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 . We con- centrate 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 and the . We shall see how a transistor or an operational amplifier can be used as a gate, in preparation for our discussion of in Chapter 3.

Energy Sources

The Chemical Cell intended. Cells are connected in series and in parallel The most common small-scale source of electrical to form batteries of 9 volts, 12 volts etc., capable of energy is the chemical cell. Chemical cells are con- delivering various currents (Figure 2-2). structed from various materials, usually of two chem- ically dissimilar substances, called a and an , separated by a liquid or a paste medium called . The anode serves as a source of 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 -zinc type whose internal structure is drawn in Figure 2-1.

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.

Cells and batteries are designed to have a charge capac- ity expressed in ampere-hours (Ah) or milliampere- hours (mAh). Capacities for typical cell types are listed in Table 2-1. The larger the current drawn from Figure 2-1. Internal structure of the carbon-zinc cell. 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 A chemical cell is designed to produce an electro- for a digital watch or a hearing aid might be tiny motive force (emf) of 1.5 volts and to have a size and a whereas a battery in a nuclear submarine might be as shape appropriate to the device for which it is large as an average refrigerator. Research is being 2-1 Aspects of Technology carried out in major corporations like Union Carbide, solar cell has a lifetime that, in principle, is infinite. Sony and others to produce cells of ever-increasing The physics of the silicon solar cell is basically the capacity and lifetime.1 physics of the PN junction that we have dis- cussed in Chapter 1. We shall concentrate here on the Table 2-1. Charge Capacities of Some Cell Types.2 practical uses of the cell as an alternative source of power and the practical details of its power output for Type Description Elements Capacity various light and load conditions. D Gen Purpose Carbon-Zn 1500 Each silicon solar cell (Figure 2-3) can convert solar C Gen Purpose Carbon-Zn 700 energy directly into electrical energy by a process AA General Carbon-Zn 300 called photovoltaic conversion. Essentially a large-area AAA Heavy Duty Zn Chloride 120 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 Example Problem 2-1 an excess of holes (P type). One layer of the cell is Cell Lifetime made thin enough to enable photons of light to pene- trate to the junction and there to interact with free Ordinary flashlights use D cells. A fresh D cell has a electrons. A free , in absorbing a photon, typical charge capacity of 1500 mAh. If 25 mA are acquires enough energy to take part in electrical con- drawn from the cell continuously, how long in hours duction. This means that the number of minority should the cell last? charge carriers in each semiconductor type increases —holes in the P-material and free electrons in the N- Solution: material. These carriers, if they reach the junction The number of milliampere-hours can be written I x before recombining, cross the junction in response to t, where I is in mA and t is in hours. Thus the cross-junction . Once across the junc- t = 1500 mA-hours/25 mA = 60 hours. tion they are free to move through an external circuit The D cell should be expected to last 60 hours. and deliver power to a load.

The 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 metal variable) DC current. One such instrument you will annular ring use in this course is the Agilent Model E3640A pro- grammable power supply. This supply can be made metal P-TYPE SILICON to function as a voltage source or as a current source. base plate N-TYPE SILICON More details on this instrument can be found in Appendix A. Figure 2-3. The disk-shaped silicon solar cell.

The Solar Cell The solar cell is a less common source of electrical A single cell is typically able to deliver about 0.5 volt energy than is the chemical cell, though its importance to an open circuit (called the open circuit voltage VOC) increases daily. Many hand calculators used by stud- and a certain maximum current to a shorted load ents today are powered by solar cells. In contrast to (called the short circuit current ISC). To form a practical the chemical cell, the solar cell, by its name, derives power source, a number of cells must be connected in energy not from the dissociation of chemicals, but series to form arrays with voltage outputs of 6, 9, 12 from sunlight or the ambient light in buildings. The volts, and so forth, and in parallel to give a desired 2-2 Aspects of Technology output current. Most arrays have a flat geometry, con- This curve is obtained by connecting the array to a sistent with the need to capture maximum sunlight. load and then graphing I as a function of V as Some are fabricated on a substrate and are the resistance is changed. You can see that as the load fragile while others are made on a metallic backing resistance increases the output current decreases. and are flexible, enabling them to be bent into conven- Superimposed on the figure is the output power P ient shapes and to be used in demanding applications (the product of I and V). P goes through a maximum as in pleasure boats and spacecraft. Connecting a solar for a certain V and therefore also for a certain resis- array to a circuit is simple—you connect the array to tance R. R is equal to the array’s internal resistance. the circuit with two . Thus maximum power is obtained from an array Though we have described a silicon solar array as a when it is connected to a load whose resistance is power source, the power it can deliver is relatively equal to the internal resistance of the array. low; it is therefore not often used in a stand-alone way. Most often it functions as a trickle charger for a The Selenium Photocell higher-power primary source like a lead-acid battery The selenium photocell functions in practice much or a gell-cell. Under normal conditions the battery like a solar array in that it converts solar energy into supplies power to the main load (house wiring, etc) electrical energy. The advantage of selenium photo- and is independent of the array. When convenient voltaic cells over other cells is that their response is (during periods of non-usage), the battery is very close to that of the human eye. Their efficiency as recharged by being disconnected from the main load energy converters of the total spectrum is not as high and connected to the array. as other photocells, and so they are not used as Silicon solar arrays are commonly described by sources of energy as are solar cells. three parameters: the maximum power, PMAX, they can Figure 2-5 shows the cross-section of an idealized deliver to a load of a common type (like a lead-acid barrier-layer selenium photocell. The steel support battery), the open circuit voltage, VOC, and the short plate “A” provides the rear (positive) contact, and circuit current, ISC. These parameters are quoted for the carries a layer of metallic selenium “B”, which is a few array for one full sun, which is the illumination hundreds of a millimeter in thickness. “C” is a thin received in an outdoor position on the equator at high transparent electrically-conductive layer applied by noon on a summer day. cathodic sputtering; it is reinforced along its edge by a sprayed on negative contact ring “D” and protected IV Characteristic of a Solar Cell from damage by lacquering. The rear support of the Many of the properties of a silicon solar cell or array photocell is protected from corrosion by a metallic are described by its IV characteristic curve (Figure 2- spray coating “E”; this also improves electrical 4). contact.

200 Maximum Power 1600 A B C D 180 1400 160 Short Circuit Current Isc 1200 140 120 1000 100 800 80 600 60 E

400 Output Power (mW)

40Output Current (mA) Open Circuit Voltage Voc Figure 2-5. Cross-section of a selenium photocell. 20 200 0 0 0 1 2 3 4 5 6 7 8 9 Output Voltage (V) 10 11 12 This kind of photoelectric cell is used chiefly for light meters, exposure meters, and other devices involving Figure 2-4. A typical IV characteristic for a solar cell (or light. They are usually specified by curves of closed- array) subject to some level of illumination. The power goes circuit current versus illumination in lux. through a maximum in the “knee” region of the current.

2-3 Aspects of Technology 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 1821. The voltage, though small, is measurable with a high- quality digital multimeter, or if amplified by a signal conditioner or amplifier. Thermocouples, being made of , 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 thermo- couple 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 non- Figure 2-6. Response curves for various thermocouple com- linearly on temperature T. However, if the tempera- binations. Some are more common than others, for example, ture change DT is small enough then V follows a CR-AL, Fe-CN, and Cu-CN. linear relationship

V = sDT , [2-1] Of all of these combinations types K and J are the most used in undergraduate science laboratories. You where DT is the temperature difference between the will likely be using a type K in this course. If you do junction temperature and a reference temperature and use a thermocouple to measure temperature you must s is the Seebeck coefficient (temperature coefficient) of take special precautions to provide a temperature the particular thermocouple combination. reference and to calibrate the combination correctly. Many different thermocouple combinations have Alternatively, you can use a thermocouple with a been found to be useable in this way (Table 2-2). A special signal conditioner. These issues we postpone combination is chosen for its sensitivity (temperature for Chapter 6. dependence) and temperature range (Figure 2-6). When certain crystalline materials (such as Rochelle Table 2-2. Standard Thermocouple Types and Useful Temp- salt or quartz) and (such as barium titanante) erature Ranges. are deformed, a voltage develops across them. This phenomenon is called the piezoelectric effect. The force Letter Metals Approx Temp or pressure on a piezoelectric material produces a Designation Range (˚C) voltage that is directly proportional in sign and mag- Type K Chromel/Alumel –200 to 1250 nitude to the applied stress. Common piezoelectric Type J Iron/Constantan 0 to 750 devices are the buzzer and pressure sensor. We Type T Copper/Constantan –200 to 350 discuss these further in Chapter 6. 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

2-4 Aspects of Technology Arguably, most resistors to be found in consumer electronic devices today are made from semi- conductor 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 ten. The fourth band gives the manufacturer’s toler- A large-scale discrete resistor can be made from virtu- ance. The tolerance is the manufacturer’s estimate of ally any conductor, from copper to carbon. However, the uncertainty in the resistance, based on quality most resistors are fabricated from a section of wire cut control employed at the factory. An example in to a certain calculated length or an amount of carbon reading a color code is given in Example Problem 2-2. compressed to a certain shape and dimension, cylin- drical being the most common in consumer electron- ics. A cut-away view of the carbon composition type Example Problem 2-2 is drawn in Figure 2-7. 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 104 ± 10%) .

In this example the manufacturer guarantees that if Figure 2-7. A cutaway view of a carbon composition resis- the resistance is measured with a reputable instru- tor. ment, the result will fall within ±10%, or ±8 x 104 W, of the value specified by the color code. Resistors of 1 % Color Code and 0.5 % tolerance are available at higher cost. The resistance value of a carbon composition resistor Power Rating is indicated by a color code painted in four bands on A resistor can transfer only so much heat to the sur- the resistor’s body (Table 2-3). rounding air at room temperature before undergoing an unacceptable change in resistance. Carbon compos- ition resistors are rated as to the maximum power Table 2-3. Resistor Color Code they can dissipate without the resistance drifting out- Bands 1, 2, 3 Band 4 side the tolerance range. The ratings most commonly Black 0 Green 5 Gold 5% available off the shelf are 1/8, 1/4, 1/2, 1, 2, 5, and 10 Brown 1 Blue 6 Silver 10% watts. The rating is largely a factor of the resistor’s Red 2 Violet 7 No Color 20% volume and surface area (Figure 2-8). Orange 3 Grey 8 The larger the surface area the greater the power Yellow 4 White 9 dissipation. Should a manufacturer’s rating be exceeded a resistor can heat up sufficiently to self- destruct. Forced air cooling increases the effective Beginning with the band closest to one end of the power dissipation. resistor, they give, respectively, the first significant Higher-power resistors are also available, though digit, the second significant digit, and the multiple of they are not often called for in modern low power 2-5 Aspects of Technology devices. These resistors are nearly always wire- this case the fast-blow provides a better measure wound and have a large surface area. Other types of of protection. The functionality of higher-power fuses resistors are the carbon film and metal film types that is effected by devices called circuit breakers. are designed to produce low levels of electrical . Much research is under way to develop smaller, stabler and electrically “quieter” resistors from new Temperature Dependence of Resistance materials. The resistance of many materials is observed to depend on temperature in a way that can be described by the following empirical function:

RT 2 = RT1[1 +a (T2 – T1 )] , …[2-2] 2 W

where T1 and T2 are temperatures. The proportionality factor a is called the temperature coefficient of resistance. 1 W a is a characteristic of the material of which the resis- tor 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 1/2 W that all of the coefficients listed in the table are posit- ive with the exception of carbon. This means that as 1/4 W the temperature increases, the resistance of carbon Figure 2-8. Examples of resistors having the same resistance decreases. but different body sizes and power ratings.

Table 2-4. Temperature Coefficients of Various Materials. The Fuse A fuse (Figure 2-9) is a resistor that is actually a safety Material Coefficient element placed in series with a device to protect it Nickel 6.7 x 10–3 from electrical and/or heat damage. It can be found Copper 4.3 x 10–3 –3 in nearly every consumer electronic device as well as Silver 4.1 x 10 –3 in the AC mains. Iron 4.0 x 10 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. Platinum Resistance Thermometer (PRTD) The resistance of any material depends on tempera- ture. This means that any material can, in principle, The active element in a fuse is usually a metal strip, serve as a temperature sensor. If the resistance can be which is designed to melt if certain conditions are accurately measured and if the material’s a value is exceeded. If the strip melts, the circuit is opened and known, then the temperature can be calculated. the device in series with the fuse is protected from Alternatively, for a special material like platinum, electrical damage. Fuses are rated according to the temperature can be obtained from standard tables current and voltage, though it is the power delivered of resistance (see the file PRTD.dat). This is the theory the fuse element that heats it to the melting point. of operation of the Platinum Resistance Temperature Fuses are categorized as of the slow-blow or fast- Detector (PRTD). blow variety. The fast-blow variety is the quicker reac- Platinum is a metal ideally suited for the sensing of ting of the two. Sensitive equipment can sometimes be temperature because its resistance is stable and damaged if the fuse rating is exceeded only briefly. In repeatable at high temperatures and in harsh environ-

2-6 Aspects of Technology ments. We shall return to this subject in Chapter 6. where T is the absolute temperature, R is the resis- tance and A, B and C are constants to be determined in a curvefit process. We discuss the in The Thermistor more detail in Chapter 6, along with the fitting of A thermistor is in essence a thermal resistor, a resistor eq[2-3] in Appendix F. whose resistance changes with temperature more dramatically than is adequately described by eq[2-2]. For example, the resistance-vs-temperature response The Strain Gauge of a typical commonly-available thermistor, the Radio The strain gauge, as its name implies, is a device for Shack type #271-110, is shown in Figure 2-10. 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 Thermistor Type RS#271-110 support (Figure 2-11). If the support is bent or strained then the wire element is stretched a small 150 amount, causing its resistance to change (in accordance with eq[1-3]). Since the change in 100 resistance is very small, the strain gauge is almost always used in conjunction with a null-detection 50 circuit involving a Wheatstone bridge (described below). We shall return to the strain gauge in Chapter

T (degC) 0 6.

-50 0 1.105 2.105 3.105 R (Ohms) Figure 2-10. Resistance vs temperature of a Radio Shack #271-110 thermistor.

Thermistors are made from a variety of materials, that include evaporated films, carbon or carbon composi- tions, -like semiconductors of of copper, cobalt, manganese, magnesium, nickel, titanium or uranium. can be molded or compressed into various clever shapes to fit a wide range of applications. These devices have a resistance Figure 2-11. Structure of a strain gauge. change characteristic of 4 to 6%/˚C with generally a negative temperature coefficient (NTC). Thermistors made of barium or strontium titanate ceramics have a The Photoresistor positive temperature coefficient (PTC). A broad range of materials have a resistance that As can be seen from Figure 2-10, the resistance of a depends on the intensity of light falling on them. The thermistor depends on temperature in a highly non- most well-known examples are cadmium sulphide linear way. The dependence can be approximated (CdS) and cadmium selenide (CdSe). The composition empirically by the so-called Steinhart-Hart equation: of a cadmium sulphide photocell, deliberately design-

1 3 ed to exploit this property is illustrated in cross- = A + Bln(R) + C(ln( R)) , …[2-3] section in Figure 2-12. T

2-7 Aspects of Technology Active region The Voltage Divider l (photoconductive One application of resistors connected in series is the material) voltage divider (Figure 2-14a). In the figure, a voltage Ohmic Ohmic source is shown connected across three series resistors contact contact (any number of resistors greater than one would suf- fice for our argument). The node between each resis- l tor is connected to a terminal of a rotary . By manually positioning the switch on the terminals A, Figure 2-12. Construction of a CdS photocell and its circuit B, or C three fractions of the applied voltage V can be symbol. made to appear as the output voltage Vout.

The resistance R of a CdS photocell is observed to depend on light intensity according to an empirical relationship of the form: R 1 B A

– K R = RoI , [2-4] R2 (a) V where Ro (W) is a constant, I (fc) is the intensity of light C Vout and K is a constant which is less than 1. Figure 2-13 R3 shows the resistance of a cell with Ro = 2000 W 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 Vout (b)

CdSPhotocell.dat Figure 2-14. A voltage divider activated by a rotary switch (a) and a voltage divider in the form of a (b). 104 ) W When the switch is at A, 103

Vout = V , 2

Resistance ( 10

R2 + R3 1 and when at B, V = V , 10 out R + R + R 10-2 10-1 100 101 102 103 1 2 3 Intensity (fc) R and when at C, V = 3 V . Figure 2-13. Log-log plot of resistance vs light intensity for out R + R + R the Radio Shack type 276-1657 CdS photocell. 1 2 3

This divider gives discrete values of Vout. If continu- ous 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, indica- ted by the arrow (connected to the center tap in Figure 2-15), that can be moved continuously over a carbon 2-8 Aspects of Technology element or a series of closely-spaced wire windings. In The Current Divider this way more precise values of Vout can be chosen Two resistors connected in parallel (Figure 2-16) form than is possible with the rotary switch. The potentio- a current divider. It is useful to have a formula for I1 or meter was in fact widely used as an audio volume I2 in terms of the “input current” I. control in legacy consumer electronics. Similar devices called potentiometer actuators are used as position sensors in robotics (discussed in more detail I1 R1 in Chapter 6).

R2

I I2 + –

V

Figure 2-16. Two resistors connected in parallel.

Let us solve for I1. The same voltage V that appears across the resistor combination appears across R1. Thus we can write

R1R2 V = I = I1 R1, R1 + R2

R so that I = I 2 . …[2-5] Figure 2-15. Examples of , a single (top) and 1 R + R dual (bottom). The center tap of each set of three pins con- 1 2 nects to the wiper. These controls are largely obsolete. This circuit enables us to obtain the current we desire,

I1 , from an available current I.

Example Problem 2-3 Voltage Divider Example Problem 2-4 Current Divider A circuit like the one shown in Figure 2-14 has a In the circuit shown in Figure 2-16, you are given source of 10 V and two resistors in series, R1 = 100 W that I = 1 A, R1 and R2 are 100 W and 200 W respec- and R2 = 200 W. What is the voltage drop across R2? tively. What is the current through R1? Solution: According to the treatment of the previous section Solution: the voltage is given by According to eq[2-5],

R 200W R2 200 2 I1 = x1 = x1 V2 = x10V = x10V R1 + R2 100 + 200 R1 + R2 100W+200W

=6.67 V. =2/3 A. The available current is 1 ampere, but only 2/3

ampere flows through R1.

2-9 Aspects of Technology The Wheatstone Bridge circuit must be used with a voltage source and an A Wheatstone bridge is a diamond shaped arrange- instrument whereby the voltage (or the current flow) ment of resistors (Figure 2-17). 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 R1 Rv ammeter, and therefore can be quite high. You should be able to show that if the reading on a A b the ammeter is zero (when the bridge is said to be V balanced) then the following relationship between Rx and Rv applies: R2 Rx R2 Rx = Rv . …[2-6] R1 Figure 2-17. A Wheatstone bridge. Thus if the bridge is balanced by varying Rv, then the unknown Rx can be calculated. A Wheatstone bridge has desireable electrical proper- Wheatstone bridges are often used with sensors ties and is found in a number of sensor circuit (such as the strain gauge discussed earlier) which designs. R1 and R2 are usually fixed resistors, often of produce a very small change in a sensed variable. This high precision, which are mounted on the sensor very small change then results in a deviation from the board itself or in the controlling electronics. Rx is the null condition which, if the ammeter is sensitive sensing element or “unknown” in the form of a enough, is easily detected and to high precision. thermistor, a strain gauge, or other resistance sensor. Rv is a resistor whose resistance can be varied. This

Capacitors For reasons of space, we restrict our attention to large-scale non-IC types.

General The can be of almost any non-conductive As we have seen in Chapter 1 a capacitor is modelled material, , plastic, oil, glass or even air. A as a set of parallel metal plates. Practical large-value, capacitor’s value is often printed on the are made by sandwiching a dielectric capacitor’s body. between two thin metal plates and then rolling the assembly into a tubular shape (Figure 2-18). Specifications Capacitors, like resistors, are categorized in a number of different ways: for example, the 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 (60 Hz), in an audio frequency application (£ 20 kHz) or a application (MHz region). The capacitor used in the Figure 2-18. A fixed-value tubular capacitor. smoothing section of a power supply is of a large value (greater than 1 µF) and is often of the polar or

2-10 Aspects of Technology electrolytic type. Non-polar capacitors with values of observed when placing the capacitor into a circuit. order 0.001 to 0.01 µF are usually used at audio freq- The positive terminal of the capacitor must be connec- uencies, and capacitors with values less than 0.001 µF ted to the higher potential in the circuit. If this is not are usually used at radio frequencies. This usage is observed, the capacitor may break down. Also, a largely determined by the capacitor’s impedance polarized capacitor requires a polarizing (DC) voltage (Chapter 1). and cannot withstand a reverse current; it cannot be used in a situation in which a DC voltage is absent Polarized Capacitors and/or in which an existing AC voltage reverses the Power or electrolytic capacitors made from aluminum capacitor’s polarity. All other capacitor types are non- and are “polarized”. This means that the polar. More details on capacitors are listed in Table 2- polarity markings on the capacitor’s body must be 5.

Table 2-5. Fact sheet on commonly-used non-IC capacitors.

TYPE TYPICAL TYPICAL APPLICATIONS & VALUE RANGE TOLERANCE CHARACTERISTICS Aluminum 0.68 - 200, 000 µF – 10 % - + 75 % Power-supply filtering, bypass, . Electrolytic Used where large values are needed.

Tantalum 0.001 - 1000 µF 5 - 20 % Bypass, coupling, decoupling. Very stable, Electrolytic long life

Ceramic 1pF - 2.2 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 0.001 - 10 µF 5 - 20 % Blocking, filtering, transient suppression. Good (Mylar) for audio. Small size with medium stability.

Paper 0.001 - 10 µF 10 - 20 % General purpose. Large size, low cost, medium stability, and poor moisture characteristics.

Polystyrene 51 pF - 0.15 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 paten- ted 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 film that either absorbs or exudes water vapour as the relative humidity of the ambient air rises or falls. Figure 2-19. The Vaisala Humicap humidity sensor.

2-11 Aspects of Technology As the dielectric constant of the capacitor changes so humidity reading. We have a few more details on this does the capacitance. The capacitance is measured by type of sensor in Chapter 6 since it is used in the the electronics of the instrument and converted to a UTSC weather station.

Inductors We confine our attention here to large-scale non-IC types of .

Inductors, Chokes and Coils Specifications published for inductors usually give the An is modelled as a coil of wire wound on a Q value, test frequency, and current rating. The Q support or a form (Figure 2-20). The form may be of value indicates how sharp the response of the coil is magnetic material, non-magnetic, or even non-existent when resonating at the test frequency. The current (the inside of the coil being air). You may recall from rating is the amount of current the wire making up Chapter 1 that the interesting property of an inductor the coil can safely carry without self-destructing. (The is its . Inductance is the property respon- wire making up the coil can be of various gauges.) sible for producing an emf across the coil when the current through the coil is made to change with time. 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 -bound). Coils used above 30 MHz are usually wound on non-ferrous materials Figure 2-20. An inductor of the simplest geometry is one such as brass or copper to minimize power losses to that is wound on a circular toroidal shaped form. Because of eddy currents. Two iron core types are illustrated in its efficiency, this kind of inductor with an iron form is Figure 2-22. commonly used in the low pass filter section of the power supplies of high quality audio .

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 2-22. A selection of inductor types: chokes (top) and iron cores (bottom).

Figure 2-21. Examples of chokes and coils. 2-12 Aspects of Technology The The Transformer Equation A transformer is a special type of inductor consisting A working relationship exists between the AC volt- of two coils. The coils are wound close together but in ages appearing across the primary and secondary such a way as to be electrically insulated from each windings of an ideal transformer. (An ideal trans- other. One coil is called the primary winding, the other former is one in which no energy is lost to heat.) If v1 the secondary. The normal use of a transformer is to and v2 are the voltages developed across primary and obtain a desired AC voltage across the secondary secondary, and if the windings have n1 and n2 turns of from an available AC voltage applied across the wire, respectively, then it can be shown that primary. A transformer works in this way because of an effect called mutual induction. If the two coils are n2 v2 = v1 . …[2-7] close enough together the magnetic flux produced by n1 the current in coil 1 passes through coil 2 and vice versa. Thus a changing current in coil 1 induces an If n2/n1 is greater than 1 then v2 is greater than v1, i.e., emf across coil 1 and across coil 2. the voltage across the secondary exceeds the voltage In order for mutual induction to occur a means across the primary—thus the source of the name must exist to enable the flux produced by the current transformer. This kind of transformer is called a step in coil 1 to pass through coil 2. This is called “flux up transformer. If n2/n1 is less than 1 then v2 is less linkage”. Linkage is achieved by placing the coils than v1 and the situation is reversed; the transformer close together, by interleaving the coils (winding them is a step down type. together) or by using a closed loop of some magnetic As we have stated, a transformer is placed in a cir- material like iron to guide the flux. The diagram of a cuit to obtain a desired AC voltage from an available toroidal core transformer is drawn in Figure 2-23a. one. The most commonly available AC voltage is the The circuit symbol for a transformer is drawn in 115 volts supplied by the AC mains. are Figure 2-23b. 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 Primary Secondary step down transformers. This topic in “high power” is Coil 1 B Coil 2 n1 n2 beyond the intended scope of these notes. i1 + Transformers are very non-ideal devices; because of (a) eddy current losses, they tend to lose energy to heat v1 L1 L2 v2 – and they tend to distort current waveforms. They are therefore to be avoided in modern circuit designs wherever possible. Indeed, in modern low-power magnetic material for flux loop mostly digital consumer devices they are rarely to be seen at all. n1 n2 i1 i2 + + Example Problem 2-5 source v1 v2 load (b) Transformer

– – A transformer like the one shown in Figure 2-23 has L1 L2 its primary connected to the 115V AC mains. If the mean that the coils are wound in the same number of turns in the primary and secondary are sense, i.e., clockwise or counterclockwise 1000 and 500, respectively, what is the voltage to be Figure 2-23. An ideal transformer (a) is given the circuit expected across the secondary? symbol (b). Solution: According to the treatment of the previous section the voltage is given by

2-13 Aspects of Technology n 500 V = sec ondary x115V = x115V (discussed in more detail in Chapter 6). The active sec ondary element in a rain gauge is a spoon or a cup in which nprimary 1000 the rain drops. The handle of the spoon is balanced on a pivot so that once the spoon fills with water it tips = 57.5 V. out. A magnet is attached to the handle end of the spoon. As the spoon tips the magnet comes into The transformer is a step-down type. 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 The Inductor in Sensors emf is registered as an electrical pulse which is then counted. An inductor is often part of a sensor whose function is to count something. An example is the rain gauge

An Analog Waveform Revisited

In a science lab an analog waveform can be produced From its beginning, analog electronics was focussed by a signal generator (Figure 2-24). By analog wave- on the issues of routing an analog signal from one form is meant a waveform that is a continuous func- point to another in a circuit without distorting the sig- tion of time. An analog waveform has the property nal in any way, that is, by introducing changes in that at any instant of clocktime it has a definite value amplitude or phase. The difficulties achieving this to of displacement or voltage. Or in other words, the satisfaction of the consumer was one of the things between any two clocktimes it has an infinite number to drive the digital revolution in the audio industry. of displacement or voltage values. Most waveforms The waveform we have chosen here as an example we encounter in our everyday lives are analog in is a pure sinusoid, a special case. Analog waveforms nature. The sounds that we hear with our ears are may in general consist of a number of superposed continuously-varying waves of air pressure. The sinusoids, in other words, a number of components. voltage signal we obtain from the wall sockets in our One example of a waveform consisting of the super- homes and labs is an analog waveform. The “real position of 1 kHz and 2 kHz components is shown in world” is arguably an analog one. Figure 2-25. Audio waveforms that we hear every day consist of a wide range of frequencies and amplitudes, all changing in complicated ways with time.

Figure 2-24. The output from a signal generator has an ana- log waveform.4 Figure 2-25. A waveform consisting of two component wave- forms of frequency 1 kHz and 2 kHz. 2-14 Aspects of Technology DTMF A practical application of waveforms consisting of Table 2-6. Dialing Digits and their associated dualtone two components, or tones, is in the Dual Tone Multiple frequencies. Frequency (DTMF) method of conveying information via the telephone line. This application we literally Keypad Character Frequencies hear every day, every time we use a telephone. 0 941 Hz and 1336 Hz In spite of the digital revolution, telephony is an 1 697 Hz and 1209 Hz analog medium at heart (because speech is analog?). 2 697 Hz and 1336 Hz Digital information (e.g., a telephone number) is sent 3 697 Hz and 1477 Hz over a telephone line as a two-tone signal. Each 4 770 Hz and 1209 Hz character on the keypad of a telephone has its own 5 770 Hz and 1336 Hz 6 770 Hz and 1477 Hz combination of two-tone signals (Table 2-6). Dual 7 852 Hz and 1209 Hz tones are decoded by special ICs in routing equip- 8 852 Hz and 1336 Hz ment. Some instruments, in particular the Telulex 9 852 Hz and 1477 Hz Model SG-100/A signal generator (described in Ap- * 941 Hz and 1209 Hz pendix 1) is equipped with the firmware to perform # 941 Hz and 1477 Hz this decoding. A 697 Hz and 1633 Hz It sometimes happens that when complex wave- B 770 Hz and 1633 Hz forms pass through a system some components are C 852 Hz and 1633 Hz modified in amplitude and phase more than others. A D 941 Hz and 1633 Hz 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.

2-15 Aspects of Technology 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 unchang- ed. 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 Thus dividing eq[2-8b] by [2-8a] we get The story of filters begins with the idea of the v Z impedance divider. We have seen in Chapter 1 how a G = out = 2 . …[2-9] voltage divider can be made from two series resistors. vin Z 1 + Z 2 The equivalent in AC circuits is two series imped- ances Z1 and Z2 (Figure 2-26). G in fact is what is known in mathematics as a com-

plex number. This is because Z1 and Z2 are themselves

complex numbers (Chapter 1). But if the form of Z1 system and Z2 are known then |G| and the phase angle f can be calculated. Let us consider an example. Z1 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 2- vin vout Z2 27. The system is called an RC filter.

R Figure 2-26. In its most general form a filter can be thought vin C vout of as an impedance divider. Figure 2-27. An RC low pass filter. In electronics jargon the circuit is called a four-terminal network. There are four terminals—two inputs and In a rigorous mathematical treatment, we would deal two outputs. The circuit can also be regarded as a with G as a . To avoid this, we system (within the dashed rectangle). The input volt- bypass the mathematics and simply state the results. age v is the stimulus applied to the system and the in The absolute value of G, |G|, is given by output voltage vout the response. We can quantify this circuit’s effect on the input by finding the ratio of the 1 output voltage to input voltage and the phase angle | G(w)|= , …[2-10a] 2 2 2 between the two signals. This ratio, which we shall 1+w R C call G, can be measured with a DMM, the phase angle f with an oscilloscope. and f (w ) = ArcTan(–wRC) . …[2-10b] The input and output voltages are: These expressions are functions of the angular freq-

vin = i(Z1 + Z2 ) , …[2-8a] uency w. f is the angle the output voltage leads the input voltage. To examine the frequency dependence of these functions more carefully, we have plotted and vout = iZ2 . …[2-8b] 2-16 Aspects of Technology them in log-log graphs (Figures 2-28). With study, the meaning of Figures 2-28 should be Example Problem 2-6 evident. Low frequency components of the input Interpreting the Effect of a Filter on a Signal Applied signal are transferred to the output without change in to it amplitude or phase. But high frequency components are both attenuated and phase shifted. This is just the You are given that a signal consists of the sum of kind of action performed by a filter—in this case, a low sinusoids of 1000 Hz and 10000 Hz of equal pass filter. Even if the circuit in Figure 2-27 were, in amplitude. The signal is input to the low pass filter fact, invisible to you, you could still infer the equival- whose response curves are shown in Figures 2-28. ent circuit from measurements of the responses Describe the signal to be expected at the filter’s |G(w)| and f (w). Let us see in the following example output. problem how to interpret filter response curves in detail. Solution: From a study of the curves we can make the following predictions: Gain vs Frequency At a frequency of 1000 Hz, 1.0 • |G|, the ratio of the output to the input signal, should be about 0.9 • f should be about –0.25 radians (–14 degrees) At a frequency of 10000 Hz, • |G| should be about 0.3 0.5 • f should be about –1.25 radians (–72 degrees) Gain G

The conclusion to be drawn is that the 1000 Hz 0.0 signal should be affected very little by the filter; at 100 101 102 103 104 105 106 the output its amplitude should be reduced by about 10% and retarded in phase by about 14 degrees. The Log Frequency (Hz) filter’s effect on the 10000 Hz signal should be greater. The 10000 Hz signal should have its output Phase Shift vs Frequency reduced by a factor of 70% and be retarded in phase 0.5 by 1.25 radians, or approximately 72 degrees. Clearly, the filter should selectively attenuate and 0.0 phase shift the 10000 Hz signal more than the 1000 Hz signal. -0.5

-1.0 We have assumed in this discussion that the capacitor Radians -1.5 is perfectly ideal and therefore dissipates no energy to heat. In a real capacitor, however, some energy will -2.0 inevitably be lost, meaning that the curves for a real 100 101 102 103 104 105 106 RC filter will deviate to a lesser or greater extent from Log Frequency (Hz) what is shown in Figures 2-28. We shall take up this subject again in Appendix C Figure 2-28. f Plots of |G| and from eqs[2-10] for the RC where we show how a computer application can be W low pass filter. Here C= 4.7 µF and R = 10 . used to measure |G| and f. Our next topic is the subject of .

2-17 Aspects of Technology 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 semicon- ductor determining how the diode is used. Diodes made from germanium and silicon are mostly used as 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 band. A selection of specifications for a few of these Diodes designed for rectification or signal detection diode types is listed in Table 2-6. The peak inverse purposes are made of germanium or silicon and pack- voltage (PIV) is the maximum reverse voltage the aged much like resistors but without the color code. diode can sustain without suffering electrical break-

The body is commonly black and of a size consistent down. The forward current If is the maximum current with the current-handling capability (larger size for the diode can sustain in the forward direction and the larger currents). The cathode end of the body is forward voltage drop is the corresponding voltage usually indicated by a rounding of the body or by a drop across the diode.

Table 2-6. Selected specifications for a number of /signal diodes @25 ˚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 Description Vmax PIV If max Ir max Vf AV RS# (V) (V) (A) @ PIV (µA) (V) 1N34 Ge signal 1.0 60 0.05 30

1N60 Ge signal 1.0 50 0.03 40

Si rectifier 50 35 6 25 0.9 276-1661

1N4001 Si rectfier 1.6 50 1 10 276-1101

Si rectifier 1 1000 2.5 1 276-1114

Of the two diode types, the germanium diode has the The advantage of an intrinsically lower forward voltage A special type of silicon diode, related to the solar cell drop (typically 0.3 volts as compared with 0.7 volts for and called a photodiode, is especially designed to detect silicon). This low forward voltage drop results in a light. It is usually much smaller than a solar cell, low power loss and more efficient diode, making it sometimes as small as the head of a pin. A photo- superior in many ways to silicon. This lower voltage graph showing a number of photodiode products is drop becomes important in very low signal environ- reproduced in Figure 2-29. ments (signal detection from audio to FM frequencies) The photodiode has a very fast response time, often and in low level logic circuits. The disadvantage of the of the order of nanoseconds. It is used reversed- germanium diode is its larger current for biased. In this mode the current which flows across reverse voltages (Figure 1-38). This makes the silicon the junction is linearly proportional to the intensity of diode the diode of choice for rectification. the light striking the diode (described in Chapter 1 2-18 Aspects of Technology and shown in Figure 1-27). A simple circuit employ- diodes are fabricated from semiconductor compounds ing a photodiode in a light intensity meter is drawn in such as Gallium Nitride, Indium Phosphide (InP), Figure 2-30. Gallium Phosphide (GaP), Gallium Arsenide (GaAs), and Gallium Arsenide Phosphide (GaAsP). An LED is designed to emit light of a specific color when for- ward 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). Figure 2-29. A selection of . 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 turn- on voltage, the diode emits light. Information regard- ing typical LEDs is given in Figure 2-31. Specifications for a selection of LEDs are listed in Table 2-7.

I LED LED symbol case

Figure 2-30. A simple light intensity meter using a photo- anode cathode diode. As the intensity of the light increases the resistance cathode of the diode decreases and the current detected increases. anode (b) (a) Vin

In addition to the usual specifications published for diodes, photodiodes are described by a responsivity R factor R defined as follows:

I = RP , LED

(c) where I is the measured photocurrent (A) flowing through the diode and P is the optical power (W) Figure 2-31. Information on LEDs, package (a), circuit incident on the diode. R depends on the wavelength. symbol (b) and circuit (c). The wavelength response characteristics depend on the material from which the photodiode is made (silicon or other materials), details of the diode fabri- The anode of an LED is identified by the longer of the cation process, and the optical filter, if any, between two lead wires (a). An LED can pass only a small the light sensor and the active photodiode surface. current (typically 20 mA) without self-destructing. For this reason an LED is nearly always used with a series The Light-Emitting Diode (LED) current-limiting resistor (c). If Vin is of the order of 6V As its name implies, a light emitting diode (LED) is a then the current limiting resistor R should be about PN diode especially designed to emit light. It is rela- 220 W. Some LEDs are designed for use with a 5 volt tively inexpensive, efficient, consumes far less power source and have the current limiting resistor built-in. than an incandescent lamp and has a long life. These

2-19 Aspects of Technology Table 2-7. Specifications for a selection of LEDs @25 ˚C that you will most likely encounter in this course.

Type Description Vmax PIV If max Vf AV P max Peak Wave- RS# (V) (V) (A) (V) (mW) length (nm) Wide Angle 5.2 2.1 697 276-310 red LED

Yellow 2.8 4.1 0.1 1.9 130 590 Jumbo LED

Green 0.025 2.1 75 276-022 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? peak, or peak-to-peak values. f is the angle, in radians The idea of an amplifier is illustrated in Figure 2-32. A or degrees, that the output signal leads or lags the signal of amplitude Vin is applied to a system and has input signal. To give an example, Figure 2-33 shows its amplitude increased to a value Vout. This process the input and output signals for an amplifier with a takes energy. The energy is drawn from a source like gain of 10 and a phase shift of 180 degrees. 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.

Energy from supply Vout Vin

amp

Figure 2-32. The idea of amplification. An input signal con- Figure 2-33. A screen save from a TekTDS210 digital oscil- trols the energy drawn from a power supply so as to give loscope. At the top is shown the input signal (on CH1) ap- rise to an output signal increased in amplitude. plied to an inverting opamp of the type shown in Figure 2- 45. 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 Amplifiers are described by the same parameters used CH1 (5.04V/504mV) is 10 and the phase shift is 180 deg- for a filter: the gain G and phase shift f . G is the ratio rees since the output is inverted with respect to the input. of the output to input voltages expressed as rms, 2-20 Aspects of Technology Amplifiers to be Described than is the BJT and FET since it so easy to use and Two of the most popular discrete amplifier devices in figures in thousands if not millions of applications. use today are the bipolar junction transistor (BJT) and We shall therefore discuss in the next section the BJT the field effect transistor (FET). The only briefly in anticipation of spending most of our (IC) type of amplifier called the operational amplifier time on the opamp. All of the signal conditioning (opamp) is even more important in a practical sense circuits reproduced in Chapter 6 use opamps.

The Transistor Amplifier The two most important transistor types are the bipolar junction transistor (BJT) and the field effect transistor (FET). The latter was the first to be invented but the former was the first to be widely adopted by the electronics industry. Except for special applications today, discrete have largely been replaced by ICs. And the few examples of discrete transistors to be found today are largely FETs. Therefore we begin our discussion of transistors with the BJT, not because it is state-of-the-art, but because in many respects it is a natural advance on PN junction technology.

The Bipolar Junction Transistor the PNP. Current flows from collector to emitter We discuss here the bipolar junction transistor (for through the NPN and in the reverse direction convenience we shall just use the word transistor). A through the PNP. We shall focus on the NPN class in transistor can be used to amplify an AC signal as well our discussion here, though the PNP class is of equal as a DC signal, but before it will work at all, it must importance. first be “prepared” with certain DC voltages set up between its terminals or DC currents made to flow through its body. We begin, therefore, with the issue collector base emitter collector base emitter of DC preparation or bias and defer until later a C E C E discussion of the response of the transistor to an AC N P N P N P 5 signal. B B IC IC Classes C E C E There are two general classes of transistor: the NPN and the PNP. Both classes are made from germanium, silicon and more exotic materials like gallium IB IB (b) arsenide. Both classes consist of three sections of B (a) B doped semiconductor arranged in a kind of sandwich Figure 2-34. Composition and circuit symbol of bipolar (Figure 2-34). These sections are called the collector, junction transistors: NPN class (a) and PNP class (b). the base and the emitter, and are each provided with an electrical connection. The origin of the nomencla- ture NPN and PNP should be clear from the order of the sections in the figure. Electrical Characteristics of the NPN Transistor To make our task of explaining how a transistor To make a transistor work, two external DC voltages works as easy as possible we can think of both classes must be applied to it (Figure 2-35). These voltages 6 as having the same geometry. The base is the center may be derived from two separate power sources, as material, the collector and emitter are the outer is implied in the figure, or from a single source. Thus materials. The base is lightly doped, the emitter and there are two loop currents: a base current IB induced collector are more heavily doped. (For an explanation by the voltage VBE between the base and emitter and a of doping see Chapter 1.) And the emitter is more collector current IC induced by the voltage VCE bet- heavily doped than the collector. The two classes ween collector and emitter. IC is typically two orders differ in the direction the current flows—into the base of magnitude larger than IB and VCE is much larger terminal of the NPN and out of the base terminal of 2-21 Aspects of Technology than VBE. germanium and 0.7 V for silicon) and the base- collector junction reverse biased by a few volts.

VCE Transistor Characteristics IC Much of a transistor’s electrical behavior is summar- ized in its families of characteristic curves. One family is called the collector characteristics (Figure 2-37). These N P N E C curves show how the collector current depends on the collector-emitter voltage when the base current is B + – held constant at various values. To function as a lin- ear amplifier, a transistor must be operated in a state IB VBE represented by a point on the graph where the varia- Figure 2-35. Biasing of an NPN transistor. bles depend linearly on one other. This range, called the plateau region, is where the collector current is directly proportional to the base current and is rela- Recalling our study of the PN junction diode in tively independent of small changes in the collector- Chapter 1 you should recognize (Figure 2-36) that the emitter voltage. In this region the transistor can be base emitter junction functions like a PN diode. The modelled as a current source in series with a diode (Figure 2-38). purpose of the base-emitter voltage VBE is to turn on the base-emitter junction, that is, to reduce the resis- tance of that junction to a low value, thereby allowing a collector current to flow. Alternatively, the resis- IC IB3 tance of the base-emitter junction would be so high as IB2 to reduce the flow of the collector current IC to a point where the transistor could not function as intended. IB1 Plateau region

VCE IC VCE

Figure 2-37. The family of IC vs VCE curves of a typical BJT. IC IC N P N E C C IB B IC = b IB + – = hFE IB B IB VBE Figure 2-36. An attempt to illustrate how a small base- VPN emitter current in a transistor (bottom loop) controls a much larger collector-emitter current (top loop). E Figure 2-38. Model of a typical NPN transistor.

The base-emitter junction works as a kind of valve. Small variations in V (and therefore in I ) produce BE B The three currents in a transistor, IB, IC and IE are small changes in the base-emitter resistance, which in proportional to one another in the following way: turn cause large variations in IC. Small variations in IB causing large variations in I is “amplification in C IC = aI E , action”. Thus an NPN transistor is normally operated with the = b IB = hFE IE , …[2-9] base-emitter junction forward biased (0.3 volts for 2-22 Aspects of Technology where a and b, which are approximately constant, are called the alpha- and beta-parameters. a and b are • The CE amplifier has both current and voltage themselves related by gain. It is used as a general purpose amplifier. • The CC amplifier has current gain but a voltage a gain of only unity (V ~ 0.6 V so V /V ~ 1). It b = . …[2-10] BE EC BC 1– a is used as a coupling stage when high input im- pedance and low output impedance are required. Typically b is about 99 and a about 0.99. These num- • The CB amplifier has voltage gain but a current bers show that the ratio IC/IB is large, implying that gain of only unity (IC/IE ~ 1). It is used in high the transistor can be used to amplify current. Since frequency circuits since the capacitance linking

VCE/VBE is also large (at least for some configurations output to input is small. as we shall show in the next section), the transistor can be used to amplify voltage. In order to design a working amplifier based on one of these configurations the transistor must be proper- Transistor Configurations ly biased, as we have already stated. This means that Since a transistor has three electrical terminals, a sig- the transistor must be operated in an electrical state nal can be applied between any pair of its terminals characterized by values of IB, IC and VCE making up a three different ways. This leads to three configura- point in the plateau region of the collector curves tions (Figure 2-39). The two terminals on the left in (Figure 2-37). Only in this region does the amplifier each figure represents the input, the two terminals on function linearly with the collector current being the right the output. One terminal is common to both directly proportional to the base current and more-or- input and output. The configurations are therefore less independent of the collector-emitter voltage. A called the common emitter (CE), the common base (CB) point in this region is also far removed from a state in and the common collector (CC). which maximum current flows through the transistor, the so-called “saturated” state (corresponding to VCE = 0) or a state in which no current flows through the transistor at all, the state of “cut off” (corresponding

C C C to IC = 0). This point is called an operating or quies- in B cent point. To do this, we must add external resistors, out out capacitors, etc., to the transistor to effect the necessary B in current limiting. This topic would take us into what is E E E usually covered in a course in electronics and beyond the intended scope of these notes. In the event that Common emitter, CE Common collector, CC (a) (b) you have to use a transistor circuit in this course the circuit diagram will be given.

E C The Phototransistor in out (c) Still on the subject of transistors, there is a transistor B B that is especially constructed to allow light to pene- Common base, CB trate to the base-emitter junction. It is used as a detector of light. In this case it is the energy of the Figure 2-39. The configurations of an NPN transistor: com- light falling on the base (rather than an external mon emitter (CE), common collector (CC), and common power supply) that provides the energy to induce a base (CB). For simplicity, we have omitted external com- collector current IC to flow across the base-emitter ponents from the diagrams. junction. The greater the light intensity the greater the collector current (Figure 2-40).

The collector current IC is observed to depend Each configuration has advantages and disadvantag- directly on the light intensity Il in a relationship of es that can be summarized in the following points. the form: 2-23 Aspects of Technology

IC @h fe Il , Rs I where hfe is the current gain of the transistor (defined in the previous section). There is no external connection to the base (Figures 2-41). This device is V more sensitive than is a photodiode, but is slower to react to changes in light intensity. We discuss this device in more detail in Chapter 6. Figure 2-41a. A simple light-intensity meter using a photo- transistor.

unused 1 k I 0 - 1 mA

Figure 2-41b. A circuit for uswing a phototransistor like a photodiode. Figure 2-40. Collector characteristic curves for a typical phototransistor. This concludes our discussion of discrete amplifier devices. We now move on in the next section to the operational amplifier.

2-24 Aspects of Technology The Operational Amplifier The operational amplifier, or opamp for short, is a much easier device to employ in a circuit of one’s own design than is a discrete transistor. For one thing, an opamp, unlike a transistor, needs no bias. An opamp is fabricated as a single IC and is intended to be used like a black box.7 One needn’t be concerned with its internal structure. One need only connect it correctly to a voltage source, provide the appropriate feedback element (resistor, capacitor, whatever) and then ensure that the signal applied to its input has an amplitude small enough not to induce unwanted distortion in the output. Here we describe the properties of the opamp and how to construct useful devices with it.

The Need to Know The opamp is in many respects the goal of our review I+ of amplifier devices. Thousands of signal conditioning V+ circuits that are used with sensors employ opamps as straight signal amplifiers, as filters or for other Ro purposes. It is useful to have a working knowledge of Vin Ri opamps so as to better understand how sensor devices A (V+ – V–) Vout do their job. I– It is instructive for the user, whether student or pro- V– fessional engineer, to regard an opamp as an ideal element first, then later as the real device that it is. Therefore, we begin by explaining what is meant by Figure 2-43. The equivalent circuit of an opamp IC. The an ideal opamp and then consider the ideal opamp in input resistance Ri is very large, at least 1 MW, and the a number of what are called “linear” applications, output resistance Ro is very small, of the order of ohms. where the output is directly proportional to the input.

The Ideal OpAmp The opamp has two inputs, labelled “+” and “–“, and A view of the bare bones of an opamp is drawn in one output. A ground line is common to them all. Figure 2-42. Shown is the opamp IC itself (the Often, one or the other of the inputs is connected to triangle), the two signal inputs (“+” and “–“), the ground. If the “+” input is grounded and a signal is output, the power supply lines V++ and V–– and the applied between the “–“ input and ground, then the ground line. (The power lines, most often ±15 volts output signal is inverted (or phase shifted by 180˚) usually derived from the same power supply, are relative to the input. If the “–“ input is grounded and nearly always omitted from circuit diagrams, and we a signal is applied between the “+” input and ground, shall omit them from now on.)8 The equivalent circuit then the output signal is not inverted. For these reas- of the ideal opamp IC itself is drawn in Figure 2-43. ons the “–“ and “+” inputs are called, respectively, the inverting and non-inverting inputs.

reference Characteristics voltage V++ (+ 15 V) An opamp has the important characteristic that its I+ V+ + output voltage Vout is proportional to the difference between its input voltages (V – V ). For this reason it w + – I– A(j ) V– – is said to have a differential input. Another character- Vout sample istic is a very large gain when no feedback element is voltage = A (V+ – V–) in place (Figure 2-44). (A feedback element—resistor, V– – (– 15 V) capacitor, whatever—is nearly always connected between the output and one of the inputs.) The gain Figure 2-42. Schematic of an opamp. The reference and without feedback is called the open loop gain. sample voltages can be applied to either input. As we have stated, over frequencies of interest, an opamp behaves as a nearly ideal device. By this we 2-25 Aspects of Technology mean it has an input resistance so high it can be regarded as effectively infinite, and an output resis- RF tance so low it can be regarded as zero (Figure 2-43). R1 This means that an opamp can be described to a good S approximation by the following rules: – Vi Vin + Rule 1: The input currents I+ and I– are zero Vout

(a consequence of Ri » ¥ ). (a)

Rule 2: The voltages V+ and V– are equal (a consequence of V being very small). in RF

R1 I1 S I– Io Gain dB (b) 100 open loop Ro Vin Vi Ri – A Vi Vout

closed loop 40 Figure 2-45. An opamp with feedback (a) and its equivalent circuit (b).

log f Vout = –AVi . …[2-11] Figure 2-44. Gain curves of a typical opamp with and with- where A denotes the very large open-loop gain factor out feedback. and the “–“ sign indicates phase inversion. Summing the currents flowing into node S we have These rules make up what is called the ideal amplifier Vin – Vi Vout – Vi approximation. We shall see in what follows that these + – I- = 0. …[2-12] rules are, indeed, approximations, and are not strictly R1 RF true. But by making them we can calculate many useful properties of opamp circuits. Assuming I– = 0 (Rule 1) and substituting eq[2-12] Thus before we look at the opamp from the point of into eq[2-11] and expanding, we have view of being a real device we study it in a number of circuits we can analyze using the ideal amplifier æ 1 1 1 ö Vin approximation. Vout ç + + ÷ = – . è RF AR1 ARF ø R1 The OpAmp With Feedback One of the simplest opamp circuits for the beginner to Since A>>1 the second and third terms in parentheses are negligible and can be dropped. Thus we are left study is one that has a single input resistor R1 and a with single feedback resistor RF (Figure 2-45a). The non- V V inverting input is tied to ground and the input signal out » – in R R Vin is applied between the inverting input and F 1 ground. The equivalent circuit of the amplifier is drawn in V R so that G = out = – F . …[2-13] Figure 2-45b. You should be able to see that this Vin R1 circuit is just the circuit of Figure 2-43 with R1 and RF added. Since the inverting input is used here we can This is the amplifier’s midband closed-loop gain. It is write 2-26 Aspects of Technology the midband gain in the sense of being the gain when Rule 2 we have: the frequency is neither very low nor very high—or when the effects of frequency are negligible. Since Vi Vin = V+ = V– = Vout ! …[2-16] = V+ – V– » 0 the summing node S is at zero potential or “virtual ground”. Thus the gain is +1, and the output and input signals We can calculate the input and output impedances are in phase. The circuit is technically known as a of the amplifier as a whole. Note that voltage follower. The impedance between the non- inverting input and ground is very high. This circuit Vin is typically used to match a device whose output Rin = @R1 . …[2-14] I1 impedance is high to a device whose input imped- ance is low. Impedance matching is important in elec- Detailed analysis would show that tronics. It is often (though not always) desired that maximum power be transferred from one stage to

(R1 + RF ) another, and this can only be achieved if the imped- Rout = Ro << Ro . …[2-15] ances are matched in this way. AR1 Noninverting Amplifier with Gain The conclusion we draw is that the opamp with feed- If we add two resistors to the previous circuit we get back in the above configuration has a large input im- the circuit in Figure 2-47. pedance (equal to R1) and a low output impedance (much less than the output impedance of the opamp itself). These are desireable characteristics. Eq[2-13] is the DC closed-loop gain. The closed loop + gain curve is drawn in Figure 2-44 over a wide freq- uency range along with the open loop gain. The DC – R2 Vin I closed loop gain is arbitrarily shown as 100 or 40 dB Vout (representative of the Motorola 741, a common op- I– = 0 R1 amp in many signal conditioning circuits). The closed loop gain curve is flat out to a frequency at which it meets the open loop gain curve. Clearly, feedback GAIN R R bw R enhances the amplifier’s frequency response or band- 1 2 IN 10 1 kW 9 kW 100 kHz 400 MW width and reduces its low frequency gain. 100 100 W 9.9 kW 10 kHz 280 MW Noninverting Unity Gain Amplifier 1000 100 W 99.9 kW 1 kHz 80 MW Figure 2-47. One of the odder opamp circuits is one that has no A noninverting amplifier with gain. Shown external components as such: the output is tied direct- below the figure are typical specifications for a Motorola ly to the inverting input (Figure 2-46). 741.

According to Rule 1, I– = 0. The voltage at the invert- + ing input is given by the voltage divider equation

– R1 Vin V– = Vout Vout R1 + R2

= Vin , Figure 2-46. Noninverting unity-gain amplifier. applying Rule 2. Thus the closed-loop gain is

Vin is applied to the non-inverting input. Applying 2-27 Aspects of Technology V R + R G = out = 1 2 . …[2-17] I Vin R1 R – Thus the amplifier has gain but does not invert. The A input impedance is very high, as it was in the prev- I + Vout = – RI ious example. This circuit is typically used as a general-purpose amplifier.

Inverting Amplifier With Gain Figure 2-49. Current to voltage converter. We briefly return to the inverting amplifier with gain (reproduced in Figure 2-48). Typical values of exter- nal components are tabled below the figure. and Vout = –IR . …[2-19]

The output voltage is proportional to the input cur- I rent. This function might look a little unusual, but the circuit, called a current to voltage converter, is often R1 R2 R2 – G = – employed as a first stage in matching a sensor to A R1 conditioning electronics (see Figure 6-13). Sensors Vin + often have to be placed some distance from the con- Vout trolling electronics and the connecting cables can be quite long. To sidestep the voltage drop that would otherwise occur in a long connecting cable the sensor is designed as a current source. This means that at the

GAIN R1 R2 bw RIN controlling end the current must be converted to a 1 10 kW 10 kW 1 MHz 10 kW voltage. 10 1 kW 10 kW 100 kHz 1 kW 100 1 kW 100 kW 10 kHz 1 kW Sum Amplifier 1000 100 W 100 kW 1 kHz 100 W With the circuit shown in Figure 2-50, signals can be Figure 2-48. Inverting amplifier with gain. Shown below effectively added together. We can show that the the figure are typical specifications for a Motorola 741. output voltage Vout is proportional to the algebraic sum of the input currents.

R Here G = – 2 . …[2-18] R1 S RF R1

The amplifier has gain but inverts (shown by the – minus sign). The input impedance is essentially R1. V1 R2 V2 + Current to Voltage Converter Vout The current to voltage amplifier (Figure 2-49) is a variation of the inverting amplifier. Summing the currents flowing into node A we have Figure 2-50. A sum amplifier. This circuit is shown with two inputs, but in principle could have any number of V – 0 inputs. I + out = 0 , R

V Summing the currents flowing into node S we have: so that I = – out , R

2-28 Aspects of Technology

V1 V2 Vout sum and difference amplifiers can be identified in + + = 0 . many signal conditioner circuits for sensors, as we R1 R2 RF shall see in Chapter 6..

In the event that RF = R1 = R2 we have the simple result: Real OpAmps We hope that with the examples we have chosen you Vout = – (V1 + V2) . … [2-20] can appreciate the usefulness of the ideal amplifier The output equals the sum of the inputs (with inver- approximation. Though “not quite true” and leading sion). to expressions of gain that are “not quite correct” the approximations are nevertheless good enough to Difference Amplifier provide the functionality we need most of the time. The circuit of Figure 2-51 gives an output propor- However, there are times when we need to take tional to the difference between the two inputs. account of how real opamps differ from the ideal. The Assuming an ideal opamp we neglect the currents following list of parameters points out characteristics entering the inverting and non-inverting inputs. Thus and limitations of the typical opamp you should be we can add the currents flowing into nodes A and B, aware of:

V1 – V– Vout – V– + = 0 , … [2-21] Ao (open loop voltage gain) R1 RF Typically 100,000 or 100 dB

V2 – V+ 0 – V+ + = 0 . … [2-22] Zin (input impedance) R2 R3 Typically 1 MW for BJTs, 1 MMW for FETs. The larger this number is the better. Also Vout = A (V+ – V–) . … [2-23]

Zout (output impedance) Typically a few hundred ohms A I (input bias current) V1 R1 RF B – Typically a fraction of a µA for BJTs and a few picoA V– Vx A for FETs. The smaller this number is the better. V+ + Vout = A Vx = A(V+ – V–) V2 R2 R3 VCC (supply voltage range) Typical limits are ± 3 volts to ± 15 volts B

Figure 2-51. A difference amplifier. VI (max) (input voltage range) Typically 2 volts less than VCC

V (input-offset voltage) If we take for simplicity R1 = R2 = RF = R3 (different IO Typically a few mV values lead to a weighting of the inputs), V+ and V– can be eliminated from eqs[2-21], [2-22] and [2-23] to give fT (Transition Frequency) The transition frequency is the frequency at which the æ 2 ö open loop gain curve falls to unity (or the frequency V 1+ = V – V . out è Aø 2 1 at which Log(gain) = 0). For the 741 fT = 1 MHz. f T can also be used as a gain-bandwidth product, i.e., fT = G x bandwidth. Opamps with much larger f s than the For A >> 1, V = V – V . T out 2 1 741 have been on the market for some years. Thus the circuit can be used to subtract signals. The 2-29 Aspects of Technology Gain At this stage you should be able to test your know- ledge of opamps. Here is an example. 1000 Example Problem 2-7 10 Properties of an OpAmp

1 The opamp shown in Figure 2-54 may be considered to be ideal. What is the gain to be expected of this 3 5 6 log f 6 circuit? If the opamp’s fT is 1 x 10 Hz, what is the bandwidth to be expected? Gain bandwidth fT 1 1 x 106 106 10 1 x 105 106 1000 1 x 103 106 + Figure 2-52. The gain-bandwidth product of an opamp is a Vin – Vout constant. The data below the figure are for a typical 100 kW Motorola 741. 200 kW

Slew Rate Figure 2-54. An op amp amplifier. An opamp is expected to faithfully reproduce the swing or skew in the signal applied to it. But if the Solution: frequency and amplitude of the input signal are large The gain of the amplifier is given by eq[2-17] where enough then the output signal may not be able to R and R are 200 kW and 100 kW, respectively. Thus accurately follow the slew in the input (Figure 2-53). 1 2 This “inertia” or “lag” is quantified by engineers with G = (200 kW + 100 kW)/200kW = 1.5. a parameter called the slew rate, expressed in volts per second. Typical values are in the range 1 V/µs to 10 The gain-bandwidth product, f , is given as 1 x 106 V/µs. One effect of slew rate limiting is that the band- T Hz. Therefore the bandwidth to be expected is: width of the amplifier is greater for small input signals than it is for large input signals. 6 5 bw = fT/G = 1 x 10 /1.5 = 6.67 x 10 Hz.

This bandwidth is quite large, meaning that the 50 kHz output waveform circuit could be used through the audio range of Vout frequencies and well beyond.

y

x 1 KHz output waveform Figure 2-53. The slew rate is given by y/x, where x is in µs and y is in volts. The higher the frequency the greater the slew rate limiting becomes apparent.

2-30 Aspects of Technology The Idea of a Gate As will be seen in Chapter 3, each bit in a binary number is physically implemented in the solid state by a gate, a device whose output can exist in one of two states, one representing a “0”, the other a “1”. The simplest gate is an ordinary switch, like a light switch, which can be manually set to an ON position or an OFF position. An equivalent, semiconductor gate is a PN diode or transistor, or even an opamp, as we shall see here.

Switch Gate logic HIGH output. A gate in the form of a manual switch (Figure 2-55) is On the other hand, if the voltage applied between the simplest kind of gate to understand. base and emitter equals or exceeds the base-emitter turn on voltage, as shown in the circuit on the right, then the base and collector currents are large, and the collector-emitter voltage is therefore LOW (most of the voltage V is dropped across R). The transistor is said to be in a saturated state. The collector output is R R therefore also at a logic LOW. Thus a logic HIGH input results in a logic LOW output. V HIGH LOW V volts ~ 0 volts V V

Figure 2-55. Gates in the form of manual . R HIGH R V volts Floating or grounded V ³ VPN The switch is connected in series with a resistor R and LOW ~ 0 volts a source of voltage V (the actual values of R and V are non- not important to our argument). The output voltage conducting conducting representing the logic state is taken across the switch. When the switch is OPEN no current flows through R or the switch and therefore the top of the switch is at “OFF” Logic 1 “ON” Logic 0 V volts, or a logic HIGH. When the switch is Figure 2-56. CLOSED, current flows down through R and the Gates in the form of transistors. switch, and the output is at 0 volts, or a logic LOW.

Transistor Gate OpAmp Gate The advantage of a transistor switch over a manual switch is that the transistor switch is controlled by a An opamp used as an open loop comparator can also voltage (more accurately the base current) and, in work as a switch (Figure 2-57). If Vin is positive by principle, can be made very fast. This functionality more than a few hundreds of microvolts then Vout can be achieved with the circuits of Figure 2-56. The rises more-or-less to the voltage of the positive power output voltage representing the output logic state is supply (a logic HIGH). If on the other hand Vin is taken between the collector and ground. If the voltage negative by more than a few hundreds of microvolts applied between the base and emitter of the transistor then Vout falls to the voltage of the negative power on the left is zero, or at least small—less than the supply (a logic LOW). This circuit more closely base-emitter turn-on voltage—then the base current is resembles a voltage-controlled switch than the trans- zero and the collector current is very small; the istor switch since it requires a negligible current. transistor is effectively non-conducting or “cut off”. The collector output is therefore at a logic HIGH. Here, a logic LOW (or an undefined logic) results in a 2-31 Aspects of Technology

+ As we have stated above one gate like the ones shown here is required to “implement” each bit in a binary Vin – Vout number. We shall have more to say on this subject in Chapter 3.

Figure 2-57. An opamp comparator can be used as a gate. Remember, the power supply lines are not shown here.

IC Switching Often in the sciences one is interested in controlling a relatively high-current device like an oven or a motor from a computer. Special IC switches have been developed for these tasks. The switches are usually controlled with a small current. This topic is included here because you will be using some form of solid state switch in your project in this course.

The SCR The Triac

Figure 2-58. Figure 2-59.

2-32 Aspects of Technology Practice Problems

1. A carbon composition resistor has color bands: yellow, violet, red, silver 4. The resistance of a photoresistor of R0 = 2000 W. Express the resistance in standard form. What is the light intensity in foot-candles?

2. The following circuit has two resistors. Based on 5. Show circuit of centre-tapped transformer. the circuit values is it expected that one of the Calculate peak and rms values. resistors should eventually burn out? If so, which one and why? 6. A sinusoidal waveform is described by the following expression

V = 5.0sin(2p 60t) Volts. 100 kW 10 kW 100 V 1/4 W 1/2 W What is (i) the peak value of voltsge? (ii) the peak-to-peak value of voltage? (iii) the rms value of voltage? (iv) the frequency in Hz? 3. Compute the current flowing through each resistor in the following circuit. 7. Two or three examples of opamp circuits. Calculate gain etc.

3 W

W 5 V 6 W 5

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EndNotes for Chapter 2 1 For details on the cells and batteries available on today’s market see the Enercell Battery Guidebook (Master Publishing, 1990, 1985) available at many Radio Shack stores. 2 Cells are able to rejuvenate themselves slightly if run intermittently. These figures are for continuous use and are taken from the reference in endnote 1. 3 Some electronics texts contain descriptions of various monolithic technologies that are employed in the manufacture of small-scale resistors, capacitors and inductors. One of them is: R. Boylestad and L. Nashelsky, Electronic Devices & Circuit Theory (Prentics-Hall, 5th Ed., 1992). See also the text in endnote 6. 4 The original signal represented by this display was analog. However, the signal shown here is actually a digital one since it was sampled by a digital oscilloscope. The spacing between samples is so very small, however, that the representation is an analog one to a good approximation. 5 In these notes we use the word “bias” in the manner in which it is actually used in the jargon of electronics. to denote a DC voltage. The phrases “voltage bias”, “reverse bias” and “bias” all refer to a DC voltage. 6 For details on the structure and actual fabrication of a transistor you should consult a text on transistor technology. A good beginning is A. C. Melissinos, Principles of Modern Technology (Cambridge U. Press 1990). 7 An opamp is formally described as a high gain differential DC coupled amplifier especially designed to be used with feedback. Its equivalent circuit may include more than 20 transistors. A number of stages make up its internal structure, the most important of which are a differential amplifier input (consisting of bipolar junction transistors or field effect transistors), an intermediate gain stage and a push pull output stage. The gain of the basic opamp without feedback, referred to as the open loop gain, is typically 103 to 10 6. Being DC coupled, the opamp is useable from DC to an upper bound frequency set by its structural design. 8 For historical reasons the discussion of the opamp in this section concerns the bipolar “work horse” opam, the 741. In most of the sensor designs produced by Vernier Software the opamp of choice is the unipolar Texas Instruments TLC721.

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