Dave Shattuck University of Houston University of Houston ECE 3355 Electronics Lecture Notes Set 5 Version 36 Diodes Dr. Dave Shattuck Dept. of ECE, Univ. of Houston Dave Shattuck University of Houston University of Houston Diodes We will cover material from Sections 3.1 through 3.5 and 4.1 through 4.7 from the 7th Edition of the Sedra and Smith text. We will not cover all of the detail that is in the textbook.
Dave Shattuck University of Houston University of Houston Overview of this Part Diodes In this part, we will cover the following topics: Semiconductor Physics Overview Diode Plots, Load Lines, Diode Models The Guess-and-Test Method Useful Diode Circuits Dave Shattuck University of Houston University of Houston Diodes are like oneway valves for current. They only conduct in one
direction. This makes them very useful for some kinds of applications, but also make them inherently nonlinear devices, which makes solving diode circuits harder. Diodes It is actually possible to make a one-way valve for water flow, although it is not shown here. Your heart has one way valves. A diode is an electronic analog for the valves in your heart. Dave Shattuck University of Houston
University of Houston One Way Valves Diodes are like oneway valves for current. They only conduct in one direction. This is analogous to the valves in your heart, through which blood passes in only one direction. Heart Valves allow blood to flow in only one direction. Dave Shattuck University of Houston University of Houston SEMICONDUCTORS
AND THE PN JUNCTION There are conductors, and insulators. Semiconductors are somewhere in between in terms of their conductivity. (An aside: Semiinsulators is too hard to pronounce, and has consecutive i's.) (Another aside: Semiconductors are not the people who collect tickets on large trucks.) Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION Semiconductors have a valence of 4 they form covalent bonds with each other. With sufficient energy, an electron can break a bond, and we produce
1) a free electron and 2) a hole. Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION Free electrons can move. Thus, a material with free electrons will conduct electricity. A free electron is called a mobile charge carrier. (This is sort of redundant.) Holes can also move; this motion is virtual, but conceptually and effectively works the same way as with free electrons. Thus, a material with holes will conduct electricity. A hole is also called a mobile charge carrier. Dave Shattuck
University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION A string of silicon atoms are shown below. Si Si Si Si Si Si Si Si Si Si Si
Si Si Si Si Si Si Si Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION A string of silicon atoms are shown below. A hole has been added, by removing an electron (typically, this is done by doping, that is by adding impurities.).
Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si
hole Dave Shattuck University of Houston SEMICONDUCTORS AND THE PN JUNCTION University of Houston A string of silicon atoms are shown below. Now, we put a voltage across the string of silicon atoms. Si - Si Si Si Si
Si Si Si Si Si Si Si Si Si Si Si Si Si hole + Dave Shattuck
University of Houston SEMICONDUCTORS AND THE PN JUNCTION University of Houston A string of silicon atoms are shown below. As the electrons move, due to the voltage, the hole moves in the opposite direction. Si - Si Si Si Si Si Si
Si Si Si Si Si Si Si Si Si Si Si hole + Dave Shattuck University of Houston SEMICONDUCTORS
AND THE PN JUNCTION University of Houston A string of silicon atoms are shown below. As the electrons move, due to the voltage, the hole moves in the opposite direction. Si - Si Si Si Si Si Si Si Si
Si Si Si Si Si Si Si Si Si hole + Dave Shattuck University of Houston SEMICONDUCTORS AND THE PN JUNCTION University of Houston
A string of silicon atoms are shown below. As the electrons move, due to the voltage, the hole moves in the opposite direction. Si - Si Si Si Si Si Si Si Si Si Si Si
Si Si Si Si Si Si hole + Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION A string of silicon atoms are shown below. A hole propagates in direction of more negative
voltage. It acts like a positively charged mobile charge carrier. That is how we treat it. Si - Si Si Si Si Si Si Si Si Si Si Si Si Si
Si Si Si Si hole + Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION In a pure semiconductor, there are equal numbers of holes and free electrons, since every time a free electron gets away, a hole is created. We call a pure semiconductor an intrinsic
semiconductor. People who make semiconductors go to great trouble to make pure silicon crystals, called wafers. Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION In pure silicon wafers, the concentration of free electrons, called n, must be the same as the concentration of holes, called p, so ni = p i where ni is called the intrinsic density of free electrons, and pi is called the intrinsic density of holes. The values of n and p are functions of temperature, which makes sense, since it will determine the number of free electron/hole pairs. It follows that temperature will
dramatically affect the conductivity. Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION There are two ways that charges move: 1) due to electric fields, called drift 2) due to concentration gradients, called diffusion Well, all this is fine, but pretty useless. The market for temperature dependent conductors is pretty limited. The key step comes next. We add impurities. No. Really, what do we do? Ans: No, really, this is what we do. We add special kinds of impurities to increase the number of free electrons, or the number or holes.
Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION By introducing a whole bunch of atoms with a valence of 3, we obtain an excess of holes. (More holes than free electrons.) These atoms are called acceptors, and result in a change in the semiconductor to what we call a p material. In p materials, holes are the majority carriers, and free electrons are the minority carriers. Dave Shattuck University of Houston University of Houston
SEMICONDUCTORS AND THE PN JUNCTION By introducing a whole bunch of atoms with a valence of 5, we obtain an excess of free electrons. (More free electrons than holes.) These atoms are called donors, and result in a change in the semiconductor to what we call a n material. In n materials, free electrons are the majority carriers, and holes are the minority carriers. Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION We can put the n material next to the p material.
Right after we put these areas together, there is a concentration gradient. The only things able to move, though, are the mobile charge carriers. There is diffusion. When a hole meets a free electron, they annihilate each other. This is called recombination. We build up a depletion region, at the junction, which is depleted of mobile charge carriers. Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION When the carriers move, they leave behind a net charge density. This charge density produces an electric field which opposes the diffusion current. Therefore, the diffusion does not go on forever, but reaches an equilibrium condition.
This, in turn, produces a potential distribution in the junction. Take care. This is a local voltage drop, not a battery. It is a potential barrier to more flow of charge carriers. Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION The diffusion produces a potential distribution in the junction, which is a potential barrier to more flow of charge carriers. The voltage at the junction acts as a barrier, a hindrance to majority carrier flow. Since there are a few, but not many, minority carriers, the current will be pretty small unless this barrier is lowered. This barrier can be lowered by biasing, or the external application of voltage across the junction.
Dave Shattuck University of Houston University of Houston SEMICONDUCTORS AND THE PN JUNCTION When the voltage is applied to reduce the barrier, this is called forward biasing. With sufficient voltage, current will flow. When it is applied to increase the barrier, this is called reverse biasing. Very little current will flow. Current only flows in one direction. This is pretty neat. This is called rectification. Remember, that this is a passive device. We call this device a diode. Dave Shattuck University of Houston
University of Houston Are these diodes really useful? This is a good question. The answer is, YES! You bet they are. They are definitely worth the trouble. We will look at what kinds of things we can do with diodes, once we learn how to model them, and solve circuits that have them included. Go back to Overview slide. Dave Shattuck University of Houston University of Houston Diode Models Thus far, we have mostly had linear
components. We had nonlinear circuits when we talked about amplifiers and saturation, but we tried to avoid saturation. Now, here we have a fundamental, nonlinear device. It is not only nonlinear, it is also fundamentally polar, in that it is not symmetrical. We begin by looking at ways to model the diode. Dave Shattuck University of Houston University of Houston Diode Models We begin by looking at ways to model the diode. We need a schematic symbol for the diode, which follows. We call the p region side the anode and the n region side the cathode.
Dave Shattuck University of Houston University of Houston We show here a plot of iD as function of vD for a diode. Note the reference polarities are shown in the diagram. Diode Models Dave Shattuck University of Houston
University of Houston Diode Problem Solutions There will be 4 different ways that we could solve diode problems. 1. Use actual data for the diode, typically in the form of a plot. 2. Use the diode equation, typically in the form of a plot, or using iterative methods. 3. Use the ideal diode approximation. 4. Use the piecewise linear diode model. Actually, the ideal diode is simply a special case of the piecewise linear diode model, as we shall see. Dave Shattuck University of Houston University of Houston Diode Plots
There will be 4 different ways that we could solve diode problems. The first one is: 1. Use actual data for the diode, typically in the form of a plot. The actual data for the diode is plotted, and then the characteristics for the circuit are plotted on the same axes. The plot of the characteristics of the circuit is called a load line. Dave Shattuck University of Houston University of Houston Load Lines A load line is a plot of the characteristics of the circuit. The assumption is that the circuit, connected to the diode, is linear, and can be
modeled using Thvenin's Theorem. Thvenin's Theorem leads to a relationship that can be plotted, which turns out to be a straight line. This straight line is called a load line. Dave Shattuck University of Houston University of Houston Diode Models There will be 4 different ways that we could solve diode problems. The last three are: 2. Use the diode equation, typically in the form of a plot, or using iterative methods. 3. Use the ideal diode approximation. 4. Use the piecewise linear diode model. The last three approaches involve the idealization of the diode in a variety of ways. Which one will be useful? This depends on the need for
accuracy. These idealizations are called diode models. Dave Shattuck University of Houston University of Houston Diode Equation The first, and most accurate model for the diode is called the diode equation. iD I s e vD nVT 1 .
Where iD and vD are defined in the diagram shown. Dave Shattuck University of Houston University of Houston Diode Equation In the diode equation, iD I s e vD nVT
1 . The quantities IS = the saturation current, n = the material constant, typically in the range from 1 to 2, and VT = the thermal voltage. Dave Shattuck University of Houston Diode Equation University of Houston In the diode equation, iD I s e
vD nVT kT 1 , where VT . q VT = the thermal voltage, and k = Boltzmann's constant = 1.38 x 10-23 [Joules/Kelvin] T = the absolute temperature in [Kelvins] q = the magnitude of the electronic charge = 1.602 x 10-19 [Coulombs]. Dave Shattuck University of Houston
Diode Equation University of Houston In the diode equation, iD I s e vD nVT kT 1 , where VT . q VT = the thermal voltage, and
k = Boltzmann's constant = 1.38 x 10-23 [Joules/Kelvin] T = the absolute temperature in [Kelvins] q = the magnitude of the electronic charge = 1.602 x 10-19 [Coulombs]. Note that the thermal voltage has units of voltage, but only varies with temperature. Thus, the name, thermal voltage. Dave Shattuck University of Houston Diode Equation University of Houston We can see that the diode equation qualitatively
models the behavior of the diode, outside the reverse breakdown region. iD I s e vD nVT 1 . Dave Shattuck University of Houston University of Houston Diode Equation
Look at the plot for negative voltages. The term in the brackets is dominated by the -1 for voltages with significant magnitude, thus, iD = -IS. vD nV iD I s e T 1 . The current goes to a value, then stays mostly flat. It seems to saturate. Thus, the name, saturation current. Dave Shattuck University of Houston Diode Equation
University of Houston Look at the plot for positive voltages. The term in the brackets is dominated by the exponential for voltages with significant magnitude. Thus, we have the exponential shaped curve, in the forward bias region. iD I s e vD nVT 1 .
Dave Shattuck University of Houston Ideal Diode Model University of Houston The ideal diode model is presented graphically in the diagram that follows. i D on off Ideal Diode Model vD i
D + vD - Dave Shattuck University of Houston University of Houston Ideal Diode Model In this model, the diode can be in one of two states: it is either off, or it is on. In the off state, the current is zero, independent of voltage. This is the same as an open circuit. In the on state, i D the voltage is on zero,
off i independent of vD D current. This is the same as a short circuit. Ideal Diode Model + vD - Dave Shattuck University of Houston Ideal Diode Model University of Houston In this model, the diode can be in one of two states: it is either off, or it is on. In general, when we
solve a circuit using this model, we do not know which state the diode is in. We might have a good idea, but we do not know. i D on off Ideal Diode Model vD i D + vD - Dave Shattuck
University of Houston Ideal Diode Model University of Houston In this model, the diode can be in one of two states: it is either off, or it is on. In general, when we solve a circuit using this model, we do not know which state the diode is in. Therefore, we use the following approach. We guess, and then we test i that guess. D on off Ideal Diode Model vD i
D + vD - Dave Shattuck University of Houston University of Houston Ideal Diode Model We guess, and then we test that guess. How do we test? We use what we know. In the off state, the current is zero, independent of voltage. This is the same as an open circuit. This only happens when the voltage vD is negative. In the on state, the voltage is zero, independent of current. This is the same as a short circuit. This only happens when the current iD is positive. The underlined phrases become the tests that we use to decide if our guess are good ones.
Dave Shattuck University of Houston University of Houston Ideal Diode Model Lets try out this on some simple circuits. Dave Shattuck University of Houston University of Houston Ideal Diode Model Here are some more to try. Dave Shattuck University of Houston University of Houston
Ideal Diode Model These are a little bit harder, but involve the same approach. Dave Shattuck University of Houston University of Houston Analysis with the Piecewise-Linear Diode Model The next diode model is the 3355 Piecewise Linear Diode Model. This model with its characteristic curve, is given i D here. 1 rd
-I Vf S Piecewise Linear Diode vD i D + vD - 3355 Piecewise-Linear Diode Model This diode model is more accurate than the ideal diode model. It is not a widely used model, but we will use it to practice using special models. Dave Shattuck
University of Houston University of Houston i D 1 rd -I Vf S Piecewise Linear Diode vD i D + vD -
Dave Shattuck University of Houston University of Houston 3355 Piecewise-Linear Diode Model Labels The -Is and Vf are labels for axis values. The rd is the inverse of the slope of the line indicated. i D 1 rd -I Vf S Piecewise Linear Diode vD
i D + vD - 3355 Piecewise-Linear Diode Model Parameters IS = reverse saturation current. Vf = Thevenin Voltage for diode in the forward biased region. rd = resistance of diode in the conducting i D region. 1 Dave Shattuck University of Houston University of Houston
rd -I Vf S Piecewise Linear Diode vD i D + vD - Dave Shattuck University of Houston University of Houston
3355 Piecewise-Linear Diode Model Parameters Vf = Thevenin Voltage for diode in the forward biased region. (In previous years, we called this the threshold voltage Vthres, which is too long, or Vth, which looked like a Thevenin voltage, or VT, which looked like the thermal voltage. If you look at old exams, you may notice any of these different versions.) i D 1 rd -I Vf S Piecewise Linear Diode vD
i D + vD - 3355 Piecewise-Linear Diode Model Regions There are four regions of the plot for nonzero values of IS, Vf and rd. There is an equivalent circuit that can be used to represent the diode in each region, and a test for that region. Dave Shattuck University of Houston University of Houston i D
1 rd -I Vf S Piecewise Linear Diode vD i D + vD - Dave Shattuck University of Houston University of Houston 3355 Piecewise-Linear Diode
Model Region 1 Behavior: Constant current, independent of voltage Model: Current source Test: Is vD 0? i D 1 rd Region 1 -I Vf S Piecewise Linear Diode vD i D
+ vD - 3355 Piecewise-Linear Diode Model Region 2 Behavior: Zero voltage, independent of current Model: Wire (zero valued voltage source) Test: Is -IS iD 0? Dave Shattuck University of Houston University of Houston Region 2 i D 1 rd -I Vf S
Piecewise Linear Diode vD i D + vD - Dave Shattuck University of Houston University of Houston 3355 Piecewise-Linear Diode Model Region 3 Behavior: Zero current, independent of voltage Model: Open circuit (zero valued current source)
Test: Is 0 vD Vf? Region 3 i D 1 rd -I Vf S Piecewise Linear Diode vD i D + vD -
3355 Piecewise-Linear Diode Model Region 4 Dave Shattuck University of Houston University of Houston Behavior: Linear relationship between voltage and current Model: Thevenin equivalent Test: Is Vf vD? -- or -- Is iD 0? i D 1 rd Region 4 -I Vf S
Piecewise Linear Diode vD i D + vD - Dave Shattuck University of Houston University of Houston 3355 Piecewise-Linear Diode Model Compared to Ideal Diode Note that the ideal diode is just the piecewise linear model, but with zero values of IS, Vf, and rd.
i D 1 rd -I Vf S Piecewise Linear Diode vD i D + vD - Dave Shattuck University of Houston
University of Houston Using the Piecewise Linear Diode Model - 1 Lets try out this on some simple circuits. Solve using values of IS = 1[mA], Vf = 1[V], and rd = 1[kW]. Dave Shattuck University of Houston University of Houston Using the Piecewise Linear Diode Model - 2 Here are some more to try.
Solve using values of IS = 1[mA], Vf = 1[V], and rd = 1[kW]. Dave Shattuck University of Houston University of Houston Using the Piecewise Linear Diode Model - 3 These are a little bit harder, but involve the same approach. Solve using values of IS = 1[mA], Vf = 1[V], and rd = 1[kW]. Dave Shattuck University of Houston University of Houston
Some Other Practice Circuits - 1 Here is another circuit to practice on. Dave Shattuck University of Houston University of Houston Some Other Practice Circuits - 2 Here is another circuit to practice on. Dave Shattuck University of Houston University of Houston Nonlinear Circuits
Thus far, we have considered only analysis for constant voltages. What if the input for a circuit is not a constant? Dave Shattuck University of Houston University of Houston Nonlinear Circuits Thus far, we have considered only analysis for constant voltages. What if the input for a circuit is not a constant? Answer: Conceptually, we need to apply the same analysis, an infinite number of times. Practically, of course, this would take a long time. Dave Shattuck
University of Houston University of Houston Super Diode A diode with improved characteristics can be obtained by putting a diode in the feedback loop of an op amp. This diagram is taken from Sedra and Smith Dave Shattuck University of Houston University of Houston Super Diode Limits
This will appear to work as an ideal diode. However, as the frequency components of vI go up, its behavior degrades due to the time it takes for the op amp to leave saturation. This diagram is taken from Sedra and Smith Dave Shattuck University of Houston University of Houston Super-Duper Diode This is an improved version. The diode D2 prevents the op amp from saturating when diode D1 is off. This allows the circuit to respond to higher frequency inputs.
This diagram is taken from Sedra and Smith Dave Shattuck University of Houston University of Houston Astable Multivibrator Here is a circuit that can produce a square wave output with no input. Lets analyze it. First question: Does this op amp have negative feedback? This diagram is taken from Sedra and Smith, 7th Edition, Figure 18.26, page
1413 Dave Shattuck University of Houston University of Houston Astable Multivibrator The output voltage vO is a square wave. The non-inverting input is a voltage divider away from that output voltage. The inverting input is always chasing the output, but can only change exponentially because of the capacitor. It is a first-order step response, with a periodically changing source voltage, which is the output. This diagram is taken from Sedra and Smith, 7th Edition, Figure 18.26, page 1413
Dave Shattuck University of Houston University of Houston Rectifier Circuits Thus far, we have considered only analysis for constant voltages. What if the input for a circuit is not a constant? Conceptually, we need to apply the same analysis, an infinite number of times. Practically, of course, this would take a long time. Instead, we need to use some insight. Take the case of the circuit called the half-wave rectifier. Dave Shattuck University of Houston
University of Houston Half-Wave Rectifier Lets analyze this circuit, using our ECE3455 Piecewise Linear Diode Model, with IS = 0, Vf = 0.7[V] and rd = 0. For vs > Vf, the diode will turn on, and the output vo(t) will be just Vf less than the input. For vs < Vf, the diode will turn off, and the output vo(t) will be zero. Dave Shattuck University of Houston University of Houston Half-Wave Rectifier
Analysis For vs > Vf, the diode will turn on, and the output vo(t) will be just Vf less than the input. This diagram assumes Vf = 0.7[V]. For vs < Vf, the diode will turn off, and the output vo(t) will be zero. Dave Shattuck University of Houston University of Houston Half-Wave Rectifier Analysis
The output waveform looks very much like the input, but only the positive part goes through. If we think of positive voltage as what we want, the part that is right, then we say that the voltage has been rectified. This circuit is called a rectifier. Notice that only half of the circuit gets to the output. We call this circuit a half-wave rectifier. Dave Shattuck University of Houston University of Houston Full-Wave Rectifier The bridge rectifier is a circuit which is also called a fullwave rectifier. Essentially, this means that both halves of the input go through the output, but with the same polarity.
Dave Shattuck University of Houston University of Houston Full-Wave Rectifier, Analysis 1 In this circuit, the load voltage vL is positive for all values of the input. The output is driven for both half-cycles of the input. Thus, it is called a full-wave rectifier. Dave Shattuck University of Houston University of Houston Full-Wave Rectifier, Analysis 2 Note that the output of this circuit has a significant dc component, even though there is no dc
component at the input. Therefore, it is a nonlinear circuit, since superposition does not hold. Dave Shattuck University of Houston University of Houston DC Power Supply Requirement Since this circuit has a significant dc component, with no dc component at the input, it can be used to produce a dc power supply. A dc power supply must be a nonlinear circuit. Dave Shattuck University of Houston University of Houston DC Power Supplies, Peak Detector Power Supplies use a
rectifier with a capacitor at the output. We start with a half-wave rectifier, since it is simpler. Show Fig. 3.32 from Sedra and Smith. This is a half-wave rectifier with a capacitor, which holds the peak value of the input source, vI(t). Dave Shattuck University of Houston University of Houston DC Power Supplies, Peak Detector This circuit will hold the peak value only
because there is nothing connected at the output. When we connect a load, something different happens. Dave Shattuck University of Houston University of Houston Here we have connected a load, R, at the output. Look carefully at the diagram for the output voltage, vO(t). Note that it no longer holds the peak value, but decreases exponentially.
DC Power Supplies Dave Shattuck University of Houston University of Houston There is a short time period, which is referred to here as the Conduction interval Dt, where the diode is on, and conducts. During this time, vO(t) = vI(t). DC Power Supplies DC Power Supplies
Dave Shattuck University of Houston University of Houston There is a longer time period, which is about as long as the period of the input wave, where the diode is off. During this time, the resistor and capacitor make a natural response circuit, and vO t V p e t t2
RC . Dave Shattuck University of Houston University of Houston The total waveform, vO(t), is a complicated combination of a sinusoid, and a decaying exponential, even for a simple diode model. A more accurate diode model makes for a very complicated solution.
DC Power Supplies Dave Shattuck University of Houston University of Houston DC Power Supplies, Approximations The waveform, vO(t), is often approximated as a simpler case, that is a dc component equal to Vp, and an ac component whose peak-topeak value is called Vr, the ripple voltage. Dave Shattuck University of Houston
University of Houston DC Power Supplies, Approximations The dc component of vO(t) is often approximated by the zero-to-peak input sinusoid, perhaps decreased by the threshold voltage of the diode, and/ or by half the ripple voltage. Dave Shattuck University of Houston University of Houston
DC Power Supplies, Approximations The ac component of vO(t) which we called the ripple voltage, or Vr, can also be approximated. The following is a derivation of a simple estimate of the ripple voltage, Vr, which is defined as the peak to peak voltage on the output of the power supply. Dave Shattuck University of Houston University of Houston
Ripple Voltage Approximation The ac component of vO(t) which we called the ripple voltage, or Vr, can also be approximated. 1. Assume an ideal diode. (If the input amplitude is much larger than Vf, we make little error in ignoring Vf. If the input amplitude is not much larger than Vf, we can make a more accurate estimate by using a better diode model.) 2. Assume that RC >> T, which we make possible by picking C large. 3. Since RC >> T, we can treat the exponential decay as a straight line. Dave Shattuck University of Houston University of Houston Ripple Voltage Approximation The ripple voltage, or Vr, can be approximated. 4. The charge gained by capacitor during charging,
Qacq, is Qacq = C Vr . 5. The charge lost during discharge, Qlost, is Qlost = iL (T-Dt) iL T . 6. Here, we have assumed that (T-Dt) T, since it discharges for almost the entire period. Dave Shattuck University of Houston University of Houston Ripple Voltage Approximation The ripple voltage, or Vr, can be approximated. 7. The voltage is a straight line, with a slope we will call m, and a peak equal to Vp. So, the current is just that voltage divided by R, V p mt iL .
R Dave Shattuck University of Houston University of Houston Ripple Voltage Approximation The ripple voltage, or Vr, can be approximated. 8. Now, since RC >> T, we assume that m = 0. Then, with Qacq = Qlost, and plugging in we get Vp CVr iLT T . R Solving, we get V pT Vp IL Vr
, RC fRC fC where IL is the load current, which is almost constant with time, and so is expressed as a dc quantity. Dave Shattuck University of Houston Ripple Voltage Approximation University of Houston The ripple voltage, or Vr, can be approximated. 9. With a full wave rectifier, the frequency is effectively doubled, so V pT Vp IL
Vr , 2 RC 2 fRC 2 fC which is a very handy little equation. It is surprisingly accurate, considering the number of approximations used to get it. Dave Shattuck University of Houston University of Houston Testing the Ripple Voltage Approximation But, if we are making this many assumptions, shouldnt we test them? Yes. How? By performing The DC Power Supply laboratory exercise. This is called Experiment V. There
are lots of ways to go wrong when performing this lab. Here are 4 of them. Dave Shattuck University of Houston University of Houston DC Power Supply Lab Error 1 1) Careless use of resistance substitution box. Do not turn large scale down to zero before turning the smaller scale up to nine. If you do this, you will effectively short out the output, resulting in a very large current, and you will let the magic smoke out of the fuse. Dave Shattuck University of Houston University of Houston DC Power Supply Lab Error 2
2) Careless setting of ac/dc setting on ammeter. If you look for 0.5A of current through the load, with the ammeter set to measure the ac component, you will let the magic smoke out of the fuse. Dave Shattuck University of Houston University of Houston 3) DC Power Supply Lab Error 3 Grounding both sides of the transformer. The oscilloscope reference clips are connected to ground. If you connect these clips on both sides of the transformer, you will have shorted diode B using the reference clips of the oscilloscope probes. Significant current will flow through them, and they will get very hot. Be careful how you connect the scope clips.
Dave Shattuck University of Houston University of Houston 4) DC Power Supply Lab Error 4 The voltage regulator will have several Volts across it, and half an Amp through it. This can be about 5[W]. Will it get hot? Not if it is big. Is it big? No. So, will it get hot? Yes. Several students have walked around with small burn marks in the shape of voltage regulators on their fingers. This is not required. Use heat sinks, and be careful. Dave Shattuck University of Houston
University of Houston Linear Small-Signal Model of the Diode Remember amplifiers, biasing, and small signals? We shall look at a similar thing for diodes. Clearly, diode characteristics are nonlinear. However, in some regions, the characteristics can be replaced by a straight line. Dave Shattuck University of Houston University of Houston Linear Small-Signal Model of the Diode If the characteristic is viewed as a straight line, for signal purposes the device is just a resistor. The value of the resistance is the inverse slope of the iD vs vD characteristic, at the Q point. This will apply for small signals, around the Q point.
Q Point slope = Dave Shattuck University of Houston University of Houston Linear Small-Signal Model of the Diode In other words, if we apply a dc voltage or current to the diode, we place the diode at a Q point. Then, we can treat the diode as if it were a resistor, equal to the inverse of the slope of the diode characteristic, as long as we stay close to that point. Q Point slope =
Dave Shattuck University of Houston University of Houston Linear Small-Signal Model of the Diode In other words, if we apply a dc voltage or current to the diode, we place the diode at a Q point. Then, we can treat the diode as if it were a resistor, equal to the inverse of the slope of the diode characteristic, as long as we stay close to that point. We stay close by using only small signals, which are called small signals. slope = Dave Shattuck
University of Houston University of Houston Linear Small-Signal Model of the Diode In other words, if we apply a dc voltage or current to the diode, we place the diode at a Q point. Then, we can treat the diode as if it were a resistor, equal to the inverse of the slope of the diode characteristic, as long as we stay close to that point. We call this resistance the dynamic resistance of the diode, and label it rd. It can be expressed as: di rd D dvD
Qpt 1 slope =