Voltage Drops Are Falling on My Head: Working Factors, Linearization, Temperature Coefficients, and Thermal Runaway
As we speak’s matter was initially going to be known as “Small Adjustments Attributable to Varied Issues”, as a result of I couldn’t consider a greater title. Then I modified the title. This one’s not a lot better, although. Sorry.
What I had in thoughts was the Shockley diode equation and another vaguely associated topics.
Table of Contents
My Lecturers Lied to Me
My introductory circuits class in school included a bit about diodes and transistors.
The splendid diode equation is that this:
$$start{array}{} V = 0 & textual content{if } I > 0 cr I = 0 & textual content{if } V < 0 finish{array} $$
In different phrases, a diode acts like a brief circuit with optimistic present, to stop any voltage drop, and it acts like an open circuit with adverse voltage, to stop any present movement.
However that’s not sensible.
So the subsequent smartest thing is that we simply assume there’s a diode drop of 0.7V or so:
$$ start{array}{} V = 0.7 & textual content{if } I > 0 cr I = 0 & textual content{if } V < 0.7 finish{array} $$
However that’s not a lot better.
So then we discovered that the pn junction equation, which applies to issues like diodes and npn transistors and photo voltaic cells, has an exponential relationship:
$$ V = frac{kT}{q} ln frac{I}{I_s} $$
the place ( okay ) is Boltzmann’s fixed (( okay approx 1.380 instances 10^{23} J/Ok )), ( T ) is the temperature in levels Kelvin, ( q ) is the cost of an electron (( q approx 1.602 instances 10^{19} C )), and ( I_s ) is a few attribute present of the junction in query. What’s “attribute” right here is admittedly the present density, so for diodes and transistors ( I_s ) will increase linearly with the world of the junction. Double the world and also you double ( I_s ). At 25°C, ( frac{kT}{q} approx 25.7 )mV, so if you hear “26 millivolts” batted round lots in semiconductor principle, that’s the place it comes from.
And truly, that’s not fairly true both; in actuality there’s a “+1” within the equation:
$$ V = frac{kT}{q} ln left(frac{I}{I_s} + 1right) $$
However for all sensible functions you possibly can neglect concerning the “+1”, since for actual units, ( I_s ) tends to be within the subpicoampere vary.
So we’re left with ( V = frac{kT}{q} ln I/I_s ): at room temperature, double the present, and also you enhance the junction voltage by about 18 millivolts; enhance the present by an element of 10, and also you enhance the junction voltage by about 59 millivolts.
Nice. That’s kind of what I’ve been utilizing in my psychological mannequin of diodes and bipolar transistors for the final 20 years. This offers you the equation for ( V_{BE} ) by way of base present, or for those who fold the achieve β into ( I_s ), by way of collector present.
Besides that’s not true both. My academics lied to me! In doing analysis for this text, I discovered they neglected an element of n (or η for those who like Greek letters):
$$ V = frac{nkT}{q} ln left(frac{I}{I_s} + 1right) $$
This issue ( n ) known as the ideality issue, and it’s apparently between 1 and a couple of for many units. (Although for those who’ve acquired your head within the sand, and don’t need to take into account units which have areas of operation with ( n > 1 ), then by definition ( n approx 1 ) and every part is hunkydory.)
And that’s not true both, as a result of there are parasitic sequence resistances and different odd results, which you study in additional superior areas of research.
It’s common for academics to misinform you. They must! Every part we use in scientific modeling is an approximation; actuality has all these ugly elements that will offer you info overload and ship you working away, for those who heard about them suddenly. For instance, we consider cube as cubes, however actually they’ve the perimeters and corners rounded off, with little indentations for the pips, and the surfaces aren’t completely parallel or completely easy as a result of manufacturing limitations, and anyway you might have quantum physics coming into the combination telling you that the atoms are shifting round unpredictably, doing no matter humorous stuff they do in quantumland.
So if you wish to know extra about why pn junctions work the way in which they do, you’re taking programs on machine physics, whereas for those who simply need issues to get executed precisely, you take care of these results empirically, like measure the ideality issue (Microchip has a great appnote on utilization of diodeconnected transistors; most of the commerciallyavailable 2N3904 transistors, if utilized in a diodeconnected method, have ideality elements across the 1.0041.005 vary) and simply take care of it. For the remainder of us, simply neglect about ( n ) and faux it’s equal to 1.
However that’s not what this text is about.
SmallSign Evaluation: Working Factors and Linearization
So let’s say that you’ve {an electrical} circuit put collectively, and all of the currents and voltages are fixed, and every part’s glad. You measure it and diligently determine what all these currents and voltages are. That’s known as an working level.
Now you modify one of many enter currents or voltages, and add a very small sign ( x(t) ) to it, and measure one of many different indicators ( y(t) ) and see the way it pertains to ( x(t) ). That is known as smallsignal evaluation, and it typically depends on the idea that for small adjustments in any of the variables or parameters, programs are linear in a small area round any explicit working level. It’s the identical approach used to outline derivatives: it’s simply the restrict of the ratio of 1 variable to a different when deviations are small. This concept can also be known as linearization: for some vector of inputs ( X ) and vector of outputs ( Y ) round any given working level ( (X_0, Y_0) ), we will approximate the outputs by ( Y approx Y_0 + J(X_0, Y_0) instances (X – X_0) ) and J is the Jacobian, which is only a massive matrix of partial derivatives ( J_{ij} = partial y_i / partial x_j ) . Blah blah blah. It’s laborious to take a look at this summary stuff and see what’s occurring, so let’s take a look at a extra concrete and helpful instance.
Let’s say that now we have a diode with a 0.70V drop when it conducts 1 mA from a present supply. In parallel with the diode is a 1μF capacitor, and we give the capacitor somewhat whack by discharging it from, say, 0.70V to 0.69V and we need to know the dynamics for it to recuperate. What does the voltage appear like?
Apart from simply doing it, or working a simulation in SPICE, the linearization method says, Hmm, nicely, I’ve this approximate equation — lemme hear it once more:
$$ V = frac{kT}{q} ln frac{I}{I_s} $$
Yeah! — and we’ll take the spinoff (in case you don’t bear in mind your calculus, ( ln a/b = ln a – ln b ) and ( frac{d}{dx} ln x = frac{1}{x} ) ), and get
$$ frac{partial V}{partial I} = frac{kT}{q} instances frac{1}{I} $$
At room temperature, that is roughly 26mV divided by 1mA = 26Ω. That’s it! No ( I_s ) within the equation, not even the diode drop V. It solely relies on ( frac{kT}{q} ) and the diode present: actually easy. That’s the incremental resistance of any pn junction carrying 1mA of present, if it comes near the Shockley equation with ideality issue of 1. So what’s going to occur is the capacitor will decay again to its ultimate voltage with a time fixed of about 26Ω × 1μF = 26μs.
If we had 5mA flowing via the diode as an alternative of 1mA, the incremental resistance could be 5.2Ω, and if we had 200μA moderately than 1mA, the incremental resistance could be 130Ω. Obtained it?
In npn transistors we will do the identical factor: the collector present ( I_C ) is an exponential perform of the baseemitter voltage ( V_{BE} = frac{kT}{q} ln frac{I_C}{I_s} ); if we had an amplifier and had been modulating the baseemitter voltage, the collector present variations could be thoughtabout ( Delta I_C = g_m Delta V_{BE} ), the place ( g_m ) known as the transconductance, and it’s simply equal to ( I_C / frac{kT}{q} ). The upper the collector present, the upper the transconductance.
This type of evaluation illustrates one necessary relationship in bipolar transistors. In case you’re keen to bump up the present within the transistor by an element of Ok, the transconductance additionally goes up by an element of Ok, whereas the parasitic capacitances typically don’t change. So for those who run via the equations, you’ll discover a circuit time fixed proportional to ( C/g_m ), and the time fixed will go down by an element of Ok. In different phrases, there’s a stronglycorrelated relationship between circuit velocity and quiescent energy. As much as the purpose when circuit dynamics are decided by different elements, for those who’re keen to double the facility, you possibly can nearly double the velocity. If you would like decrease energy, it’s a must to tolerate a slower response. This comes into play with opamps as nicely; the micropower opamps typically have a a lot smaller gainbandwidth product than opamps with greater quiescent present.
Right here’s one other instance: let’s say now we have a differential pair with 2mA of present, and the voltage throughout the differential pair is 0. Oh, and every part is properly at room temperature, so ( frac{kT}{q} approx 26{rm mV} ). If the transistors are completely matched, every one has 1mA flowing, and a few voltage throughout the ( V_{BE} ) junction. Let’s say it’s 0.7V. Now let’s apply 1mV throughout the differential pair: one transistor could have ( V_{BE} approx 0.6995V ) and the opposite could have ( V_{BE} approx 0.7005V ). In case you run via the maths, this raises the present in a single transistor by an element of ( e^{0.5{rm mV} / 26 {rm mV}} approx 1.0194 ) and the opposite will lower by about the identical issue. The distinction between the currents is roughly 38.5μA. That’s what we get if we remedy the exponential equations.
Or we may use a linearization method. Have a look at every of the transistors: they every have 1mA flowing via them, and subsequently the transconductance ( g_m approx 1/26 Omega ), so a change of 0.5mV × ( g_m ) in every of them is ( 0.5{rm mV} instances 1/26 Omega = 19.2mu A ), so one goes up by about 19.2 μA, the opposite goes down by about 19.2 μA, and the distinction adjustments by 38.4 μA. The linear approximation is simple and offers us basically the identical outcome.
Tempco!
OK, again to the pnjunction equation for a transistor:
$$V_{BE} = frac{kT}{q} ln frac{I_C}{I_s}$$
Bear in mind I mentioned you could possibly fold the achieve β into ( I_s ) so you could possibly write V_{BE} by way of collector present? The V_{BE} drop relies on the bottom present, however because the collector present ( I_C = beta I_B ) I simply lumped that issue of β in with the fixed ( I_s ). In any case, we don’t actually care what ( I_s ) is, simply that it’s some fixed for any given transistor. Besides that β isn’t utterly fixed; it’s a perform of temperature, and likewise of present. And for all I do know, ( I_s ) isn’t precisely a continuing both. So let’s simply rewrite this manner:
$$V_{BE} = (1+delta)frac{kT}{q} ln frac{I_C}{I_s} + epsilon(T – 25^circ, ln frac{I_C}{I_s})$$
the place ( 1+delta ) is our ideality issue, and that ε is a few perform; its magnitude is comparatively small and it sweeps the error all into one bucket that claims we don’t actually know the way this behaves.
As a result of it’s small, we will take a linear approximation of ( epsilon(T – 25^circ, ln frac{I_C}{I_s}) ) once more, and say
$$V_{BE} = left(frac{kT}{q} + frac{kT}{q}delta + epsilon_Iright) ln frac{I_C}{I_s} + epsilon_T (T – 25^circ) + epsilon_2(T – 25^circ, ln frac{I_C}{I_s})$$
the place ( epsilon_2 ) is REALLY small, as a result of it simply handles all of the quadratic and better phrases.
The worth ( epsilon_T ) right here produces a time period that’s proportional to temperature change. That is known as a temperature coefficient, or tempco for brief. Normally temperature coefficients are constants of proportionality, measured in models of 1/°C, so that they describe how a lot one thing adjustments in relative phrases, however typically they signify absolute deviation, like within the equation above.
We are able to’t actually predict very nicely what ( delta ) and ( epsilon_I ) and ( epsilon_T ) are, but when we examined a complete bunch of transistors, we may get a statistical thought of how they behave for a given semiconductor course of. That is known as characterization, and perhaps we will decide that 99.9999% of all transistors of a given sort are anticipated to have ( 0.003 < delta < 0.005 ), ( epsilon_I < 10mu V ), and ( epsilon_T < 5mu V / ^circ C ). (These aren’t actual numbers; I’m simply making them up.) If we’re assured sufficient, and it is smart from a advertising and marketing and enterprise standpoint, we’d resolve to place this info within the datasheet to assist out clients, or at the least publish some characterization graphs.
Transistor databooks used to publish numerous helpful characterization information. Examine the 2N2222A datasheets from ON Semiconductor and Fairchild. Fairchild doesn’t publish any characterization graphs of their 2N2222A datasheet. Phooey. Whereas ON Semi does. ON Semi was as soon as a part of Motorola, which in its heyday used to publish some actually useful info in transistor databooks, and ON Semi has retained this for the commonest transistors. (In case you’re at a storage sale and occur to identify an outdated copy of a transistor databook from GE or RCA or Motorola, snap it up! They don’t write ‘em like that anymore.) There are ten characterization graphs, every part from a graph of the DC present achieve h_{FE} (basically a synonym for β) over the 100μA to 500mA vary, to turnon and turnoff instances, to present gainbandwidth product as a perform of the working level present, to a graph of voltage temperature coefficients:
The underside curve, R_{θVB} for V_{BE}, is actually the identical factor as what I described as ( epsilon_T ); it’s given as a perform of collector present, and is in absolute phrases: mV/°C. The way in which you’d learn the graph right here is that at 15mA collector present, the tempco is 1.75mV/°C, so if the temperature on the npn junction went up by 10°C, you’ll count on the V_{BE} drop to lower by about 17.5mV.
There are temperature coefficients for plenty of issues in electronics. Opamp datasheets will virtually at all times provide the typical temperature coefficient for offset voltage: within the MCP6022, for instance, it’s ±3.5μV/°C. Voltage references are one other element: the LM4041 has a spec of not more than ±100ppm/°C, whereas the TL431 doesn’t give a tempco instantly, simply an allowed voltage deviation over the rated temperature vary. Resistors will let you know the temperature coefficient of resistance; Yageo’s backyard selection thickfilm chip resistors have a tempco of ±100ppm/°C for values within the 10Ω – 10MΩ vary, and ±200ppm/°C for the low and highvalue resistors. That’s fairly typical, and what you should preserve in perspective is that over a 50°C vary, for example, ±100ppm/°C will flip right into a ±5000ppm = ±0.5% change, which is along with the ±1% base tolerance. So these ±1% resistors are actually solely ±1% for those who deal with them properly and preserve them at a continuing temperature.
Temperature coefficients of digital parts normally fall into two classes.
The primary class is when the temperature coefficient is centered round some recognized quantity. An instance is the baseemitter voltage tempco of the 2N2222. We’re caught with it, and if it issues to us, now we have to care about it, and design our circuit to deal with that habits. One other is the resistance of copper wire, with a tempco of roughly 3930ppm/°C.
The opposite class happens when the temperature coefficient is centered round zero, as within the LM4041 or in resistors. On this case, somebody has executed the work to make use of supplies in a intelligent method (e.g. manganin for resistors) or has designed an builtin circuit in such a method to cancel out the temperature coefficient as a lot as moderately attainable. So if you see ±100ppm/°C, it means the producer has tried to provide a zero tempco, however some components may be somewhat under zero or somewhat above zero, and in the event that they hadn’t been intelligent, the tempco may be nonzero on common, and far greater.
Quartz crystals are significantly attentiongrabbing on this respect. The temperature coefficient of the resonant frequency relies on the alignment of the crystal surfaces with the crystal lattice. Scientists and engineers have recognized this, and because of this, most of the quartz crystals utilized in digital oscillators are of the AT reduce selection, the place the tempco is close to zero round room temperature. The 32.768kHz crystals used for timekeeping are XY reduce, with a tempco additionally round zero at room temperature. In these circumstances, there are nonetheless variations with temperature, they’re simply minimized round zero, and since this variation is predictable, the tempco is given as a parabolic temperature coefficient, in ppm/°C^{2}, so the XYcut tempco yields a frequency vs. temperature curve that appears like
$$ f = f_0 left(1 + b(TT_0)^2right)$$
In an XYcut timing crystal just like the Epson FC1610AN, f_{0} = 32.768kHz, T_{0} = 25°C, and b = 0.04ppm/°C^{2}.
The Wahwahwahwahwonder of Operational Amplifiers
And I’m wondering,
I wahwahwahwahwonder,
why,
why why why why why
she ran away
And I’m wondering,
the place she’s going to keep,
my little runaway
arunrunrunrunrunaway
— Del Shannon, Runaway
Considered one of my electronics lessons in school was an analog electronics lab. We studied all kinds of stuff you could possibly do with bipolar transistors. In one of many labs we needed to design an opamp out of discrete transistors. In observe, you’ll by no means do that, as a result of there’s no method you could possibly come near the efficiency of even the awful 741 opamp. The purpose was for us to study one thing about how business opamps work in observe, and to see that we may make it work even when we had been caught with discrete transistors.
Right here’s the circuit equal from the LM741 opamp, the one we prefer to hate:
Doesn’t it look lots like hieroglyphics?
To know how an opamp works, it helps to disregard the main points and deal with the large image. Right here I’ve annotated the circuit diagram:
The enter stage is made up of a differential pair of NPN and PNP transistors Q1This fall; via the magic of transistor circuits, the distinction in voltage between the inputs is was a present sign proportional to that voltage distinction, and despatched into the singleended Darlington amplifier made up of Q15 and Q17. Resistors R7, R8, and the unlabeled transistor (Q16?) kind a levelshifting circuit; C1 is the interior compensation capacitor that feeds again into the bottom of Q15; and transistors Q14 and Q20 kind a pushpull output stage, with Q15 (the second Q15? Come on, Nationwide/TI, proofread your datasheets!) performing as a present restrict. The remainder of the circuitry is used to setup bias currents and act as an energetic load for the enter stage.
The extentshifting circuit is form of attentiongrabbing, and it’s a must to perceive one thing about pushpull output levels to understand it.
Let’s say you might have this circuit:
When the output stage shaped by Q1 and Q2 is sourcing present, Q1 carries present and V_{out} is one V_{BE} drop under V_{in}.
When the output stage shaped by Q1 and Q2 is sinking present, Q2 carries present and V_{out} is one V_{BE} drop above V_{in}.
This voltage shift, which relies on the path of output present, known as crossover distortion. Proper round zero present, the output voltage has to shift up or down by two V_{BE} drops, or someplace within the 1.21.5V vary.
Within the LM741 schematic, the 2 resistors R7 and R8 kind a form of adjustable voltage regulator throughout the unnamed transistor. The voltage throughout every resistor is roughly proportional to the resistance (present into the bottom terminal is small), so R8 sees a V_{BE} drop and R7 sees about 4.5K/7.5K = 0.6V_{BE}, for a complete voltage drop of 1.6V_{BE} or about 1.01.2V. This voltage shift pulls aside the transistors Q14 and Q20 so the crossover distortion is decreased by about 80%.
Our lab opamp was a lot easier than the LM741 schematic. We had some room to design our personal circuit, but it surely needed to be based mostly on 2N3904 and 2N3906 NPN and PNP transistors. I appear to recollect it had a restrict of solely 6 or 8 transistors, and it didn’t must be as nicelybehaved because the 741 (I can’t consider I’m saying that; it’s like saying somebody didn’t must behave as properly as Dick Cheney), but it surely had explicit achieve necessities up to some megahertz, which could be difficult on a solderless breadboard.
I had acquired my circuit working, and was making measurements for my lab writeup, once I heard a POP on the opposite facet of the lab, together with a couple of alternative fourletter phrases, and perhaps 30 seconds later that particular scent wafted via the room. , That Scent. Each electronics pupil ought to expertise it at the least as soon as, however hopefully not fairly often. Sure, a element has overheated and lets the magic smoke out, sharing unstable natural compounds with the entire room. I seemed over and noticed the man in query flip the facility off, throw some transistors away, and substitute them with new ones.
A couple of minutes after that, I heard one other POP. I seemed over and it was the identical man, and he changed the transistors once more. I knew the man; he was a very good pupil, however that day he was being silly. (Whereas scripting this, I acquired curious and seemed him up on Google. He’s now a profitable companion in a enterprise consulting agency. I suppose EE simply wasn’t his factor.) It dawned on me what the issue was. Here’s what he used as an output stage in his circuit:
There have been different parts apart from those proven right here (one thing has to supply base present to the transistors; I believe he had resistors from the diodes to V_{CC} and V_{EE}), however ignore that for a second. The diodes basically cancel out the V_{BE} drops and take away the entire crossover distortion, making the output voltage equivalent to the enter voltage. Very intelligent. His circuit did, in truth, work for some time, however then, after a minute or two, would go POP and die in a pant of pungent smoke.
Now, there’s a difficulty right here. Let’s take a look at one of many graphs we noticed earlier, from the 2N2222A datasheet:
You’ll word that the V_{BE} temperature coefficient is adverse. That implies that for a set quantity of collector present, if the transistor heats up, the basetoemitter voltage goes down. However what occurs for those who preserve the voltage throughout the baseemitter junction mounted? Effectively, let’s say you had been offering 0.7V and acquired 10mA. Now the transistor heats up by 1 diploma C, so the baseemitter voltage goes down by about 1.8mV, so that you solely want 0.6982V to get 10mA. However you might have 0.7V. And we mentioned that each 18mV nearly doubles the present. In case you run the numbers, growing baseemitter voltage by 1.8mV ought to enhance the present by about 7%, to 10.7mA. So a 1 diploma C rise in temperature elevated collector present by 7%, from 10mA to 10.7mA.
Attentiongrabbing.
When the transistor conducts extra present, it dissipates energy and heats up extra. So perhaps this causes it to rise one other diploma. And this, in flip, causes the required V_{BE} drop to go down by 1.8mV, and enhance the present one other 7%, to about 11.5mA.
What we’ve acquired is a scenario the place extra present causes the junction temperature to go up, which causes extra present to movement. A optimistic suggestions loop. That is known as thermal runaway. And finally, one in every of three issues occurs:

The additional energy dissipation that heats up the transistor is balanced by environmental cooling (convection if the transistor is simply sitting in air), and causes the junction temperature to stabilize.

The present will increase sufficient that the tempco decreases in magnitude (at 100mA, the tempco is just about 1.4mV/°C), and this causes the present to stabilize. Although for those who run the numbers, at 100mA, a 1.4mV lower in required V_{BE} causes a couple of 5.5% enhance in present, to 105.5mA. That is nonetheless a reasonably vital enhance.

One thing else occurs (POP!) that disrupts the suggestions loop.
So so long as the man’s output present draw was low, the transistors had an opportunity of surviving. However as quickly as there was sufficient present, the V_{BE} voltage dropped sufficient to trigger each output transistors to conduct, and thermal runaway took over, till the junction overheated and cracked the package deal, letting the magic smoke out and stopping the movement of present.
The 741 opamp design has three design options to stop thermal runaway:
 The extentshifting circuit to cut back crossover distortion doesn’t utterly eradicate it, so each transistors are by no means on on the identical time.
 There are emitter resistors within the output stage. These are known as emitter ballast resistors, they usually’re used to melt the knee of the transistor’s present vs. V_{BE} curve at excessive currents.
 Emitter resistor R9 is related to a transistor that finally conducts and robs base present from the NPN output machine, inflicting an energetic present restrict. (I’m unsure why there isn’t one on the PNP facet.)
Different Varieties of Thermal Runaway
There are many different mechanisms for thermal runaway, so it’s best to control energy dissipation in your circuit design, in addition to the temperature coefficients. Three necessary ones in energy electronics are the next:

The bottomemitter voltage tempco is normally adverse for bipolar energy transistors. This implies you possibly can’t put them instantly in parallel, or the same form of factor will occur: transistor A and B every carry 1A of present, however then B heats up somewhat greater than A, so it tells A, “Hey, look, I can carry extra present now, I’ll take 1.1A and you’re taking 0.9A”, after which B heats up somewhat extra, and it says, “Hey, I can carry extra present now, I’ll take 1.2A and you’re taking 0.8A” and finally B takes virtually the entire present. That is known as present hogging. Even for those who put resistors in sequence with the bottom, the adverse collectoremitter voltage tempco for bipolar energy transistors implies that present hogging will happen. If you wish to parallel bipolar transistors, it’s a must to add emitter ballast resistors.

The onresistance tempco is normally optimistic for MOSFETs, usually growing by an element of 1.52.5 between room temperature and the utmost working temperature of the transistor. Whereas this implies you can parallel MOSFETs (if one heats up, its onresistance will go up and that may cut back the present it conducts, in comparison with the opposite MOSFETs in parallel), it has a adverse consequence for designs the place the MOSFET load is a continuing present, like an influence converter or a motor controller. Let’s say the MOSFET carries 10A of present, so it heats up, and its onresistance will increase, so it heats up extra, which makes its onresistance enhance additional… till issues both stabilize otherwise you hear a loud POP. What you mainly must do is plan on the MOSFET resistance being its most worth. If the thermal administration of your system retains the MOSFET junction temperature under its most restrict, you’re OK, and ultimately you’ll be conservative: as an alternative of it attending to 150°C, it’d solely get to 125°C, so its onresistance is rather less, which implies the facility dissipation goes to be lower than you deliberate for.

The temperature coefficient of magnetic saturation is usually adverse — I’m not 100% positive that is the case for all magnetic supplies, however Murphy’s Regulation says it’s — which implies that when your inductors and transformers warmth up, their inductance can drop. And for those who’re utilizing them in a switching energy converter, this implies their ripple present will enhance, which implies they’ll warmth up extra, till you get smoke and/or arcing. (I discussed this in an earlier article.)
So don’t you surprise why, WHY WHY WHY WHY WHY they ran away — be vigilant and also you’ll keep away from thermal runaway.
Abstract
We coated some miscellaneous circuit design subjects at the moment:

The bottomemitter voltage in a bipolar transistor ( V_{BE} = frac{nkT}{q} ln frac{I_C}{I_s} ) the place n is the ideality issue, normally barely larger than 1.0 for commerciallyavailable transistors. This makes the present an exponential perform of baseemitter voltage.

Linearization can assist you perceive the dynamic resistance of a element with a nonlinear V/I relationship, and remedy circuit evaluation issues extra simply.

Many digital parts have parameters that change with temperature; the temperature coefficient tells how a lot they range with temperature, and for those who’re fortunate it’s specified within the element datasheet.

Sure temperature coefficients may cause a optimistic suggestions loop that causes parts to warmth up extra once they get hotter, which known as thermal runaway.
Thanks for studying, and don’t let the magic smoke out!
© 2015 Jason M. Sachs, all rights reserved.
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