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9.0 m ladder rests against the side of a wall the bottom of the ladder is 1.5 m from thebase wall derter the measure of the angle between the ladder and the ground to the nearest degree?
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How many 1500 sq ft houses can you get on 1 acre?
This is weird. We have to assume that the walls have zero thickness, so that thebase of the walls doesn't take up any of the real estate.(1 acre) x (43,560 square ft per acre) / (1,500 square ft per house) = 29.04 houses.That means 29 houses, with 60 square ft left over.Each house gets 2.069 square ft to use for a lawn or a driveway, whichever they prefer.
Is it possible to recreate 2G's in a room?
Sure, but not for very long. Extreme DEceleration (negative acceleration, slowing down)is easy to create, at any time in any place, simply by falling down or walking into a wall.Extreme ACceleration isn't so simple. One possibility might be to have a motor or a personspin you in an office swivel-chair, creating a mini-centrifuge. Spinning fast enough ... with thebase nailed to the floor for stability ... you could synthesize many G right there in the privacyof your own room.We worked out a rough idea of how fast you have to spin, and it seeems pretty reasonable:If you're spinning in a circle with a 1-meter radius (you're 1 meter from the center), thenyou have to spin about once every 2 seconds for 1 G centripetal acceleration, or aboutonce every 1.4 seconds for 2 Gs centripetal acceleration.
Info on baseball?
Baseball was founded in 1871 by Alexander Cartwright. In the early days, it was called "Rounders." Strikes were not called at the time, and gloves weren't used until the early 1900's. Perhaps the most famous baseball player ever was Babe Ruth, the first slugger, in the 30's and 40's of the 1900's. He hit 714 home runs, something that would last until Henry "Hank" Aaron broke the record on April 8th, 1974. He would later have a record of 755 until Barry Bonds, who hit 763 in his career.Anyways, as the years went by in baseball, many milestones have been broken. 6 great milestones to achieve are:500 Home Runs (hitting)3,000 hits (hitting).300 Batting Average (hitting)300 Wins (Pitching)3.00 ERA or under (pitching)20 years (Career)Perhaps the most famous milestone of the year 2011 was Derek Jeter's 3000th hit, in which he hit a home run. He would later get five hits in five at-bats in a New York Yankees win.The most successful franchise of all thirty are the New York Yankees. They are the only Major League Baseball team to have their own television channel (YES Network), the most World Series Championships (27), and the most money of all teams.The least successful team are arguably the Chicago Cubs. Only two World Championship wins, and one of the worst seasons in baseball, from 1966, where they had a 59 win-103 loss season. By July 21st, they are 39 wins-60 losses, and are fifth out of six in the NL Central.By 2011, the objectives of the game are:Rule 1.01 to 1.0411.00-Objectives of the Game.1.01 Baseball is a game between two teams of nine players each, under direction of amanager, played on an enclosed field in accordance with these rules, under jurisdiction ofone or more umpires.1.02 The objective of each team is to win by scoring more runs than the opponent.1.03 The winner of the game shall be that team which shall have scored, in accordancewith these rules, the greater number of runs at the conclusion of a regulation game.1.04 THE PLAYING FIELD. The field shall be laid out according to the instructionsbelow, supplemented by Diagrams No. 1, No. 2 and No. 3 on adjoining pages.The infield shall be a 90-foot square. The outfield shall be the area between twofoul lines formed by extending two sides of the square, as in Diagram 1. The distance fromhome base to the nearest fence, stand or other obstruction on fair territory shall be 250 feetor more. A distance of 320 feet or more along the foul lines, and 400 feet or more to centerfield is preferable. The infield shall be graded so that the base lines and home plate arelevel. The pitcher's plate shall be 10 inches above the level of home plate. The degree ofslope from a point 6 inches in front of the pitcher's plate to a point 6 feet toward home plateshall be 1 inch to 1 foot, and such degree of slope shall be uniform. The infield and outfield,including the boundary lines, are fair territory and all other area is foul territory.It is desirable that the line from home base through the pitchers plate to second baseshall run East-Northeast.It is recommended that the distance from home base to the backstop, and from thebase lines to the nearest fence, stand or other obstruction on foul territory shall be 60 feet ormore. See Diagram 1.When location of home base is determined, with a steel tape measure 127 feet, 3⅜inches in desired direction to establish second base. From home base, measure 90 feettoward first base; from second base, measure 90 feet toward first base; the intersection ofthese lines establishes first base. From home base, measure 90 feet toward third base; fromsecond base, measure 90 feet toward third base; the intersection of these lines establishesthird base. The distance between first base and third base is 127 feet, 3⅜ inches. Allmeasurements from home base shall be taken from the point where the first and third baselines intersect.The catcher's box, the batters' boxes, the coaches' boxes, the three-foot first baselines and the next batter's boxes shall be laid out as shown in Diagrams 1 and 2.Rule 1.04 to 1.072The foul lines and all other playing lines indicated in the diagrams by solid blacklines shall be marked with paint or non-toxic and non-burning chalk or other white material.The grass lines and dimensions shown on the diagrams are those used in manyfields, but they are not mandatory and each club shall determine the size and shape of thegrassed and bare areas of its playing field.NOTE: (a) Any Playing Field constructed by a professional club after June 1,1958, shall provide a minimum distance of 325 feet from homebase to the nearest fence, stand or other obstruction on the right andleft field foul lines, and a minimum distance of 400 feet to thecenter field fence.(b) No existing playing field shall be remodeled after June 1, 1958, insuch manner as to reduce the distance from home base to the foulpoles and to the center field fence below the minimum specified inparagraph (a) above.1.05 Home base shall be marked by a five-sided slab of whitened rubber. It shall be a17-inch square with two of the corners removed so that one edge is 17 inches long, twoadjacent sides are 8½ inches and the remaining two sides are 12 inches and set at an angle tomake a point. It shall be set in the ground with the point at the intersection of the linesextending from home base to first base and to third base; with the 17-inch edge facing thepitcher's plate, and the two 12-inch edges coinciding with the first and third base lines. Thetop edges of home base shall be beveled and the base shall be fixed in the ground level withthe ground surface. (See drawing D in Diagram 2.)1.06 First, second and third bases shall be marked by white canvas or rubber-coveredbags, securely attached to the ground as indicated in Diagram 2. The first and third basebags shall be entirely within the infield. The second base bag shall be centered on secondbase. The bags shall be 15 inches square, not less than three nor more than five inchesthick, and filled with soft material.1.07 The pitcher's plate shall be a rectangular slab of whitened rubber, 24 inches by 6inches. It shall be set in the ground as shown in Diagrams 1 and 2, so that the distancebetween the pitcher's plate and home base (the rear point of home plate) shall be 60 feet, 6inches.3GRASS LINEBACKSTOP5' CIRCLE 5' CIRCLERADIUS FROMHOME BASE60'37' 37'60'6"1' MIN10' MAX1' MIN10' MAX13' 13'6'13'20'15'45'-0" 45'-0"6'90' 0"90' 0"FOUL LINEFOUL LINE95' RADIUSNEXT BATTER'S BOXNEXT BATTER'S BOXLEGENDBATTER'S BOX,CATCHER'S BOX, FOUL LINE,PITCHER'S PLATE, COACH'S BOXBASE LINES26' CIRCLE127-3 3/8"127-3 3/8"18' CIRCLENEXT BATTER'S BOXCOACH'SBOXCOACH'SBOXGRANDSTAND OR FENCE 60' FROM BASEOR FOUL LINE3'DIAGRAM NO. 1GRASS LINES3' 3'4LAYOUT ATSECOND BASELAYOUT ATTHIRD BASEFOUL LINEDIAGRAM NO. 2LEGEND1st, 2nd, 3rd BASESBATTER'S BOXCATCHER'S BOXHOME BASEPITCHER'S PLATEAA15"15"9090LAYOUT ATFIRST BASEFOUL LINEA9090B 6" 17" 6"DCB4'0"43"3'0"8'0"4'0"LAYOUT AT HOME BASELAYOUT AT PITCHER'S PLATESEE DIAGRAM NO. 3E81 "281 "23'0"ABCDE5
What is follow through on a tattoo machine and how does it affect how a tattoo machine runs?
Tattoo MachinesClick on the link to your right for more information.The tattoo machine ('gun' is a misnomer) is really a basic doorbellcircuit (you know--you push a button and somewhere in the kitchen thislittle arm bangs the hell out of a bell thingie). For you techies outthere it's a DC coil and spring point(s) machine. Both doorbell and tatmachine were invented before household current was available.It is essentially in 3 sections: The base, the mechanism, and thesanitary tube. The base really is the bulk of the metal; a rabbit earwith a screw in it, bent at 90 degrees to hold coils. In the frontthere's a round hole to hold the sanitary tube.Some people think the base looks like the handle of a gun. The basehouses the mechanism, which consists of two coils of wire wrapped aroundan iron core.At the top of the mechanism is a set of silver contact "points" (likethe end of a wire); one usually on a spring mechanism, the other eitherthe end, or on the end of a screw.The spring connects to the base and a bar, which is connected to theneedle arm (90 degrees offset). The needle arm is connected to theneedles (which are soldered onto the bar), and moves up and down insidethe sanitary tube.The coils connect to a DC power supply (between 6 - 12VDC), via a springcoiled U-cable. The U-cable is called a "clip cord," designed to moveeasily between machines but also stay in place and not fall out andspark all over the place. The springs hold the cable in/onto themachine.One side of the coils is connected to the power supply, the other end tothe point on the screw on the bunny ear, which is insulated from thebase. Through the points, the current flows via the coils and the baseof the machine. This causes the coils to become electromagnetic. Theelectro-magnet pulls down the bar, which does two things: pulls down theneedles, and opens the points. The points being open turn off themagnet. The spring assembly brings back the bar, which causes theneedles to move up *AND* make contact with the points. This causes thewhole cycle to happen again making the needles go up and down.Most machines have a large capacitor across the coils/points, whichkeeps the points from arcing and pitting, and wearing out so quickly. Acapacitor is a device that holds energy kind of like a battery, butcharges and discharges much faster (parts of a second rather than 3 or 4hours). The capacitor charges while the points are open, so when theyclose, the difference in voltage across them is nill. The points arereally an automatic switch controlled by the spring to turn the thingoff and on quickly. In old cars where there were points there was acondenser (aka capacitor) for the same reason.The sanitary tube sucks up the ink in capillary fashion, and the needlesload up as long as there's ink in the small portion of the tube.It'scalled "sanitary" because of the cutout at the bottom of the tube, whichcan be rinsed out.My understanding is that there are three layers of skin: Scaly layer,epidermis, and dermis. Tattoo machines are adjusted to penetrate intothe dermis layer but NOT *through* it (below it is the fat layer of thebody).When the needles go into the sanitary tube they have a layer of ink onand between them. The needles make little holes in the skin, and the inkis deposited into the holes. This is why the skin has to be stretched soblobs of ink don't stay. Otherwise, the skin will latch onto theneedles, grab the ink from them and generally make a mess.Ink just put into the scaly layer would be replaced quickly and fadeaway. While ink into the epidermis will stay, my conjecture is that thedermis makes for more ink and perhaps a more vivid image.Machines are really of two types: Liners, and shaders. They areexactlythe same, but are set up differently. The gap for a liner isaround thethickness of a dime, and a shader is the thickness of a nickel.Liner needles are usually arranged on the bar in a circular pattern.Shader needles are usually straight (like a comb), although Spaulding &Rogers sells a 15-needle round shader. The needles are small sewingmachine needles, usually made of stainless steel. Liners are in 1, 3, 4,5, & 7-needle combinations, set in a round configuration. Note: Therecan really be any number of them but these seem to be most common.Shader needles are in a straight row and usually are in groups of 4, 6,7, 9 needles. The sanitary tubes are designed especially for thecombination of needles, so there's a special tube for each differentnumber of needles in a needle bar assemblyo is a needle. is a cut down needle (shorter & no point)Liners:Single needle 3-needle 5-needleo o o o. . o o oo oShaders:4-needle 6-needleoooo oooooo8-needle shaders are grouped so that 7 needles form a circle with 1 inthe middle. There are also 14-needle shaders.8-needle Magnums:o 5-needle 7-needleo o o o o o oo o o o o o o o o oo ooShaders are mounted on flat needle bars while liners are mounted onround barsThere are two other types of machines. Spaulding & Rogers revolution(don't know of an artist that uses this one), which is a DC motor thatturns a cam that raises and lowers the needle bar assembly through asanitary tube.DO TATTOO NEEDLES BECOME DULL WITH USE?Tattoo needles do not dull with age, but instead become sharper by therepetitive honing motion they experience in the tattoo machine.This happens because the metal of the sanitary tube rubs against theneedles, and the softer metal (the needles) will wear. The problem withthese sharpened needles is that they sharpen into flat razor-like edges,and begin cutting the skin instead of piercing small holes.Since a tattoo is created by the conical shape of the needletransferring pigment into the skin with the aid of a wetting agent, theneedle's shape is as important as its sharpness. Pigment does nottransfer into the skin as efficiently when the shape is altered, and canalso lead to scarring.Another problem with needles is the occurrence of burs or barbs when theneedles hit the side or bottom of the pigment caps.While it is possible to use the same set of needles for more than eighthours (on the same client, of course), correct needle configuration,setup, and alignment of the needle and machine are very critical.
How do you change the bulb for the instrument panel on a 1995 Subaru Legacy wagon?
I'm doing it now on my 1996 Legacy. I had to order the bulds from Radio Shack. Remove the cup holder first and then you'll see that you have to unplug the wiring harness for hazards, blower and another one. They are little brown flat screw type bolts that are kinda flush to the panel. Twist and pull out with tweezers and you'll see you have to remove the bulbs manually. Hope this helps and that your year of car matches what mine is. Check this out:Replacing the lights behind the centerconsoleEvery major button or control in the center console should be backlit when the headlights are on.Sometimes the little bulbs burn out. The previous owner of my car demonstrated that they tend to burnout faster if you soak them with a can or two of cola. The good news is that with some care, you can fixthe burned out lights yourself. This page details the steps I followed for replacing several different lights.If none of the interior controls are lit up, check the dimmer ring on the headlight switch and makesure it is turned to the brightest setting. The interior lights don't show up very well during the daytime,so you may want to do this work in a dark or shaded location.General instructions for replacing the micro bulbsEach of the minature bulbs behind the buttons or switches in a Subaru has a base that is the right size forits location. I recommend replacing only one bulb at a time or keeping track of where each bulb base wasremoved from. You don't want to get poor lighting results because you plugged the wrong light base intoa given socket (even though it may fit). You may be able to buy the complete bulb assemblies at aSubaru dealer, but in my case I was trying not to put any more money into these repairs than I had to.1. Remove the bulb to be replaced by twisting it ~1/8th turn counterclockwise. If the bulb doesn'tfall out of its socket, you may need tweezers or fine pliers to grab the base of the bulb and removeit.2. Use a pin or fine screwdriver to unwrap the little wires from their canals in the base of the lightassembly. Once the wires are more or less straight, you should be able to pull the bulb out of thebase.3. When separated, the base and removed bulb will look something like this:Base: Bulb:4. Radio Shack stores sell micro bulbs that will fit and work very well as replacement bulbs, butyou'll have to fit them into the Subaru light bases. They are Radio Shack #7219 and come in apackage of two. The bulbs are 12 volts · 60 mA. The other number on the package is 272-1092C,http://www.med.uc.edu/pstp/students/fortner/rulights.htm (1 of 4) [6/29/2003 7:17:32 AM]Subaru Salvation Projectalthough I don't know if that matters or not. The 2-pack should be less than $2.5. The Radio Shack bulbs are slightly shorter than the Subaru bulbs, so you may need to cut a shortpiece of plastic to make the bulb stick out as far as the original bulb sticks out. I used a little ringcut from the ink tube on a Bic Rollerstick and slid it over the wires like this:6. Some of the lights have little green covers on them (the ones behind the climate control switchesare like this). The green covers will fit the Radio Shack bulbs very well and will also make iteasier to determine how much bulb should stick out of the base.7. Feed the wires from the Radio Shack bulb through the holes in the light base (one wire per hole toavoid shorting out the circuit).8. Wrap the wires through the grooves in the light base, making sure to follow the path that theoriginal wires were wrapped along. The loops on the bulb side of the base are the most important,since they form the electrical contact with the light socket. Before you trim the excess wire, itshould look something like this:9. Trim the excess wires, make sure the two wires don't touch each other at any point, and plug thelight assembly back into the socket it came out of.10. Turn the base ~1/8th turn clockwise to lock the light in position.Foglight, Rear Defroster, or Cruise ControlswitchesAll of these switches have two light bulbs: one for backlighting the symbol or text, another for the littlelight that indicates the button is in the "on" position.1. Remove the switch from the instrument panel and disconnect the plug connected to the rear of theswitch. It may help to remove the instrument panel first, so that you can get at the back side of theswitches and pop them out more easily.2. Remove the light assembly and replace the bulb according to the general instructions.3. Reconnect the plug into the back of the switch and test for lights.4. Pop the switch back into place and reassemble the instrument panel.http://www.med.uc.edu/pstp/students/fortner/rulights.htm (2 of 4) [6/29/2003 7:17:32 AM]Subaru Salvation ProjectHazard Light switchThis switch has only one bulb that backlights the symbol. The only difficult part is getting the switch outso you can work on it (the bulb is located on the top side of the switch so you have to disassemble thepanel pretty much completely).1. Remove the cup holder, including the two screws and the socket that holds the tray.2. Remove the whole center vent assembly (entire piece surrounding the heater controls, vents, andhazard switch). It should pop out fairly easily (anchor points seem to be beside each vent).3. Unplug the wires from the back of the hazard switch.4. The next trick is to get the vent assembly apart from the trim piece that holds the hazard switch.m Remove the two black screws holding the bottom of the vents to the trim piece.m Loosen or remove the 4 small screws that hold the vent top & bottom together (two goldcolored screws on each side).m Look in through the back of each vent and note that there are about 4 pop-in type "teeth"holding the vent snapped together with the trim piece.m Pop the vent assembly loose from the trim piece.5. You should be able to get at the light bulb (on top of the switch) without detaching the hazardswitch from the trim piece, but it may be easier to go ahead and unscrew the two screws holdingthe hazard switch in place on the trim and remove the switch.6. Remove the light assembly and replace the bulb according to the general instructions.7. Reconnect the plug into the back of the switch and test for lights.8. If you detached the hazard switch from the trim, reattach it.9. Pop the vent assembly back onto the back of the trim piece, making sure that all the "teeth" popback into place.10. Replace and tighten all screws removed from the whole center vent/trim assembly.11. Pop the whole center vent assembly back into place.12. Reinstall the cup holder socket and screws and slide the cup holder tray back into place.Climate control panelThe entire panel for the vent selection, fan speed, and internal temperature control is lit by three bulbs atthe back of the control assembly. Replacing them is a fairly involved repair, but worth it if you want tosee those controls at night. I think the little indicators beneath each vent selection (floor, vent, recirc,defrost, etc.) are LEDs. All of mine work, so I haven't had to mess with them. The light in the A/C switchis also separate, and mine works so I haven't had to mess with it either.1. Remove the center vent and trim according to steps 1-3 for replacing the hazard switch.2. Pop the sliding knob off of the temperature control slider.http://www.med.uc.edu/pstp/students/fortner/rulights.htm (3 of 4) [6/29/2003 7:17:32 AM]Subaru Salvation Project3. Remove the 4 screws holding the control panel in place.4. There are three plugs going to the back of the control panel (one for fan speed control, one forA/C, one for all other switches). Unplug all three.5. The cable attached to the temperature slider will prevent you from removing the whole controlpanel assembly.6. In order to pull the panel out, you need to disassemble the sliding part from the rest of the panel.This is somewhat complicated.m There is a cover made of softer black plastic on top of the back part of the assembly. Workwith the clips near each end to free this piece and slide it up and out.m Looking at the top of the assembly, you should now see a small circuit board held verticalbetween two supports.m On the back side of each support is a tab that secures the ends of the circuit board.m As you lift upward on the small circuit board, use a small screwdriver to pry the tabsoutward (away from the back of the assembly) to release the ends of the small circuit boardand slide the circuit board up and out of it supports. It will remain attached by a short greyribbon wire.m Remove the two small silver screws from the bottom of the assembly.m Lift the little clips near where those screws were and slide the front part away from the restof assembly, leaving the A/C switch, the slider and cable still in the dashboard.7. Now you should be able to look at the back of the main circuit board (across the whole back ofthe vent control assembly) and see the bases for three bulbs.8. If you don't know which bulbs are burned out, plug in the main plug to the little circuit board andcarefully test the lights (don't short anything out on any of the wires or pins).9. Remove any burned out light assemblies and replace the bulbs according to the generalinstructions. The light nearest the fan speed switch has a considerably longer base than the others,so don't get this mixed up with other bulbs. All three of these lights should have little greensheaths covering the bulbs.10. Reconnect the plugs into the back of the assembly and test for lights (again, be careful not to shortthings out).11. Unplug the system again and reassemble it. Once you have slid the front and back parts of theassembly back together and replaced the small silver screws, slide the small circuit board downinto its supports. Don't forget to put the black plastic cover back on behind the vent controlassembly, and the temperature slider knob back in place.12. Plug all three connections back into the back of the whole climate control assembly, and mount itback in place with the four screws.13. Replace the center vent assembly, cup holder socket and screws, and cup holder tray.
What is bias compensation and bias stabilisation?
Temperature Compensation Of BJT Differential AmplifiersThe bipolar junction transistor (BJT) emitter-coupled differential-pair circuit is a familiar amplifier stage in the repertoire of analog designers, but has asurprising obscurity that needs to be revealed. This TechNote examines the emitter-circuit current source, I0, of BJT diff-amps and the effects on amplifier gain of different implementations for it.The widespread belief that a BJT current source can temperature-compensate the diff-amp is true, but the conditions for it do not appearto be widely known, based on most designs. The typical circuitis shown below.+VRL1RL2vo1vo2vi1RB1Q1RB2Q2vi2RE1RE2I0This is a differential-input, differential-output voltageamplifier. Both input and output quantities are differential, and the incremental gain of the circuit is:v v - vA × v- A × v v vvA = o = o 2 o1= v 2 i2 v1 i1 = o2- o1 =vi= -a 2 ×vi 2 - vi1vi 2 - vi1RL 2vi 2v = 0i1vi1v = 0i2re1 + re 2 + RE1 + RE 2 + RB1 /(b1 + 1) + RB2 /(b 2 + 1) R -  - a1 ×L1  re1 + re 2 + RE1 + RE 2 + RB1 /(b1 + 1) + RB2 /(b 2 + 1) The condition for differential amplification is that Av1 = Av2. The circuit is made symmetrical for:RE = RE1 = RE2 ; RB = RB1 = RB2 ; RL = RL1 = RL2 ; b = b1 = b2, Q1, Q2 matchedThen the gain simply becomes:Av = 2 × Av1= 2 × Av 2= -a ×re+ RERL+ RB/(b + 1)= -a × RLrMA goal of good design is to make Av a fixed value. The choice of resistors with a low temperature coefficient (TC) and sufficiently tight accuracy is one factor. This is usually easy to achieve, though for high-precision design, the change in resistance due to change in ambient temperature is afactor to be considered. Evenmore so are thermals, changes in resistance due to changes in power dissipation with vi. For very precise designs, the change in resistance with applied voltage must be considered too.Other transistorparameters than thetwo (re and b) of the BJT T model used here - namely, ro - also need to be included for precision design. Wewill assume that theBJTs have a sufficiently high Early voltage that ro need not come into our list of considerations -- at least not here. In practice, this assumption is often valid.BJTs are typically the least ideal elements of the circuit. From the gain formula, it is evident that two BJT parameters affect gain, theincremental emitter resistance, re, and b. For high b -- that is, for b >> 1 -- the gain factor,a = bb + 1approaches 1. For a typical b value of 200, then a = 0.995, contributing a gainerror of 0.5%. If that is too much error, a-compensationtechniques are required. Usually, this error can be compensated by including it in the gain formula, as we have done. What is more important is how much it drifts with temperature. Typical TC(b) @ 1%/°C, then for large b, a has nearly a zero TC of around 50 ppm; a is not much of a problem.The transresistance expression of Av -- the denominator -- is the resistance across which the input voltage develops the common (emitter) current. Theoutput current is modified bya, which accounts for loss along the way from theemitter circuit. This transresistance, rM, also includes b in the RB term. If RB is kept small, and the inputs are driven by voltage sources, then this b is of no concern. If the sources are high in resistance, then the RB term will affect gain by b variation with temperature. Its 1%/°C variation is scaled down by the extent to which RB/(b + 1) is not dominant in rM. Thus, keepingthis term negligible is another design factor.The most troublesome term in rM is re, for it varies with temperature and emitter current, IE, according to:re =VT| I E |= kT / qe| I E |@ 26 mV , T = 300 K| I E |Thus re varies with the thermal voltage, VT, which varies in proportion with absolute temperature:dVT = VTdT TAt 300°K (about 80°F), this is 1/300°K or about 0.33%/°K = 0.33%/°C. For laboratory-quality instrument design, let us suppose the temperature range over which the equipment ought to be able to operate within its specifications is 15°C from room temperature, about 25°C ± 15°C, or 10°Cto 40°C. Over a 15°C change from ambient, VT changes about 5% -- far too much for most precision designs. Therefore, VT variation in gain needs to be compensated.The simplest compensation for re is to make it a negligible term (along with the RB term) in rM. This is accomplished by making REdominant. ForRE >> re, the drift in re affects gain far less than 5%. In many cases, dominant external emitter resistance solves the drift problem, but at the expense of gain and power dissipation. By increasing I0, then re is reduced proportionally, though circuit power increases. This is undesirable for power-limited equipment and it also exacerbates thermals by increasing DPD(vi) in the BJTs.In some cases, re cannot be made negligible, and some compensation for it is desired. One of the most common schemes is to make I0 track re and cancel its effect, at least approximately. To make I0 have the TC of VT, the simplest approach is to use a BJT current source implementation of I0. The b-ejunction voltage of the current-source BJT then decreases with temperature, I0 increases, and decreases re.Current-Source CircuitsThe first circuit sourcing I0 that we will consider is simply a resistor, R0, returned to a negative supply. This long-tailed current source approaches an ideal current source as the supply voltage, -V, approaches negative infinity, along with the value of R0. It does nothing to compensate for the TC of re.The second implementation to consider is shown below.I0Q0R0-VThis simple circuit has a voltage acrossR0 of V - VBE(Q0). As temperature, T, increases, VBE decreases, but not with the TC of VT. The other major BJT parameter affecting VBE is the saturation current, IS, as found in thep-n junction (b-ejunction) voltage equation:VBE= VT × lnI C , I C( )>> I S I S T For a typical BJT, such as a PN3904, IS ≈ 10-14 A. Then 1 mA of current produces a VBE @ 0.65 V.Both VT and IS contribute to the TC(VBE). IS has a greater effect than VT and of opposite polarity on VBE, resulting in a combined effect of about -2 mV/°C for VBE. (For more on BJT TC effects, see the volume, Signal-Processing Circuits of Analog Circuit Design, available at http://www.innovatia.com.) It is therefore more important to cancel IS effects than those of VT. Depending on the relative values of V and VBE, the effect of the TC(VBE) can be scaled by choice of RE and supply voltage, V, which is often constrained bysystem- level design. By adding a resistor network between the emitter and ground, a Thévenin equivalent supply voltage and value of R0 can be independently set. Ifscaled properly, as Tincreases, VBE decreases and I0 increases. If the increase is made to besuch that the reduction in redue to it cancels the increase in re due to VT, then re and gain remain constant.The TC(re) is calculated as follows, bydifferentiating re with respect to T:      Idre =d  VT  = 1  × dVT- VT× dI E= VT ×  1× dVT  - VT ×  1× dI E  = r× [TC%(V) - TC%(I )]EdT dT I E  I E  dT2 dTI E  VTdT I E  I EdT  e T Ewhere, TC% is the fractional change in TC.The TC%(I0) = TC%(IE) can be determined as follows. The only change across R0 is due to VBE. Therefore, thefractional change in I0 with T is:TC%( I0) = dI 0 / dT I 0- (dV / dT) / R= BE 0I 0= - dVBE / dT V - VBE= + 2 mV/°CV - VBEFor TC%(I0) = TC%(VT) = 1/T@0.33%/°C, and the voltage across R0, V - VBE = 0.6 V. With −V = −1.25 V, this is not an attractivecompensation scheme. Thepolarity of TC(I0) is correct for compensation, but not its magnitude, which leads to the next scheme, shown below.I0R1Q0R2R0-VThis implementation of I0 is more versatileand more common in occurrence than theprevious scheme. The base divider provides extra freedom forsetting TC%(I0) which, for ignored TC(b), is now:  R   dV   2 ×V - VBE  - BE TC%(I ) =1 × dI 0 =1 × d  R1 + R2   =1 ×  dT 0  I 0 dTI 0 dT  R0 + (R1 R2 ) /(b + 1) I 0 R0 + ( R1 R2 ) /(b + 1) dV  dV  - BE 1 ×  - BE =  dT  =VBE dT  =- TC%(VBE ) R  R  V R  VBE 2  ×V - V R1 + R2  2  × R1 + R2 - 1VBE 2  × R1 + R2 - 1VBEThe divider ratio that gives the correct compensation can now be found. When TC%(I0) is set equal to ×TC%(VT), then: R2 V = -TC%(VBE )+ 1 = +2 mV/°C/VBE+ 1 =0.6 V+ VBEor, R1 + R2 VBETC%(VT )0.33 %/°CVBER2R1 + R2= 0.6 V + VBEV@ 1.25 VVfor VBE = 0.65 V. This result is interesting; whatever the value of V, the unloaded divider voltage must be1.25 V for gain compensation. This is also the voltage of bandgap references, as well it should be. Bandgapcircuits use the negative TC(VBE) and scale it to cancel thepositive TC(VT). When this is done the resulting bandgap voltage always comes out to be close to 1.25 V, and varies slightly with BJT doping levels.Another current-source variation that is often used to provide rough temperature compensation is to insert a diode in series with R2, as shown below.I0R1Q0D1R2 R0-VThe usual explanation is that the TC of the diode compensates for the TC of the BJT b-ejunction, resultingin a more stable I0. A typical example is to use a 1N4152 diode to compensate a PN3904. The diode and BJT b-ejunctions are quite different, however. The diode doping levels are far less than even the BJT base, in order to achieve a higher breakdown voltage. The emitter minority carrier concentration is madeintentionally large for good emitter injection efficiency into thebase, at the expense of VBE reverse breakdown, which is typically around 7 V, much below the 60 V of the diode. The point is that although both junctions are silicon, they are rather unmatched.Suppose, however, that a similar BJT is used as a diode, with base connected to collector. Then the junction matching is better (though not as good as adjacent integrated BJTs), and allowing for a @ 1, then applying KVL around the BJT input loop:  I× R - V× ln(I / I )V × ln I 0  = IT I D× R2- I 0× R0, or,I = D 2 T 0 D0 R D  0where, ID is the diode current. If the junction currents are equal, the TC dueto VT is removed and the TC%(I0) @ 0%/°C. This is useful for applications where a stable current source is needed, but it does not compensate re of the diff-amp. The currents must deliberately be set unequal to achieve the desired TC, and for a compensating polarity of TC, it must be positive. Consequently, we must have ID > I0.The TC%(I0) is found through implicit differentiation of I0 in the above equation:1 dI 1 d  I  I  dV TC%( I ) =× 0 =×  - V ×ln 0  - ln 0  × T 0  T    I 0 dTVI 0 × R0 dT1  I I D   I D dT = - T ×  TC%( I ) +× ln 0   0   I 0 × R0 T  I D  With additional algebraic manipulation:(V / I× R ) × ln(I / I )TC%( I 0) = - T 0 0 0 DT × (1 + VT / I 0 × R0 )Then to compensate, set TC%(I0) = TC%(VT) = 1/Tand solve:I  I× R D = exp1 + 0 0 I 0 VT Because of the exponentialfunction, practical current ratios require that the voltage across R0 be not much larger than VT. For I0 = 2 mA, R0 = 22 W, and VT = 26 mV, then the voltage across R0 is 44 mV, or 1.69×VT, andID = 14.77×I0 = 29.5 mA, larger than is desired in most designs. Such small values of R0 are required to keep R0 from dominating the emitter circuit so that the TC of VBE can be expressed.Yet in many designs, R0 is relatively large and its voltage drop far exceeds VT. As a consequence, the TC%(VT) of re is not correctly compensated and a TC drift in gain exists.The previous scheme, which omitted the base diode, was only slightly better in allowing for larger R0 voltage. Perhaps we should go in the oppositedirection and add a diodeor two in the emitter.The TC of the combined junctions would bemultiplied by the number of them, and that would allow RE to be made proportionally larger. It is usually not desirable to add a large number of series diodes because the static (dc) stability of I0 is not benefited. Consequently, use of the diff-amp current source to temperature-compensatere results in a circuit requiring careful static design. I0 is then made sensitive to junction parameters, and these parameters, such as IS, have a somewhatwide tolerance amongdiscrete transistors,even of the same part number.Expect as much as 50 mV of variation among PN3904 BJTs at the same current and temperature. This compensation method is best suited for monolithic integration.ClosureThe widespread belief that a BJT current source can temperature-compensate a BJT diff-amp is true, but it often does not. Temperature compensation of I0 for a constant re results in low voltage across the current- source external emitter resistance, R0 -- so low that it can make accurate setting of I0 infeasible.Consequently, except for more elaborate schemes which amplify VT, the dominant-RE approach to diff-amp gain stability appears to still be the best.
