Transistors : Feedback

If some percentage of an amplifier’s output signal is connected to the input, so that the amplifier amplifies part of its own output signal, we have what is known as feedback. Feedback comes in two varieties: positive (also called regenerative), and negative (also called degenerative). Positive feedback reinforces the direction of an amplifier’s output voltage change, while negative feedback does just the opposite. A familiar example of feedback happens in public-address (“PA”) systems where someone holds the microphone too close to a speaker: a high-pitched “whine” or “howl” ensues, because the audio amplifier system is detecting and amplifying its own noise. Specifically, this is an example of positive or regenerative feedback, as any sound detected by the microphone is amplified and turned into a louder sound by the speaker, which is then detected by the microphone again, and so on . . . the result being a noise of steadily increasing volume until the system becomes “saturated” and cannot produce any more volume. One might wonder what possible benefit feedback is to an amplifier circuit, given such an annoying example as PA system “howl.” If we introduce positive, or regenerative, feedback into an amplifier circuit, it has the tendency of creating and sustaining oscillations, the frequency of which determined by the values of components handling the feedback signal from output to input. This is one way to make an oscillator circuit to produce AC from a DC power supply. Oscillators are very useful circuits, and so feedback has a definite, practical application for us. See “Phase shift oscillator” , Ch 9 for a practical application of positive feedback. Negative feedback, on the other hand, has a “dampening” effect on an amplifier: if the output signal happens to increase in magnitude, the feedback signal introduces a decreasing influence into the input of the amplifier, thus opposing the change in output signal. While positive feedback drives an amplifier circuit toward a point of instability (oscillations), negative feedback drives it the opposite direction: toward a point of stability. An amplifier circuit equipped with some amount of negative feedback is not only more stable, but it distorts the input waveform less and is generally capable of amplifying a wider range of frequencies. The tradeoff for these advantages (there just has to be a disadvantage to negative feedback, right?) is decreased gain. If a portion of an amplifier’s output signal is “fed back” to the input to oppose any changes in the output, it will require a greater input signal amplitude to drive the amplifier’s output to the same amplitude as before. This constitutes a decreased gain. However, the advantages of stability, lower distortion, and greater bandwidth are worth the tradeoff in reduced gain for many applications. Let’s examine a simple amplifier circuit and see how we might introduce negative feedback into it, starting with Figure below. Common-emitter amplifier without feedback. The amplifier configuration shown here is a common-emitter, with a resistor bias network formed by R1 and R2. The capacitor couples Vinput to the amplifier so that the signal source doesn’t have a DC voltage imposed on it by the R1/R2 divider network. Resistor R3 serves the purpose of controlling voltage gain. We could omit it for maximum voltage gain, but since base resistors like this are common in common-emitter amplifier circuits, we’ll keep it in this schematic. Like all common-emitter amplifiers, this one inverts the input signal as it is amplified. In other words, a positive-going input voltage causes the output voltage to decrease, or move toward negative, and vice versa. The oscilloscope waveforms are shown in Figure below. Common-emitter amplifier, no feedback, with reference waveforms for comparison. Because the output is an inverted, or mirror-image, reproduction of the input signal, any connection between the output (collector) wire and the input (base) wire of the transistor in Figure below will result in negative feedback. Negative feedback, collector feedback, decreases the output signal. The resistances of R1, R2, R3, and Rfeedback function together as a signal-mixing network so that the voltage seen at the base of the transistor (with respect to ground) is a weighted average of the input voltage and the feedback voltage, resulting in signal of reduced amplitude going into the transistor. So, the amplifier circuit in Figure above will have reduced voltage gain, but improved linearity (reduced distortion) and increased bandwidth. A resistor connecting collector to base is not the only way to introduce negative feedback into this amplifier circuit, though. Another method, although more difficult to understand at first, involves the placement of a resistor between the transistor’s emitter terminal and circuit ground in Figure below. Emitter feedback: A different method of introducing negative feedback into a circuit. This new feedback resistor drops voltage proportional to the emitter current through the transistor, and it does so in such a way as to oppose the input signal’s influence on the base-emitter junction of the transistor. Let’s take a closer look at the emitter-base junction and see what difference this new resistor makes in Figure below. With no feedback resistor connecting the emitter to ground in Figure below (a) , whatever level of input signal (Vinput) makes it through the coupling capacitor and R1/R2/R3 resistor network will be impressed directly across the base-emitter junction as the transistor’s input voltage (VB-E). In other words, with no feedback resistor, VB-E equals Vinput. Therefore, if Vinput increases by 100 mV, then VB-E increases by 100 mV: a change in one is the same as a change in the other, since the two voltages are equal to each other. Now let’s consider the effects of inserting a resistor (Rfeedback) between the transistor’s emitter lead and ground in Figure below (b). (a) No feedback vs (b) emitter feedback. A waveform at the collector is inverted with respect to the base. At (b) the emitter waveform is in-phase (emitter follower) with base, out of phase with collector. Therefore, the emitter signal subtracts from the collector output signal. Note how the voltage dropped across Rfeedback adds with VB-E to equal Vinput. With Rfeedback in the Vinput — VB-E loop, VB-E will no longer be equal to Vinput. We know that Rfeedback will drop a voltage proportional to emitter current, which is in turn controlled by the base current, which is in turn controlled by the voltage dropped across the base-emitter junction of the transistor (VB-E). Thus, if Vinput were to increase in a positive direction, it would increase VB-E, causing more base current, causing more collector (load) current, causing more emitter current, and causing more feedback voltage to be dropped across Rfeedback. This increase of voltage drop across the feedback resistor, though, subtracts from Vinput to reduce the VB-E, so that the actual voltage increase for VB-E will be less than the voltage increase of Vinput. No longer will a 100 mV increase in Vinput result in a full 100 mV increase for VB-E, because the two voltages are not equal to each other. Consequently, the input voltage has less control over the transistor than before, and the voltage gain for the amplifier is reduced: just what we expected from negative feedback. In practical common-emitter circuits, negative feedback isn’t just a luxury; its a necessity for stable operation. In a perfect world, we could build and operate a common-emitter transistor amplifier with no negative feedback, and have the full amplitude of Vinput impressed across the transistor’s base-emitter junction. This would give us a large voltage gain. Unfortunately, though, the relationship between base-emitter voltage and base-emitter current changes with temperature, as predicted by the “diode equation.” As the transistor heats up, there will be less of a forward voltage drop across the base-emitter junction for any given current. This causes a problem for us, as the R1/R2 voltage divider network is designed to provide the correct quiescent current through the base of the transistor so that it will operate in whatever class of operation we desire (in this example, I’ve shown the amplifier working in class-A mode). If the transistor’s voltage/current relationship changes with temperature, the amount of DC bias voltage necessary for the desired class of operation will change. A hot transistor will draw more bias current for the same amount of bias voltage, making it heat up even more, drawing even more bias current. The result, if unchecked, is called thermal runaway. Common-collector amplifiers, (Figure below) however, do not suffer from thermal runaway. Why is this? The answer has everything to do with negative feedback. Common collector (emitter follower) amplifier. Note that the common-collector amplifier (Figure above) has its load resistor placed in exactly the same spot as we had the Rfeedback resistor in the last circuit in Figure above (b): between emitter and ground. This means that the only voltage impressed across the transistor’s base-emitter junction is the difference between Vinput and Voutput, resulting in a very low voltage gain (usually close to 1 for a common-collector amplifier). Thermal runaway is impossible for this amplifier: if base current happens to increase due to transistor heating, emitter current will likewise increase, dropping more voltage across the load, which in turn subtracts from Vinput to reduce the amount of voltage dropped between base and emitter. In other words, the negative feedback afforded by placement of the load resistor makes the problem of thermal runaway self-correcting. In exchange for a greatly reduced voltage gain, we get superb stability and immunity from thermal runaway. By adding a “feedback” resistor between emitter and ground in a common-emitter amplifier, we make the amplifier behave a little less like an “ideal” common-emitter and a little more like a common-collector. The feedback resistor value is typically quite a bit less than the load, minimizing the amount of negative feedback and keeping the voltage gain fairly high. Another benefit of negative feedback, seen clearly in the common-collector circuit, is that it tends to make the voltage gain of the amplifier less dependent on the characteristics of the transistor. Note that in a common-collector amplifier, voltage gain is nearly equal to unity (1), regardless of the transistor’s ?. This means, among other things, that we could replace the transistor in a common-collector amplifier with one having a different ? and not see any significant changes in voltage gain. In a common-emitter circuit, the voltage gain is highly dependent on ?. If we were to replace the transistor in a common-emitter circuit with another of differing ?, the voltage gain for the amplifier would change significantly. In a common-emitter amplifier equipped with negative feedback, the voltage gain will still be dependent upon transistor ? to some degree, but not as much as before, making the circuit more predictable despite variations in transistor ?. The fact that we have to introduce negative feedback into a common-emitter amplifier to avoid thermal runaway is an unsatisfying solution. Iis it possibe to avoid thermal runaway without having to suppress the amplifier’s inherently high voltage gain? A best-of-both-worlds solution to this dilemma is available to us if we closely examine the problem: the voltage gain that we have to minimize in order to avoid thermal runaway is the DC voltage gain, not the AC voltage gain. After all, it isn’t the AC input signal that fuels thermal runaway: its the DC bias voltage required for a certain class of operation: that quiescent DC signal that we use to “trick” the transistor (fundamentally a DC device) into amplifying an AC signal. We can suppress DC voltage gain in a common-emitter amplifier circuit without suppressing AC voltage gain if we figure out a way to make the negative feedback only function with DC. That is, if we only feed back an inverted DC signal from output to input, but not an inverted AC signal. The Rfeedback emitter resistor provides negative feedback by dropping a voltage proportional to load current. In other words, negative feedback is accomplished by inserting an impedance into the emitter current path. If we want to feed back DC but not AC, we need an impedance that is high for DC but low for AC. What kind of circuit presents a high impedance to DC but a low impedance to AC? A high-pass filter, of course! By connecting a capacitor in parallel with the feedback resistor in Figure below, we create the very situation we need: a path from emitter to ground that is easier for AC than it is for DC. High AC voltage gain reestablished by adding Cbypass in parallel with Rfeedback The new capacitor “bypasses” AC from the transistor’s emitter to ground, so that no appreciable AC voltage will be dropped from emitter to ground to “feed back” to the input and suppress voltage gain. Direct current, on the other hand, cannot go through the bypass capacitor, and so must travel through the feedback resistor, dropping a DC voltage between emitter and ground which lowers the DC voltage gain and stabilizes the amplifier’s DC response, preventing thermal runaway. Because we want the reactance of this capacitor (XC) to be as low as possible, Cbypass should be sized relatively large. Because the polarity across this capacitor will never change, it is safe to use a polarized (electrolytic) capacitor for the task. Another approach to the problem of negative feedback reducing voltage gain is to use multi-stage amplifiers rather than single-transistor amplifiers. If the attenuated gain of a single transistor is insufficient for the task at hand, we can use more than one transistor to make up for the reduction caused by feedback. An example circuit showing negative feedback in a three-stage common-emitter amplifier is Figure below. Feedback around an “odd” number of direct coupled stages produce negative feedback. The feedback path from the final output to the input is through a single resistor, Rfeedback. Since each stage is a common-emitter amplifier (thus inverting), the odd number of stages from input to output will invert the output signal; the feedback will be negative (degenerative). Relatively large amounts of feedback may be used without sacrificing voltage gain, because the three amplifier stages provide much gain to begin with. At first, this design philosophy may seem inelegant and perhaps even counter-productive. Isn’t this a rather crude way to overcome the loss in gain incurred through the use of negative feedback, to simply recover gain by adding stage after stage? What is the point of creating a huge voltage gain using three transistor stages if we’re just going to attenuate all that gain anyway with negative feedback? The point, though perhaps not apparent at first, is increased predictability and stability from the circuit as a whole. If the three transistor stages are designed to provide an arbitrarily high voltage gain (in the tens of thousands, or greater) with no feedback, it will be found that the addition of negative feedback causes the overall voltage gain to become less dependent of the individual stage gains, and approximately equal to the simple ratio Rfeedback/Rin. The more voltage gain the circuit has (without feedback), the more closely the voltage gain will approximate Rfeedback/Rin once feedback is established. In other words, voltage gain in this circuit is fixed by the values of two resistors, and nothing more. This is an advantage for mass-production of electronic circuitry: if amplifiers of predictable gain may be constructed using transistors of widely varied ? values, it eases the selection and replacement of components. It also means the amplifier’s gain varies little with changes in temperature. This principle of stable gain control through a high-gain amplifier “tamed” by negative feedback is elevated almost to an art form in electronic circuits called operational amplifiers, or op-amps. You may read much more about these circuits in a later chapter of this book! REVIEW:Feedback is the coupling of an amplifier’s output to its input.Positive, or regenerative feedback has the tendency of making an amplifier circuit unstable, so that it produces oscillations (AC). The frequency of these oscillations is largely determined by the components in the feedback network.Negative, or degenerative feedback has the tendency of making an amplifier circuit more stable, so that its output changes less for a given input signal than without feedback. This reduces the gain of the amplifier, but has the advantage of decreasing distortion and increasing bandwidth (the range of frequencies the amplifier can handle).Negative feedback may be introduced into a common-emitter circuit by coupling collector to base, or by inserting a resistor between emitter and ground.An emitter-to-ground “feedback” resistor is usually found in common-emitter circuits as a preventative measure against thermal runaway.Negative feedback also has the advantage of making amplifier voltage gain more dependent on resistor values and less dependent on the transistor’s characteristics.Common-collector amplifiers have much negative feedback, due to the placement of the load resistor between emitter and ground. This feedback accounts for the extremely stable voltage gain of the amplifier, as well as its immunity against thermal runaway.Voltage gain for a common-emitter circuit may be re-established without sacrificing immunity to thermal runaway, by connecting a bypass capacitor in parallel with the emitter “feedback resistor.”If the voltage gain of an amplifier is arbitrarily high (tens of thousands, or greater), and negative feedback is used to reduce the gain to reasonable levels, it will be found that the gain will approximately equal Rfeedback/Rin. Changes in transistor ? or other internal component values will have little effect on voltage gain with feedback in operation, resulting in an amplifier that is stable and easy to design. Lessons In Electric Circuits copyright (C) 2000-2010 Tony R. Kuphaldt

Transistor ratings and packages

Like all electrical and electronic components, transistors are limited in the amounts of voltage and current each one can handle without sustaining damage. Since transistors are more complex than some of the other components you’re used to seeing at this point, these tend to have more kinds of ratings. What follows is an itemized description of some typical transistor ratings. Power dissipation: When a transistor conducts current between collector and emitter, it also drops voltage between those two points. At any given time, the power dissipated by a transistor is equal to the product (multiplication) of collector current and collector-emitter voltage. Just like resistors, transistors are rated for how many watts each can safely dissipate without sustaining damage. High temperature is the mortal enemy of all semiconductor devices, and bipolar transistors tend to be more susceptible to thermal damage than most. Power ratings are always referenced to the temperature of ambient (surrounding) air. When transistors are to be used in hotter environments (>25o, their power ratings must be derated to avoid a shortened service life. Reverse voltages: As with diodes, bipolar transistors are rated for maximum allowable reverse-bias voltage across their PN junctions. This includes voltage ratings for the emitter-base junction VEB , collector-base junction VCB , and also from collector to emitter VCE . VEB , the maximum reverse voltage from emitter to base is approximately 7 V for some small signal transistors. Some circuit designers use discrete BJTs as 7 V zener diodes with a series current limiting resistor. Transistor inputs to analog integrated circuits also have a VEB rating, which if exceeded will cause damage, no zenering of the inputs is allowed. The rating for maximum collector-emitter voltage VCE can be thought of as the maximum voltage it can withstand while in full-cutoff mode (no base current). This rating is of particular importance when using a bipolar transistor as a switch. A typical value for a small signal transistor is 60 to 80 V. In power transistors, this could range to 1000 V, for example, a horizontal deflection transistor in a cathode ray tube display. Collector current: A maximum value for collector current IC will be given by the manufacturer in amps. Typical values for small signal transistors are 10s to 100s of mA, 10s of A for power transistors. Understand that this maximum figure assumes a saturated state (minimum collector-emitter voltage drop). If the transistor is not saturated, and in fact is dropping substantial voltage between collector and emitter, the maximum power dissipation rating will probably be exceeded before the maximum collector current rating. Just something to keep in mind when designing a transistor circuit! Saturation voltages: Ideally, a saturated transistor acts as a closed switch contact between collector and emitter, dropping zero voltage at full collector current. In reality this is never true. Manufacturers will specify the maximum voltage drop of a transistor at saturation, both between the collector and emitter, and also between base and emitter (forward voltage drop of that PN junction). Collector-emitter voltage drop at saturation is generally expected to be 0.3 volts or less, but this figure is of course dependent on the specific type of transistor. Low voltage transistors, low VCE , show lower saturation voltages. The saturation voltage is also lower for higher base drive current. Base-emitter forward voltage drop, kVBE , is similar to that of an equivalent diode, ?0.7 V, which should come as no surprise. Beta: The ratio of collector current to base current, ? is the fundamental parameter characterizing the amplifying ability of a bipolar transistor. ? is usually assumed to be a constant figure in circuit calculations, but unfortunately this is far from true in practice. As such, manufacturers provide a set of ? (or “hfe”) figures for a given transistor over a wide range of operating conditions, usually in the form of maximum/minimum/typical ratings. It may surprise you to see just how widely ? can be expected to vary within normal operating limits. One popular small-signal transistor, the 2N3903, is advertised as having a ? ranging from 15 to 150 depending on the amount of collector current. Generally, ? is highest for medium collector currents, decreasing for very low and very high collector currents. hfe is small signal AC gain; hFE is large AC signal gain or DC gain. Alpha: the ratio of collector current to emitter current, ?=IC/IE .   ? may be derived from ?, being ?=?/(?+1) . Bipolar transistors come in a wide variety of physical packages. Package type is primarily dependent upon the required power dissipation of the transistor, much like resistors: the greater the maximum power dissipation, the larger the device has to be to stay cool. Figure below shows several standardized package types for three-terminal semiconductor devices, any of which may be used to house a bipolar transistor. There are many other semiconductor devices other than bipolar transistors which have three connection points. Note that the pin-outs of plastic transistors can vary within a single package type, e.g. TO-92 in Figure below. It is impossible to positively identify a three-terminal semiconductor device without referencing the part number printed on it, or subjecting it to a set of electrical tests. Transistor packages, dimensions in mm Transistor packages, dimensions in mm. Small plastic transistor packages like the TO-92 can dissipate a few hundred milliwatts. The metal cans, TO-18 and TO-39 can dissipate more power, several hundred milliwatts. Plastic power transistor packages like the TO-220 and TO-247 dissipate well over 100 watts, approaching the dissipation of the all metal TO-3. The dissipation ratings listed in Figure above are the maximum ever encountered by the author for high powered devices. Most power transistors are rated at half or less than the listed wattage. Consult specific device datasheets for actual ratings. The the semiconductor die in the TO-220 and TO-247 plastic packages is mounted to a heat conductive metal slug which transfers heat from the back of the package to a metal heatsink, not shown. A thin coating of thermally conductive grease is applied to the metal before mounting the transistor to the heatsink. Since the TO-220 and TO-247 slugs, and the TO-3 case are connected to the collector, it is sometimes necessary to electrically isolate the these from a grounded heatsink by an interposed mica or polymer washer. The datasheet ratings for the power packages are only valid when mounted to a heatsink. Without a heatsink, a TO-220 dissipates approximately 1 watt safely in free air. Datasheet maximum power disipation ratings are difficult to acheive in practice. The maximum power dissipation is based on a heatsink maintaining the transistor case at no more than 25oC. This is difficult with an air cooled heatsink. The allowable power dissipation decreases with increasing temperature. This is known as derating. Many power device datasheets include a dissipation versus case termperaure graph. REVIEW:Power dissipation: maximum allowable power dissipation on a sustained basis.Reverse voltages: maximum allowable VCE , VCB , VEB .Collector current: the maximum allowable collector current.Saturation voltage is the VCE voltage drop in a saturated (fully conducting) transistor.Beta: ?=IC/IBAlpha: ?=IC/IE ?= ?/(?+1)TransistorPackages are a major factor in power dissipation. Larger packages dissipate more power. Lessons In Electric Circuits copyright (C) 2000-2010 Tony R. Kuphaldt

Current mirrors Transistors

An often-used circuit applying the bipolar junction transistor is the so-called current mirror, which serves as a simple current regulator, supplying nearly constant current to a load over a wide range of load resistances. We know that in a transistor operating in its active mode, collector current is equal to base current multiplied by the ratio ?. We also know that the ratio between collector current and emitter current is called ?. Because collector current is equal to base current multiplied by ?, and emitter current is the sum of the base and collector currents, ? should be mathematically derivable from ?. If you do the algebra, you’ll find that ? = ?/(?+1) for any transistor. We’ve seen already how maintaining a constant base current through an active transistor results in the regulation of collector current, according to the ? ratio. Well, the ? ratio works similarly: if emitter current is held constant, collector current will remain at a stable, regulated value so long as the transistor has enough collector-to-emitter voltage drop to maintain it in its active mode. Therefore, if we have a way of holding emitter current constant through a transistor, the transistor will work to regulate collector current at a constant value. Remember that the base-emitter junction of a BJT is nothing more than a PN junction, just like a diode, and that the “diode equation” specifies how much current will go through a PN junction given forward voltage drop and junction temperature: If both junction voltage and temperature are held constant, then the PN junction current will be constant. Following this rationale, if we were to hold the base-emitter voltage of a transistor constant, then its emitter current will be constant, given a constant temperature. (Figure below) Constant VBE gives constant IB, constant IE, and constant IC. This constant emitter current, multiplied by a constant ? ratio, gives a constant collector current through Rload, if enough battery voltage is available to keep the transistor in its active mode for any change in Rload‘s resistance. To maintain a constant voltage across the transistor’s base-emitter junction use a forward-biased diode to establish a constant voltage of approximately 0.7 volts, and connect it in parallel with the base-emitter junction as in Figure below. Diode junction 0.7 V maintains constant base voltage, and constant base current. The voltage dropped across the diode probably won’t be 0.7 volts exactly. The exact amount of forward voltage dropped across it depends on the current through the diode, and the diode’s temperature, all in accordance with the diode equation. If diode current is increased (say, by reducing the resistance of Rbias), its voltage drop will increase slightly, increasing the voltage drop across the transistor’s base-emitter junction, which will increase the emitter current by the same proportion, assuming the diode’s PN junction and the transistor’s base-emitter junction are well-matched to each other. In other words, transistor emitter current will closely equal diode current at any given time. If you change the diode current by changing the resistance value of Rbias, then the transistor’s emitter current will follow suit, because the emitter current is described by the same equation as the diode’s, and both PN junctions experience the same voltage drop. Remember, the transistor’s collector current is almost equal to its emitter current, as the ? ratio of a typical transistor is almost unity (1). If we have control over the transistor’s emitter current by setting diode current with a simple resistor adjustment, then we likewise have control over the transistor’s collector current. In other words, collector current mimics, or mirrors, diode current. Current through resistor Rload is therefore a function of current set by the bias resistor, the two being nearly equal. This is the function of the current mirror circuit: to regulate current through the load resistor by conveniently adjusting the value of Rbias. Current through the diode is described by a simple equation: power supply voltage minus diode voltage (almost a constant value), divided by the resistance of Rbias. To better match the characteristics of the two PN junctions (the diode junction and the transistor base-emitter junction), a transistor may be used in place of a regular diode, as in Figure below (a). Current mirror circuits. Because temperature is a factor in the “diode equation,” and we want the two PN junctions to behave identically under all operating conditions, we should maintain the two transistors at exactly the same temperature. This is easily done using discrete components by gluing the two transistor cases back-to-back. If the transistors are manufactured together on a single chip of silicon (as a so-called integrated circuit, or IC), the designers should locate the two transistors close to one another to facilitate heat transfer between them. The current mirror circuit shown with two NPN transistors in Figure above (a) is sometimes called a current-sinking type, because the regulating transistor conducts current to the load from ground (“sinking” current), rather than from the positive side of the battery (“sourcing” current). If we wish to have a grounded load, and a current sourcing mirror circuit, we may use PNP transistors like Figure above (b). While resistors can be manufactured in ICs, it is easier to fabricate transistors. IC designers avoid some resistors by replacing load resistors with current sources. A circuit like an operational amplifier built from discrete components will have a few transistors and many resistors. An integrated circuit version will have many transistors and a few resistors. In Figure below One voltage reference, Q1, drives multiple current sources: Q2, Q3, and Q4. If Q2 and Q3 are equal area transistors the load currents Iload will be equal. If we need a 2·Iload, parallel Q2 and Q3. Better yet fabricate one transistor, say Q3 with twice the area of Q2. Current I3 will then be twice I2. In other words, load current scales with transistor area. Multiple current mirrors may be slaved from a single (Q1 – Rbias) voltage source. Note that it is customary to draw the base voltage line right through the transistor symbols for multiple current mirrors! Or in the case of Q4 in Figure above, two current sources are associated with a single transistor symbol. The load resistors are drawn almost invisible to emphasize the fact that these do not exist in most cases. The load is often another (multiple) transistor circuit, say a pair of emitters of a differential amplifier, for example Q3 and Q4 in “A simple operational amplifier”, Ch 8 . Often, the collector load of a transistor is not a resistor but a current mirror. For example the collector load of Q4 collector , Ch 8 is a current mirror (Q2). For an example of a current mirror with multiple collector outputs see Q13 in the model 741 op-amp , Ch 8 . The Q13 current mirror outputs substitute for resistors as collector loads for Q15 and Q17. We see from these examples that current mirrors are preferred as loads over resistors in integrated circuitry. REVIEW:A current mirror is a transistor circuit that regulates current through a load resistance, the regulation point being set by a simple resistor adjustment.Transistors in a current mirror circuit must be maintained at the same temperature for precise operation. When using discrete transistors, you may glue their cases together to do this.Current mirror circuits may be found in two basic varieties: the current sinking configuration, where the regulating transistor connects the load to ground; and the current sourcing configuration, where the regulating transistor connects the load to the positive terminal of the DC power supply. Lessons In Electric Circuits copyright (C) 2000-2010 Tony R. Kuphaldt

transistors : Biasing calculations

Although transistor switching circuits operate without bias, it is unusual for analog circuits to operate without bias. One of the few examples is “TR One, one transistor radio” TR One, Ch 9 with an amplified AM (amplitude modulation) detector. Note the lack of a bias resistor at the base in that circuit. In this section we look at a few basic bias circuits which can set a selected emitter current IE. Given a desired emitter current IE, what values of bias resistors are required, RB, RE, etc? The simplest biasing applies a base-bias resistor between the base and a base battery VBB. It is convenient to use the existing VCC supply instead of a new bias supply. An example of an audio amplifier stage using base-biasing is “Crystal radio with one transistor . . . ” crystal radio, Ch 9 . Note the resistor from the base to the battery terminal. A similar circuit is shown in Figure below. Write a KVL (Krichhoff’s voltage law) equation about the loop containing the battery, RB, and the VBE diode drop on the transistor in Figure below. Note that we use VBB for the base supply, even though it is actually VCC. If ? is large we can make the approximation that IC =IE. For silicon transistors VBE?0.7V. Base-bias Silicon small signal transistors typically have a ? in the range of 100-300. Assuming that we have a ?=100 transistor, what value of base-bias resistor is required to yield an emitter current of 1mA? Solving the IE base-bias equation for RB and substituting ?, VBB, VBE, and IE yields 930k?. The closest standard value is 910k?. What is the the emitter current with a 910k? resistor? What is the emitter current if we randomly get a ?=300 transistor? The emitter current is little changed in using the standard value 910k? resistor. However, with a change in ? from 100 to 300, the emitter current has tripled. This is not acceptable in a power amplifier if we expect the collector voltage to swing from near VCC to near ground. However, for low level signals from micro-volts to a about a volt, the bias point can be centered for a ? of square root of (100·300)=173. The bias point will still drift by a considerable amount . However, low level signals will not be clipped. Base-bias by its self is not suitable for high emitter currents, as used in power amplifiers. The base-biased emitter current is not temperature stable. Thermal run away is the result of high emitter current causing a temperature increase which causes an increase in emitter current, which further increases temperature. Variations in bias due to temperature and beta may be reduced by moving the VBB end of the base-bias resistor to the collector as in Figure below. If the emitter current were to increase, the voltage drop across RC increases, decreasing VC, decreasing IB fed back to the base. This, in turn, decreases the emitter current, correcting the original increase. Write a KVL equation about the loop containing the battery, RC , RB , and the VBE drop. Substitute IC?IE and IB?IE/?. Solving for IE yields the IE CFB-bias equation. Solving for IB yields the IB CFB-bias equation. Collector-feedback bias. Find the required collector feedback bias resistor for an emitter current of 1 mA, a 4.7K collector load resistor, and a transistor with ?=100 . Find the collector voltage VC. It should be approximately midway between VCC and ground. The closest standard value to the 460k collector feedback bias resistor is 470k. Find the emitter current IE with the 470 K resistor. Recalculate the emitter current for a transistor with ?=100 and ?=300. We see that as beta changes from 100 to 300, the emitter current increases from 0.989mA to 1.48mA. This is an improvement over the previous base-bias circuit which had an increase from 1.02mA to 3.07mA. Collector feedback bias is twice as stable as base-bias with respect to beta variation. Inserting a resistor RE in the emitter circuit as in Figure below causes degeneration, also known as negative feedback. This opposes a change in emitter current IE due to temperature changes, resistor tolerances, beta variation, or power supply tolerance. Typical tolerances are as follows: resistor— 5%, beta— 100-300, power supply— 5%. Why might the emitter resistor stabilize a change in current? The polarity of the voltage drop across RE is due to the collector battery VCC. The end of the resistor closest to the (-) battery terminal is (-), the end closest to the (+) terminal it (+). Note that the (-) end of RE is connected via VBB battery and RB to the base. Any increase in current flow through RE will increase the magnitude of negative voltage applied to the base circuit, decreasing the base current, decreasing the emitter current. This decreasing emitter current partially compensates the original increase. Emitter-bias Note that base-bias battery VBB is used instead of VCC to bias the base in Figure above. Later we will show that the emitter-bias is more effective with a lower base bias battery. Meanwhile, we write the KVL equation for the loop through the base-emitter circuit, paying attention to the polarities on the components. We substitute IB?IE/? and solve for emitter current IE. This equation can be solved for RB , equation: RB emitter-bias, Figure above. Before applying the equations: RB emitter-bias and IE emitter-bias, Figure above, we need to choose values for RC and RE . RC is related to the collector supply VCC and the desired collector current IC which we assume is approximately the emitter current IE. Normally the bias point for VC is set to half of VCC. Though, it could be set higher to compensate for the voltage drop across the emitter resistor RE. The collector current is whatever we require or choose. It could range from micro-Amps to Amps depending on the application and transistor rating. We choose IC = 1mA, typical of a small-signal transistor circuit. We calculate a value for RC and choose a close standard value. An emitter resistor which is 10-50% of the collector load resistor usually works well. Our first example sets the base-bias supply to high at VBB = VCC = 10V to show why a lower voltage is desirable. Determine the required value of base-bias resistor RB. Choose a standard value resistor. Calculate the emitter current for ?=100 and ?=300. Compare the stabilization of the current to prior bias circuits. An 883k resistor was calculated for RB, an 870k chosen. At ?=100, IE is 1.01mA. For ?=300 the emitter currents are shown in Table below. Bias circuitIC ?=100IC ?=300base-bias1.02mA3.07mAcollector feedback bias0.989mA1.48mAemitter-bias, VBB=10V1.01mA2.76mA Table above shows that for VBB = 10V, emitter-bias does not do a very good job of stabilizing the emitter current. The emitter-bias example is better than the previous base-bias example, but, not by much. The key to effective emitter bias is lowering the base supply VBB nearer to the amount of emitter bias. How much emitter bias do we Have? Rounding, that is emitter current times emitter resistor: IERE = (1mA)(470) = 0.47V. In addition, we need to overcome the VBE = 0.7V. Thus, we need a VBB >(0.47 + 0.7)V or >1.17V. If emitter current deviates, this number will change compared with the fixed base supply VBB,causing a correction to base current IB and emitter current IE. A good value for VB >1.17V is 2V. The calculated base resistor of 83k is much lower than the previous 883k. We choose 82k from the list of standard values. The emitter currents with the 82k RB for ?=100 and ?=300 are: Comparing the emitter currents for emitter-bias with VBB = 2V at ?=100 and ?=300 to the previous bias circuit examples in Table below, we see considerable improvement at 1.75mA, though, not as good as the 1.48mA of collector feedback. Bias circuitIC ?=100IC ?=300base-bias1.02mA3.07mAcollector feedback bias0.989mA1.48mAemitter-bias, VBB=10V1.01mA2.76mAemitter-bias, VBB=2V1.01mA1.75mA How can we improve the performance of emitter-bias? Either increase the emitter resistor RB or decrease the base-bias supply VBB or both. As an example, we double the emitter resistor to the nearest standard value of 910?. The calculated RB = 39k is a standard value resistor. No need to recalculate IE for ? = 100. For ? = 300, it is: The performance of the emitter-bias circuit with a 910 emitter resistor is much improved. See Table below. Bias circuitIC ?=100IC ?=300base-bias1.02mA3.07mAcollector feedback bias0.989mA1.48mAemitter-bias, VBB=10V1.01mA2.76mAemitter-bias, VBB=2V, RB=4701.01mA1.75mAemitter-bias, VBB=2V, RB=9101.00mA1.25mA As an exercise, rework the emitter-bias example with the base resistor reverted back to 470?, and the base-bias supply reduced to 1.5V. The 33k base resistor is a standard value, emitter current at ? = 100 is OK. The emitter current at ? = 300 is: Table below below compares the exercise results 1mA and 1.38mA to the previous examples. Bias circuitIC ?=100IC ?=300base-bias1.02mA3.07mAcollector feedback bias0.989mA1.48mAemitter-bias, VBB=10V1.01mA2.76mAemitter-bias, VBB=2V, RB=4701.01mA1.75mAemitter-bias, VBB=2V, RB=9101.00mA1.25mAemitter-bias, VBB=1.5V, RB=4701.00mA1.38mA The emitter-bias equations have been repeated in Figure below with the internal emitter resistance included for better accuracy. The internal emitter resistance is the resistance in the emitter circuit contained within the transistor package. This internal resistance REE is significant when the (external) emitter resistor RE is small, or even zero. The value of internal resistance RE is a function of emitter current IE, Table below.   REE = KT/IEm   where:   K=1.38×10-23 watt-sec/oC, Boltzman's constant   T= temperature in Kelvins ?300.   IE = emitter current   m = varies from 1 to 2 for Silicon   REE ? 0.026V/IE = 26mV/IE For reference the 26mV approximation is listed as equation REE in Figure below. Emitter-bias equations with internal emitter resistance REE included.. The more accurate emitter-bias equations in Figure above may be derived by writing a KVL equation. Alternatively, start with equations IE emitter-bias and RB emitter-bias in Figure previous, substituting RE with REE+RE. The result is equations IE EB and RB EB, respectively in Figure above. Redo the RB calculation in the previous example emitter-bias with the inclusion of REE and compare the results. The inclusion of REE in the calculation results in a lower value of the base resistor RB a shown in Table below. It falls below the standard value 82k resistor instead of above it. REE?REE ValueWithout REE83kWith REE80.4k Bypass Capacitor for RE One problem with emitter bias is that a considerable part of the output signal is dropped across the emitter resistor RE (Figure below). This voltage drop across the emitter resistor is in series with the base and of opposite polarity compared with the input signal. (This is similar to a common collector configuration having

Transistor : Biasing techniques

In the common-emitter section of this chapter, we saw a SPICE analysis where the output waveform resembled a half-wave rectified shape: only half of the input waveform was reproduced, with the other half being completely cut off. Since our purpose at that time was to reproduce the entire waveshape, this constituted a problem. The solution to this problem was to add a small bias voltage to the amplifier input so that the transistor stayed in active mode throughout the entire wave cycle. This addition was called a bias voltage. A half-wave output is not problematic for some applications. In fact, some applications may necessitate this very kind of amplification. Because it is possible to operate an amplifier in modes other than full-wave reproduction and specific applications require different ranges of reproduction, it is useful to describe the degree to which an amplifier reproduces the input waveform by designating it according to class. Amplifier class operation is categorized with alphabetical letters: A, B, C, and AB. For Class A operation, the entire input waveform is faithfully reproduced. Although I didn’t introduce this concept back in the common-emitter section, this is what we were hoping to attain in our simulations. Class A operation can only be obtained when the transistor spends its entire time in the active mode, never reaching either cutoff or saturation. To achieve this, sufficient DC bias voltage is usually set at the level necessary to drive the transistor exactly halfway between cutoff and saturation. This way, the AC input signal will be perfectly “centered” between the amplifier’s high and low signal limit levels. Class A: The amplifier output is a faithful reproduction of the input. Class B operation is what we had the first time an AC signal was applied to the common-emitter amplifier with no DC bias voltage. The transistor spent half its time in active mode and the other half in cutoff with the input voltage too low (or even of the wrong polarity!) to forward-bias its base-emitter junction. Class B: Bias is such that half (180o) of the waveform is reproduced. By itself, an amplifier operating in class B mode is not very useful. In most circumstances, the severe distortion introduced into the waveshape by eliminating half of it would be unacceptable. However, class B operation is a useful mode of biasing if two amplifiers are operated as a push-pull pair, each amplifier handling only half of the waveform at a time: class B push pull amplifier: Each transistor reproduces half of the waveform. Combining the halves produces a faithful reproduction of the whole wave. Transistor Q1 “pushes” (drives the output voltage in a positive direction with respect to ground), while transistor Q2 “pulls” the output voltage (in a negative direction, toward 0 volts with respect to ground). Individually, each of these transistors is operating in class B mode, active only for one-half of the input waveform cycle. Together, however, both function as a team to produce an output waveform identical in shape to the input waveform. A decided advantage of the class B (push-pull) amplifier design over the class A design is greater output power capability. With a class A design, the transistor dissipates considerable energy in the form of heat because it never stops conducting current. At all points in the wave cycle it is in the active (conducting) mode, conducting substantial current and dropping substantial voltage. There is substantial power dissipated by the transistor throughout the cycle. In a class B design, each transistor spends half the time in cutoff mode, where it dissipates zero power (zero current = zero power dissipation). This gives each transistor a time to “rest” and cool while the other transistor carries the burden of the load. Class A amplifiers are simpler in design, but tend to be limited to low-power signal applications for the simple reason of transistor heat dissipation. Another class of amplifier operation known as class AB, is somewhere between class A and class B: the transistor spends more than 50% but less than 100% of the time conducting current. If the input signal bias for an amplifier is slightly negative (opposite of the bias polarity for class A operation), the output waveform will be further “clipped” than it was with class B biasing, resulting in an operation where the transistor spends most of the time in cutoff mode: Class C: Conduction is for less than a half cycle (

The cascode amplifier

While the C-B (common-base) amplifier is known for wider bandwidth than the C-E (common-emitter) configuration, the low input impedance (10s of ?) of C-B is a limitation for many applications. The solution is to precede the C-B stage by a low gain C-E stage which has moderately high input impedance (k?s). See Figure below. The stages are in a cascode configuration, stacked in series, as opposed to cascaded for a standard amplifier chain. See “Capacitor coupled three stage common-emitter amplifier” Capacitor coupled for a cascade example. The cascode amplifier configuration has both wide bandwidth and a moderately high input impedance. The cascode amplifier is combined common-emitter and common-base. This is an AC circuit equivalent with batteries and capacitors replaced by short circuits. The key to understanding the wide bandwidth of the cascode configuration is the Miller effect. The Miller effect is the multiplication of the bandwidth robbing collector-base capacitance by voltage gain Av. This C-B capacitance is smaller than the E-B capacitance. Thus, one would think that the C-B capacitance would have little effect. However, in the C-E configuration, the collector output signal is out of phase with the input at the base. The collector signal capacitively coupled back opposes the base signal. Moreover, the collector feedback is (1-Av) times larger than the base signal. Thus, the small C-B capacitance appears (1-Av) times larger than its actual value. This capacitive gain reducing feedback increases with frequency, reducing the high frequency response of a C-E amplifier. The approximage voltage gain of the C-E amplifier in Figure belowb is -RL/REE. The emitter current is set to 1.0 mA by biasing. REE= 26mV/IE = 26mV/1.0ma = 26 ?. Thus, Av = -RL/REE = -4700/26 = -181. The pn2222 datasheet list Ccbo = 8 pF.[FAR] The miller capacitance is Ccbo(1-Av). Gain Av = -181, negative since it is inverting gain. Cmiller = Ccbo(1-Av) = 8pF(1-(-181)=1456pF A common-base configuration is not subject to the Miller effect because the grounded base shields the collector signal from being fed back to the emitter input. Thus, a C-B amplifier has better high frequency response. To have a moderately high input impedance, the C-E stage is still desirable. The key is to reduce the gain (to about 1) of the C-E stage which reduces the Miller effect C-B feedback to 1·CCBO. The total C-B feedback is the feedback capacitance 1·CCB plus the actual capacitance CCB for a total of 2·CCBO. This is a considerable reduction from 181·CCBO. The miller capacitance for a gain of -2 C-E stage is Cmiller = Ccbo(1-Av)= Cmiller = Ccbo(1-(-1)) = Ccbo·2. The way to reduce the common-emitter gain is to reduce the load resistance. The gain of a C-E amplifier is approximately RC/RE. The internal emitter resistance REE at 1mA emitter current is 26?. For details on the 26?, see “Derivation of REE”, see REE. The collector load RC is the resistance of the emitter of the C-B stage loading the C-E stage, 26? again. CE gain amplifier gain is approximately Av = RC/RE=26/26=1. This Miller capacitance is Cmiller = Ccbo(1-Av) = 8pF(1-(-1)=16pF. We now have a moderately high input impedance C-E stage without suffering the Miller effect, but no C-E dB voltage gain. The C-B stage provides a high voltage gain, AV = -181. Current gain of cascode is ? of the C-E stage, 1 for the C-B, ? overall. Thus, the cascode has moderately high input impedance of the C-E, good gain, and good bandwidth of the C-B. SPICE: Cascode and common-emitter for comparison. The SPICE version of both a cascode amplifier, and for comparison, a common-emitter amplifier is shown in Figure above. The netlist is in Table below. The AC source V3 drives both amplifiers via node 4. The bias resistors for this circuit are calculated in an example problem cascode. SPICE waveforms. Note that Input is multiplied by 10 for visibility. *SPICE circuit from XCircuit v3.20 V1 19 0 10 Q1 13 15 0 q2n2222 Q2 3 2 A q2n2222 R1 19 13 4.7k V2 16 0 1.5 C1 4 15 10n R2 15 16 80k Q3 A 5 0 q2n2222 V3 4 6 SIN(0 0.1 1k) ac 1 R3 1 2 80k R4 3 9 4.7k C2 2 0 10n C3 4 5 10n R5 5 6 80k V4 1 0 11.5 V5 9 0 20 V6 6 0 1.5 .model q2n2222 npn (is=19f bf=150 + vaf=100 ikf=0.18 ise=50p ne=2.5 br=7.5 + var=6.4 ikr=12m isc=8.7p nc=1.2 rb=50 + re=0.4 rc=0.3 cje=26p tf=0.5n + cjc=11p tr=7n xtb=1.5 kf=0.032f af=1) .tran 1u 5m .AC DEC 10 1k 100Meg .end The waveforms in Figure above show the operation of the cascode stage. The input signal is displayed multiplied by 10 so that it may be shown with the outputs. Note that both the Cascode, Common-emitter, and Va (intermediate point) outputs are inverted from the input. Both the Cascode and Common emitter have large amplitude outputs. The Va point has a DC level of about 10V, about half way between 20V and ground. The signal is larger than can be accounted for by a C-E gain of 1, It is three times larger than expected. Cascode vs common-emitter banwidth. Figure above shows the frequency response to both the cascode and common-emitter amplifiers. The SPICE statements responsible for the AC analysis, extracted from the listing: V3 4 6 SIN(0 0.1 1k) ac 1 .AC DEC 10 1k 100Meg Note the “ac 1” is necessary at the end of the V3 statement. The cascode has marginally better mid-band gain. However, we are primarily looking for the bandwidth measured at the -3dB points, down from the midband gain for each amplifier. This is shown by the vertical solid lines in Figure above. It is also possible to print the data of interest from nutmeg to the screen, the SPICE graphical viewer (command, first line): nutmeg 6 -> print frequency db(vm(3)) db(vm(13)) Index frequency db(vm(3)) db(vm(13)) 22 0.158MHz 47.54 45.41 33 1.995MHz 46.95 42.06 37 5.012MHz 44.63 36.17 Index 22 gives the midband dB gain for Cascode vm(3)=47.5dB and Common-emitter vm(13)=45.4dB. Out of many printed lines, Index 33 was the closest to being 3dB down from 45.4dB at 42.0dB for the Common-emitter circuit. The corresponding Index 33 frequency is approximately 2Mhz, the common-emitter bandwidth. Index 37 vm(3)=44.6db is approximately 3db down from 47.5db. The corresponding Index37 frequency is 5Mhz, the cascode bandwidth. Thus, the cascode amplifier has a wider bandwidth. We are not concerned with the low frequency degradation of gain. It is due to the capacitors, which could be remedied with larger ones. The 5MHz bandwith of our cascode example, while better than the common-emitter example, is not exemplary for an RF (radio frequency) amplifier. A pair of RF or microwave transistors with lower interelectrode capacitances should be used for higher bandwidth. Before the invention of the RF dual gate MOSFET, the BJT cascode amplifier could have been found in UHF (ultra high frequency) TV tuners. REVIEWA cascode amplifier consists of a common-emitter stage loaded by the emitter of a common-base stage.The heavily loaded C-E stage has a low gain of 1, overcoming the Miller effectA cascode amplifier has a high gain, moderately high input impedance, a high output impedance, and a high bandwidth. Lessons In Electric Circuits copyright (C) 2000-2010 Tony R. Kuphaldt

The common-collector amplifier

Our next transistor configuration to study is a bit simpler for gain calculations. Called the common-collector configuration, its schematic diagram is shown in Figure below. Common collector amplifier has collector common to both input and output. It is called the common-collector configuration because (ignoring the power supply battery) both the signal source and the load share the collector lead as a common connection point as in Figure below. Common collector: Input is applied to base and collector. Output is from emitter-collector circuit. It should be apparent that the load resistor in the common-collector amplifier circuit receives both the base and collector currents, being placed in series with the emitter. Since the emitter lead of a transistor is the one handling the most current (the sum of base and collector currents, since base and collector currents always mesh together to form the emitter current), it would be reasonable to presume that this amplifier will have a very large current gain. This presumption is indeed correct: the current gain for a common-collector amplifier is quite large, larger than any other transistor amplifier configuration. However, this is not necessarily what sets it apart from other amplifier designs. Let’s proceed immediately to a SPICE analysis of this amplifier circuit, and you will be able to immediately see what is unique about this amplifier. The circuit is in Figure below. The netlist is in Figure below. Common collector: Output equals input less a 0.7 V VBE drop. Unlike the common-emitter amplifier from the previous section, the common-collector produces an output voltage in direct rather than inverse proportion to the rising input voltage. See Figure above. As the input voltage increases, so does the output voltage. Moreover, a close examination reveals that the output voltage is nearly identical to the input voltage, lagging behind by about 0.7 volts. This is the unique quality of the common-collector amplifier: an output voltage that is nearly equal to the input voltage. Examined from the perspective of output voltage change for a given amount of input voltage change, this amplifier has a voltage gain of almost exactly unity (1), or 0 dB. This holds true for transistors of any ? value, and for load resistors of any resistance value. It is simple to understand why the output voltage of a common-collector amplifier is always nearly equal to the input voltage. Referring to the diode current source transistor model in Figure below, we see that the base current must go through the base-emitter PN junction, which is equivalent to a normal rectifying diode. If this junction is forward-biased (the transistor conducting current in either its active or saturated modes), it will have a voltage drop of approximately 0.7 volts, assuming silicon construction. This 0.7 volt drop is largely irrespective of the actual magnitude of base current; thus, we can regard it as being constant: Emitter follower: Emitter voltage follows base voltage (less a 0.7 V VBE drop.) Given the voltage polarities across the base-emitter PN junction and the load resistor, we see that these must add together to equal the input voltage, in accordance with Kirchhoff’s Voltage Law. In other words, the load voltage will always be about 0.7 volts less than the input voltage for all conditions where the transistor is conducting. Cutoff occurs at input voltages below 0.7 volts, and saturation at input voltages in excess of battery (supply) voltage plus 0.7 volts. Because of this behavior, the common-collector amplifier circuit is also known as the voltage-follower or emitter-follower amplifier, because the emitter load voltages follow the input so closely. Applying the common-collector circuit to the amplification of AC signals requires the same input “biasing” used in the common-emitter circuit: a DC voltage must be added to the AC input signal to keep the transistor in its active mode during the entire cycle. When this is done, the result is the non-inverting amplifier in Figure below. Common collector (emitter-follower) amplifier. The results of the SPICE simulation in Figure below show that the output follows the input. The output is the same peak-to-peak amplitude as the input. Though, the DC level is shifted downward by one VBE diode drop. Common collector (emitter-follower): Output V3 follows input V1 less a 0.7 V VBE drop. Here’s another view of the circuit (Figure below) with oscilloscopes connected to several points of interest. Common collector non-inverting voltage gain is 1. Since this amplifier configuration doesn’t provide any voltage gain (in fact, in practice it actually has a voltage gain of slightly less than 1), its only amplifying factor is current. The common-emitter amplifier configuration examined in the previous section had a current gain equal to the ? of the transistor, being that the input current went through the base and the output (load) current went through the collector, and ? by definition is the ratio between the collector and base currents. In the common-collector configuration, though, the load is situated in series with the emitter, and thus its current is equal to the emitter current. With the emitter carrying collector current and base current, the load in this type of amplifier has all the current of the collector running through it plus the input current of the base. This yields a current gain of ? plus 1: Once again, PNP transistors are just as valid to use in the common-collector configuration as NPN transistors. The gain calculations are all thesame, as is the non-inverting of the amplified signal. The only difference is in voltage polarities and current directions shown in Figure below. PNP version of the common-collector amplifier. A popular application of the common-collector amplifier is for regulated DC power supplies, where an unregulated (varying) source of DC voltage is clipped at a specified level to supply regulated (steady) voltage to a load. Of course, zener diodes already provide this function of voltage regulation shown in Figure below. Zener diode voltage regulator. However, when used in this direct fashion, the amount of current that may be supplied to the load is usually quite limited. In essence, this circuit regulates voltage across the load by keeping current through the series resistor at a high enough level to drop all the excess power source voltage across it, the zener diode drawing more or less current as necessary to keep the voltage across itself steady. For high-current loads, a plain zener diode voltage regulator would have to shunt a heavy current through the diode to be effective at regulating load voltage in the event of large load resistance or voltage source changes. One popular way to increase the current-handling ability of a regulator circuit like this is to use a common-collector transistor to amplify current to the load, so that the zener diode circuit only has to handle the amount of current necessary to drive the base of the transistor. (Figure below) Common collector application: voltage regulator. There’s really only one caveat to this approach: the load voltage will be approximately 0.7 volts less than the zener diode voltage, due to the transistor’s 0.7 volt base-emitter drop. Since this 0.7 volt difference is fairly constant over a wide range of load currents, a zener diode with a 0.7 volt higher rating can be chosen for the application. Sometimes the high current gain of a single-transistor, common-collector configuration isn’t enough for a particular application. If this is the case, multiple transistors may be staged together in a popular configuration known as a Darlington pair, just an extension of the common-collector concept shown in Figure below. An NPN darlington pair. Darlington pairs essentially place one transistor as the common-collector load for another transistor, thus multiplying their individual current gains. Base current through the upper-left transistor is amplified through that transistor’s emitter, which is directly connected to the base of the lower-right transistor, where the current is again amplified. The overall current gain is as follows: Voltage gain is still nearly equal to 1 if the entire assembly is connected to a load in common-collector fashion, although the load voltage will be a full 1.4 volts less than the input voltage shown in Figure below. Darlington pair based common-collector amplifier loses two VBE diode drops. Darlington pairs may be purchased as discrete units (two transistors in the same package), or may be built up from a pair of individual transistors. Of course, if even more current gain is desired than what may be obtained with a pair, Darlington triplet or quadruplet assemblies may be constructed. REVIEW:Common-collector transistor amplifiers are so-called because the input and output voltage points share the collector lead of the transistor in common with each other, not considering any power supplies.The common-collector amplifier is also known as an emitter-follower.The output voltage on a common-collector amplifier will be in phase with the input voltage, making the common-collector a non-inverting amplifier circuit.The current gain of a common-collector amplifier is equal to ? plus 1. The voltage gain is approximately equal to 1 (in practice, just a little bit less).A Darlington pair is a pair of transistors “piggybacked” on one another so that the emitter of one feeds current to the base of the other in common-collector form. The result is an overall current gain equal to the product (multiplication) of their individual common-collector current gains (? plus 1). Lessons In Electric Circuits copyright (C) 2000-2010 Tony R. Kuphaldt

Meter check of a transistor

Bipolar transistors are constructed of a three-layer semiconductor “sandwich,” either PNP or NPN. As such, transistors register as two diodes connected back-to-back when tested with a multimeter’s “resistance” or “diode check” function as illustrated in Figure below. Low resistance readings on the base with the black negative (-) leads correspond to an N-type base in a PNP transistor. On the symbol, the N-type material corresponds to the “non-pointing” end of the base-emitter junction, the base. The P-type emitter corresponds to “pointing” end of the base-emitter junction the emitter. PNP transistor meter check: (a) forward B-E, B-C, resistance is low; (b) reverse B-E, B-C, resistance is ?. Here I’m assuming the use of a multimeter with only a single continuity range (resistance) function to check the PN junctions. Some multimeters are equipped with two separate continuity check functions: resistance and “diode check,” each with its own purpose. If your meter has a designated “diode check” function, use that rather than the “resistance” range, and the meter will display the actual forward voltage of the PN junction and not just whether or not it conducts current. Meter readings will be exactly opposite, of course, for an NPN transistor, with both PN junctions facing the other way. Low resistance readings with the red (+) lead on the base is the “opposite” condition for the NPN transistor. If a multimeter with a “diode check” function is used in this test, it will be found that the emitter-base junction possesses a slightly greater forward voltage drop than the collector-base junction. This forward voltage difference is due to the disparity in doping concentration between the emitter and collector regions of the transistor: the emitter is a much more heavily doped piece of semiconductor material than the collector, causing its junction with the base to produce a higher forward voltage drop. Knowing this, it becomes possible to determine which wire is which on an unmarked transistor. This is important because transistor packaging, unfortunately, is not standardized. All bipolar transistors have three wires, of course, but the positions of the three wires on the actual physical package are not arranged in any universal, standardized order. Suppose a technician finds a bipolar transistor and proceeds to measure continuity with a multimeter set in the “diode check” mode. Measuring between pairs of wires and recording the values displayed by the meter, the technician obtains the data in Figure below. Unknown bipolar transistor. Which terminals are emitter, base, and collector? ?-meter readings between terminals. The only combinations of test points giving conducting meter readings are wires 1 and 3 (red test lead on 1 and black test lead on 3), and wires 2 and 3 (red test lead on 2 and black test lead on 3). These two readings must indicate forward biasing of the emitter-to-base junction (0.655 volts) and the collector-to-base junction (0.621 volts). Now we look for the one wire common to both sets of conductive readings. It must be the base connection of the transistor, because the base is the only layer of the three-layer device common to both sets of PN junctions (emitter-base and collector-base). In this example, that wire is number 3, being common to both the 1-3 and the 2-3 test point combinations. In both those sets of meter readings, the black (-) meter test lead was touching wire 3, which tells us that the base of this transistor is made of N-type semiconductor material (black = negative). Thus, the transistor is a PNP with base on wire 3, emitter on wire 1 and collector on wire 2 as described in Figure below. BJT terminals identified by ?-meter. Please note that the base wire in this example is not the middle lead of the transistor, as one might expect from the three-layer “sandwich” model of a bipolar transistor. This is quite often the case, and tends to confuse new students of electronics. The only way to be sure which lead is which is by a meter check, or by referencing the manufacturer’s “data sheet” documentation on that particular part number of transistor. Knowing that a bipolar transistor behaves as two back-to-back diodes when tested with a conductivity meter is helpful for identifying an unknown transistor purely by meter readings. It is also helpful for a quick functional check of the transistor. If the technician were to measure continuity in any more than two or any less than two of the six test lead combinations, he or she would immediately know that the transistor was defective (or else that it wasn’t a bipolar transistor but rather something else — a distinct possibility if no part numbers can be referenced for sure identification!). However, the “two diode” model of the transistor fails to explain how or why it acts as an amplifying device. To better illustrate this paradox, let’s examine one of the transistor switch circuits using the physical diagram in Figure below rather than the schematic symbol to represent the transistor. This way the two PN junctions will be easier to see. A small base current flowing in the forward biased base-emitter junction allows a large current flow through the reverse biased base-collector junction. A grey-colored diagonal arrow shows the direction of electron flow through the emitter-base junction. This part makes sense, since the electrons are flowing from the N-type emitter to the P-type base: the junction is obviously forward-biased. However, the base-collector junction is another matter entirely. Notice how the grey-colored thick arrow is pointing in the direction of electron flow (up-wards) from base to collector. With the base made of P-type material and the collector of N-type material, this direction of electron flow is clearly backwards to the direction normally associated with a PN junction! A normal PN junction wouldn’t permit this “backward” direction of flow, at least not without offering significant opposition. However, a saturated transistor shows very little opposition to electrons, all the way from emitter to collector, as evidenced by the lamp’s illumination! Clearly then, something is going on here that defies the simple “two-diode” explanatory model of the bipolar transistor. When I was first learning about transistor operation, I tried to construct my own transistor from two back-to-back diodes, as in Figure below. A pair of back-to-back diodes don’t act like a transistor! My circuit didn’t work, and I was mystified. However useful the “two diode” description of a transistor might be for testing purposes, it doesn’t explain how a transistor behaves as a controlled switch. What happens in a transistor is this: the reverse bias of the base-collector junction prevents collector current when the transistor is in cutoff mode (that is, when there is no base current). If the base-emitter junction is forward biased by the controlling signal, the normally-blocking action of the base-collector junction is overridden and current is permitted through the collector, despite the fact that electrons are going the “wrong way” through that PN junction. This action is dependent on the quantum physics of semiconductor junctions, and can only take place when the two junctions are properly spaced and the doping concentrations of the three layers are properly proportioned. Two diodes wired in series fail to meet these criteria; the top diode can never “turn on” when it is reversed biased, no matter how much current goes through the bottom diode in the base wire loop. See Bipolar junction transistors, Ch 2 for more details. That doping concentrations play a crucial part in the special abilities of the transistor is further evidenced by the fact that collector and emitter are not interchangeable. If the transistor is merely viewed as two back-to-back PN junctions, or merely as a plain N-P-N or P-N-P sandwich of materials, it may seem as though either end of the transistor could serve as collector or emitter. This, however, is not true. If connected “backwards” in a circuit, a base-collector current will fail to control current between collector and emitter. Despite the fact that both the emitter and collector layers of a bipolar transistor are of the same doping type (either N or P), collector and emitter are definitely not identical! Current through the emitter-base junction allows current through the reverse-biased base-collector junction. The action of base current can be thought of as “opening a gate” for current through the collector. More specifically, any given amount of emitter-to-base current permits a limited amount of base-to-collector current. For every electron that passes through the emitter-base junction and on through the base wire, a certain, number of electrons pass through the base-collector junction and no more. In the next section, this current-limiting of the transistor will be investigated in more detail. REVIEW:Tested with a multimeter in the “resistance” or “diode check” modes, a transistor behaves like two back-to-back PN (diode) junctions.The emitter-base PN junction has a slightly greater forward voltage drop than the collector-base PN junction, because of heavier doping of the emitter semiconductor layer.The reverse-biased base-collector junction normally blocks any current from going through the transistor between emitter and collector. However, that junction begins to conduct if current is drawn through the base wire. Base current may be thought of as “opening a gate” for a certain, limited amount of current through the collector. Lessons In Electric Circuits copyright (C) 2000-2010 Tony R. Kuphaldt

BIPOLAR JUNCTION TRANSISTORS

The invention of the bipolar transistor in 1948 ushered in a revolution in electronics. Technical feats previously requiring relatively large, mechanically fragile, power-hungry vacuum tubes were suddenly achievable with tiny, mechanically rugged, power-thrifty specks of crystalline silicon. This revolution made possible the design and manufacture of lightweight, inexpensive electronic devices that we now take for granted. Understanding how transistors function is of paramount importance to anyone interested in understanding modern electronics. My intent here is to focus as exclusively as possible on the practical function and application of bipolar transistors, rather than to explore the quantum world of semiconductor theory. Discussions of holes and electrons are better left to another chapter in my opinion. Here I want to explore how to use these components, not analyze their intimate internal details. I don’t mean to downplay the importance of understanding semiconductor physics, but sometimes an intense focus on solid-state physics detracts from understanding these devices’ functions on a component level. In taking this approach, however, I assume that the reader possesses a certain minimum knowledge of semiconductors: the difference between “P” and “N” doped semiconductors, the functional characteristics of a PN (diode) junction, and the meanings of the terms “reverse biased” and “forward biased.” If these concepts are unclear to you, it is best to refer to earlier chapters in this book before proceeding with this one. A bipolar transistor consists of a three-layer “sandwich” of doped (extrinsic) semiconductor materials, either P-N-P in Figure below(b) or N-P-N at (d). Each layer forming the transistor has a specific name, and each layer is provided with a wire contact for connection to a circuit. The schematic symbols are shown in Figure below(a) and (d). BJT transistor: (a) PNP schematic symbol, (b) physical layout (c) NPN symbol, (d) layout. The functional difference between a PNP transistor and an NPN transistor is the proper biasing (polarity) of the junctions when operating. For any given state of operation, the current directions and voltage polarities for each kind of transistor are exactly opposite each other. Bipolar transistors work as current-controlled current regulators. In other words, transistors restrict the amount of current passed according to a smaller, controlling current. The main current that is controlled goes from collector to emitter, or from emitter to collector, depending on the type of transistor it is (PNP or NPN, respectively). The small current that controls the main current goes from base to emitter, or from emitter to base, once again depending on the kind of transistor it is (PNP or NPN, respectively). According to the standards of semiconductor symbology, the arrow always points against the direction of electron flow. (Figure below) Small electron base current controls large collector electron current flowing against emitter arrow. Bipolar transistors are called bipolar because the main flow of electrons through them takes place in two types of semiconductor material: P and N, as the main current goes from emitter to collector (or vice versa). In other words, two types of charge carriers — electrons and holes — comprise this main current through the transistor. As you can see, the controlling current and the controlled current always mesh together through the emitter wire, and their electrons always flow against the direction of the transistor’s arrow. This is the first and foremost rule in the use of transistors: all currents must be going in the proper directions for the device to work as a current regulator. The small, controlling current is usually referred to simply as the base current because it is the only current that goes through the base wire of the transistor. Conversely, the large, controlled current is referred to as the collector current because it is the only current that goes through the collector wire. The emitter current is the sum of the base and collector currents, in compliance with Kirchhoff’s Current Law. No current through the base of the transistor, shuts it off like an open switch and prevents current through the collector. A base current, turns the transistor on like a closed switch and allows a proportional amount of current through the collector. Collector current is primarily limited by the base current, regardless of the amount of voltage available to push it. The next section will explore in more detail the use of bipolar transistors as switching elements. REVIEW:Bipolar transistors are so named because the controlled current must go through two types of semiconductor material: P and N. The current consists of both electron and hole flow, in different parts of the transistor.Bipolar transistors consist of either a P-N-P or an N-P-N semiconductor “sandwich” structure.The three leads of a bipolar transistor are called the Emitter, Base, and Collector.Transistors function as current regulators by allowing a small current to control a larger current. The amount of current allowed between collector and emitter is primarily determined by the amount of current moving between base and emitter.In order for a transistor to properly function as a current regulator, the controlling (base) current and the controlled (collector) currents must be going in the proper directions: meshing additively at the emitter and going against the emitter arrow symbol. Lessons In Electric Circuits copyright (C) 2000-2010 Tony R. Kuphaldt

The Shockley Diode

Our exploration of thyristors begins with a device called the four-layer diode, also known as a PNPN diode, or a Shockley diode after its inventor, William Shockley. This is not to be confused with a Schottky diode, that two-layer metal-semiconductor device known for its high switching speed. A crude illustration of the Shockley diode, often seen in textbooks, is a four-layer sandwich of P-N-P-N semiconductor material, Figure below. Shockley or 4-layer diode Unfortunately, this simple illustration does nothing to enlighten the viewer on how it works or why. Consider an alternative rendering of the device’s construction in Figure below. Transistor equivalent of Shockley diode Shown like this, it appears to be a set of interconnected bipolar transistors, one PNP and the other NPN. Drawn using standard schematic symbols, and respecting the layer doping concentrations not shown in the last image, the Shockley diode looks like this (Figure below) Shockley diode: physical diagram, equivalent schematic diagram, and schematic symbol. Let’s connect one of these devices to a source of variable voltage and see what happens: (Figure below) Powered Shockley diode equivalent circuit. With no voltage applied, of course there will be no current. As voltage is initially increased, there will still be no current because neither transistor is able to turn on: both will be in cutoff mode. To understand why this is, consider what it takes to turn a bipolar junction transistor on: current through the base-emitter junction. As you can see in the diagram, base current through the lower transistor is controlled by the upper transistor, and the base current through the upper transistor is controlled by the lower transistor. In other words, neither transistor can turn on until the other transistor turns on. What we have here, in vernacular terms, is known as a Catch-22. So how can a Shockley diode ever conduct current, if its constituent transistors stubbornly maintain themselves in a state of cutoff? The answer lies in the behavior of real transistors as opposed to ideal transistors. An ideal bipolar transistor will never conduct collector current if no base current flows, no matter how much or little voltage we apply between collector and emitter. Real transistors, on the other hand, have definite limits to how much collector-emitter voltage each can withstand before one breaks down and conduct. If two real transistors are connected in this fashion to form a Shockley diode, each one will conduct if sufficient voltage is applied by the battery between anode and cathode to cause one of them to break down. Once one transistor breaks down and begins to conduct, it will allow base current through the other transistor, causing it to turn on in a normal fashion, which then allows base current through the first transistor. The end result is that both transistors will be saturated, now keeping each other turned on instead of off. So, we can force a Shockley diode to turn on by applying sufficient voltage between anode and cathode. As we have seen, this will inevitably cause one of the transistors to turn on, which then turns the other transistor on, ultimately “latching” both transistors on where each will tend to remain. But how do we now get the two transistors to turn off again? Even if the applied voltage is reduced to a point well below what it took to get the Shockley diode conducting, it will remain conducting because both transistors now have base current to maintain regular, controlled conduction. The answer to this is to reduce the applied voltage to a much lower point where too little current flows to maintain transistor bias, at which point one of the transistors will cutoff, which then halts base current through the other transistor, sealing both transistors in the “off” state as each one was before any voltage was applied at all. If we graph this sequence of events and plot the results on an I/V graph, the hysteresis is evident. First, we will observe the circuit as the DC voltage source (battery) is set to zero voltage: (Figure below) Zero applied voltage; zero current Next, we will steadily increase the DC voltage. Current through the circuit is at or nearly at zero, as the breakdown limit has not been reached for either transistor: (Figure below) Some applied voltage; still no current When the voltage breakdown limit of one transistor is reached, it will begin to conduct collector current even though no base current has gone through it yet. Normally, this sort of treatment would destroy a bipolar junction transistor, but the PNP junctions comprising a Shockley diode are engineered to take this kind of abuse, similar to the way a Zener diode is built to handle reverse breakdown without sustaining damage. For the sake of illustration I’ll assume the lower transistor breaks down first, sending current through the base of the upper transistor: (Figure below) More voltage applied; lower transistor breaks down As the upper transistor receives base current, it turns on as expected. This action allows the lower transistor to conduct normally, the two transistors “sealing” themselves in the “on” state. Full current is quickly seen in the circuit: (Figure below) Transistors are now fully conducting. The positive feedback mentioned earlier in this chapter is clearly evident here. When one transistor breaks down, it allows current through the device structure. This current may be viewed as the “output” signal of the device. Once an output current is established, it works to hold both transistors in saturation, thus ensuring the continuation of a substantial output current. In other words, an output current “feeds back” positively to the input (transistor base current) to keep both transistors in the “on” state, thus reinforcing (or regenerating) itself. With both transistors maintained in a state of saturation with the presence of ample base current, each will continue to conduct even if the applied voltage is greatly reduced from the breakdown level. The effect of positive feedback is to keep both transistors in a state of saturation despite the loss of input stimulus (the original, high voltage needed to break down one transistor and cause a base current through the other transistor): (Figure below) Current maintained even when voltage is reduced If the DC voltage source is turned down too far, though, the circuit will eventually reach a point where there isn’t enough current to sustain both transistors in saturation. As one transistor passes less and less collector current, it reduces the base current for the other transistor, thus reducing base current for the first transistor. The vicious cycle continues rapidly until both transistors fall into cutoff: (Figure below) If voltage drops too low, both transistors shut off. Here, positive feedback is again at work: the fact that the cause/effect cycle between both transistors is “vicious” (a decrease in current through one works to decrease current through the other, further decreasing current through the first transistor) indicates a positive relationship between output (controlled current) and input (controlling current through the transistors’ bases). The resulting curve on the graph is classically hysteretic: as the input signal (voltage) is increased and decreased, the output (current) does not follow the same path going down as it did going up: (Figure below) Hysteretic curve Put in simple terms, the Shockley diode tends to stay on once its turned on, and stay off once its turned off. No “in-between” or “active” mode in its operation: it is a purely on or off device, as are all thyristors. A few special terms apply to Shockley diodes and all other thyristor devices built upon the Shockley diode foundation. First is the term used to describe its “on” state: latched. The word “latch” is reminiscent of a door lock mechanism, which tends to keep the door closed once it has been pushed shut. The term firing refers to the initiation of a latched state. To get a Shockley diode to latch, the applied voltage must be increased until breakover is attained. Though this action is best described as transistor breakdown, the term breakover is used instead because the result is a pair of transistors in mutual saturation rather than destruction of the transistor. A latched Shockley diode is re-set back into its nonconducting state by reducing current through it until low-current dropout occurs. Note that Shockley diodes may be fired in a way other than breakover: excessive voltage rise, or dv/dt. If the applied voltage across the diode increases at a high rate of change, it may trigger. This is able to cause latching (turning on) of the diode due to inherent junction capacitances within the transistors. Capacitors, as you may recall, oppose changes in voltage by drawing or supplying current. If the applied voltage across a Shockley diode rises at too fast a rate, those tiny capacitances will draw enough current during that time to activate the transistor pair, turning them both on. Usually, this form of latching is undesirable, and can be minimized by filtering high-frequency (fast voltage rises) from the diode with series inductors and parallel resistor-capacitor networks called snubbers: (Figure below) Both the series inductor and parallel resistor-capacitor “snubber” circuit help minimize the Shockley diode’s exposure to excessively rising voltage. The voltage rise limit of a Shockley diode is referred to as the critical rate of voltage rise. Manufacturers usually provide this specification for the devices they sell. REVIEW:Shockley diodes are four-layer PNPN semiconductor devices. These behave as a pair of interconnected PNP and NPN transistors.Like all thyristors, Shockley diodes tend to stay on once turned on (latched), and stay off once turned off.To latch a Shockley diode exceed the anode-to-cathode breakover voltage, or exceed the anode-to-cathode critical rate of voltage rise.To cause a Shockley diode to stop conducting, reduce the current going through it to a level below its low-current dropout threshold. Les