ECE 271 Lesson One Page 1of 25
Key Lecture Concepts for CoE225/EE 271 (Mostly Digital Electronics) by
R.B.Comely, Revision Summer 05
All Copyrights Reserved
Suggestions for Learning from the Lessons: The lessons are written so that you can learn by interactive discussions during the class and not be concerned about taking notes. Therefore the lesson overview and the bold statements should be read at least once before coming to class so that you are somewhat familiar with the subjects and can then learn better during the interactive discussions in class. This will reduce the time needed outside of class to master the topics to be tested on exams.
Note that the sentences inserted between brackets ([-]) in these lessons are not unimportant but can be left unread for continuity of reading comprehension of the key ideas that initially should be mastered before the related details are learned. Bold statements normally have to be read several times from different viewpoints to obtain thorough understanding of the subjects they address. The statements in bold type concisely present the main ideas and can be used to review the important concepts in a lesson.
LESSON ONE: Two-Terminal Nonlinear Devices.
Lesson Introduction and Overview: There are two important learning objectives for this lesson. The first is to understand the meaning of the symbols and the nonlinear current versus voltage (I/V) characteristics for two-terminal electronic devices. In the first three weeks of this course you will learn how circuit engineers use devices with these nonlinear characteristics to design circuits that can perform digital operations, e.g. NOR and AND. {Example linear and nonlinear device characteristics are sketched at the bottom of this page, along with a characteristic which models a nonlinear characteristic using linear segments.} You also will learn how two terminal nonlinear devices, particularly a device called the diode, are used to design circuits which can amplify and change the shape of electrical analog signal waveforms. Analog, versus digital, signals vary continuously and relatively slowly with time, having all possible amplitude values, versus digital signals which have two distinct values, except when switching between the two values. The concept of analog versus digital signals is illustrated by the waveforms in the margin.
The second learning objective is to show how circuits with nonlinear devices are analyzed by approximating sections of the nonlinear device I/V curve by linear (straight-line) characteristics. These straight-line characteristics can be used to construct a circuit model to replace the diode in a circuit. One circuit model is a resistor in series with a battery, as shown beneath the linear diode model below.
Example circuits with diodes will be analyzed by replacing the diodes by their models and then finding the voltages and currents, using the linear circuit analysis tools from ECE 231. By analyzing circuits with nonlinear devices in lessons 1-3, some of the digital as well as analog applications of circuits with nonlinear devices will become apparent to you.
A) Introduction to Actual Diode Characteristic, Equation, and Symbol.
Current voltage characteristic curves for one type of two-terminal device, the p-n junction diode made in silicon, are shown for different devices in fig1.1. {The figures are at the end of each lesson and are drawn large so that notes can be written on the figure. When a figure is referred to in the text, it should be held next to the text while reading the text, as if they were on the same page.} The current voltage curves for two different diodes are shown in figl.l a, pg.l 0, using a mA current scale. Note that as the voltage increases positively from zero the diode appears to conduct current only when the voltage reaches about 0.4 [v] for diode Band 0.6 [v] for diode A. This "turn-on" voltage is called the threshold voltage. Once the voltage exceeds the threshold voltage, the current rapidly increases for further increases in voltage. {The voltage needs to change by only small amounts to obtain relatively large changes in current.} Note that for values less than the threshold voltage, including negative values of voltage, there is no current, even for voltages as large as at least 50 [v] for these particular diodes.
Note the circuit symbol for the diode is an arrow touching a bar, as shown in the insert in fig1.1a. If the voltage dropped across a diode is positive on the arrow side (the anode) with respect to the bar side (the cathode), the diode voltage, VD, is said to be positive and the diode is said to be forward biased. If VD is positive the first quadrant curve describes how the current varies with the voltage drop. Note again from the characteristic for diode A that the diode conducts current only if the voltage is greater than 0.6 [v]. This voltage value is the called the threshold voltage, or turn-on voltage, for diode A. Note that the threshold voltage for diode B is 0.4 [v].
If the voltage drop is such that the voltage on the anode is less than the voltage on the cathode, the diode is described as being reversed biased and VD is said to be negative. For negative voltages, the characteristic of the third quadrant must be used. For diodes A and B the current is very small for all diode voltages that are negative. It appears to be zero for the current scale used for fig1.1 a. For example it seems as if diode B conducts current only when it is forward biased by more than 0.4 volts and that the diode does not pass current if the diode is reversed biased (the cathode voltage positive with respect to the anode, the reverse biased case). Note that the polarity 9f the diode voltage drop depends on the voltage and current sources of the circuit to which the diode is attached and not on the direction of the arrow! ! !
A mathematical model for diodes is given by equation la. Equation 1a is the form of the equation that is useful if the current is known and the voltage drop is the unknown. The three parameters of the diode are defined beneath the equation. [The values for IS and nVT describe the diode just as the value of two ohms describes a resistor.] Please look carefully at the equations and memorize them and the definitions of the three parameters: a) IS b) n and c) VT.
a) IS is the reverse saturation current, the constant current value that is observed when VD is more negative than about 100 [mv] for silicon pn junction diodes at normal room temperatures. The reverse saturation current is a sensitive function of temperature, doubling every ten degrees in silicon diodes at room temperature. [For silicon diodes the saturation current usually will normally have values between one μA and 10 fA. However, since modem diodes can have cross-sectional areas smaller than one hundredth of a human hair and as large as several square feet, as required for microelectronics and the power industry, the range of possible values for different types of diodes can be even larger. Note also that capital letters are use for voltage or current, e.g. VD, the voltage is DC; while V is the symbol for a voltage that may have ac voltage super imposed on a DC voltage. This detail is not important at this time.]
b) nVT is the product of the thermal voltage and the ideality factor, n. For convenience, the value of the nVT product is usually taken in this course to be 25 [mv], 0.025 [vI. [The ideality factor n must lie between 1 and 2. It varies with voltage but is often constant over several decades of current and usually has a value between 1.1 and 1.2.Table 1.1 (pg. 9) shows calculated values for nVT for different values of temperature using the equation VT= kT/q, where k is the Boltzmann factor 1.38*10-23 joules/°K, and q is thechargeonanelectron,1.6*10-19 coulombs. Equations and constants to obtain the values in the table are also given for the convenience of the reader. Please check a few of the calculated values.]
Diode A in fig1.1a has values for Is and nVT of 10-10 mA and 25 mV. The same diode curve is shown in fig1.1 b but with the voltage and current scales much smaller (fA and mV). (Values to plot these curves were obtained by inserting various VD values into equation 1.1a.) Fig1.lb shows that there is indeed a current when the diode is reversed biased and that it increases with reverse voltage until it saturates at the Is value of 10-10mAwhen the voltage is about 100mV, or four times the value of nVT. When forward biased, the diode conducts immediately with voltage. However, remember that the current scale is in fA versus the mA scale in fig1.1a. Thus there is actually no significant current at the mA level until the voltage reaches 0.6 [v] in the forward direction.
In fig1.1lc diode A is compared with a diode that has a much smaller value for IS, 10-14 mA. This Is value is a typical value for a GaAs diode. Note that the threshold voltage for the GaAs diode is greater, about 0.8 [v]. Note again for both diodes that once the threshold voltage is exceeded there can be very large increases in current for relatively small changes in voltage, indicative of a device with high conductance. The current is seen to change by tens of mA, for less than a 50mV change in applied voltage.
If diode characteristics for these devices are plotted on semi-log graph paper, as in fig1.1ld, straight lines are obtained because of the exponential nature of equation 1.1. One advantage of using the semi-log paper is that we can observe the change in voltage over a much larger current range. [Diodes seldom have constant values with voltage changes for n and IS because of surface effects and semiconductor material effects at very large and very small current density levels. However, linear behavior over 4 or 5 decades on semi-log paper is often observed. The deviation from linear behavior for small and large currents can be observed from diode I/V plots on semi-log paper. ]
Returning to fig1.1c, note that the dotted straight lines can be used to approximate the change in current with changes in voltage in the highly conducting regions. Linear increases in device current with increases in device voltage can be modeled in circuits
by resistors. This linear approximation is the basis for the use of circuit models with resistors and batteries for nonlinear devices for regions of operation where the I/V curve is nearly linear. For diode A, a 30 mA change in current occurs for only a 40 mV change in voltage or the diode behaves approximately as if it a resistor of only 4/3 ohms.
Exercise 1.1. For a diode with IS = 10-10 [mA] and nVT = 0.025 [v], find vD when ID = 2.779 [mA], 0.0444 [mA], and 0.666 [mA]. For each current calculate the power consumed in the diode. Answers: vD = 0.6012, 0.4978 and 0.3928[v]; P = 1.67 mW, 22 mW, 0.2616 mW. Note that the diode voltage changes relatively slowly with large current changes due to the logarithm function.
Exercise 1.2 How much current would be required to increase the diode voltage to 0.8059 [v]? Answer: ten amperes. Note that it is difficult to get more than a 0.7 volts drop across a diode without passing a large amount of current through a diode. A diode with a large cross-sectional area and a high power consumption rating would be needed.
Do you know what a one-watt power consumption rating means? What would happen if the diode dropped 0.6 [v] when 2 amperes of current flowed through it? Answer: The power consumed would be 1.2 W, which would exceed the maximum power rating of the diode.
This would result in excessive heating of the diode and the diode I/V curve would be changed, perhaps becoming an open circuit.
Exercise 1.3. What is the resistance value corresponding to the straight line approximating the GaAs diode curve in fig1.1c? Note that the line was drawn as a tangent to the diode curve at slightly lower currents than for the silicon diode. [Answer: 1.9 +/– ~.04 ohms.]
B) Review of Circuits One Concepts and Methods Used in Electronics.
Examples and exercises illustrating basic circuit analysis concepts and methods learned in Circuits One will be handed out in class. Being able to apply these concepts quickly is essential for analysis of circuits in digital electronics. About 45 minutes of class time will be available to interact with the class to practice particularly the five concepts used over and over in this course: voltage division, potential difference, node analysis, and voltage and current sources. The professor should be informed immediately if a student needs more review instructional time as almost all students who fail Electronics One do so because of a weakness in understanding and applying these concepts.
C) Linear Models and a Five Step Approach to Solve Simple Diode Circuits.
A general 5-step approach for diode circuit analysis using linear models will be presented. The simple circuits to be analyzed are in fig1.2c along with a step-by-step analysis. The unknowns for the problems are the diode voltage and current, VD and ID, and the voltage with respect to ground, VX. A voltage and current pair determine a single point on the characteristic. It is called the “Q point”. {As will be learned in ECE 372 Q stands for quiescent or quiet. The voltage and current of a Q pt. are the values that would be measured for the device in a particular circuit, if there were no ac voltages in the circuit.} Before introducing the five steps, the values for the device models for the three regions will be discussed in detail.
Assume that the nonlinear curves for a diode characteristic can be modeled by the three-segment characteristic shown in Fig1.2a. Note that for diode voltages greater than 0.5 volt there is a 50mA change in current for a 0.5[v] change. This behavior corresponds to a 10 W resistor. Fig1.2b shows more clearly the models that can be used for each of the three regions of the diode represented by lines. For a diode with a forward voltage across it greater than 0.5 [v], a battery of 0.5 volts in series with a 10 W resistor can replace the diode. The battery accounts for the portion of the total voltage applied to the circuit that must be dropped across the diode without causing any current flow. It can be considered to be a voltage drop that must be subtracted from the applied voltage to the diode to obtain the voltage that is applied across the internal resistance (10 W) of the diode. In no way should the battery be considered to be an energy source that causes current to flow! The 10 W internal resistance models only the forward biased conducting region of the diode curve. It accounts for the increase in diode current for voltage increases above 0.5 volts. {A classic error is to replace the diode by a battery and resistor when the voltage across the diode is less than the threshold voltage.}