material and free electrons in the N- material. These carriers, if they reach the junction before recombining, cross the junction in response to the cross-junction electric field. Once across the junction they are free to move through an external circuit and deliver power to a load. The Power Supply Next to the chemical cell the most common source of electrical energy in a laboratory is a power supply. Basically, a power supply converts the input from the mains at 110 V AC to some DC voltage at a (possibly variable) DC current. One such instrument you will use in this course is the Agilent Model E3640A programmable power supply. This supply can be made to function as a voltage source or as a current source. More details on this instrument can be found in Appendix A. The Solar Cell The solar cell is a less common source of electrical energy than is the chemical cell, though its importance increases daily. Many hand calculators used by students today are powered by solar cells. In contrast to the chemical cell, the solar cell, by its name, derives energy not from the dissociation of chemicals, but from sunlight or the ambient light in buildings. The 2-2 metal annular ring metal base plate P-TYPE SILICON N-TYPE SILICON electrodes Figure 2-3. The disk-shaped silicon solar cell. A single cell is typically able to deliver about 0.5 volt to an open circuit (called the open circuit voltage V OC ) and a certain maximum current to a shorted load (called the short circuit current I SC ). To form a practical power source, a number of cells must be connected in series to form arrays with voltage outputs of 6, 9, 12 volts, and so forth, and in parallel to give a desired

3 output current. Most arrays have a flat geometry, consistent with the need to capture maximum sunlight. Some are fabricated on a glass substrate and are fragile while others are made on a metallic backing and are flexible, enabling them to be bent into convenient shapes and to be used in demanding applications as in pleasure boats and spacecraft. Connecting a solar array to a circuit is simple you connect the array to the circuit with two wires. Though we have described a silicon solar array as a power source, the power it can deliver is relatively low; it is therefore not often used in a stand-alone way. Most often it functions as a trickle charger for a higher-power primary source like a lead-acid battery or a gell-cell. Under normal conditions the battery supplies power to the main load (house wiring, etc) and is independent of the array. When convenient (during periods of non-usage), the battery is recharged by being disconnected from the main load and connected to the array. Silicon solar arrays are commonly described by three parameters: the maximum power, P MAX, they can deliver to a load of a common type (like a lead-acid battery), the open circuit voltage, V OC, and the short circuit current, I SC. These parameters are quoted for the array for one full sun, which is the illumination received in an outdoor position on the equator at high noon on a summer day. IV Characteristic of a Solar Cell Many of the properties of a silicon solar cell or array are described by its IV characteristic curve (Figure 2-4). Aspects of Technology This curve is obtained by connecting the array to a load resistor and then graphing I as a function of V as the resistance is changed. You can see that as the load resistance increases the output current decreases. Superimposed on the figure is the output power P (the product of I and V). P goes through a maximum for a certain V and therefore also for a certain resistance R. R is equal to the array s internal resistance. Thus maximum power is obtained from an array when it is connected to a load whose resistance is equal to the internal resistance of the array. The Selenium Photocell The selenium photocell functions in practice much like a solar array in that it converts solar energy into electrical energy. The advantage of selenium photovoltaic cells over other cells is that their response is very close to that of the human eye. Their efficiency as energy converters of the total spectrum is not as high as other photocells, and so they are not used as sources of energy as are solar cells. Figure 2-5 shows the cross-section of an idealized barrier-layer selenium photocell. The steel support plate A provides the rear (positive) contact, and carries a layer of metallic selenium B, which is a few hundreds of a millimeter in thickness. C is a thin transparent electrically-conductive layer applied by cathodic sputtering; it is reinforced along its edge by a sprayed on negative contact ring D and protected from damage by lacquering. The rear support of the photocell is protected from corrosion by a metallic spray coating E ; this also improves electrical contact Output Current (ma) Short Circuit Current Isc Open Circuit Voltage Voc Output Voltage (V) Maximum Power Figure 2-4. A typical IV characteristic for a solar cell (or array) subject to some level of illumination. The power goes through a maximum in the knee region of the current Output Power (mw) A B C D E Figure 2-5. Cross-section of a selenium photocell. This kind of photoelectric cell is used chiefly for light meters, exposure meters, and other devices involving light. They are usually specified by curves of closedcircuit current versus illumination in lux. 2-3

4 The Thermocouple A thermocouple is a junction of two dissimilar metals, like copper and constantan, that produces an open circuit voltage that depends on the temperature. The effect is called the thermoelectric or Seebeck effect, named after Thomas Seebeck who discovered it in The voltage, though small, is measurable with a highquality digital multimeter, or if amplified by a signal conditioner or amplifier. Thermocouples, being made of wire, are very rugged and inexpensive and can operate over a wide range of temperature, and also to a high temperature. Since the Seebeck voltage is so small, a thermocouple is impractical for use as a source of electrical energy; but as a temperature sensor it works very well. In general, the emf V is observed to depend nonlinearly on temperature T. However, if the temperature change T is small enough then V follows a linear relationship Figure 2-6. Response curves for various thermocouple combinations. Some are more common than others, for example, CR-AL, Fe-CN, and Cu-CN. V = s T, [2-1] where T is the temperature difference between the junction temperature and a reference temperature and s is the Seebeck coefficient (temperature coefficient) of the particular thermocouple combination. Many different thermocouple combinations have been found to be useable in this way (Table 2-2). A combination is chosen for its sensitivity (temperature dependence) and temperature range (Figure 2-6). Table 2-2. Standard Thermocouple Types and Useful Temperature Ranges. Letter Designation Metals Approx Temp Range ( C) Type K Chromel/Alumel 200 to 1250 Type J Iron/Constantan 0 to 750 Type T Copper/Constantan 200 to 350 Type E Chromel/Constantan 200 to 900 Type S Pa/Pa 10% Rhodium 0 to 1450 Type R Pa/Pa 13% Rhodium 0 to 1450 Of all of these combinations types K and J are the most used in undergraduate science laboratories. You will likely be using a type K in this course. If you do use a thermocouple to measure temperature you must take special precautions to provide a temperature reference and to calibrate the combination correctly. Alternatively, you can use a thermocouple with a special signal conditioner. These issues we postpone for Chapter 6. Piezoelectricity When certain crystalline materials (such as Rochelle salt or quartz) and ceramics (such as barium titanante) are deformed, a voltage develops across them. This phenomenon is called the piezoelectric effect. The force or pressure on a piezoelectric material produces a voltage that is directly proportional in sign and magnitude to the applied stress. Common piezoelectric devices are the buzzer and pressure sensor. We discuss these further in Chapter

5 Resistors Arguably, most resistors to be found in consumer electronic devices today are made from semiconductor materials and exist in the form of monolithic integrated circuits (ICs). A treatment of the subject would take us into areas of technology and engineering that lie beyond the intended scope of these notes. 3 We confine our attention here to discrete large-scale resistor types that you might encounter in a research project in the science lab. Carbon Composition Type A large-scale discrete resistor can be made from virtually any conductor, from copper to carbon. However, most resistors are fabricated from a section of wire cut to a certain calculated length or an amount of carbon compressed to a certain shape and dimension, cylindrical being the most common in consumer electronics. A cut-away view of the carbon composition type is drawn in Figure 2-7. ten. The fourth band gives the manufacturer s tolerance. The tolerance is the manufacturer s estimate of the uncertainty in the resistance, based on quality control employed at the factory. An example in reading a color code is given in Example Problem 2-2. Example Problem 2-2 Reading a Color Code A resistor has color bands in the order: grey, red, yellow and silver. What is the resistance? Solution: The numbers corresponding to the colors are: 8, 2, 4 and 10%. According to the code the resistance is: (82 x 10 4 ± 10%) ohms. Figure 2-7. A cutaway view of a carbon composition resistor. Color Code The resistance value of a carbon composition resistor is indicated by a color code painted in four bands on the resistor s body (Table 2-3). Table 2-3. Resistor Color Code Bands 1, 2, 3 Band 4 Black 0 Green 5 Gold 5% Brown 1 Blue 6 Silver 10% Red 2 Violet 7 No Color 20% Orange 3 Grey 8 Yellow 4 White 9 Beginning with the band closest to one end of the resistor, they give, respectively, the first significant digit, the second significant digit, and the multiple of In this example the manufacturer guarantees that if the resistance is measured with a reputable instrument, the result will fall within ±10%, or ±8 x 10 4 Ω, of the value specified by the color code. Resistors of 1 % and 0.5 % tolerance are available at higher cost. Power Rating A resistor can transfer only so much heat to the surrounding air at room temperature before undergoing an unacceptable change in resistance. Carbon composition resistors are rated as to the maximum power they can dissipate without the resistance drifting outside the tolerance range. The ratings most commonly available off the shelf are 1/8, 1/4, 1/2, 1, 2, 5, and 10 watts. The rating is largely a factor of the resistor s volume and surface area (Figure 2-8). The larger the surface area the greater the power dissipation. Should a manufacturer s rating be exceeded a resistor can heat up sufficiently to selfdestruct. Forced air cooling increases the effective power dissipation. Higher-power resistors are also available, though they are not often called for in modern low power 2-5

6 devices. These resistors are nearly always wirewound and have a large surface area. Other types of resistors are the carbon film and metal film types that are designed to produce low levels of electrical noise. Much research is under way to develop smaller, stabler and electrically quieter resistors from new materials. 2 W 1 W 1/2 W 1/4 W Figure 2-8. Examples of resistors having the same resistance but different body sizes and power ratings. this case the fast-blow fuse provides a better measure of protection. The functionality of higher-power fuses is effected by devices called circuit breakers. Temperature Dependence of Resistance The resistance of many materials is observed to depend on temperature in a way that can be described by the following empirical function: R T 2 = R T1 [ 1 +α( T 2 T 1 )], [2-2] where T 1 and T 2 are temperatures. The proportionality factor α is called the temperature coefficient of resistance. α is a characteristic of the material of which the resistor is made and varies between about 2 x 10 2 C 1 and 2 x 10 5 C 1 for various materials (Table 2-4). Notice that all of the coefficients listed in the table are positive with the exception of carbon. This means that as the temperature increases, the resistance of carbon decreases. The Fuse A fuse (Figure 2-9) is a resistor that is actually a safety element placed in series with a device to protect it from electrical and/or heat damage. It can be found in nearly every consumer electronic device as well as in the AC mains. Table 2-4. Temperature Coefficients of Various Materials. Material Coefficient Nickel 6.7 x 10 3 Copper 4.3 x 10 3 Silver 4.1 x 10 3 Iron 4.0 x 10 3 Platinum 3.9 x 10 3 Mercury 9.9 x 10 4 Carbon 7.0 x 10 4 Figure 2-9. Two types of fuse, fast and slow blow. The active element in a fuse is usually a metal strip, which is designed to melt if certain conditions are exceeded. If the strip melts, the circuit is opened and the device in series with the fuse is protected from electrical damage. Fuses are rated according to current and voltage, though it is the power delivered the fuse element that heats it to the melting point. Fuses are categorized as of the slow-blow or fastblow variety. The fast-blow variety is the quicker reacting of the two. Sensitive equipment can sometimes be damaged if the fuse rating is exceeded only briefly. In Platinum Resistance Thermometer (PRTD) The resistance of any material depends on temperature. This means that any material can, in principle, serve as a temperature sensor. If the resistance can be accurately measured and if the material s α value is known, then the temperature can be calculated. Alternatively, for a special material like platinum, the temperature can be obtained from standard tables of resistance (see the file PRTD.dat). This is the theory of operation of the Platinum Resistance Temperature Detector (PRTD). Platinum is a metal ideally suited for the sensing of temperature because its resistance is stable and repeatable at high temperatures and in harsh environ- 2-6

7 ments. We shall return to this subject in Chapter 6. The Thermistor A thermistor is in essence a thermal resistor, a resistor whose resistance changes with temperature more dramatically than is adequately described by eq[2-2]. For example, the resistance-vs-temperature response of a typical commonly-available thermistor, the Radio Shack type # , is shown in Figure T (degc) Thermistor Type RS# where T is the absolute temperature, R is the resistance and A, B and C are constants to be determined in a curvefit process. We discuss the thermistor in more detail in Chapter 6, along with the fitting of eq[2-3] in Appendix F. The Strain Gauge The strain gauge, as its name implies, is a device for measuring strain. The strain is determined from the change that occurs in the device s resistance. It is in essence a long section of wire firmly fixed to a support (Figure 2-11). If the support is bent or strained then the wire element is stretched a small amount, causing its resistance to change (in accordance with eq[1-3]). Since the change in resistance is very small, the strain gauge is almost always used in conjunction with a null-detection circuit involving a Wheatstone bridge (described below). We shall return to the strain gauge in Chapter R (Ohms) Figure Resistance vs temperature of a Radio Shack # thermistor. Thermistors are made from a variety of materials, that include evaporated films, carbon or carbon compositions, ceramic-like semiconductors of oxides of copper, cobalt, manganese, magnesium, nickel, titanium or uranium. Thermistors can be molded or compressed into various clever shapes to fit a wide range of applications. These devices have a resistance change characteristic of 4 to 6%/ C with generally a negative temperature coefficient (NTC). Thermistors made of barium or strontium titanate ceramics have a positive temperature coefficient (PTC). As can be seen from Figure 2-10, the resistance of a thermistor depends on temperature in a highly nonlinear way. The dependence can be approximated empirically by the so-called Steinhart-Hart equation: 1 T = A + Bln R ( ) + C ln( R) ( )3, [2-3] Figure Structure of a strain gauge. The Photoresistor A broad range of materials have a resistance that depends on the intensity of light falling on them. The most well-known examples are cadmium sulphide (CdS) and cadmium selenide (CdSe). The composition of a cadmium sulphide photocell, deliberately designed to exploit this property is illustrated in crosssection in Figure

8 Ohmic contact λ Active region (photoconductive material) Ohmic contact Figure Construction of a CdS photocell and its circuit symbol. λ The Voltage Divider One application of resistors connected in series is the voltage divider (Figure 2-14a). In the figure, a voltage source is shown connected across three series resistors (any number of resistors greater than one would suffice for our argument). The node between each resistor is connected to a terminal of a rotary switch. By manually positioning the switch on the terminals A, B, or C three fractions of the applied voltage V can be made to appear as the output voltage V out. The resistance R of a CdS photocell is observed to depend on light intensity according to an empirical relationship of the form: B A R = R o I K, [2-4] where R o (Ω) is a constant, I (fc) is the intensity of light and K is a constant which is less than 1. Figure 2-13 shows the resistance of a cell with R o = 2000 Ω and K = 0.75 plotted on a log-log graph. Clearly, this kind of dependence makes the CdS cell an obvious sensor of light intensity. We shall return to this device in Chapter 6. V V R 2 R 3 C Vout Vout (b) (a) CdSPhotocell.dat Figure A voltage divider activated by a rotary switch (a) and a voltage divider in the form of a potentiometer (b). Resistance (Ω) Intensity (fc) Figure Log-log plot of resistance vs light intensity for the Radio Shack type CdS photocell. When the switch is at A, V out = V, and when at B, V out = and when at C, V out = R 2 + R 3 + R 2 + R 3 V, R 3 + R 2 + R 3 V. This divider gives discrete values of V out. If continuous values are desired then a special, variable, resistor called a potentiometer may be substituted (Figure 2-14b and 2-15). The potentiometer is equipped with a wiper, indicated by the arrow (connected to the center tap in Figure 2-15), that can be moved continuously over a carbon 2-8

9 element or a series of closely-spaced wire windings. In this way more precise values of V out can be chosen than is possible with the rotary switch. The potentiometer was in fact widely used as an audio volume control in legacy consumer electronics. Similar devices called potentiometer actuators are used as position sensors in robotics (discussed in more detail in Chapter 6). Aspects of Technology The Current Divider Two resistors connected in parallel (Figure 2-16) form a current divider. It is useful to have a formula for I 1 or I 2 in terms of the input current I. I 1 R 2 I I 2 + V Figure Two resistors connected in parallel. Let us solve for I 1. The same voltage V that appears across the resistor combination appears across. Thus we can write V = I R 2 + R 2 = I 1, Figure Examples of potentiometers, a single (top) and dual (bottom). The center tap of each set of three pins connects to the wiper. These controls are largely obsolete. Example Problem 2-3 Voltage Divider A circuit like the one shown in Figure 2-14 has a source of 10 V and two resistors in series, = 100 Ω and R 2 = 200 Ω. What is the voltage drop across R 2? Solution: According to the treatment of the previous section the voltage is given by V 2 = R 2 + R 2 x10v = =6.67 V. 200Ω 100Ω+ 200Ω x10v so that I 1 = I R 2 + R 2. [2-5] This circuit enables us to obtain the current we desire, I 1, from an available current I. Example Problem 2-4 Current Divider In the circuit shown in Figure 2-16, you are given that I = 1 A, and R 2 are 100 Ω and 200 Ω respectively. What is the current through? Solution: According to eq[2-5], I 1 = R x1 = + R x1 =2/3 A. The available current is 1 ampere, but only 2/3 ampere flows through. 2-9

10 The Wheatstone Bridge A Wheatstone bridge is a diamond shaped arrangement of resistors (Figure 2-17). V a R1 R2 A Rv Rx Figure A Wheatstone bridge. A Wheatstone bridge has desireable electrical properties and is found in a number of sensor circuit designs. R1 and R2 are usually fixed resistors, often of high precision, which are mounted on the sensor board itself or in the controlling electronics. Rx is the sensing element or unknown in the form of a thermistor, a strain gauge, or other resistance sensor. Rv is a resistor whose resistance can be varied. This b circuit must be used with a voltage source and an instrument whereby the voltage (or the current flow) between points a and b can be measured. Often the circuit is employed as a null detector, that is, Rv is varied until the ammeter connected between a and b reads zero. The sensitivity of the bridge is thus a function of the sensitivity of the ammeter, and therefore can be quite high. You should be able to show that if the reading on the ammeter is zero (when the bridge is said to be balanced) then the following relationship between Rx and Rv applies: Rx = R2 R1 Rv. [2-6] Thus if the bridge is balanced by varying Rv, then the unknown Rx can be calculated. Wheatstone bridges are often used with sensors (such as the strain gauge discussed earlier) which produce a very small change in a sensed variable. This very small change then results in a deviation from the null condition which, if the ammeter is sensitive enough, is easily detected and to high precision. Capacitors For reasons of space, we restrict our attention to large-scale non-ic capacitor types. General As we have seen in Chapter 1 a capacitor is modelled as a set of parallel metal plates. Practical large-value, capacitors are made by sandwiching a dielectric between two thin metal plates and then rolling the assembly into a tubular shape (Figure 2-18). Figure A fixed-value tubular capacitor. The dielectric can be of almost any non-conductive material, paper, plastic, oil, glass or even air. A capacitor s capacitance value is often printed on the capacitor s body. Specifications Capacitors, like resistors, are categorized in a number of different ways: for example, the frequency and voltage range over which they are to be used, whether they are of polar or non-polar type (more on this below), and the materials of their manufacture. Generally, a capacitor is used either in a power application at low frequencies (60 Hz), in an audio frequency application ( 20 khz) or a radio frequency application (MHz region). The capacitor used in the smoothing section of a power supply is of a large value (greater than 1 µf) and is often of the polar or 2-10

11 electrolytic type. Non-polar capacitors with values of order to 0.01 µf are usually used at audio frequencies, and capacitors with values less than µf are usually used at radio frequencies. This usage is largely determined by the capacitor s impedance (Chapter 1). Polarized Capacitors Power or electrolytic capacitors made from aluminum and tantalum are polarized. This means that the polarity markings on the capacitor s body must be Aspects of Technology observed when placing the capacitor into a circuit. The positive terminal of the capacitor must be connected to the higher potential in the circuit. If this is not observed, the capacitor may break down. Also, a polarized capacitor requires a polarizing (DC) voltage and cannot withstand a reverse current; it cannot be used in a situation in which a DC voltage is absent and/or in which an existing AC voltage reverses the capacitor s polarity. All other capacitor types are nonpolar. More details on capacitors are listed in Table 2-5. Table 2-5. Fact sheet on commonly-used non-ic capacitors. TYPE TYPICAL VALUE RANGE Aluminum Electrolytic , 000 µf TYPICAL TOLERANCE 10 % % APPLICATIONS & CHARACTERISTICS Power-supply filtering, bypass, coupling. Used where large values are needed. Tantalum Electrolytic µf 5-20 % Bypass, coupling, decoupling. Very stable, long life Ceramic 1pF µf 5-30 % Transient decoupling, bypass. Value changes with frequency and temperature. Mica 1 pf - 1 µf 1-30 % Timing, Oscillator, and AF circuits. Very stable. Polypropylene 1 pf - 10 µf 2-10 % Blocking, bypass, coupling, and timing circuits. Filter, noise suppression. Good for audio through UHF. Polyester (Mylar) µf 5-20 % Blocking, filtering, transient suppression. Good for audio. Small size with medium stability. Paper µf % General purpose. Large size, low cost, medium stability, and poor moisture characteristics. Polystyrene 51 pf µf 1-5 % Timing and tuned circuits. Small capacitance change with temperature. Excellent stability. Good in audio circuits. Capacitors in Sensors A few words are in order about the use of capacitors as sensing elements. One clever example is the patented Humicap sensor manufactured by Vaisala Inc. (Figure 2-19) for measuring relative humidity. The basic principle of humidity measurement is the same in both the HUMICAP and INTERCAP sensors. The dielectric in these sensors is a thin polymer film that either absorbs or exudes water vapour as the relative humidity of the ambient air rises or falls. Figure The Vaisala Humicap humidity sensor. 2-11

12 As the dielectric constant of the capacitor changes so does the capacitance. The capacitance is measured by the electronics of the instrument and converted to a humidity reading. We have a few more details on this type of sensor in Chapter 6 since it is used in the UTSC weather station. Inductors We confine our attention here to large-scale non-ic types of inductors. Inductors, Chokes and Coils An inductor is modelled as a coil of wire wound on a support or a form (Figure 2-20). The form may be of magnetic material, non-magnetic, or even non-existent (the inside of the coil being air). You may recall from Chapter 1 that the interesting property of an inductor is its inductance. Inductance is the property responsible for producing an emf across the coil when the current through the coil is made to change with time. Figure An inductor of the simplest geometry is one that is wound on a circular toroidal shaped form. Because of its efficiency, this kind of inductor with an iron form is commonly used in the low pass filter section of the power supplies of high quality audio amplifiers. Specifications published for inductors usually give the Q value, test frequency, and current rating. The Q value indicates how sharp the response of the coil is when resonating at the test frequency. The current rating is the amount of current the wire making up the coil can safely carry without self-destructing. (The wire making up the coil can be of various gauges.) Inductor Forms The type of form on which a coil is wound affects a coil s inductance and frequency response. Iron forms or cores are used at low frequencies (up to 100 khz). Coils used at frequencies up to 30 MHz are usually space-wound (air core) or wound on cores made of ferrite (iron filings epoxy-bound). Coils used above 30 MHz are usually wound on non-ferrous materials such as brass or copper to minimize power losses to eddy currents. Two iron core types are illustrated in Figure The terms inductor, choke, and coil are often used interchangeably in electronics jargon. But an inductor called a coil is usually intended to resonate or peak at a certain frequency, while a choke is intended to attenuate (i.e., choke ) a group of frequencies (Figure 2-21). (For the meaning of these terms see the discussion of the filter later in this chapter.) Figure A selection of inductor types: chokes (top) and iron cores (bottom). Figure Examples of chokes and coils. 2-12

13 The Transformer A transformer is a special type of inductor consisting of two coils. The coils are wound close together but in such a way as to be electrically insulated from each other. One coil is called the primary winding, the other the secondary. The normal use of a transformer is to obtain a desired AC voltage across the secondary from an available AC voltage applied across the primary. A transformer works in this way because of an effect called mutual induction. If the two coils are close enough together the magnetic flux produced by the current in coil 1 passes through coil 2 and vice versa. Thus a changing current in coil 1 induces an emf across coil 1 and across coil 2. In order for mutual induction to occur a means must exist to enable the flux produced by the current in coil 1 to pass through coil 2. This is called flux linkage. Linkage is achieved by placing the coils close together, by interleaving the coils (winding them together) or by using a closed loop of some magnetic material like iron to guide the flux. The diagram of a toroidal core transformer is drawn in Figure 2-23a. The circuit symbol for a transformer is drawn in Figure 2-23b. v 1 Primary Coil 1 n 1 i 1 Secondary Coil 2 n 2 magnetic material for flux loop i 1 L source v 1 v 2 load L 1 B L 2 n 1 n 2 L 2 v 2 mean that the coils are wound in the same sense, i.e., clockwise or counterclockwise Figure An ideal transformer (a) is given the circuit symbol (b). i 2 + (a) (b) Aspects of Technology The Transformer Equation A working relationship exists between the AC voltages appearing across the primary and secondary windings of an ideal transformer. (An ideal transformer is one in which no energy is lost to heat.) If v 1 and v 2 are the voltages developed across primary and secondary, and if the windings have n 1 and n 2 turns of wire, respectively, then it can be shown that v 2 = n 2 n 1 v 1. [2-7] If n 2 /n 1 is greater than 1 then v 2 is greater than v 1, i.e., the voltage across the secondary exceeds the voltage across the primary thus the source of the name transformer. This kind of transformer is called a step up transformer. If n 2 /n 1 is less than 1 then v 2 is less than v 1 and the situation is reversed; the transformer is a step down type. As we have stated, a transformer is placed in a circuit to obtain a desired AC voltage from an available one. The most commonly available AC voltage is the 115 volts supplied by the AC mains. Transformers are therefore the first stage in most consumer devices that obtain their power from the mains. As well, the AC mains voltage is derived from high-voltage lines with step down transformers. This topic in high power is beyond the intended scope of these notes. Transformers are very non-ideal devices; because of eddy current losses, they tend to lose energy to heat and they tend to distort current waveforms. They are therefore to be avoided in modern circuit designs wherever possible. Indeed, in modern low-power mostly digital consumer devices they are rarely to be seen at all. Example Problem 2-5 Transformer A transformer like the one shown in Figure 2-23 has its primary connected to the 115V AC mains. If the number of turns in the primary and secondary are 1000 and 500, respectively, what is the voltage to be expected across the secondary? Solution: According to the treatment of the previous section the voltage is given by 2-13

14 V sec ondary = n sec ondary n primary x115v = x115v = 57.5 V. The transformer is a step-down type. The Inductor in Sensors An inductor is often part of a sensor whose function is to count something. An example is the rain gauge (discussed in more detail in Chapter 6). The active element in a rain gauge is a spoon or a cup in which the rain drops. The handle of the spoon is balanced on a pivot so that once the spoon fills with water it tips out. A magnet is attached to the handle end of the spoon. As the spoon tips the magnet comes into contact with the end of an inductor. The inductor s inductance rises suddenly, causing a change to occur in the emf across the inductor. This brief change of emf is registered as an electrical pulse which is then counted. An Analog Waveform Revisited In a science lab an analog waveform can be produced by a signal generator (Figure 2-24). By analog waveform is meant a waveform that is a continuous function of time. An analog waveform has the property that at any instant of clocktime it has a definite value of displacement or voltage. Or in other words, between any two clocktimes it has an infinite number of displacement or voltage values. Most waveforms we encounter in our everyday lives are analog in nature. The sounds that we hear with our ears are continuously-varying waves of air pressure. The voltage signal we obtain from the wall sockets in our homes and labs is an analog waveform. The real world is arguably an analog one. From its beginning, analog electronics was focussed on the issues of routing an analog signal from one point to another in a circuit without distorting the signal in any way, that is, by introducing changes in amplitude or phase. The difficulties achieving this to the satisfaction of the consumer was one of the things to drive the digital revolution in the audio industry. The waveform we have chosen here as an example is a pure sinusoid, a special case. Analog waveforms may in general consist of a number of superposed sinusoids, in other words, a number of components. One example of a waveform consisting of the superposition of 1 khz and 2 khz components is shown in Figure Audio waveforms that we hear every day consist of a wide range of frequencies and amplitudes, all changing in complicated ways with time. Figure The output from a signal generator has an analog waveform. 4 Figure A waveform consisting of two component waveforms of frequency 1 khz and 2 khz. 2-14

15 DTMF A practical application of waveforms consisting of two components, or tones, is in the Dual Tone Multiple Frequency (DTMF) method of conveying information via the telephone line. This application we literally hear every day, every time we use a telephone. In spite of the digital revolution, telephony is an analog medium at heart (because speech is analog?). Digital information (e.g., a telephone number) is sent over a telephone line as a two-tone signal. Each character on the keypad of a telephone has its own combination of two-tone signals (Table 2-6). Dual tones are decoded by special ICs in routing equipment. Some instruments, in particular the Telulex Model SG-100/A signal generator (described in Appendix 1) is equipped with the firmware to perform this decoding. It sometimes happens that when complex waveforms pass through a system some components are modified in amplitude and phase more than others. A system which selectively modifies components of waveforms is called a filter. Filters appear again and again in sensors and signal conditioning circuitry. That brings us to the next section where we examine filters in detail. Aspects of Technology Table 2-6. Dialing Digits and their associated dualtone frequencies. Keypad Character Frequencies Hz and 1336 Hz Hz and 1209 Hz Hz and 1336 Hz Hz and 1477 Hz Hz and 1209 Hz Hz and 1336 Hz Hz and 1477 Hz Hz and 1209 Hz Hz and 1336 Hz Hz and 1477 Hz * 941 Hz and 1209 Hz # 941 Hz and 1477 Hz A 697 Hz and 1633 Hz B 770 Hz and 1633 Hz C 852 Hz and 1633 Hz D 941 Hz and 1633 Hz 2-15

16 The Analog Filter Filters exist in many places in electric circuits, in forms that are intended and those that are not. Any circuit that consists of a resistor and a capacitor, or a resistor and an inductor in close proximity, can serve as an analog filter. A filter is really a frequency selective attenuator, in the sense that it alters the frequency makeup of a waveform by changing the amplitude and/or phase of a range of frequency components of the waveform, leaving other frequency components unchanged. A filter that does not amplify, which we discuss here is called a passive filter. A filter that does amplify is called an active filter. We shall discuss these kinds of filters (called amplifiers) later in this chapter. The Impedance Divider The story of filters begins with the idea of the impedance divider. We have seen in Chapter 1 how a voltage divider can be made from two series resistors. The equivalent in AC circuits is two series impedances Z 1 and Z 2 (Figure 2-26). vin Z1 system Z2 vout Thus dividing eq[2-8b] by [2-8a] we get G = v out v in = Z 2 Z 1 + Z 2. [2-9] G in fact is what is known in mathematics as a complex number. This is because Z 1 and Z 2 are themselves complex numbers (Chapter 1). But if the form of Z 1 and Z 2 are known then G and the phase angle φ can be calculated. Let us consider an example. The RC Low Pass Filter Replacing Z1 in Figure 2-26 with a resistance R and Z2 with a capacitance C, the circuit reduces to Figure The system is called an RC filter. Figure In its most general form a filter can be thought of as an impedance divider. v in R C v out Figure An RC low pass filter. In electronics jargon the circuit is called a four-terminal network. There are four terminals two inputs and two outputs. The circuit can also be regarded as a system (within the dashed rectangle). The input voltage v in is the stimulus applied to the system and the output voltage v out the response. We can quantify this circuit s effect on the input by finding the ratio of the output voltage to input voltage and the phase angle between the two signals. This ratio, which we shall call G, can be measured with a DMM, the phase angle φ with an oscilloscope. The input and output voltages are: v in = i( Z 1 + Z 2 ), [2-8a] and v out = iz 2. [2-8b] In a rigorous mathematical treatment, we would deal with G as a complex number. To avoid this, we bypass the mathematics and simply state the results. The absolute value of G, G, is given by G(ω) = 1 1+ω 2 R 2 C 2, [2-10a] and φ(ω ) = ArcTan( ωrc). [2-10b] These expressions are functions of the angular frequency ω. φ is the angle the output voltage leads the input voltage. To examine the frequency dependence of these functions more carefully, we have plotted 2-16

17 them in log-log graphs (Figures 2-28). With study, the meaning of Figures 2-28 should be evident. Low frequency components of the input signal are transferred to the output without change in amplitude or phase. But high frequency components are both attenuated and phase shifted. This is just the kind of action performed by a filter in this case, a low pass filter. Even if the circuit in Figure 2-27 were, in fact, invisible to you, you could still infer the equivalent circuit from measurements of the responses G(ω) and φ(ω). Let us see in the following example problem how to interpret filter response curves in detail. Gain G Gain vs Frequency Example Problem 2-6 Interpreting the Effect of a Filter on a Signal Applied to it You are given that a signal consists of the sum of sinusoids of 1000 Hz and Hz of equal amplitude. The signal is input to the low pass filter whose response curves are shown in Figures Describe the signal to be expected at the filter s output. Solution: From a study of the curves we can make the following predictions: At a frequency of 1000 Hz, G, the ratio of the output to the input signal, should be about 0.9 φ should be about 0.25 radians ( 14 degrees) At a frequency of Hz, G should be about 0.3 φ should be about 1.25 radians ( 72 degrees) Radians Log Frequency (Hz) Phase Shift vs Frequency Log Frequency (Hz) Figure Plots of G and φ from eqs[2-10] for the RC low pass filter. Here C= 4.7 µf and R = 10 Ω. The conclusion to be drawn is that the 1000 Hz signal should be affected very little by the filter; at the output its amplitude should be reduced by about 10% and retarded in phase by about 14 degrees. The filter s effect on the Hz signal should be greater. The Hz signal should have its output reduced by a factor of 70% and be retarded in phase by 1.25 radians, or approximately 72 degrees. Clearly, the filter should selectively attenuate and phase shift the Hz signal more than the 1000 Hz signal. We have assumed in this discussion that the capacitor is perfectly ideal and therefore dissipates no energy to heat. In a real capacitor, however, some energy will inevitably be lost, meaning that the curves for a real RC filter will deviate to a lesser or greater extent from what is shown in Figures We shall take up this subject again in Appendix C where we show how a computer application can be used to measure G and φ. Our next topic is the subject of diodes. 2-17

18 Diodes We have described in Chapter 1 some of the physics of the semiconductor diode. Diodes are fabricated as a junction of P- and N-type semiconductor materials, with the type of semiconductor determining how the diode is used. Diodes made from germanium and silicon are mostly used as rectifiers and signal detectors. Diodes made from exotic materials such as GaAsP and others are used as light detectors and sources. All diodes are tested by manufacturers and sold with specifications as to the maximum voltage and current they can sustain. Rectifier/Signal Diodes Diodes designed for rectification or signal detection purposes are made of germanium or silicon and packaged much like resistors but without the color code. The body is commonly black and of a size consistent with the current-handling capability (larger size for larger currents). The cathode end of the body is usually indicated by a rounding of the body or by a band. A selection of specifications for a few of these diode types is listed in Table 2-6. The peak inverse voltage (PIV) is the maximum reverse voltage the diode can sustain without suffering electrical breakdown. The forward current I f is the maximum current the diode can sustain in the forward direction and the forward voltage drop is the corresponding voltage drop across the diode. Table 2-6. Selected specifications for a number of rectifier/signal C that you will most likely encounter in this course. We have included the generic type number (in the form 1N#) and the Radio Shack catalog number where known. Type RS# Description Vmax (V) PIV (V) If max (A) Ir PIV (µa) 1N34 Ge signal Vf AV (V) 1N60 Ge signal N Si rectifier Si rectfier Si rectifier Of the two diode types, the germanium diode has the advantage of an intrinsically lower forward voltage drop (typically 0.3 volts as compared with 0.7 volts for silicon). This low forward voltage drop results in a low power loss and more efficient diode, making it superior in many ways to silicon. This lower voltage drop becomes important in very low signal environments (signal detection from audio to FM frequencies) and in low level logic circuits. The disadvantage of the germanium diode is its larger leakage current for reverse voltages (Figure 1-38). This makes the silicon diode the diode of choice for rectification The Photodiode A special type of silicon diode, related to the solar cell and called a photodiode, is especially designed to detect light. It is usually much smaller than a solar cell, sometimes as small as the head of a pin. A photograph showing a number of photodiode products is reproduced in Figure The photodiode has a very fast response time, often of the order of nanoseconds. It is used reversedbiased. In this mode the current which flows across the junction is linearly proportional to the intensity of the light striking the diode (described in Chapter 1

19 and shown in Figure 1-27). A simple circuit employing a photodiode in a light intensity meter is drawn in Figure Figure A selection of photodiodes. Aspects of Technology diodes are fabricated from semiconductor compounds such as Gallium Nitride, Indium Phosphide (InP), Gallium Phosphide (GaP), Gallium Arsenide (GaAs), and Gallium Arsenide Phosphide (GaAsP). An LED is designed to emit light of a specific color when forward biased, mostly red or green, but sometimes other colors, such as yellow, blue and white. LEDs are used as replacements for incandescent lamps, in indicator devices of all kinds ranging from ON/OFF indicators to large billboard displays in subways. We shall spend a few moments here on the LED because you will be using an LED indicator box in your study of the RS-232 interface (Appendix B). An LED, unlike a rectifier diode, is encapsulated in a transparent covering. When the LED is forward biased by a voltage equal to or greater than the turnon voltage, the diode emits light. Information regarding typical LEDs is given in Figure Specifications for a selection of LEDs are listed in Table 2-7. I LED case LED symbol Figure A simple light intensity meter using a photodiode. As the intensity of the light increases the resistance of the diode decreases and the current detected increases. cathode (a) anode anode Vin (b) cathode In addition to the usual specifications published for diodes, photodiodes are described by a responsivity factor R defined as follows: I = RP, where I is the measured photocurrent (A) flowing through the diode and P is the optical power (W) incident on the diode. R depends on the wavelength. The wavelength response characteristics depend on the material from which the photodiode is made (silicon or other materials), details of the diode fabrication process, and the optical filter, if any, between the light sensor and the active photodiode surface. The Light-Emitting Diode (LED) As its name implies, a light emitting diode (LED) is a PN diode especially designed to emit light. It is relatively inexpensive, efficient, consumes far less power than an incandescent lamp and has a long life. These (c) R LED Figure Information on LEDs, package (a), circuit symbol (b) and circuit (c). The anode of an LED is identified by the longer of the two lead wires (a). An LED can pass only a small current (typically 20 ma) without self-destructing. For this reason an LED is nearly always used with a series current-limiting resistor (c). If Vin is of the order of 6V then the current limiting resistor R should be about 220 Ω. Some LEDs are designed for use with a 5 volt source and have the current limiting resistor built-in. 2-19

20 Table 2-7. Specifications for a selection of C that you will most likely encounter in this course. Type RS# Description Wide Angle red LED Yellow Jumbo LED Vmax (V) PIV (V) If max (A) Vf AV (V) P max (mw) Peak Wavelength (nm) Green LED Amplification We have seen in Chapter 1 that a carbon composition resistor continuously radiates or dissipates heat energy to the surrounding air. Most circuit elements dissipate heat in a similar way including the capacitor and inductor because they all possess some amount of resistance. In other words, capacitors and inductors are not ideal elements. For this reason most circuit designs require some amplification or boosting of voltage, current or power to offset losses of energy. What is an Amplifier? The idea of an amplifier is illustrated in Figure A signal of amplitude V in is applied to a system and has its amplitude increased to a value V out. This process takes energy. The energy is drawn from a source like a battery or a power supply. Amplification should be thought of as a process in which a smaller signal controls a larger signal and not like an image being magnified by a magnifying lens. The amp in the figure can be a transistor or an operational amplifier. peak, or peak-to-peak values. φ is the angle, in radians or degrees, that the output signal leads or lags the input signal. To give an example, Figure 2-33 shows the input and output signals for an amplifier with a gain of 10 and a phase shift of 180 degrees. Vin Energy from supply Vout amp Figure The idea of amplification. An input signal controls the energy drawn from a power supply so as to give rise to an output signal increased in amplitude. Amplifiers are described by the same parameters used for a filter: the gain G and phase shift φ. G is the ratio of the output to input voltages expressed as rms, Figure A screen save from a TekTDS210 digital oscilloscope. At the top is shown the input signal (on CH1) applied to an inverting opamp of the type shown in Figure At the bottom is shown the output (on CH2). The gain is 10 since the ratio of the peak-to-peak values of CH2 to CH1 (5.04V/504mV) is 10 and the phase shift is 180 degrees since the output is inverted with respect to the input. 2-20