Semiconductor Diodes Terminal Characteristics Objective The PN junction semiconductor diode is a real device whose steady-state terminal volt-ampere approximates that for the idealized diode definition. Although they have significantly different terminal characteristics it is nevertheless common practice for both devices to be represented by the same icon. Hence some care is needed to distinguish which diode the icon implies; generally however this is unambiguously clear from context. The diode is an important circuit element in its own right, as well as being important in understanding the operation of other devices, in particular but not limited to the bipolar junction transistor. As is true generally for semiconductor devices the diode terminal volt-ampere relation is nonlinear. Approximating the diode by a simpler PWL model is very useful for reasons noted elsewhere. In this note on diodes a qualitative description of junction phenomena leading to the basic diode terminal relation is presented. This is intended to provide a conceptual background against which to better appreciate junction characteristics. Then the characteristic of a representative1N4004 diode is examined (via a computer analysis using a nonlinear diode model) to illustrate theoretical expectations. Some often useful generalizations are made about diode characteristics. Then the idealized diode is used to describe modeling of real device characteristics. Finally a useful computer model approximating an idealized diode is described, primarily for a limited pedagogical use. Addendum: a) For the present we assume that the diode internal physical processes are fast enough to be able to adapt essentially instantaneously to changes in diode terminal voltage. The practical meaning of ‘instantaneous’ is that physical changes in the diode state are more or less complete before terminal voltages and currents change significantly. However the internal response time although it usually is very short still is finite, and in a number of increasingly common applications a diode may not respond quite fast enough for the reaction to be 'instantaneous'. This aspect of the dynamic behavior of the diode we consider separately later. b) Computed terminal characteristics are used to illustrate the discussion of device characteristics. There are some aspects of this use that should be appreciated. The computations are derived from mathematical models, not real devices. However model parameters have been selected to closely characterize measured terminal properties, and the models are extremely valuable in predicting device behavior in a circuit. Still they do not in general reflect all the physical interactions in the operation of a real device, and the distinction between a model and the device modeled ought to be kept in mind always. Indeed in many cases the mathematical description of the model is not a description of the device physical processes themselves but rather is a 'behavioral' model simulating device terminal behavior mathematically without direct reference to physics. The point is simply that computer models are invaluable but not infallible. Introduction A detailed technical examination of the fabrication technology and the physical phenomena associated with a semiconductor junction is no simple undertaking, and it is not to be found here. On the other hand a broad qualitative appreciation of semiconductor junction physics can be of enormous help in the application of semiconductor devices in electronic circuits. Hence a review of a qualitative discussion of semiconductor physics such as is found in the ECE311 text is recommended. While there are several semiconductors of technological interest it is sufficient for our needs to consider only silicon semiconductors. Silicon exhibits a remarkable confluence of metallurgical, chemical, electrical, and mechanical properties that give it general commercial preeminence as a semiconductor material. The silicon semiconductor diode is a two-terminal element exhibiting which unlike (say) a resistor exhibits non-bilateral behavior, i.e., current flow through the device is easier in one direction than the other.
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The conventional icon representing a semiconductor diode is drawn below; the equation shown is a theoretical expression (not derived here) for the diode volt-ampere relation. Conventional voltage and current polarity definitions are indicated in the drawing. The icon reflects the non-bilateral behavior of the junction, i.e., there is a direction (forward) of ‘easy’ current flow, and a direction (reverse) of ‘hard’ current flow. The icon is an arrow that ‘points’ in the direction of easy current flow; forward bias corresponds to V ≥ 0 and reverse bias corresponds to V ≤ 0.. The 'emission' parameter 1 ≤ N ≤ 2 allows heuristically for the effect of different diode fabrication methods and construction. q is the electron charge, k is Boltzman's constant, and T is the Kelvin temperature. At room temperature q/kT ≈ 40, so that a forward bias of about 0.2 volt or more is sufficient to make the exponential term >> 1. Is is a temperature-dependent device parameter reflecting various semiconductor material properties. Is is typically a very small current, nanoamperes or less for diodes not specifically designed to carry high currents.. Hence forward-bias voltages of several tenths volt are necessary to bring the diode current above the microampere level. Forward Bias The computed forward-bias volt-ampere characteristic of a 1N4004 diode (PSpice model used to compute the characteristic) is shown below for several temperatures; this is representative of small-geometry diode characteristics. Note that the forward-bias current does not reach a current about the milliampere level until a threshold (‘knee’) voltage of roughly 0.5 volt is crossed. It is useful to note, as is generally true for
diodes of the 1N4004 type, that roughly 0.1-volt change in forward bias increases the current by about an order of magnitude. Note further that the forward-bias voltage needed for a given current decreases as the temperature increases, i.e., as the average thermal energy of the carriers increases. For silicon the bias voltage needed for a given current is reduced roughly 2 millivolt per ° C temperature increase. Because of the large current range for a forward-bias junction a logarithmic re-plot of the characteristics as shown below is informative. Note the close adherence to an exponential dependence of current on forwardbias voltage over the several orders of magnitude plotted. For diode operation in the milliampere current range around room temperature the bias will be roughly 0.6 to 0.7 volt. Note again that around room temperature a bias voltage increase of 50 to 100 millivolts or so increases the current by roughly an order of magnitude.
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At the risk of a compounded sophistry the PSpice 1N4004 diode model is used to estimate the emission parameter by plotting data as shown in the figure to the right. Actually the precise value of the emission parameter is 1.984 and the calculated value of the ordinate in the figure following is 51.6 at room temperature; this value is built into the model explicitly. On the other hand the model quite accurately reflects the actual device characteristics, and the computation serves to suggest what an experimental determination almost certainly would show, i.e.,
Reverse Bias If the diode voltage polarity is negative the diode is said to be ‘reverse-biased’. In the theoretical expression for the diode current this corresponds to the exponential becoming much less than 1 with a few tenths volt reverse bias. The following figure plots the reverse-bias current for several temperatures. Note the considerable difference between the reverse-bias current level and the forward-bias current range.
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Incidentally what is measured experimentally as the reverse-bias current ordinarily is not actually Is. Is generally is so small that it is difficult to measure directly and, in addition, other conduction phenomena tend to mask the current. Suppose, for example, there is a resistance of 10 Megohm shunted across the 1N4004 diode; contamination of one sort or another, e.g., skin oils, could do this. A reverse-bias voltage of just 1 volt then leads to a ‘reverse’ current through this shunting resistance of 100 nA, an order of magnitude larger, for example, than Is for the 1N4004. For forward bias of course this comparatively small current is not significant. This sort of shunting is evidenced by an apparent reverse-bias current that increases as the reverse-bias voltage magnitude increases. To determine Is experimentally preferably measure the forward-bias current for I >> Is, and plot ln(I) vs. junction voltage V. This is a line which extrapolated to V = 0 provides ln(Is). Idealized Diode Basic circuit analysis courses introduce the concept of idealized lumped-circuit elements. These are fictional constructs that embody some essential aspect of real device operation. For example the idealized linear resistor embodies the property of power consumption implicit in Ohm’s Law. There is a not entirely unnatural tendency to identify the canonical resistor icon with, for example, a familiar commercial cylindrical composite device with colored bands identifying resistance value and tolerance. In fact however the icon represents only the dissipation characteristic of that or in fact most other physical devices. Real devices, in which several physical phenomena generally operate concurrently, are described to some degree of approximation by a combination of idealized circuit elements. Thus a real resistor may need to be described for some uses by a combination of idealized resistors, idealized capacitors, and idealized inductors. The idealized resistor icon need not even represent a specific component; it might for example represent collective power consumption by an unspecified device, e.g., by a motor under load, or by a TV set. At this point we review a special idealized circuit element –the idealized diode. The idealized diode is an abstract approximation to a property of a ‘real’ diode, in the same general sense that an idealized resistor is an abstract approximation to a property of a ‘real’ resistor. That is it abstracts a particular aspect of the real diode operation. In later discussion we compare the idealized diode volt-ampere relation to that of real diodes, and use idealized diodes as part of the representation of the volt-ampere relation of various devices incorporating diodes, e.g., the bipolar transistor. Temporarily however the idealized device can be viewed simply as a fictional construct for purposes of an abstract discussion, a construct that later will turn out fortuitously to be useful in the real world. The idealized diode is defined as shown to the right. Note particularly the polarity assumptions for the voltage and the current in terms of which the diode volt-ampere property is defined. The idealized diode is in a limited sense analogous to a perfect mechanical knife switch, i.e., current flows without dissipating energy when the switch is closed (the ON state of the diode) and no current flows (and there is no dissipation) when the switch is open (the OFF state of the diode). However a mechanical switch requires an additional mechanism or intervention of some sort actually to open or close the switch; the idealized diode switches automatically on the basis of the voltage or current level. (To help avoid a common conceptual difficulty note carefully that the diode characteristic itself is not discontinuous at the origin; it is the slope of the diode characteristic that is discontinuous. If it were otherwise there would be difficulties with Conservation of Energy (KVL) and/or Conservation of Charge (KCL) principles.) The idealized diode is ‘piecewise linear’ (PWL), i.e., it is linear except for the discontinuity in slope (i.e. first derivative) at V=I=0. What this means insofar as the analysis of an idealized diode circuit is concerned is that instead of analyzing (with attendant difficulties) one non-linear circuit we may use two relatively simpler linear analyses, one for each segment of the characteristic. Latter we consider this partitioning in relation to the mathematical technique of approximating a non-linear curve by a set of secants; in the limit as the number of secants approaches ∞ (and secant length -> 0) a highly accurate approximation to direct use of the non-linear curve is obtained. This is basically the procedure generally ECE 414-Diodes
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used, for example, to estimate the area under a curve. There are of course some bounds to the charm of this simplification; having to perform too large a number of linear calculations, for example, tends to make a direct numerical analysis more attractive. However experience has demonstrated (and will do so again later) that even a crude linearized circuit approximation often can provide truly remarkable effective assistance in a circuit design. Illustrative Idealized Diode Circuit Analysis First some abstract remarks to provide a general background, and then a specific illustration of a circuit analysis in which, for simplicity, we consider only circuits which, except for idealized diodes, are linear, i.e., involve circuit elements which have linear terminal volt-ampere relations. Linear elements include the idealized resistor, capacitor, inductor, transformer, and independent and controlled voltage and current sources. Since each idealized diode by definition either is in an open-circuit (OFF) state or a short-circuit (ON) state it follows that for specified diode states the circuit behavior is linear. As source voltages and/or source currents vary diodes may change states, i.e., a diode which is initially open-circuit may become short-circuit, or vice versa. Each diode change in state in general changes the network topology, e.g., a diode switching to an open-circuit condition effectively removes from the active circuit any elements with which it is series. However after the diode change of state the circuit, although topographically not the same electrically as before the change, nevertheless is again a linear circuit. Since the circuit topology remains unchanged unless and until a diode changes state circuit variables are linearly related, i.e., the relationship between any pair of variables graphs as a segment of a line. In general as the strength of an independent-source variable is increased monotonically from -∞ to + ∞ branch voltages and currents change, and eventually a diode (generally) will change state. At that point the relationship between the variables plotted changes (the circuit topology and so the application of Kirchoff’s laws has changed), and a different line segment is involved. Because of the monatomic character of the assumed source change it follows that in a linear circuit a given diode will change state no more than once if at all. Hence for a circuit involving N diodes there can be at most N changes of one or another diode state, and so at most N+1 line segments are involved in a complete description of the circuit performance. Note however that there may be fewer segments in special circumstances although there cannot be more. While in general there are no more than N+1 segments needed in describing the performance of a particular N-diode circuit the number of conceivable combinations of diode states is 2N. If there is more than one diode in the circuit then (since 2N > (N+1) for N > 1) there are more conceivable diode state combinations than there are segments. For example, for N = 2 the maximum number of segments is 3, but there are four possible combinations of diode states to consider. It follows that not all conceivable combinations of diode states actually are realized in any specific circuit involving more than one diode. (As a simple illustration consider a pair of back-to-back diodes; the diodes cannot both be short circuit concurrently, nor can they both be open-circuit concurrently. (Parenthetical comment: consider the relationship between the current through and the voltage across a back-to-back diode pair. Is this relationship piecewise linear?) For a voltage or current discontinuity to occur at the point where one segment ends and another begins violates the energy conservation requirement (for voltage) or the charge conservation requirement (for current), and cannot occur. The discontinuity always must be in the slope of the two adjacent segments. Note that with zero voltage across and zero current through the diode at the point where it changes state a physical distinction at that point between forward-bias (ON) and reverse-bias (OFF) operation is moot. As noted before a mathematical existence theorem proves that a solution of a valid linear circuit exists and moreover that solution is unique. It follows from this that within the domain of each segment individually there is a unique solution. By induction then there is one and only one result for the analysis of a PWL circuit. This unique solution can be identified by just three necessary and sufficient conditions: Within the domain of each segment a) KVL must be satisfied; b) KCL must be satisfied; c) The volt-ampere (constitutive) relations of the individual circuit elements must be satisfied. It is with respect to item c) that uncertainties arise in a PWL circuit analysis, since the portion of the diode volt-ampere relation applicable depends on its initially unknown circuit state. Thus it appears that the ECE 414-Diodes
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results of a circuit analysis really must be known a priori to determine the appropriate diode state to use for the analysis to obtain the results. Fortunately there is a straightforward if indirect means to resolve this difficulty. Simply assume a diode state for each diode (it can be simply a random guess, but an educated guess can simplify the analysis), and analyze the corresponding linear circuit under the assumed circumstances. The solution process itself, absent a procedural error, assures the satisfaction of KVL and KCL. Similarly no question arises about satisfaction of the circuit element volt-ampere relations other than those for the diodes. Absent an error the only uncertainty in the analysis is whether or not the correct assumption was made about diode states initially. Determine separately for each diode whether the assumed diode state is consistent with the solution based on that assumption. This means simply that a diode assumed to be in an open-circuit state must be reversebiased by the calculated circuit voltages. Similarly a diode assumed to be short-circuit must carry calculated currents in its forward direction. If for a given diode the appropriate condition is not satisfied then the necessary and sufficient conditions for the unique solution are not satisfied (diode volt-ampere relation is not satisfied), and the assumption made about the diode state must be wrong. But then since a diode has just two possible states the correct diode state assumption to make immediately becomes clear. Consider, for example the circuit drawn to the left. There are two (idealized) diodes, and hence in principle four combinations of diode states to consider. But in this particular circuit it is not difficult to determine directly that D2 must be closed; if it were not there would be no current through the 5KΩ, no voltage drop across this resistor, and an inconsistent 9V forward-bias for D2. Hence D2 must be closed (i.e., short-circuit), and so carry a current of 1.8 ma in the forward direction for D2. But D1 also must be closed, since if it were not there would be an inconsistent forward-biasing voltage of 9V across it. Hence D1 carries a forward current of 0.9 ma. And despite what intuition may suggest KCL then requires I = -0.9ma (note the polarity of I carefully). A somewhat more intricate circuit involving two diodes is drawn to the right. For the present we use a straightforward brute force approach to analyzing this circuit; each possible combination of diode states is considered individually for validity. That is, we make use of the fact that a unique solution exists, as well as the known conditions to establish the correctness of a proposed solution. There are four combinations of diode states to evaluate, and we do each in turn. The methodology is straightforward albeit tedious. A specific combination of diode states is assumed; the diodes are replaced by an equivalent open- or short-circuit as appropriate. The circuit then is analyzed, and the results are used to validate (or not) the assumed diode states. Circuit A (left) assumes both diodes are open, but this cannot be. Since no current flows both D1 and D2 have forward-biasing voltages. This is inconsistent; the assumed diode states require reverse-bias. Circuit B also is inconsistent; in this case there is a forward-bias voltage of 3 volts across D1, which is assumed to be reverse-biased. And Circuit C also is inconsistent since D2 has a forwardbias voltage of 3 volts. The remaining possible diode state combination is that in Circuit D, and since there must be a unique solution (and assuming no errors in the analysis) this can be anticipated to correspond to the consistent solution. To verify this note that the current through the 5KΩ resistor is 1.8 ma while that through D2 is 0.9 ma and is properly directed. The current through D1, also is properly directed, ECE 414-Diodes
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Idealized Diode (computer model) The idea of creating an idealized diode model to simplify ‘hand’ calculations in making design estimates is discussed elsewhere as part of a review of PWL analysis. Idealized diodes are useful to simplify ‘hand’ calculations, enabling relatively quick and generally adequate analytic approximate calculations. Such calculations often provide a good indicator of the interaction of circuit components to produce a given circuit performance, as well as some idea of the relative importance of the component contributions. This kind of understanding is more difficult to come by using a numerical calculation. It also is often useful to suppress secondary aspects of actual circuit behavior to concentrate on the dominant aspects; this is also something an approximation can do. Use of simplified models supports the application of judgment to design situations. Subsequent computer analysis using non-linear device models can refine approximate designs. Since more accurate nonlinear diode models would be used for computer calculations ordinarily there is no particular computational advantage to temporizing with a less accurate computer model. It may appear peculiar therefore to degrade a nonlinear diode model to approximate an idealized diode for a computer computation.. But this apparent incongruity should be evaluated in terms of objectives. At the very least for instructional purposes, it is often convenient to use a computer analysis to compare the results of an idealized diode PWL circuit analysis with those for an analysis using a nonlinear device model. For this and similar purposes a computer model for the idealized diode is useful. This requires rather more care to develop that might appear to be the case at first. The discontinuity in slope at the origin creates some computational difficulties. It turns out, almost perversely, that a continuously differentiable nonlinear model for the idealized diode is to be preferred. (This may be considered as one indication of important distinctions between a hand calculation and a computer analysis.) There are several ways of devising a satisfactory model, but probably the simplest way is to modify an existing nonlinear diode model appropriately. The following remarks, although generally applicable, are expressed specifically for PSpice use. Suppose the diode emission parameter N is made very small, say 10-6. In effect this reduces the voltage required for a given forward bias current by a factor of one million! If about a 50 mV change ordinarily causes an order of magnitude current change in a real diode then the modified diode requires only 50 nanovolts for the same change. Hence the forward-bias diode characteristic rises quite sharply, not abruptly but continuously, within a few nanovolts of the origin. (Keep in mind that this is a computational trick; the modified nonlinear model does not correspond to a real diode.) The reverse current is not the idealized zero value but it is quite small (and can be made smaller if the need arises). There is an additional ‘catch’ however that has to be considered to avoid computational problems. Because of the extraordinarily large increase in forward current with small forward-bias voltage it is possible for the computed current magnitude to exceed the storage size limitations of the analysis program or to become so large as to cause mathematical convergence problems. To avoid this another parameter in the computer diode model can be used; the nonlinear model includes a parasitic resistance (RS) in series with the ‘real’ diode, representing for example lead resistance. This can be used as a current limiting resistance; a milliohm will do nicely to limit current magnitudes to less than about 10 kiloamperes. (Again note this is just a computational trick to avoid computational problems.) To realize this idealized diode computer model in PSpice place and select a 1N4002 diode. Then select Model from the EDIT menu, and in the dialog that opens select the middle ‘Edit’ item. In the list of model parameter that is presented change Rs to 1m and N to 1u. PSpice will use the built-in default diode model with the parameters N and RS changed as prescribed. Examples of this usage appear below.
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Diode Comparison Computation The following computer analysis makes a comparison between a 1N4002 nonlinear PSpice model (closely approximating real diode characteristics) and a diode model idealized as described above. For purposes of comparison we also use the idealized diode in series with a fixed voltage source model more closely a ‘real’ diode by allowing for a threshold ‘turn-on’ voltage of Vo as illustrated to the right. Three parallel diode branches as shown below are examined for their behavior as the voltage VS is varied. As VS increases from an initial value of –0.5 volts the diodes, initially all reverse-biased,
eventually become forward-biased. The idealized diode branches without the offset voltage ‘breaks over’ at essentially zero volts and the voltage drop across the diode does not change significantly thereafter. In the branch with the offset voltage the diode remains reverse-biased until VS reaches the 0.7v threshold, and thereafter the diode plus offset voltage remains fixed at 0.7v. The 1N4002, on the other hand, must wait for the ‘knee’ to be passed before enough current flows to cause a significant voltage drop across the series resistor. The 1N4002 bias voltage then increases slightly as the diode current increases, corresponding to small junction voltage changes needed to obtain large changes in current.
A different perspective is afforded by plotting the diode currents rather than voltages. VS and the series resistor determine the current through the idealized diode. Since the forward-bias voltage is zero; the slope corresponds as it should to a 1 kΩ resistance. Except for the 0.7v offset the same behavior is shown by the modified diode branch. ECE 414-Diodes
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For small currents, i.e., when the voltage drop across the 1k≈ resistor is small compared to the diode voltage drop, the 1N4002 characteristic has a exponential shape. There is very small current flow until the diode bias exceeds the ‘knee’ of the1N4002 characteristic at a few tenths of a volt. The diode current increases somewhat less rapidly than for the idealized diode because the forward voltage rises as current increases; there is hence less voltage drop across the series resistor. Eventually the source voltage becomes ‘large’ compared to changes in the diode voltage and the voltage drop across the resistor is essentially VS. Note that the slope approaches 1 KΩ as the source voltage increases Incidentally note that the idealized diode should be a good approximation for the real diode in circuits in which the 0.7volt (approx.) forward-bias voltage is small compared to other significant circuit voltages. Further improvement in the approximation is obtained by adding the offset voltage.
Reminder About Junction Dynamics The discussion thus far has been of steady-state junction behavior. In general for a change of state to occur a corresponding charge redistribution must occur within the junction. Inevitably there is a finite transition period during which change occurs. How important this transition period is depends on whether the charge redistribution delay is small compared to the time for which circuit voltages change significantly. If it is then the new internal steady state is reached before the external circuit can respond appreciably, and the internal redistribution delay can be ignored. In effect the device behavior can be described adequately as a sequence of steady-state conditions. This is in fact the case for a great many important applications, and in general it is presumed to be the case in subsequent discussion unless and until an explicit reconsideration is made somewhat later. Note that this does not exclude circuit dynamics from consideration, i.e., so long as significant reactive element time delays are much larger than the device time constants the latter can be neglected. Idealized Diode Circuit Illustration Assume for simplicity that the diodes in the circuit to the right are idealized diodes; we will determine the transfer relationship between Vout and Vin and show the circuit approximates the square-root voltage transfer function Vout = √Vin for 0 ≤ Vin ≤ 25v by a series of secants Although we do not consider the design procedure in detail here the basic underlying concept is straightforward. An (idealized) diode either is effectively an opencircuit, or it is effectively a short-circuit. In the former case a circuit elements in series with the diode are electrically removed from a circuit, and in the latter case they are added to the circuit. Voltage sources are used to determine the conditions for the introduction/removal of a diode branch. ECE 414-Diodes
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The square-root curve to be synthesized is plotted below (secants are not drawn). The secant approximation to be used will agree precisely with the theoretical expression at Vin = 0, 1, 4, 9, 16, and 25 volts respectively (emphasized points) i.e. a straight-lines are used to connect successive points on the curve. Note in the circuit shown that the diodes are biased so that all diodes are reversebiased (open-circuit) for Vout ≤1v, and so all diode branches for this condition are effectively open-circuit. It follows that Vout = Vin for 0 ≤ Vin < 1; this provides the first secant extending from the origin to the point (Vin, Vout) =(1,1). When Vout reaches 1 volt the diode with the 1v offset bias becomes forwardbiased, and remains so for 1v ≤ Vout ≤ 2v. The effect is to activate this diode branch. It is then a straightforward circuit calculation to determine that for this condition Vout = [(Vin - 1)/(R + R/2)][R/2] +1 = (Vin + 2)/3. This plots as a line that extends from the point (1,1) at the end of the first segment to what is the end point of this second secant at (4,2). This end point corresponds to the point at which the next diode (2v bias) turns ON and a second diode branch is activated. Note that the secants form a continuous function, although the slope changes discontinuously at the point where successive secants meet. When Vout reaches 2v (and until Vout = 3v) the first two diodes both are ON. Write (say) a node equation at the output node: (Vin – Vout)/R = (Vout – 1)/R/2 + (Vout – 2)/R/2, and simplify to Vout = (Vin – 5)/6. This secant is valid from the point (4,2) to the point (9,3). It is left as an exercise to verify that the remaining secants as predicted correspond to the remaining diodes being turned ON in succession. As each diode is turned ON it adds an additional shunt branch. Of course idealized diodes are hard to come by in practice, and so for an evaluation of circuit performance we use 1N4002 diodes (PSpice model). First however to bring the idealized diode design closer to a 1N4002 the circuit is modified as shown below. The offset voltage in each branch is divided into two parts, with a nominal 0.7v part associated with the diode. It is the combination of the fixed offset voltage and the idealized diode that is replaced for the PSpice computation by the 1N4002 diode model (indicated by the dashed rectangles). Standard resistance values (10%) of R = 68k and R/2 = 33k are used. A comparison between theoretical and computed results is facilitated by plotting Vout2 vs. Vin; this should plot (ideally) as a line with unit slope. A plot of Vin vs. Vin provides this unit slope line.
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in practice additional changes would be used to improve the design. For example the offset voltages could be provided by a resistive voltage divider; the source voltage for the divider could be adjusted to calibrate the circuit, e.g., make the experimental and theoretical voltage output agree at Vin = 5v. Since there already is a precise agreement for Vin = 0 this adjustment will force a closer fit at intermediate points. This adjustment is not done here.
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ILLUSTRATIVE PROBLEMS (1) Diode Clipping A computer analysis of the diode circuit drawn to the right serves to further illustrate diode behavior. The source (use VPWL in PSpice) presents a triangular waveform (see below) across the series combination of a diode and DC offset voltage source. The computer analysis uses the 1N4002 nonlinear PSpice diode model; this diode is a general-purpose low-power rectifier diode. The computational results are plotted below. Use PSpice to reproduce the voltage V(2) as shown. Then use an idealized diode mode both to anticipate (belatedly) and also to evaluate the computational results. It is not be difficult to recognize (assuming an idealized diode) that V(2) will be equal to the source voltage when it is less than the offset voltage, and equal to the offset voltage otherwise. Evaluate the plot in terms of expectations from the idealized analysis. Take account of ‘the threshold’ for the 1N4002 Note: The idealized diode model has a zero threshold (‘knee’) voltage while the 1N4002 threshold is 0.5 - 0.7 volts or so. Account for this in interpreting the plot. . Sketch a rough plot of the anticipated diode currents, and then compute the currents for comparison.
(2) The circuit diagram (below) shows an improved experimental realization of the theoretical Square Root transfer function described above; V(2)2 ≈ VS for 0 ≤ VS < 25 volts. Note that the theoretical value will agree with an experimental value for VS = 0 volts. A second point of agreement can be realized by a calibration step; adjust V1 (experimentally) so that experimental and theoretical agreement is obtained for VS = 25 volts. The value so obtained for this calibration step is 10.6v. Making the theoretical and experimental (virtual) characteristics agree at the two ends tends to force better agreement at intermediate points as well. Compute the transfer relation v(out) * v(out) vs. v(in); also plot v(in) on the same axes. Suggestion: Plot v(in) on the same axes to judge the efficacy of the design.
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(3) The large difference between forward- and reverse-bias conduction ability of a diode is the basis for the following (simplified) switching circuit illustration. A square-wave control voltage VC is applied to the back-to-back diode connection as shown to the right. The back-to-back diodes both are reverse-biased and there is no current through the pair, unless the voltage at the common node of the diodes is greater than VS. Use the idealized diode approximation to show that
Assume VS is a triangular waveform with a peak value of 4v and a nominal period of 1 millisecond, and VC is a square wave of amplitude 10v. Use R1=1KΩ, R2=R3=47KΩ. Use 1N4148 switching diodes for the computer analysis rather than idealized diodes: Compute and plot Vo. Keeping in mind the back-to-back diode connection evaluate the influence of the threshold voltage for the diodes? (4) Diodes may be used as a kind of voltage reference in integrated circuits. Although there are other generally preferable means to serve the purpose illustrated in the example nevertheless it is instructive to examine the principles involved. A Thevenin equivalent for a power supply consists of a voltage source in series with the 'internal' resistance of the supply. There is a voltage drop across this resistor which increases with increasing load current, so that the terminal supply voltage decreases. To limit this terminal voltage change in so far as the load is concerned a 'regulator' is added; in this illustration the diode 'tree'. The idea is to use the diode forward-bias property, i.e., large diode current changes involve exponentially smaller diode voltage changes. The circuit is designed to draw supply current greater than the maximum required by the load. This current then divides, part drawn off by the load and the remainder shunted through the diodes. As the load current demand changes the current division ratio changes. However provided the minimum current through the diodes (which occurs for maximum load current) is sufficient for diode operation above the threshold the voltage across the load will not vary greatly. And of course the maximum diode current,(for minimum load current) should not exceed the diode ratings. Compute the load voltage for the circuit as the load current varies from 0 to 20ma. Use VS = 10v, RS = 200Ω, RB = 150Ω. Note that for the maximum 20 ma current the terminal voltage will have dropped by 7 v from its no-load value. Use 1N4002 diodes. Compare the source current to the diode current. ECE 414-Diodes
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