Bipolar Transistors Fundamentals.docx

Bipolar Transistors Fundamentals Menu

1 Bipolar Transistors 1.1 Transistor Fundamentals 1.2 Transistor Biasing 1.3 Transistor Operation 1.4 Transistor Testing Using an Ohmmeter 1.5 Transistor Configurations 1.5.1 Common Emitter Circuit 1.5.1.1 Static Values 1.5.1.2 Dynamic Values 1.5.1.3 Static Characteristic Curves 1.5.1.4 PNP Common Emitter Circuit 1.5.2 Common Base Circuit 1.5.2.1 Static Values 1.5.2.2 Dynamic Values 1.5.2.3 Static Characteristic Curves 1.5.2.4 PNP Common Base Circuit 1.5.3 Common Collector Circuit 1.5.3.1 Static Values 1.5.3.2 Dynamic Values 1.5.3.3 PNP Common Collector Circuit 1.6 Operating Point 1.7 Saturation and Cutoff Operation 2 Classes of Amplifiers 3 Transistor Coupling 4 Advanced Concepts 4.1 Static and Dynamic Gain 4.1.1 Common Emitter Gain Calculations 4.1.2 Common Base Gain Calculations 4.1.3 Common Collector Gain Calculations 4.2 Biasing Techniques 4.2.1 General Bias Circuits 4.2.1.1 Single-Battery Circuit 4.2.1.2 Fixed Bias 4.2.1.3 Emitter Bias 4.2.1.4 Self-Bias 4.3 Practical Transistor Amplifier 4.3.1 General Rules

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Bipolar Transistors The transistor has revolutionized the electronics industry. Discovered in 1948, its advantages have opened many new possibilities for design engineers. The transistor has almost fully replaced the vacuum tube as a basic amplifier. It has an extremely long life, minimal power and voltage requirements, and a small physical size. The transistor is rugged and can withstand excessive vibration. A full understanding of the transistor and its circuitry will enable you to become a very effective technician when dealing with electricity and electronics.

Transistor Fundamentals A ''transistor'' is a semiconductor that can be used for signal amplification. The characteristic curve of a diode shows the nonlinear resistance property of this device. This makes a diode a good rectifier, but a poor amplifier. By definition, a transistor is a semiconductor device that can be used to control current flow. It is a threeterminal device with two effective PN junctions joined with their like material mating regions made very thin. '''Figure 1''' illustrates the formation of a transistor from two diodes.

Figure 1: Transistors as Two Diodes A diode is composed of two blocks of semiconductor material, one N type and one P type. A transistor of the simplest type consists of three blocks, joined together so as to produce either a PNP sequence or an NPN sequence. The three elements of a transistor are the emitter, the base, and the collector. The terminals are assigned the letters ''E'', ''B'', and ''C'', respectively. The transistor symbols are shown in '''Figure 2''' with their associated semiconductor block drawings. An arrowhead identifies the emitter terminal. If the arrow points away from the base, it is an NPN transistor; and if the arrow points toward the base, it is a PNP transistor.

Figure 2: Circuit Symbols for PNP and NPN Transistors

Each block of material that makes up a transistor has a different concentration of impurity. The semiconductor material that has the largest impurity concentration is the emitter. The base is a very thin, lightly doped semiconductor material. The collector is a block of semiconductor that has a higher impurity concentration than the base, but not as high as the emitter. As shown in '''Figure 2''', there are two points where a PN junction is formed: at the contact of the collector and the base, and at the contact of the emitter and the base. It should be expected that the transistor, due to its PN junctions, would be biased and, consequently, that the properties of PN junctions will play a major role in the operation of the transistor. Related articles explain how the barrier potential of a PN junction would exist across the depletion region as a result of diffusion. The emitter-base junction and the collector-base junction have barrier potentials and depletion regions. '''Figure 3''' illustrates the PN junction barrier potentials in a transistor.

Figure 3: Transistor PN Junction Barrier Potentials

Transistor Biasing If a flow of current in the emitter-base circuit is desired, apply a forward bias to the emitter-base PN junction, as shown in '''Figure 4'''. This would be a positive potential on the base with reference to the emitter. When the value of the forward bias is large enough, forward current will flow due to the majority carriers. The value of forward bias required is the same as would be expected from other diodes studied.

Figure 4: Transistor Biasing

This causes a new condition: the emitter region is much more heavily doped than the base region. There are many more current carriers in the emitter than in the base. Once the potential barrier has been overcome, the available current carriers can drift across the junction. There will not be sufficient current carriers in the base to recombine with the current carriers from the emitter. Its small number of majority carriers limits base current. As a consequence of light doping in the base region, the electrons that have drifted into the base cannot totally recombine with holes in the base region, as there is an insufficient number of holes present. The electrons, consequently, diffuse throughout the entire base, and the base appears to have a high content of minority carriers. Now the question may arise as to how to continue current flow through the transistor. How is a complete path for current flow from emitter to collector achieved? There is one more PN junction to consider: the base-collector junction. There will be a high content of minority carriers, electrons in this case, in the base. In reality, we would now like to cause a minority carrier flow through the base-collector PN junction. Reverse-biasing a junction will allow for a flow of minority carriers. Therefore, as shown in '''Figure 4''', the collector-base junction is reverse-biased. This can be seen by noting the battery polarities. A .4 V battery is responsible for the forward biasing of the emitter-base junction. The main supply battery is a 10 V battery that is connected between the emitter and the collector. The base will be 0.4 V positive with reference to the emitter. The collector, which is N-type material, is more positive than the base. This is the reverse bias of the collector-base junction. The result of reverse-biasing the collector-base junction is a flow of the minority carrier electrons present in the base region into the collector region. The potential barrier aids this process across the base-collector PN junction. The positive potential applied to the collector will attract electrons, causing a complete path for current flow from emitter to collector. If the emitter-base junction had originally been reverse-biased, there would have been no significant current flow from emitter to collector, probably only a few microamperes. Only the minority carriers (holes) of the N-type emitter would flow into the base. Once in the base, they would recombine with the base’s minority carriers (electrons). There would be a small amount of reverse current. The potential barrier of the collector-base junction would repel the holes from the emitter. Consequently, there would be no current flow from emitter to collector. It has been shown that biasing the emitter-base junction can either cause emitter-collector current to flow or prevent emitter-collector current from flowing. The emitter-base circuit can also control the amount of current through the emitter-collector circuit. In '''Figure 5''', we find the PNP and NPN transistors shown with proper biasing to allow for a current flow from emitter to collector. There are several facts that should be noted upon examining these illustrations.

Figure 5: Proper Biasing NPN and PNP Transistors First, the circuits for the two transistors are identical except for the polarity of the batteries. Second, if we examine the polarity of the respective bias batteries, we should note that the emitter-base PN junction is forward-biased in both circuits, and the collector-base junction is reverse-biased in both circuits. If the resistors in series with the collector-emitters drop 6 V, then that leaves 6 V across the collectoremitter in both circuits. For the NPN transistor, voltage at the collector would be +6 V with respect to ground. For the PNP transistor, voltage at the collector would be -6 V with respect to ground. "Hole flow" only takes place within the transistor. In the external circuit, the concern is electron flow. Electrons flow from the negative terminal of the supply battery to the positive terminal (see '''Figure 6''').

Figure 6: Proper Biasing Simplified

In the case of the NPN transistor, the N-type material of the collector is more positive than the P-type material of the base. In short, the N-type material is positive with reference to the P-type material. The base looks negative with reference to the collector. This is reverse bias for this PN junction. In the case of the PNP transistor, the P-type material of the collector is more negative than the N-type material of the base. The base looks positive with reference to the collector. This again is reverse bias for this PN junction.

Transistor Operation Now that all conditions have been met for current flow through the transistor, including the appropriate supply polarities for biasing, the complete sequence of events for transistor conduction and its ability to control current can be examined. '''Figure 7''' shows a PNP transistor with a forward bias applied to the emitter-base junction and a reverse bias applied to the base-collector junction.

Figure 7: PNP Transistor Conduction If the variable-bias battery is decreased to 0 V, there could be no emitter-base current; therefore, there could be no emitter-collector current and there would be no indication on the ammeter in series with the collector terminal. As the output of the bias battery is increased, a value will be reached at which the potential barrier of the emitter-base junction is defeated and current will flow in the emitter-base circuit. The holes in the collector are attracted to the negative potential at the collector terminal, giving a complete path for current flow from emitter to collector in the transistor. Looking at electron flow in the external circuit, electrons from the emitter will be attracted to the positive side of the supply. The attraction of the electrons produces holes. At the same time, electrons from the negative side of the supply will recombine with the holes in the collector material. As a result, there will be a complete path for current flow in the collector-emitter circuit as well.

Rather than following the individual current carriers through the transistor, the current flow from emitter to collector will be referred to as simply ''emitter-collector current''. Also, the current flow in the emitter-base circuit will be called ''emitter-base current''. An increase in the voltage applied to the base causes an increase in forward bias. An increase in forward bias causes more current carriers to enter the base. More current carriers being available in the base provides more current carriers to cross the collector-base junction. As a result, there will be an increase in the number of holes flowing into the collector. Simply stated, an increase in forward bias produces an increase in emitter-base current, which allows an increase in emitter-collector current. A decrease in the voltage applied to the base would cause a decrease in forward bias. A decrease in forward bias would produce a decrease in emitter-base current and, consequently, a decrease in emitter-collector current. An increase in forward bias generates more current carriers; therefore, the transistor decreases its opposition to current flow. A decrease in forward bias causes less current carriers to be produced, and the transistor appears to increase its opposition to current flow.

Transistor Testing Using an Ohmmeter While an ohmmeter cannot test all the characteristics of transistors, especially transistors used for high frequencies or switching, it is capable of making many simple transistor tests. Since transistor testers might not always be available, and the ohmmeter usually is available, some hints on how to test transistors using an ohmmeter are in order. Since damage to transistors could occur when using voltages above approximately 4 V, care must be taken to avoid using resistance scales where the internal voltage of the ohmmeter is greater than 4 V. This higher potential usually is found on the higher resistance scales of analog ohmmeters. Excess current might also cause damage to the transistor under test. Since the internal current limiting resistance generally increases as the resistance range is increased, the low range of the resistance scale should also be avoided. Basically, if we stay away from the highest resistance range (possible excessive voltage) and the lowest resistance range (possible excessive current), the ohmmeter should present no problems in transistor testing. Generally speaking, the RX10 and RX100 scales may be considered safe. On DMMs, the 2KL scale is designed for testing PN junctions due to the fact that most DMMs do not produce sufficient test voltage unless they are set to the 2KL range. The polarity of the battery, as well as the voltage value, must be known when using the ohmmeter for transistor testing. Although in some cases, the ground or common lead (black) is negative and the hot lead (red) is positive, this is not always the case. To use an ohmmeter or a transistor to check for bias, the transistor should be out of circuit. As shown in '''Figure 8''', the probe leads must be connected to the base and emitter or the base and collector junctions. If the resistance reading is low and reversing the leads produces a high resistance reading, the junction is good. If both resistances are low or high, the junction is bad.

Figure 8: Transistor Testing Using an Ohmmeter Both base-emitter and base-collector junctions should be checked in both directions. A failed test on either junction denotes a faulty transistor that should be replaced. The type of transistor can be determined (NPN or PNP) for a good transistor by noting the test lead connections when the junction is forward-biased. If the positive potential is applied to the base when the transistor is forward-biased, the transistor has a P base, making it an NPN transistor. If the negative lead on the base forward biases it, the transistor is a PNP transistor. It is possible to reverse the polarity of the ohmmeter leads by changing the function switch position. This means that the black or common lead becomes the positive battery and the red lead becomes the negative battery. CAUTION! Although the jacks of the meter may show a negative sign under the common and a positive sign under the other jack, these do not indicate the internal polarity of the battery connected to the jack. In addition, an ohmmeter that draws more than one milliampere should not be used for transistor testing. Testing will be the same as for the PN junction testing; only the emitter-base and base-collector junctions are tested. A reading across the emitter-collector will be near infinity for a correct reading. There are three different configurations in which to connect a transistor. Each of these has its own particular characteristics. There are also different ways to bias transistors, which will be discussed. The combination of these configurations and biasing techniques work together to produce the desired transistor circuit response.

Transistor Configurations When transistors are placed into circuits, they are in one of three configurations, known as ''common emitter'', ''common base'', and ''common collector''. '''Figure 9''' shows the common emitter, or grounded emitter, connection. The input signal is introduced into the base-emitter circuit, and the output signal is taken from the collector-emitter circuit; thus, the emitter is common to both circuits.

Figure 9: Common Emitter Transistor Circuit '''Figure 10''' shows the common base, or grounded base, connection. The input signal is introduced into the emitter-base circuit, and the output is taken from the collector-base circuit; thus, the base is common to both circuits.

Figure 10: Common Base Transistor Circuit '''Figure 11''' shows the common collector, or grounded collector, connection. The input signal is introduced into the base-collector circuit, and the output signal is taken from the emitter-collector circuit; thus, the collector is common to both circuits. This configuration is also called an ''emitter follower'' circuit.

Figure 11: Common Collector Transistor Circuit

Common Emitter Circuit The common emitter circuit is by far the most frequently used transistor amplifier configuration. In this circuit, the emitter is common to both the input and the output circuits. '''Figure 12''' shows a common emitter connected transistor.

Figure 12: Common Emitter Transistor Circuit NPN The input signal is applied to the base-emitter circuit, and the output is taken from the emitter-collector circuit. The emitter-base junction is still forward-biased, and the collector-base junction is reverse-biased. '''Figure 13''' shows the voltage and current waveforms for a common emitter transistor circuit when an AC input voltage is applied. The dotted line represents the static (DC) voltages that would occur with only DC bias applied and no AC input.

Figure 13: Voltage and Current Waveforms for a Common Emitter NPN Configuration

Static Values Using Kirchhoff’s Voltage Law, the voltage at the output when the input voltage is zero is given by the following equation: VCC = VCE + ICRL Where: VCC=collector circuit battery voltage (volts) VCE=collector to emitter voltage drop (volts) IC =collector current (amps) RL =load resistance (ohms)

Dynamic Values When the AC input voltage is applied, the bias of the base-emitter junction varies, which varies how much the transistor conducts. The result is an output that varies around the static (DC) output value. When the input voltage is increasing, it aids the forward bias of the emitter-base junction. This causes an increase in collector current and a corresponding decrease in the collector-emitter voltage drop, or VCE. This causes the collector voltage to become less positive with respect to ground. Thus, when the input voltage is increasing, the output voltage is decreasing. The input and output voltages in a common emitter transistor circuit are out of phase by 180°.

Static Characteristic Curves The relationship between the output voltage drop, or VCE, and the output collector current, or IC, in the common emitter-base circuit is described using static characteristic curves. These are curves for DC, or static operating characteristics with no AC signal applied. '''Figure 14''' shows typical common emitter static characteristic curves.

Figure 14: Common Emitter Static Characteristic Curves NPN The operation of the common emitter amplifier can now be plotted on the static characteristic curve. If the transistor were conducting at its maximum rate, IC would be at a maximum and VCE would be at a minimum. In simple terms, the transistor acts as a short. This condition is known as ''saturation''. If the transistor were conducting at its minimum rate, IC would be at a minimum and VCE would be at a maximum. In simple terms, the transistor acts as an open. This condition is known as ''cutoff''. Drawing a single straight line through these two points on the static characteristic curve yields the load line. The load line represents all possible combinations for IC, VCE, and IB for that particular circuit. If any of the individual components in that circuit are changed, the load line also changes.

PNP Common Emitter Circuit The PNP common emitter circuit ('''Figure 15''') functions the same as the NPN circuit detailed above, only the biasing and output polarities differ.

Figure 15: Common Emitter Transistor Circuit PNP The characteristic curves are shown in '''Figure 16''', and the dynamic input and output waveforms are shown in '''Figure 17'''.

Figure 16: Common Emitter Static Characteristic Curves PNP

Figure 17: Voltage and Current Waveforms for a Common Emitter PNP Configuration

Common Base Circuit The common base, or grounded base, circuit is one of three basic ways of connecting a transistor. In this circuit, the base is common to both the input and output circuits. '''Figure 18''' shows a common base connected transistor. The input signal is applied to the emitter-base circuit, and the output is taken from the collector-base circuit, normally across load resistor RL.

Static Values When the input voltage is zero, current flows as shown in '''Figure 18'''. IE flows through RE into the emitter; IC flows from the collector through RL. These currents are produced by the combination of the bias batteries VEE and VCC. Statically, VIN is equal to IERE VEE, which is some value of negative voltage. Statically, VOUT is equal to VCICRL, which is some value of positive voltage. These static V IN and V OUT values are indicated as dashed reference lines, as are the static values of IE and IC.

Figure 18: Common Base Transistor Circuit NPN

Dynamic Values When an AC input voltage is applied to the forward-biased emitter-base circuit, the bias of this junction varies. When the applied input voltage swings positive, it opposes the emitter-base circuit bias (VEE ). When the AC voltage swings negative, it aids this bias. When the input voltage is increasing, the forward bias decreases in the emitter-base circuit and IE decreases. When the input voltage is decreasing, the forward bias increases and IE increases also. The change in emitter current directly affects collector current. When IE decreases, IC decreases. The change in IC affects the voltage developed across RL. When IC decreases, VRL decreases in amplitude and subtracts less from the effect of VCC. The result is that VOUT increases. Conversely, when IC increases, VRL increases in amplitude and subtracts more from VCC. VOUTtherefore decreases. These effects are shown in '''Figure 19'''. Notice that when the input voltage increases, the output voltage increases. There is no phase reversal in a common base transistor amplifier. The collector circuit biasing battery VCC causes the output voltage to be positive DC with an AC component. The emitter circuit biasing battery VEE causes the input voltage to be negative DC with an AC component. Input and output AC components are in phase.

Figure 19: Common Base Transistor Circuit NPN Voltage and Current Waveforms

Static Characteristic Curves The relationship between the output voltage drop VCB and the output collector current IC in the common base circuit is described using static characteristic curves. These are curves of DC or static operating characteristics with no AC signal applied. '''Figure 20''' shows typical common base static characteristic curves.

Figure 20: Common Base Static Characteristic Curves NPN

The operation of the common base amplifier can be plotted just as easily as the common emitter amplifier. First, mark the point at which saturation occurs (ICmaximum, VCB minimum). Next, mark the point at which cutoff occurs (IC minimum, VCB maximum). Drawing a single straight line through these two points on the static characteristic curve yields the load line. The load line represents all possible combinations for I C, VCB, and IB for that particular circuit. If any of the individual components in that circuit are changed, the load line also changes.

PNP Common Base Circuit The PNP common base circuit functions the same as the NPN circuit detailed above. Only biasing and output polarities differ. This is shown in '''Figure 21'''.

Figure 21: Common Base Transistor Circuit PNP The proof that the PNP transistor functions the same as an NPN transistor is obvious when the static characteristics of each are compared. '''Figure 22''' shows typical common base static characteristic curves for the PNP transistor.

Figure 22: Common Base Static Characteristic Curves PNP Dynamic signal response is shown for the PNP common base configuration in '''Figure 23'''.

Figure 23: Common Base Transistor Circuit PNP Voltage and Current Waveforms

Common Collector Circuit The common collector, or emitter follower, circuit is a third way of connecting a transistor. It is the leastused configuration. In this circuit, the collector is common to both the input and the output circuits. '''Figure 24''' shows a common collector connected transistor. The input signal is applied to the collector-base circuit between the base and ground. The output signal is taken from the collector-emitter circuit between the emitter and ground. The collector is common to both the input and the output circuits. Again, the emitterbase junction is forward-biased by VEE, and the collector-base junction is reverse-biased by VCC.

Figure 24: Common Collector Transistor Circuit NPN '''Figure 25''' shows the voltage and current waveforms for a common collector transistor circuit when an AC input voltage is applied. The dotted line represents the static (DC) voltages that would occur with only DC bias applied and no AC input.

Figure 25: Voltage and Current Waveforms for NPN Common Collector Transistor Circuit

Static Values Using Kirchhoff’s Voltage Law, the voltage at the output when the input voltage is zero is given by the following equation: VCC + VEC IERL = 0

Where: VCC=Collector circuit battery voltage (volts) VEC =Emitter to collector voltage drop (volts) IE =Emitter current (amps) RL =Load resistance (ohms)

Dynamic Values When the AC input voltage is applied, the bias of the base-emitter junction varies. When the input voltage is increasing, it aids VEE and increases the forward bias of the emitter-base junction. This causes an increase in both collector current and emitter current, and a corresponding decrease in the emitter to collector voltage drop VEC. This causes the emitter voltage to become more positive and the output voltage to increase. Thus, when the input voltage is increasing, the output voltage is also increasing. Conversely, when the input voltage is decreasing, the output voltage is decreasing. Thus, the input and output voltages in a common collector transistor circuit are in phase.

PNP Common Collector Circuit The PNP common collector circuit functions the same as the NPN circuit detailed above. Only biasing and output polarities differ.

Figure 26: Common Collector Transistor Circuit PNP

Figure 27: Voltage and Current Waveforms for a PNP Common Collector Transistor Circuit

Operating Point The ''operating point'' of a transistor is the point on the static characteristic curve around which the AC signal varies. The operating point is determined by the DC values of the collector current and the collector voltage that are set by the bias voltage sources and the resistors in the circuit. The word ''quiescent'' refers to the fact that it is determined with no AC signal applied. '''Figure 28''' is the dynamic transfer characteristic curve for a transistor.

Figure 28: Properly Selected Operating Point

The base current versus the collector current is plotted for a given collector voltage. The position of the operating point on this graph determines the output signal. When the operating point lies on the linear portion of the dynamic transfer characteristic curve, the transistor operates linearly, and the output signal will be identical to the input signal, as shown in the Figure 28. '''Figure 29''' shows what happens when the operating point is not selected on the linear portion of the dynamic transfer characteristic curve. The output waveform is distorted.

Figure 29: Distortion Produced by Poor Selection of the Operating Point

Saturation and Cutoff Operation Transistor characteristics vary with time and operating point. '''Figure 30''' shows a typical static characteristic curve for a transistor. There are three regions in which a transistor may operate: active, cutoff, and saturation, as shown in '''Figure 30'''.  



The ''active region'' is the region of normal transistor operation. In this region, the emitter-base junction is forward-biased. In the ''cutoff region'', both the emitter-base junction and the collector-base junction are reverse-biased, and no conduction takes place. In this condition, the transistor presents an open circuit unless the input signal is of sufficient amplitude to forward bias the transistor. In the ''saturation region'', the emitter-base junction is forward-biased, while the collector-base junction has either a small reverse bias or a forward bias. When operating in this region, the collector is not able to collect all the charge carriers injected by the emitter. In this condition, the transistor presents a "short" circuit.

Figure 30: Active, Cutoff, and Saturation Regions of Transistor Operation

Classes of Amplifiers Amplifiers are normally designed to amplify either voltage, current, or power. They are classified according to function. When transistor amplifiers are cascaded, all stages, except the last, are called ''current amplifiers'', even though their current gain may be less than their voltage and power gains. When the function of an amplifier is to supply power to a load, such as loudspeakers or motors, it is classified as a ''power amplifier''. The last stage in any case must be designed and modified according to the final use of the signal. Amplifiers are also classified according to their bias current, which determines the input and output signal characteristics. '''Figure 31''' shows the characteristics of the three classes of amplifiers. A ''Class A'' amplifier is biased so that the output signal current flows during the entire cycle of the input signal. The operating pointswings entirely on the linear portion of the static characteristic curve. Class ''A'' amplifiers are called ''small'' signal amplifiers. A ''Class B'' amplifier is biased so that the output signal current flows during only half the input cycle. A Class ''B'' amplifier is biased right at minimum base bias current (cutoff). A ''Class C'' amplifier is biased below cutoff, so the output signal current flows during less than half of the cycle of the input signal. A Class ''C'' amplifier is used for special applications, such as with a tuned circuit. Class ''B'' and ''C'' amplifiers operate efficiently because output current is cut off during ineffective parts of

the signal cycle. Class ''B'' and ''C'' amplifiers are called ''large'' signal amplifiers.

Figure 31: Three Classes of Amplifiers and Typical Biasing Arrangements

Transistor Coupling Transistors are cascaded into stages to produce a desired output. The output of one stage is used to drive the succeeding stage, as shown in '''Figure 32'''. Signal coupling between stages can be accomplished using RC coupling, transformer coupling, and direct coupling.

Figure 32: Cascaded Amplifier Stages RC coupling of two transistor stages is shown in '''Figure 33'''. The RC network in dashed lines consists of a collector load resistor R1, a DC blocking capacitor C and an input resistor R2 for the second stage. The purpose of the capacitor is to prevent the DC voltage at the collector of transistor Q 1 from appearing at the input of transistor Q2. The reactance of this capacitor must be small compared with the input impedance of the second stage to prevent a large signal voltage loss across the capacitor. The resistance of resistor R2 usually is 7 to 15 times greater than the input impedance of the following stage to prevent shunting the signal current around the input of the stage. The upper limit value of this resistor is controlled by DC bias temperature stabilization considerations. The very low signal frequencies are attenuated by the capacitor, since capacitive reactance is inversely proportional to frequency. The high frequency response is limited by the internal capacitance of the two transistors. In general, however, the frequency response of RC coupling is very good. RC coupling in battery-operated equipment usually is limited to low-power operation to limit battery drain. Because of the dissipation of DC power in the collector load resistor, or R1, the efficiency of RC coupling is low.

Figure 33: RC Coupling Transformer coupling of two transistor stages is shown in '''Figure 34'''. The primary winding of the transformer provides the load impedance of the collector of transistor Q1. The secondary winding of the transformer introduces the AC signal into the base of transistor Q2. The power efficiency of transformer coupling approaches a theoretical maximum because there is no collector load resistor to dissipate power. For this reason, transformer coupling is used extensively in the amplifiers of portable battery-powered equipment. The frequency response of transformer coupling is not as good as that of the RC coupling. At low frequencies, the reactance of the primary side of the transformer is low, causing decreased gain. At high frequencies, gain is reduced by signal loss through the collector capacitance of transistor Q 1 and the leakage reactance between primary and secondary windings.

Figure 34: Transformer Coupling '''Figure 35''' shows direct coupling of two transistor stages. Direct coupling is used for amplification of DC signals and for amplification of very low frequencies. In direct coupling, an NPN transistor, Q1, is connected directly to a PNP transistor, or Q2. This arrangement is necessary to ensure proper biasing of each stage without the addition of additional power supplies. If the collector current of transistor Q 1 is larger than the base current of transistor Q2, then a collector load resistor, or R1, must be connected, as shown. The frequency response of direct-coupled transistors is limited only by the internal capacitances of the transistors. However, temperature variation of the bias current in one stage is amplified by all the stages, causing severe temperature instability. There is also a reduction in gain due to poor impedance matching. In addition, both AC and DC signals are amplified, since there is no simple means of eliminating the biasing voltages from the signal.

Figure 35: Direct Coupling

Advanced Concepts Static and Dynamic Gain Transistor amplifiers are devices that use small inputs to control large outputs. The relationship between the magnitude of the input and output signals is known as ''gain''. Gain is a unitless value and usually is calculated for current, voltage, and power. Since transistor amplifiers have both static (DC bias) and dynamic (AC) inputs and outputs, both static and dynamic gain can be calculated for any transistor amplifier.

Common Emitter Gain Calculations

Figure 36: Common Emitter Transistor Circuit NPN

The static current gain AI for a common emitter circuit equals the ratio of the collector current to the base current when the collector to emitter voltage drop is held constant. For the common emitter transistor circuit, the static current gain AI is also referred to as the ''static current gain factor'', or β, the Greek letter beta.

The dynamic current gain Ai for a common emitter transistor circuit equals the change in collector current for a given change in base current with the collector to emitter voltage drop held constant. If an AC signal is applied, Ai equals the ratio of the peak-to-peak variation of the collector current to the peak-to-peak variation of the base current.

Example: Determine the static and dynamic current gain of a common emitter transistor circuit with the following characteristics:

The current gain of a common emitter transistor circuit is high. Typical values of the static current gain factor are 25 to 50, with values up to 40 attainable. The high current gain is the property that makes the common emitter circuit so useful. The resistance gain, RG, of a common emitter transistor circuit is considerably lower than that for a common base transistor circuit. The input impedance is higher by a factor of about 7 (350 ohms versus 50 ohms), but the output impedance is lower by a factor of about 103 (1K ohm versus 1 megohm). The voltage gain AV of a common emitter transistor circuit is somewhat higher than that for a common base transistor circuit. This effect is partially cancelled by the smaller resistance gain. The power gain AP of a common emitter transistor circuit is high due to the squaring of the current gain of greater than one. Typical values of the power gain are 102 to 104.

Common Base Gain Calculations

Figure 37: Common Base Transistor Circuit PNP The ''static current gain'' AI for a common base transistor circuit is given by the equation below. Current gain for the common base configuration is also referenced as α, the Greek letter alpha.

The ''dynamic current gain'' Ai for a transistor is defined as "the change in output current for a given change in input current."

For the common base transistor circuit, the dynamic current gain is the change in collector current for a given change in emitter current with the collector to base voltage drop held constant.

Dynamic current gain can be determined directly from the static characteristic curves by noting the change in output current for a small change in input current with the collector to base voltage drop held constant. Another method of determining dynamic current gain is to apply an AC signal and compare the peak to peak variation of the collector current with that of the emitter current. Example: Determine the static and dynamic current gains of a common base transistor circuit with the following characteristics:

Both the static and the dynamic current gains AI and Ai for the common base transistor circuit are always less than unity. The lack of current gain is compensated for by an extremely high resistance gain. This circuit typically has very low input impedance, ranging from 50 to 150 ohms, and very high output impedance, ranging from 300 K ohms to 500 K ohms. Since approximately the same current flows in the emitter and collector circuits, a very high load resistor can be placed in the output circuit, resulting in a high voltage gain. Voltage gains up to 1,000 are possible; as a result, power gains of 100 to 1000 are also attainable.

Common Collector Gain Calculations

Figure 38: Common Collector Transistor Circuit NPN The static current gain AI for a common collector transistor circuit equals the ratio of the emitter current to the base current with the emitter collector voltage drop held constant. It has no special symbol The static current gain for a common collector transistor circuit is related to the static current gain factor β for a common emitter circuit by the following equation: The dynamic current gain Ai for a common collector transistor circuit equals the change in emitter current for a given change in base current with the emitter collector voltage drop held constant. If an AC signal is applied, Ai equals the ratio of the peak to peak variation of the base current The current gain of a common collector transistor circuit is high. Typical values of the static current gain factor are 25 to 50. The resistance gain, or RG, of a common collector transistor circuit is less than one. The base collector input circuit is reverse-biased and, therefore, of high resistance. The emitter collector output circuit is forward-biased and, therefore, of low resistance. Typical values are RIN = 3 x 105 ohms and Rout = 3 x 102 ohms. Because of its high input and low output impedance, the common collector circuit is used mainly as an impedance matching device. The voltage gain AV of a common collector transistor circuit is less than one, and the power gain AP is normally considerably less than that of either a common base or a common emitter circuit.

'''Table 1''' summarizes the characteristics of the three types of transistor circuits. '''Table 2''' summarizes transistor circuit gain equations.

Table 1: Summary of Transistor Circuit Characteristics

Table 2: Transistor Circuit Gain Equations

Biasing Techniques As previously stated, to attain a flow of current in the emitter-base circuit, forward bias must be applied to the emitter-base PN junction. This would create a positive potential on the base with reference to the emitter. When the value of forward bias is large enough, forward current will flow due to the majority carriers. The value of forward bias required is the same as would be expected for the diodes studied in other articles.

General Bias Circuits '''Figure 39''' shows a general circuit for biasing a transistor. This circuit will be applied to each of the three circuit configurations (CB, CE, and CC) by selecting the required input and output points.      

VCC is the collector supply voltage that places a reverse bias on the collector-base junction. VEE is the emitter supply voltage that biases the emitter-base junction in a forward direction. RC is the collector load resistor. RE is the emitter resistor. RB is the base resistor, and RF is the feedback resistor.

Figure 39: General Bias Circuit for Transistors The common base circuit is drawn in '''Figure 40'''. In this circuit, the signal is applied between the emitter and the base, and the output is taken from the collector and the base. The base is common to both input and output. This being the case, the base is grounded, and resistor RB of the general bias circuit is shortcircuited. RFis considered to have infinite resistance. Therefore, RF is similar to an open circuit and is omitted.

Figure 40: General Bias Circuit Converted to a CB Amplifier The general bias circuit is converted to the common emitter circuit in '''Figure 41'''. The input signal is applied between the base and the emitter; the output is taken from the collector-emitter junction. The emitter is common to both the input and the output, and it is grounded. Therefore, RE is short-circuited,

and the emitter is connected directly to ground. Again, RF is considered to have infinite resistance and is represented as an open circuit.

Figure 41: General Bias Circuit Converted to the CE Amplifier In the common collector circuit in '''Figure 42''', the input signal is applied between the base and the collector. The output signal is taken from the emitter and collector. The collector is common to both the input and the output. Therefore, it is grounded. Since the collector is the common grounded terminal, RC is short-circuited. RF is still considered an infinite resistance and is represented as an open circuit. In practice, the collector is grounded for signal voltages only through a lowreactance capacitor. Up to this point, RF seems to always have been omitted or considered as an infinite resistance. In practical circuits, RF will assume a value that is explained later.

Figure 42: General Bias Circuit Converted to a CC Amplifier

Single-Battery Circuit For simplification, two voltage sources have been used in all circuits discussed. One source is used for the forward biasing of the emitter-base junction; the other for the reverse biasing of the collector-base junction. Two batteries are unnecessary, however, and the CE amplifier in '''Figure 43''' uses only one.

Figure 43: This Circuit Converts the CE Amplifier to a Single Power Source There is no question about the reverse bias of the collector-base junction because the collector is connected through RC to the most negative point of the circuit, which is the negative supply terminal. The most positive point in the circuit is the ground, which is connected directly to the positive terminal of VCC. RF and RB form a resistance voltage divider connected directly across VCC. The voltage at B is less negative than the negative terminal of VCC by the amount of the voltage drop across RF. It is certainly negative in respect to the emitter, which is at ground or the most positive point in the circuit. Now, you can see that the emitter-base junction is forward-biased. By selecting the proper values for RF and RB, the desired forward bias voltage and current can be established. The series combination of RF and RB must be large enough so that current drain from the supply battery will be small and long life will be assured.

Fixed Bias '''Figure 44''' shows the fixed bias method. Notice that RB has been omitted. This circuit sets essentially a constant base current and is very sensitive to variations in the circuit. By the proper selection of R F, the required forward bias voltages and base current may be set up.

Figure 44: Fixed Bias Method of Connecting a Transistor

Emitter Bias Emitter bias is the better method of biasing transistor circuits (see '''Figure 45'''). This type of bias is less sensitive to changes in transistor characteristics than base bias.

Figure 45: Schematic Circuit for Emitter Biasing In this case, the forward bias VEE will establish a constant emitter current, IE, producing a voltage drop across RE. RE is selected to provide the proper forward bias. RBis the "return" to complete the emitter base circuit. A signal applied to the amplifier will produce an AC component in the collector current. However, this does not upset the emitter bias because a low-reactance path around RE is provided by bypass

capacitor C. This circuit almost guarantees a very stable operating point for the transistor; however, this advantage is overshadowed by the requirement of two power supplies or batteries.

Self-Bias The self-bias schematic is shown in '''Figure 46'''. This circuit differs from the fixed bias method in that bias resistor RF is connected to the collector rather than VCC. This method provides a more stable operating point than fixed biasing, and only one power source is needed.

Figure 46: Schematic of Transistor Self Bias If a fixed collector current is assumed at some selected operating point, the voltage VC will be constant but lower in value than VCC due to the drop across RC. Any change in I C will consequently change the value of VC. Since the base is connected to VC through RF, a certain amount of degeneration will result. What is meant by ''degeneration''? A positive signal at the input of the CE amplifier (PNP) will make the base more positive and decrease its forward bias and decrease IC. A reduction in IC means a lesser voltage drop across RC, and collector voltage VC becomes more negative as it approaches the value of negative VCC. This more negative voltage to the base through RF tends to increase the forward bias. In other words, it opposes the increase caused by the input signal. A signal from the output of a device fed back to the input in a phase relationship that opposes the input is called ''degeneration''. The major disadvantage of the self-bias scheme is the loss of amplifier gain due to degeneration.

Practical Transistor Amplifier Up to this point, it may seem that transistor circuit design is an exact science where high precision and exact values are the rule. This is not exactly the case. Practical commercial circuits are designed using general rules. Circuit values are then refined by actually building a prototype circuit and making

small value changes until the desired results are obtained. Before any general rules can be applied, the following question must be asked: What is the circuit designed to do? Once this question is answered in basic terms, the circuit can be designed easily.

General Rules The first step is to determine the circuit design requirements. For example, a 500μV sine wave that needs to be amplified to 75 mV would require a common-emitter circuit.

The first rule of thumb is that the ratio of collector resistor resistance to emitter resistor resistance should equal the voltage gain of the circuit.

A typical initial value for RE is 100 Ω. This sets a value for RC at:

The second rule of thumb is that at quiescent operation, the collector resistor should drop approximately half of the supply voltage. This would require a supply voltage (VCC) of 12V.

From this, we can calculate collector quiescent current.

This 0.4 mA must also flow through RE, yielding a voltage drop of:

Now is the time to select the bias resistors for the circuit. The values selected must bias the transistor above the turn-on point. Also, for temperature stability reasons, the bias current should be 10 times the input signal current. To determine the input signal current, we must work backwards. A collector current of 0.4 mA was calculated earlier. By looking at the transistor specification sheet, we could determine the transistor’s β = 50, a typical value.

Knowing this necessary value for input current, the bias current can be determined as around 80 µA. Since our transistor is to be an NPN silicon transistor, VBE Z 0.7 V at turn-on. Additionally, there is 0.04 V between the emitter and circuit common due to the voltage drop across R E, yielding a base-to-circuit common voltage drop of approximately 0.704 V. The transistor must be biased above this point for quiescent operation. A typical value is between 0.1 and 0.2 volts of forward bias above the turn-on point. Choose a value just under 0.2 V. This will yield a bias voltage value of about 0.9 V. With 80 µA of bias current and 0.9 V of base common voltage drop:

This means that 11.1 V must be dropped by R2.

Since this is to be an AC amplifier, the last item to be determined is the emitter bypass capacitor value. This circuit must amplify signals from 500 Hz to 15 Hz. Under worse case conditions, XC should be about 0.1X R. This condition occurs at the low frequency end; in this case, 500 Hz.

Rearranging the formula for XC, the value for C can be calculated: This value is close to the standard value of 27 μf, so a 27 μf capacitor around RE can be installed. '''Figure 47''' shows a common emitter circuit with all of the calculated values shown.

Figure 47: Single-Stage Amplifier