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Fundamentals of Transistors - Transistor Amplifiers

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Fundamentals of Transistors - Transistor Amplifiers

This chapter deals with the design and operation of the transistor as a low-frequency amplifying device based on the transistor characteristics and limitations discussed in the preceding chapters. Since it is impracticable to cover every useful type of connection, the emphasis in this section is on fundamental illustrations, such as choosing the transistor d-c operating point, stabilizing methods, matching, direct coupling, and cascading class A and B single-ended and push-pull transistor amplifiers. Some of the unique properties of transistors that are attained by the symmetrical operation of the N-P-N and P-N-P types in the same circuit are also considered.


Grounding the Transistor System

Some confusion exists about which electrode should be connected to ground in a transistor system. The basic reason for the difficulty lies in the terminology: grounded base, grounded emitter, and grounded collector. Actually, these designations do not refer to the circuit ground, but only specify which of the three electrodes is common to both the input and output circuits. A better way to specify the three basic connections would be: common base, common emitter, and common collector. These latter designations are used by many authorities. In general, the system ground can be made at any convenient point in the circuit, without consideration to the type of connection.


Fig. 5-1. Selecting the d-c
operating point.


Fig. 5-2. Fixed-bias


The D-C Operating Point

Limitations, Supply Voltage and Load.

As in the case of the vacuum tube, the problem of designing a transistor amplifier is somewhat simplified if the a-c signal is treated independently of the d-c operating point. The first step in the design could logically be the selection of the d-c operating point. (Actually, three separate conditions must be fixed; the operating point, the load line, and the supply voltage. In general, the selection of any two automatically limits the determination of the third.) The d-c operating point may be placed anywhere in the transistor characteristics, limited however by the collector maximums of voltage, current, and power dissipation. The final selection of the operating point is based primarily on the magnitude of the signals to be handled.

Suppose, for example, a transistor, whose characteristics are illustrated in Fig. 5-1, is to be used with its operating point set at Ec = 10 volts, Ic = 6 ma. Assume, also, that the maximum limits of the transistor are Ic = 18 ma, Ec = 30 volts, and collector dissipation = 100 milliwatts, as shown enclosed by the dotted lines. The supply voltage required is the value at the intersection of the load line and the collector voltage axis. Thus, for a fixed load of 1,670 ohms, the necessary supply voltage is 20 volts. If, however, the supply voltage is fixed, then the load resistance is determined by the line joining both the supply voltage (Ec at Ic= 0) and the operating point. As an illustration, assume the supply voltage is to be Ebb fixed at 30 volts. The resulting load resistance


For any selected operating point there are many combinations of load resistance and supply voltage that will permit the load line to pass through the d-c operating point.

The usual problem is one in which both the load and supply voltages are fixed. The problem then resolves itself into a choice of the operating point. In Fig. 5-1, for the conditions Ro = 1,670 ohms, and Ebb = 20 volts, the d-c operating point may be placed anywhere along the load line. It is usually desirable to design the amplifier for maximum signal handling capacity. In this case, then, the d-c operating point should be midway between the extreme limits of the base current, namely 0 and 800 microamperes. The choice of Ib = 400 microamperes sets the operating point for maximum signal capacity at Ic= 6ma, and Ec = 10 volts.

Fixed Bias.

The collector bias conditions, then, fix the d-c bias current Ib of the input base electrode; conversely, the base bias current fixes the collector bias for a given load and supply voltage. The desired base bias current can be obtained by connecting a resistor between the base and the collector terminal of the supply voltage as shown in Fig. 5-2. For Ebb = 20 volts, and Ib = 400 microamperes, the total series resistance is


This value includes the emitter to base resistance, but since re + rb is generally only a few hundred ohms, they can be neglected. The resulting circuit, with the calculated values, is illustrated in Fig. 5-2 for a N-P-N transistor. If the same characteristics were applied to a P-N-P type, the only circuit change would be a reversal of the supply battery potentials. The transistor bias indicated in this figure is called fixed bias.



Fig. 5-3. Variation of operating


Unfortunately, transistors are temperature sensitive devices; in addition some variation usually exists in the characteristics of transistors of a given type. These factors may cause a displacement of the constant base current lines along the collector current axis. Figure 5-3 illustrates the effect of this variation; the abnormal cases are purposely exaggerated. Notice the effect of this shift on the relative positions of the d-c operating point. In the low Ice unit (Fig. 5-3B) the collector voltage is too high; in the high Ico unit (Fig. 5-3C) the collector voltage is too low. To overcome this, the circuit needs degeneration, similar to that produced by an unbypassed cathode bias resistor in a vacuum-tube circuit. In transistor, circuitry, this method of degeneration is a form of automatic control of the base bias, known as self bias.

A simple method for establishing automatic control of the base bias requires the base bias resistor to be tied directly to the collector, as in Fig. 5-4. Thus, if the collector voltage is high (Fig. 5-3B) , the base current is increased, moving the d-c operating point downward along the load line; conversely, if the collector voltage is low (Fig. 5-3C) , the base bias current is decreased, moving the d-c operating point upward along the load line. The value of the selected base bias resistor is different in the self-bias case from that computed in the fixed-bias connection. For self bias, the resistor is tied to the collector voltage, which in this case is 10 volts. Then 09 ohms. The base bias resistor performs the double duty of determining the value of Ib and preventing those excessive shifts in the collector d-c operating point due to temperature change and transistor interchange. The principal limitation of self bias is that it still allows some variation of the d-c operating point, since the base bias resistor is fixed by the required operating point, and the stabilization produced by it is only a secondary effect. In addition, self bias also introduces a-c negative feedback which reduces the effective gain of the amplifier. Despite its limitations, however, self bias is very useful and works well in many applications.

The importance of temperature stability with respect to the d-c operating point cannot be taken lightly. One of the effects of a temperature rise is to increase the saturation current Ico, which, in turn, increases the collector dissipation. The increased collector dissipation increases the temperature, which increases Ico, and so on. Thus, poor temperature stability almost certainly will cause transistor burnouts, particularly if the transistor is operated near its maximum dissipation limit.


Fig. 5-4. Self-bias operation.


Fig. 5-5. Hunter-Goodrich bias

Hunter-Goodrich Bias Method.

A method of establishing tighter control on the base bias current illustrated in Fig. 5-5 is the Hunter-Goodrich method. This involves the addition of a fixed base bias operating in the reverse direction of the normal self bias. The fixed bias is introduced by resistor RF and separate voltage supply EF. To overcome this reversed fixed bias, the self bias resistor RB must be decreased to maintain the same base bias current. The reduced value of RB increases the available negative d-c feedback from the collector circuit, thus providing greater transistor stability.

As in the preceding cases, the effect of the base and emitter circuit resistances (re + rb) can be neglected in the calculations. The values of RF and EF depend upon the value of fixed bias desired. For example, assume that a fixed bias value Ib2 of 300 µa will provide the additional stability needed, and a battery EF = 10 volts is available. Then RF


In comparison, RB 25,000 ohms in the simple self bias case. Since the input resistance of the transistor is small compared to RF, practically all of the stabilizing current flows into the base-emitter circuit.

The Hunter-Goodrich bias method is extremely useful when a high degree of circuit stability is needed. Its particular disadvantage is that it requires two separate battery supplies.

Self Bias Plus Fixed Bias.

One method of obtaining additional stabilization with only one battery is shown in Fig. 5-6 (A) , the basic features of which are often used in transistor power stages. The fundamental differences between this circuit and the preceding fixed plus self bias method are the interchange of RL and Ebb, and the connection of the reverse bias resistor RF into the collector circuit. Interchanging the supply battery and the load resistor provides two points at which variations in collector voltage will appear. However, this interchange does not affect the d-c operation of the circuit. Connecting RF, as illustrated, produces essentially the same result as the Hunter-Goodrich arrangement, except that the reverse bias is no longer fixed. If the previous
circuit constants are desired:


All the other values remain the same.



Fig. 3-6. (A) Stabilization of d-c operating point with one battery. (B) Typical power
output stage.

In power amplifier circuits, the load usually consists of a transformer plus an additional stabilizing resistor. Figure 5-6 (B) illustrates one possible form of this arrangement for use as a transistor power amplifier stage.

A disadvantage of this bias method is that the d-c degeneration feedback is reduced, due to the shunting effect of resistor RF, thus reducing the stabilization. On the other hand, this method provides for greater stability than does the simple self-bias method. It provides less stability than the Hunter-Goodrich method, but requires only one battery supply.


Fig. 5-7. Equivalent voltage-current sources.


Fig. 5-8. Class A amplifier.

Current Sources.

Notice that all the bias requirements are supplied by conventional batteries, which act as constant voltage sources. At this point the conscientious reader may wonder if this does not conflict with the statements in earlier chapters that transistors are current-operated devices. Actually, the term "current source" is more than just a mathematical concept. The practical aspect can be shown as follows: Assume that a six-volt battery with negligible internal resistance is connected to a variable load resistance. Except for very low values of load, the battery terminal voltage remains constant as long as the battery remains fully charged. Now assume that a one megohm resistor is connected in series with the battery and the load resistor. In this case the current remains reasonably constant while the load resistance is varied from zero to about 0.1 megohm. Thus, the addition of a series resistor has converted the constant voltage supply into a constant current source over a fairly wide range of load resistance values. The range depends upon the value of the series resistor. Figure 5-7 illustrates the basic equivalent interchanges of supply sources. Mathematically, all that is involved is the movement of the impedance proportionality constant from one side of the equation. to the other.

That these circuits are equivalent can be shown by a simple example. Take the case of a six-volt battery in series with a resistor R = 1 megohm and a load RL = 1 megohm. Then the load current equals


a load RL = 1 megohm. Now the load current equals the source current less the amount shunted by resistor R. Since R and Ro are in parallel, the voltage drop across each resistor must be the same, and the load current equals


This checks with the previous result. The same procedure can be used to convert an a-c voltage source into an a-c current source.


Fig. 5-9. (A) Distortion due to
crowding of collector characteristic.
(B) Effect of input distortion on
output wave.

Class A Amplifiers

Basic Circuitry — Efficiency Stabilization.

Figure 5-8 represents a typical Class A transistor amplifier using d-c operating biases as described in the preceding paragraphs. The stabilizing resistor in the emitter circuit is made equal to the load impedance in this case. This condition provides maximum protection against variations in Ico, since the power available from the battery is effectively limited to the maximum collector dissipation. While the arrangement shown in Fig. 5-8 prevents transistor damage due to excessive collector variations, half of the d-c power is dissipated across the stabilizing resistor. The maximum efficiency of a class A transistor is 50%; using a stabilizing resistor whose value is equal to the load resistor reduces the efficiency to a maximum of 25%.

In general, this amount of stability control is needed only in mass production applications if transistors having a wide tolerance range are to be used. Actually, the reproducibility of transistor characteristics has improved rapidly during the past few years. There is no reason why this trend should not continue, and eventually permit the attainment of amplifier efficiency values very close to the theoretical maximum. In most circuits, between 5 and 10% of the collector d-c power (EcIc) is satisfactory for normal stabilization. In the circuit shown in Fig. 5-8, for example, a resistance of 100 ohms between the emitter and ground would be sufficient.

Bypass and Coupling Capacitors.

If the stabilizing resistor in the emitter lead is unbypassed, the amplifier gain is decreased. This is similar to the action of an unbypassed cathode resistor in a vacuum-tube amplifier. A value of 50 µf works out well for the bypass capacitor in most audio frequency applications. The self bias resistances from collector to base may also be suitably bypassed to avoid a-c degeneration. In cascaded stages, the load is unusually low, and the a-c collector voltage is also low. In this case, the bypass capacitor can be omitted with only a slight loss in the stage gain.

The value of the coupling capacitor Cc must be large enough to pass the lowest frequency to be amplified. Usually a maximum drop of 3 db in gain is permitted. At this value, the reactance of the coupling capacitor is equal to the input resistance of the stage. Since the input resistance is low for the grounded emitter and grounded base connections, relatively high capacity coupling condensers are required. For example: What is the minimum value of Cc necessary for coupling into a stage whose input resistance ri 500 ohms, if a frequency response down to 100 cps is required? At 100 cps, 20


Another characteristic of a transistor amplifier that should be mentioned is the harmonic distortion. If the circuit is wired, the distortion can be measured directly, using a suitable wave analyzer or distortion meter. In addition, distortion can be calculated under given operating conditions from the collector characteristics, using the same methods as in vacuum-tube amplifiers. These methods are described in detail in most radio engineering handbooks. The total harmonic distortion is about 5% in the typical transistor amplifier. It is caused mainly by the decreased spacing between the collector current-collector voltage curves for equal changes in base current. This crowding effect occurs at the higher values of collector current. Figure 5-9 (A) is an exaggerated illustration of this type of distortion in transistor circuits.

If the input resistance of the amplifier is high compared to the source impedance, another type of distortion, due to variations in the input circuit, is introduced. In the region of low collector current, the input resistance increases, thus reducing the amplitude of the input signal. In the high region of the collector a-c current cycle, the input resistance decreases, thus increasing the amplitude of the input signal. This type of non-linear distortion is illustrated in Fig. 5-9 (B) .

Since the two major types of distortion described above have opposite effects, it will be possible to counteract one with the other by adjusting the value of the signal generator impedance. In troubleshooting multi-stage transistor amplifiers, an output waveform similar to that indicated in Fig. 5-9 (B) would probably indicate a defect in one of the preceding stages.

When computing the harmonic distortion of a transistor amplified by conventional vacuum-tube graphical methods, the computed value is generally in the order of 1% less than the measured value. This is caused by the assumption that the signal generator resistance is negligible, a condition seldom realized in low input resistance transistor circuits. The source resistance in vacuum-tube amplifiers does not affect the determination of the harmonic distortion, since the grid current

is zero. However, the equivalent parameter in transistor amplifiers, the
base-emitter voltage, is not zero. The effect of the source may be taken into account by considering it as part of the base resistance. However, in most applications, it is more than satisfactory to simply add 1% to the calculated value of percentage distortion.


Fig. 5-10. (A) Load lines for maximum power. (B) Determination of
optimum load. (C) Power amplifier


Maximum Output Conditions.

Since the power handling capacity of the transistor is small compared to that of the vacuum tube, it is usually necessary to drive the transistor to its maximum limits. When a transistor amplifier is designed for maximum power, as in Fig. 510 (C) , it is properly termed a power amplifier, although the actual power involved may only amount to a hundred milliwatts. To obtain maximum power, the load line is selected to include the maximum possible area concurrent with the fixed limitations of maximum collector dissipation, current, and voltage. The ideal load for maximum power would be one which followed exactly the transistor limit boundaries illustrated in Fig. 5-1.

In the practical case, it is usually necessary to settle for a load line that is tangent to the limiting characteristic line. Since this curve is non-linear, there are several possible choices of load. The final choice depends primarily on the signal requirements of the circuit. Figure 5-10 (A) shows the two extreme cases: line A is the optimum load for a small signal input; line B is the optimum load for a large signal input. Since, however, the supply voltage is usually specified, the load line chosen is the one that is tangent to the limiting curve and that passes through the specified supply voltage (Ec at Ic= 0).

The calculations for determining the conditions for maximum out in a power amplifier stage, assuming a transistor with the characteristics illustrated in Fig. 5-10 (B), are as follows: Assume a battery supply Ebb = 20 volts. This determines a point on the load line for fc 0. Now hold one end of a straight edge on this point and swing the edge until it just touches a point on the maximum collector dissipation ,line. Draw a line through the two points. This is the optimum load line for the given conditions. The maximum input signal, the d-c bias resistors, and the distortion can all be computed directly from the figure by means of the methods discussed in the preceding paragraphs:


Using the standard equation derived for vacuum-tube circuits, the transistor a-c output Pac is one-eighth of the product of the peak-to-peak collector voltage and collector current:


The maximum a-c signal current can be taken directly trom the characteristic curve. In this case, ib = 600 µa peak-to-peak. (The stabilizing resistors have been omitted to simplify the illustration.)

Push-Pull Operation.

Whenever possible, transistor power amplifiers should be operated as push-pull stages. Push-pull operation has several desirable features, including the elimination of the even-order harmonics and the d-c component in the load. The first factor is particularly fortunate, insofar as transistor applications are concerned. It was noted previously that operation at high values of collector current introduces a distortion due to crowding of the collector current-voltage lines. Thus, for a given value of allowable distortion, push-pull operation will allow the transistors to be driven into the higher I, regions. In turn, each transistor delivers more power to the load than when it is connected for single-ended operation.


Fig. 5-11. Class A push-pull


Fig. 5-12. (A) Class B circuit (constant voltage). (B) Class B push-pull operation.

he operating point, load, and biasing resistors for the Class A push-pull stage are determined for each transistor exactly as if it were a single-ended type. A typical push-pull transistor amplifier is illustrated in Fig. 5-11, based on the same transistor characteristics used previously. The separate biasing arrangement indicated in this illustration permits a more exact match of the transistor characteristics. Notice that the load is twice the value computed for the single-ended stage.

Class B Transistor Amplifiers

Basic Operation — Quiescent Point.

While the efficiency of a Class A amplifier is good under operating conditions, the collector dissipation is approximately the same whether or not a signal is applied. Its efficiency for intermittent or standby operation is poor. For standby operation, as in the case of the vacuum tube, Class B operation is preferred, and the operating point of a Class B transistor amplifier should be on the Ec = 0 line. This bias condition, however, would require an extremely high resistance in series with the battery. Thus most of the available supply power would be lost in the series resistor, the only function of which was to convert the voltage source into a current source. As an alternate method, a constant voltage battery is used. This sets the d-c operating point at the collector voltage Ec = Ebb on the Ic = 0 axis. Figure 5-12 (A) shows a typical Class B transistor amplifier with a constant voltage source, using the same transistor as in previous calculations.

Push-Pull Circuitry.

Two Class B amplifiers connected as a push-pull stage, using two of the circuits illustrated in Fig. 5-12 (A) , will not operate. One transistor will always be biased in the reverse direction by the input signal, thereby causing its input resistance to become very high. This condition can be eliminated by using a center-tapped input transformer and connecting the center tap to the common emitter electrodes. This circuit is characterized by a distorted output wave. The distortion is particularly evident when the signal generator resistance is low. However, the distortion can be reduced within limits by introducing base bias into the circuit.

Figure 5-12 (B) illustrates one possible form of this latter arrangement. The value of the base bias resistor RF for minimum cross-over distortion can be determined by the conventional graphic methods of vacuum-tube Class B push-pull amplifiers when using the composite transistor characteristics. The proper bias setting may be determined experimentally by direct measurement with an oscilloscope or a distortion meter. If the experimental method is used, care must be taken to avoid setting the base bias too high. This would cause a relatively high quiescent d-c collector current to flow, and the circuit would perform in a manner similar to that of a Class AB amplifier in vacuum-tube circuits. resistor Rc may be a thermistor or some other temperature sensitive device. Rc is usually required in stages, subject to large changes in temperature to prevent excessive variation in the collector d-c operating point.


Fig. 5-13. (A) Class 11 push-pull operation without input transformer.
(B) Output waveforms.


Another arrangement for a transistor push-pull Class B stage is illustrated in Fig. 5-13 (A) . This circuit permits the elimination of the input transformers. The diodes D1 and D2 prevent each transistor from cutting off when it is biased in the negative (reverse bias) direction by the input signal, since the diodes effectively short out the signal-induced bias. The point at which this bypass action occurs is determined by the bias due to resistors RF and Rc. These resistors also furnish base bias to the transistors to minimize cross-over distortion. Figure 5-13 (B) illustrates the effect of diodes and bias resistors on distortion of the output signal.

The detailed operating characteristics of a Class B transistor push-pull amplifier are determined by the same methods used in similar vacuum tube circuits. The approximate values of the major characteristics can be calculated as illustrated in the following example: Assume that the transistors to be used in the Class B push-pull circuit have a maximum collector dissipation rating of 100 milliwatts, and assume that a battery Ebb = 10 volts is specified. The collector dissipation Pc in


Phase Inverters


Transistor push-pull amplifiers, like their vacuum-tube counterparts, require the use of a phase inverter to supply the required balanced signal input. Transistor inverters are more complicated than conventional vacuum-tube types in that they must provide a balanced current, rather than a balanced voltage, input signal. However, the principles of operation are essentially the same.


Fig. 5-14. Transistor phase


Fig. 5-15. Gain controls.

Typical Circuit.

Figure 5-14 illustrates the basic circuit of a transistor phase inverter, which provides a reasonably well-balanced output. The basic operation is as follows: the upper transistor operates as a conventional grounded emitter amplifier except that the emitter is grounded through the parallel circuit, consisting of the lower transistor emitter-base path and resistor RE. The emitter-base path has a low resistance, less than 50 ohms, so that practically all of the a-c emitter current of the top transistor flows through this path. Since the emitter current value for each transistor is the same, the collector currents are also equal if the current gains from emitter to collector are equal. For proper operation, the load resistances should be small compared to the output resistances of the transistors, and the emitter-to-collector current gains should be well matched. For the circuit illustrated, the output resistance of each transistor is the collector resistance shunted by RB. Since rc is much greater than RB, the output resistance is equal to RB. Thus RB should be about ten times RL. It is not necessary for the current gains to be exactly matched. Values which fall in the range of .92 to .97 are usually satisfactory. RL and RB are selected to provide the operating biases, which in this case are Ec = 10 volts, Ic = 4 ma, and Ib = 400 µa. The value of RE is particularly important. It must be large compared to the emitter-to-base resistance path of the lower transistor; if it is not, an appreciable portion of the a-c signal will be shunted through RE and the currents in the emitters will not be equal. In general, a value of RE that is ten times the emitter-to-base circuit resistance is satisfactory.


Transistor Gain Controls

Despite the relatively low gain of transistor amplifiers, a gain control is frequently necessary to compensate for changes in the input signal, the ambient noise level, and other variations. The design of volume controls for transistor circuits is not a difficult problem if the fact that transistors are current operated devices is kept in mind. Figure 5-15 (A) illustrates one possible form of output gain control in a R-C coupled stage. In this circuit, the output potentiometer sets both the collector d-c operating point and the level of the output signal. The coupling capacitor blocks d-c current from flowing into the load. The value of this capacitor must be large enough to pass the lowest frequency to be amplified. If the output load is a transformer, this same form of gain control is not satisfactory, since, as illustrated in Fig. 5-15 (B) , the load impedance varies with the potentiometer setting. If the coupling capacitor is omitted, circuit operation is poorer because the volume control setting changes the d-c operating point.

Figure 5-15 (C) illustrates a satisfactory form of input volume control in a transformer coupled stage. The resistance of the potentiometer should be at least ten times the value of the secondary-winding impedance to make its loading effect negligible. The arrangement illustrated in Fig. 5-15 (D) , however, is not satisfactory, because the base bias varies with changes in the volume control setting.

In multistage operation, the gain control may be located in the input or output circuit of any stage. It is usually desirable to place the control in the first stage if the signal amplitude is likely to vary appreciably. This arrangement helps to prevent the system from overloading on large signals.


Fig. 5-16. Block schematic of cascade


Fig. 5-17. Calculated three-stage cascade.


Cascade Operation

Design Considerations — Overall Power Gain.

In any given problem requiring more than one stage of amplification, several cascade arrangements are possible. This flexibility is a desirable design feature; however, it complicates the problem of selecting the best combination of the three general forms of transistor connections with respect to the input and output resistances, and to the required gain of the system Every design is fixed to some extent by the function of the circuit. but the requirement for maximum gain is invariably included.

Figure 5-16 is the block schematic of a three stage circuit. It is evident from inspection that the overall current gain of the system is he product of the individual stage gains, thus α = α1α2α3. The operating gain as defined in equation 3-45 is


On this basis, a cascade system has maximum gain when each of the stages is separately designed for a maximum value of its associated gain
Selection of Stage Connection. The first stage requires that its gain factor 36 be as large as possible. The following general rules for this stage are based on an analysis of the gain factor vs Rg characteristic:

  1. When Rg has a low value (0 to 500 ohms) , use either the grounded base or the grounded emitter connection.
  2. When R g has an intermediate value (500 to 1,500 ohms) , use the grounded emitter connection.
  3. When Rg has a high value (over 1,500 ohms) , use the grounded emitter or the grounded collector connection.

In the intermediate stage α22 is made as large as possible. This requirement generally can be met by either the transistor grounded emitter or grounded collector connection. The intermediate stage equivalent load should be less than (rc — rm) . If rc is nearly equal to rm, the grounded collector should not be used. This equality would cause the input and output resistances of the stage to become independent of the values of the connecting circuits. (An analysis of this buffer effect was covered in the discussion of input and output resistance of the grounded collector stage in Chapter 4.)

It must be noted that the intermediate stage represented by the current gain a2 in this discussion may actually consist of several intermediate stages having a total current gain equal to α2. This analysis of the three-stage circuit of Fig. 5-14, therefore, is applicable to any number of cascaded stages.

In the final stage, the gain factor RLα32 is made as large as possible. The following general rules for this stage are based on the analysis of the gain factor vs RL characteristic for the three basic transistor connections.

  1. When RL has a small value (0 to 10,000 ohms) , use a grounded collector or a grounded emitter connection.
  2. When RL has an intermediate value (10,000 to 500,000 ohms) , use a grounded emitter connection.
  3. When RL has a high value (over 500,000 ohms) , use a grounded emitter or grounded base connection.

(The numerical values listed above apply to those junction transistors with characteristics similar to the Western Electric Type 1752 transistor; however, the general values can be extended on a relative basis to cover all types.)

Based on the foregoing rules, it might appear that the choice of the grounded emitter connection is the best under all conditions. However, specific design problems of ten dictate the use of grounded base and grounded collector circuits when the coupling network, biases, feedback, and other factors are taken into consideration.

Cascade Design. As an illustration of these principles, consider the design of a three-stage cascade system using the typical junction transistor with re = 50 ohms, rb = 500 ohms, rc = 1,999,500 ohms, and rm = 1,899,500 ohms. Assume that Rg is adjustable but limited to low values. RL = 150 ohms requires the use of the grounded emitter or grounded collector connections. Assume that other design factors limit the choice to the latter case. Then for the last stage:

r11 = rb = 1,999,500 + 500 = 2,000,000 ohms;

r12 = rc - rm 1,999,500 — 1,899,500 = 100,000 ohms;

r21 = rc = 1,999,500 ohms;

r22 = rc + re — rm = 1,999,500 + 50 — 1,899,500 = 100,050 ohms.

The input resistance of the last stage (equation 3-13) is expressed as:


Since a low value of Rg is specified, the first stage must use either the grounded emitter or the grounded base connection. The load of the first stage equals the input resistance of the intermediate stage and is a low value. Therefore, the best choice for the first stage is the grounded emitter connection. Since Rg was specified as being adjustable, its value will be made equal to the input resistance,


The resulting cascade circuit is shown in Fig. 5-17. This circuit does not include biasing arrangements, coupling networks and feedback loops. The values of the elements necessary for introducing these re- quirements may be computed by the methods in preceding paragraphs.

The cascade system may be changed considerably by the addition of external resistance arms to the circuits. These have the effect of increasing the effective values of the transistor parameters. For example, consider the effect of adding a stabilizing resistor RE = 50 ohms in series with the emitter arm of the input stage. The effective resistance of the emitter is now re +RE = 50 + 50 = 100 ohms, and the general four-terminal parameters are now:


Thus, a simple change reduces the overall system gain by a factor of one-half. It is evident that even after the basic stage connections are fixed, a considerable variation in the cascade performance and resistance terminal characteristics can be attained by changes in the effective value of the transistor parameters.


Fig. 18. R-C interstage coupling; Xc less than ri at lowest frequency to be amplified; R at least 10 times ri.


Fig. 5-19. Typical decoupling

Coupling and Decoupling Circuits. To obtain the absolute maximum gain from a cascaded system, image resistance matching between stages is required. The analysis and conditions for matching the three basic transistor connections are covered in Chapters 3 and 4. The stage can be matched by interstage transformers. In i-f strips, transformer coupling is convenient and invariably used, because the transformers are also required for selectivity. In audio circuits, however, the increased gain due to the transformer is seldom worth its expense. In audio cascades, therefore, resistance-capacitance coupling is the most practical and economical choice. Figure 5-18 represents a typical R-C coupled stage. The capacitance must be large enough to pass the lowest frequency to be amplified. Its value can be computed as indicated in the preceding paragraphs dealing with single stage amplifiers. Resistor R must be large compared to the input resistance r1. The interstage loss in gain is less than one db if R is chosen to be ten times as great as ri.

When cascaded stages. are connected to produce an overall gain of 60 db or more, consideration must be given to the addition of a de-coupling circuit, as indicated by the combination R1C1, as shown in Fig. 5-19. Decoupling is required to prevent positive feedback through the battery resistance which is common to all the stages. High-gain transistor cascades almost always require a decoupling network, since even low values of battery resistance are significant when compared to the low input resistance of transistor stages. The product of R1 and C1 (time constant) should be equal to or greater than the inverse of the lowest frequency to be amplified by the stage. While this specified frequency sets the time constant, there are any number of combinations of C1 and R1 which can be used. In general, R1 is made small enough so that it does not affect the supply voltage greatly, and at the same time is not made so low that a very high value of C1 is required. The following example illustrates the calculation of the decoupling network: Suppose that for the circuit illustrated in Fig. 5-19, the d-c base bias Ib = 500 µa, and a drop of one-quarter of a volt in the battery supply through R1 can be tolerated. The maximum value of R1 equals the allowable voltage drop divided by the base current, 42 = 500 ohms. If 100 cps is the lowest frequency to be passed, then43and 44 (In this equation, f is expressed in cycles per second, R1 in ohms, and C1 in farads.) The value of C1 depends on the allowable voltage drop through R1. If a larger drop is allowable the value of C1 will decrease proportionately. In this example, assume that only a 10 µf capacitor is available, and that the maximum drop through R1 can be increased. Then R1, for the same
cut-off frequency, equals 45 and the voltage drop through R1 equals R1Ib = 1000 (500 x 10-6) =0.5 volt. The base bias resistor now must be adjusted to compensate for the reduced value of the effective supply voltage. Thus


as compared to the value (without decoupling) ,


In general then, when the value of the decoupling resistor is significant in comparison to the value of the bias resistor, RB must be decreased by an amount equal to that of R1 to maintain the specified d-c base current. In the form of an equation, this condition can be specified as:


Figure 5-20 illustrates an experimental two-stage amplifier using grounded emitter circuits designed specifically to amplify the output of a 50 ohm dynamic microphone. The output terminates in a 600 ohm line. The overall gain of the system is 46 db.

Complementary-Symmetry Circuits

Basic Theory.

The circuits discussed to this point can be used with either N-P-N or P-N-P transistors. It is necessary only that the battery supply is connected with the proper polarity. For other applications, it is possible and often very profitable to combine the two types of junction transistors into one circuit. This technique permits the design of many novel configurations that have no direct equivalent in vacuum tube circuits, since no one has yet invented a vacuum tube that emits positive particles from its cathode. Some of the characteristics of this unique property of transistors can be illustrated with the help of Fig. 5-21 (A) , which is the composite curve of N-P-N and P-N-P units having identical characteristics except for polarity. (Practical circuits are never designed for an exact match, because of the expense of selection.) For each operating point E1I1 in the N-P-N unit, there is an equivalent operating point (—E1) (—I1) for the P-N-P unit. These symmetrical properties offer innumerable possibilities in circuit applications. For example, if a peak signal current of 20 µa is applied to the base of each transistor simultaneously, the operating point of the N-P-N transistor has shifted to E2 = 8 volts, I2 = 15 ma at the instant that the input signal reaches a value of + 10 µa. But at the same instant the operating point of the P-N-P unit is at E2 = - 22 volts, and I2 = —5 ma. An increase in the base current of the N-P-N unit causes the collector current to increase; the same variation causes the collector current of the P-N-P unit to decrease. When the signal is reversed, the opposite effect occurs. The complete waveforms for this operation are shown in Fig. 5-21 (B) . Since the output of the transistors are 180° out of phase, it appears that the N-P-N and P-N-P types will operate, with their input circuits in parallel, as a push-pull stage. Furthermore, due to the complementary action of the N-P-N and P-N-P types, the circuit does not require an input transformer or a phase inverter.


Fig. 5-20. Experimental two-stage


Fig. 5.21. (A) Composite characteristics for N-P-N and P-N-P transistors. (B) Waveforms of
composite characteristics.

Symmetrical Push-Pull Operation.

Figure 5-22 illustrates the basic symmetrical push-pull circuit with numerical values based on the same typical transistor characteristics used in previous examples. The operation of this circuit is the same as that of the transistor push-pull Class A amplifier that uses only one type of transistor. The circuit is capable of supplying a high voltage gain when operating into a high impedance load. The voltage gain of the circuit shown in Fig. 5-22 is in the order of 250 (48db) . If the transistors are exactly symmetrical, the d-c collector currents supplied by each transistor cancel each other, and no d-c component flows in the load. The circuit is easily adaptable for direct connection to the voice coil of a speaker. Notice also that the same circuit can be modified by proper adjustment of the base bias for Class B push-pull operation.


Fig. 5-22. A symmetrical push-pull


Fig. 5-23. A direct-coupled symmetrical cascade.


Fig. 5-24. Two-stage symmetrical
push-pull amplifier.


Cascade Operation.

One type of symmetrical circuit that proves very practical is the cascaded arrangement illustrated in Fig. 5-23. This tandem circuit represents the simplest possible cascade, since the only components of the system are the transistors and the battery supply. The gain per stage is low compared to the maximum available gain because of the mismatch existing between the stages. However, the reduced number of components and the simplicity of the design often outweighs this disadvantage.

A circuit which incorporates the major features of both push-pull and cascaded symmetrical configurations is shown in Fig. 5-24. This arrangement can serve as a single-ended power amplifier to feed a low impedance speaker from a relatively high resistance source. The two transistors in the output circuit are operated in the grounded emitter connection. Therefore, the phase of the input signal is reversed in going from base to collector. The base of the last stage is connected directly to the collector output circuit of the input stage. Since the signal also undergoes phase reversal in the first stage, the output of the transistors on each side of the load are in phase. The stability of this circuit is very high because it incorporates 100 percent degenerative feedback. The large amount of feedback keeps the distortion very low, and also allows the load to be very small. Since the circuit is in effect a two-stage Class B push-pull amplifier, the standby collector dissipation is negligible. The amplifier is capable of delivering a constant a-c output of about 400 milliwatts using transistors rated at 100 milliwatts. In intermittent short term operation, the same amplifier can deliver about a watt without damage to the transistors.

It is apparent that complementary-symmetry circuits offer considerable promise for further investigation. Their use in the field of high quality, low-cost portable audio systems is particularly attractive because the output can be fed directly into a voice coil, thus eliminating the expensive and often troublesome output transformer.

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