The design and servicing of the transistor circuit is more compli-cated than that of the vacuum tube, because transistor input and output circuits are never inherently independent of each other. This makes it difficult for a newcomer to get the "feel" of the transistor. In the long run, however, these same complex characteristics provide for a more flexible device, one capable of many circuit applications beyond the range of the vacuum tube.

This chapter deals with the extension of the four-terminal charac-teristics developed for the grounded base to encompass the two remain-ing connections, the grounded emitter, and the grounded collector; a comparison of the major features of the three basic connections; limita-tions of the transistor; andtransistor testing methods.

**Introdudion**

In the following analysis of transistor performance in the grounded emitter and grounded collector connections, the same typical point-contact and junction transistors discussed in Chapter 3 will be used for numerical examples. For the point-contact transistor in the ground-ed base connection, the parameters are:

For the junction transistor in the grounded base connection:

Notice that since r_{m} and r_{c}. are so much greater in value than r_{b}, par-ticularly in the case of the junction transistor, for all practical purposes r_{21} r_{b}, and r_{22} r_{c}.

**Fig. 4-1. (A) The grounded emifter connection. (B) Equivalent active "T" for grounded
emitter connection.**

**Fig. 4-2. Operating circuit, grounded emitter connection.**

**The Grounded Emitter Connection**

*Equivalent Operating Circuit. *

The grounded emitter connection is illustrated in Fig. 4-1 (A) . In this case the input connection is made between the base and emitter electrodes (conventionally the emitter is shown schematically as an arrowhead resting on the base) , and the output is taken between the collector and the emitter. Thus, in this case, the emitter is the common electrode. Figure 4-1 (B) illustrates the equivalent active "T" circuit for the grounded emitter connection.

Figure 4-2 is the complete operating circuit of the grounded emit-ter connection. Notice that although the negative side of the signal generator is grounded, the polarity of the signal in this connection is reversed with respect to the emitter and base terminals shown in the grounded base connection of Fig. 3-9. Since this effective reversal of input leads is the only physical difference between the two connections, the grounded emitter, unlike the grounded base, produces a phase in-version of the input signal.

*Circuit Parameters. *

The general open-circuit characteristics derived for the grounded base connection apply equally well to the grounded emitter and grounded base connections, since the characteristics were determined on the basis of a sealed box. However, since the internal parameters of the transistor have been rearranged, the values of the general characteristics are different. It is necessary then, to evaluate the open-circuit characteristics r_{11}, r_{12}, r_{21}, and r_{22} in terms of the tran-sistor internal parameters r_{e}, r_{b} r_{c}, and r_{m}. The same basic measuring circuits, illustrated in Figs. 3-8, may be used to determine the four-terminal parameter for the grounded emitter connection:

These grounded-emitter relationships are derived as follows:

A. Using Fig. 4-1 (B) , the input loop equation on the basis of Kirch-

off's law is:

The open-circuit characteristics can now be numerically evaluated for the typical point-contact and junction transistors previously considered in Chapter 3. For the point-contact transistor in the grounded emitter connection:

Because of the large values of r_{m} and r_{c} with respect to r_{e}, r_{21} in the practical case can be approximated by —r_{m}, and r_{22} by (r_{c} — r_{m}) The emitter resistance, r_{b} = r_{12}, is the feedback resistance and is equivalent to r_{b} = r_{12} in the grounded base connection. Notice, however, that since there is phase inversion in the grounded emitter connection, re produces degenerative (negative) feedback, rather than regenerative (positive) feedback. The degenerative effect of the output current through re is similar to the degenerative action of an unbypassed cath-ode resistor in a grounded cathode vacuum tube.

Current Gain in the Grounded Emitter Connection. The current gain in terms of the general four-terminal parameters was defined by equation 3-8 as:

In terms of the transistor parameters in the grounded emitter connec-tion now being considered, the current gain is

In the case of the grounded-emitter point-contact transistor, r_{21} and r_{22} are both negative. The value of the load resistor, R_{L}, determines whether the current gain is positive or negative. If R_{L} is less than the absolute value of —r_{22}, a is positive; if R_{L} is greater than the absolute value of —r_{22}, a is negative. A negative value of current gain indicates simply that the input current is inverted in phase. This is normal in the grounded emitter connection. Theoretically, an infinite current gain is attained when R_{L}= - r_{22}. The current gain of a typical point-contact transistor with a load R_{L} = 15,000 ohms is

The current gain in the junction transistor is always negative in the grounded emitter connection, since r_{22} is always positive. The cur-rent gain for the typical grounded-emitter junction transistor with a load

The maximum current gain, as in the case of the grounded base con-nection, is:

**Fig. 4-3. Input resistance vs load resistance for typical point-contact transistor
(grounded emitter).**

*Input Resistance ri for the Grounded Emitter Connection. *

The input resistance was defined in equation 3-13 in terms of the general open circuit parameter as:

The input resistance in terms of the transistor parameters in the grounded emitter connection becomes:

**Fig. 4-4. Input resistance vs load resistance for typical junction transistor (grounded emitter).**

The effect of the value of the load resistance on the input resistance of typical transistors is illustrated in Figs. 4-3 and 4-4. The input re-sistance for the point-contact transistor starts at a value of -40 ohms for R_{L} = 0, and becomes more negative as the load resistance increases. When R_{L} —r_{22}, the input resistance is infinite. As the load resist-ance increases beyond this point, the input resistance becomes positive, decreasing in value to the limiting condition r_{1} = r_{m} = 250 ohms when the output is open-circuited. Negative values of input resistance indicate circuit instability; consequently, the point-contact transistor can be used as an oscillator in the region where R_{L} is less than -r_{22}. Circuits of this type are called "collector-controlled oscillators."

The input resistance of the junction transistor is always positive. In the typical transistor considered, the input resistance decreases from a value of 1,500 ohms at R_{L} = 0, to 550 ohms for an infinite load.

Output Resistance r_{o} for the Grounded Emitter Connection. The output resistance was defined by equation 3-21 in terms of the general four-terminal parameters as:

The output resistance in terms of the internal transistor parameters in the grounded emitter connection becomes:

The effect of the value of the signal generator resistance is illustrated for the point-contact and junction transistors in Figs. 4-5 and 4-6, re-spectively. Notice that the output resistance of the point-contact type is positive at R_{g} = 0, and decreases rapidly to zero when R_{g} is slightly less than 50 ohms. As R_{g}, is increased further, r_{o} becomes negative and gradually approaches the limiting condition, when R_{g}, is infinite, r_{i} = r_{22 = }-11,850 ohms. Thus, the point-contact transistor can have a nega-tive output resistance over a large range of generator resistance values, and this characteristic can be used in transistor oscillator design. Circuits of this type are called "base-controlled oscillators."

The output resistance of the junction transistor is always positive, and for the typical type considered, r_{o} gradually decreases from approxi-mately 273,000 ohms to 100,000 ohms as R_{g}, is increased from zero to infinity.

The range in which both the output and input resistances of the point-contact transistor are positive can be increased by adding external resistance in the emitter arm. This increases the effective value of r_{e}= r_{12}. Notice that if enough external resistance is added so that the effective emitter resistance r_{e} = R_{L} is equal to or greater than - (r_{c} - r_{m}) , the input and output resistance is positive. This stabilizing effect of adding resistance to the emitter load is frequently used in transistor circuit applications.

**Fig. 4-5. Output resistance vs generator resistance for typical point-contact transistor
(grounded emitter).**

**Fig. 4-6. Output resistance vs generator resistance for typical junction transistor
(grounded emitter).**

*Voltage Gain VG in the Grounded Emitter Connection. *

The voltage gain was defined by equation 3-24 in terms of the general four-terminal parameters as:

Notice that the voltage gain in this connection, like the current gain, is negative. Again this merely indicates that the input voltage is inverted in phase.

*Impedance Matching in the Grounded Emitter Connection. *

As in

the analysis of the grounded base connection in Chapter 3, the stability factor must be less than unity for short-circuit stability. The numerical value of 8 for the typical point-contact transistor is . This re-emphasizes the fact that the point-contact transistor in the grounded emitter connection is unstable when the output is short-circuited. The stability factor for the junction transistor

*Power Gain in the Grounded Emitter Connection.*

The numerical

values of the voltage and current gains are always negative in the stable range of operation of the grounded emitter connection. The negative sign is merely a mathematical indication of the phase inversion of the ampli-ifed signal. Since the power gain is a function of the product of the volt-age and current gains, its numerical value must be positive.

The operating gain is defined in equation 3-46 as

.Note that since r_{21} and the bracketed quantity in the denominator are squared, the numerical value of this equation is always positive. It is certainly possible to obtain an apparently valid power gain in an un-stable portion of the transistor characteristic if numerical values are haphazardly substituted. For example, evaluating the operating gain for the typical point-contact transistor when R_{L} = 1,000 ohms and R_{g} = 10 ohms,

However, Fig. 4-3 indicates that at a load of R_{L} = 1,000 ohms, the tran-sistor is unstable and will oscillate. This does not mean that the ground-ed emitter connected transistor can oscillate and supply a power gain at the same time, but rather that the operating gain equation can only be applied conditionally. Without going too deeply into the mathematic-al concepts involved, equation 3-46 can only be applied when (R_{g} + r_{11}) (R_{L} + r_{22}) - r_{12}r_{21} is greater than zero. When R_{g} and R_{L} equal zero, the worst possible case, the condition equation becomes r_{11}r_{12} — r_{12}r_{21} > 0. This is just an-other way of expressing the requirement that the stability . ,must be less than unity. As a result, the operating gain is conditional when ∂ is greater than unity.

In the typical point-contact transistor under discussion, 8 = 1.19, the conditional equation is (R_{g} + 250) (RL - 11,850) - 150 (- 23,750) > 0. A plot of this conditional characteristic is shown in Fig. 4-7. Any com-bination of generator resistance and load resistance in the stable region can be used, but the selection of operating values close to the condition-al characteristic provides the greatest operating gain.

The following example illustrates the design of a grounded emitter circuit for maximum power gain when the stability factor is greater than one. Assume that the load R_{L} is fixed at 10,000 ohms for the typical point-contact transistor. Figure 4-7 indicates than any value of R_{g}, less than 1,530 ohms will provide stable operation. Thus for R_{g} = 100 ohms

**Fig. 47. Conditional stability characteristic (grounded embitter).**

These examples prove that extremely high values of power gain can be attained by selection of R_{g}R_{L} values close to the stability characteristic. In the practical case, however, the selected values must be sufficiently removed from the instability limit to avoid the introduction of circuit oscillation by normal parameter variations.

The grounded emitter connection can be stabilized by adding resistance in the emitter arm. As an example, assume that a resistor R_{e} = 850 ohms is added in series with the emitter. The four-terminal parameters then become:

Substituting these new values, the conditional equation becomes (R_{g} + 1,100) (R_{L} — 11,000) — (1,000) (— 22,900) and must be greater than zero. A plot of the modified conditional stability characteristic is shown in Fig. 4-7. Notice the extent to which the stability area has been increased. As before, the selection of values R_{L} and R_{g} located near the limiting line provide the greatest power gain.

The maximum available power gain defined by equation 3-55,

can be applied to the grounded emitter connection provided that the stability factor is less than one. The numerical value of the maximum available gain for the typical junction transistor is:

**The Grounded Collector Connection**

* Equivalent Operating Circuit. *

The grounded collector connection is illustrated in Fig. 4-8 (A) . In this connection, the input signal is connected between the base and collector electrodes, and the output is taken between the emitter and the common collector. The equivalent active "T" is illustrated in Fig. 4-8 (B) .

The general four-terminal parameters can be measured in terms of the internal transistor parameters using the basic measuring circuits of Fig. 3-8. The four-terminal parameter equations for the grounded collector connection are:

**Fig. 4-8. (A) The grounded collector connection. (B) Equivalent active "T" for grounded
collector connection.**

**Fig. 4-9. Operating circuit, grounded collector connection.**

Figure 4-9 illustrates the operating circuit for the grounded collector connection. As in the analysis of the grounded emitter circuit, the performance characteristics for this connection can now be determined by straightforward substitution in the general four-terminal circuit equations.

*Current Gain a, of the Grounded Collector Connection. *

The current gain as defined in equation 3-8 is:

In terms of the internal transistor parameters in the grounded collector connection, the current gain becomes:

The value of r_{22} is always negative in the case of the point-contact transistor. Therefore, the load resistor R_{L} must be larger than the absolute value of r_{22} for stable operation, and the equation for maximum current gain can only be applied to the junction transistor. Numerical values for the typical junction transistor when R_{L} = 100,000 ohms are

For the point-contact transistor when RL = 15,000 ohms,

It would appear that as the load approaches the absolute value of r_{22}, extremely high current gains are attainable. For example, for the point-contact transistor when R_{h} = 11,950 ohms,

In operating circuits, however, the grounded collector current gain is limited to the same order of magnitude as in the grounded emitter con-nection. This limitation is caused by the rapid increase in input re-sistance with an increase in current gain.

*Input Resistance, r _{i,} in the Grounded Collector Circuit. *

The general input resistance is defined by equation 3-13:

In terms of grounded collector transistor parameters, the input resistance becomes

The variation of input resistance with load is illustrated for the point-contact and junction transistors in Figs. 4-10 and 4-11, respectively. The input resistance for the point-contact transistor is negative from R_{L} = 0 to R_{L}= — r_{22} = 11,850 ohms. Notice that when Rh = —r22, the input resistance is infinite or open circuited. As R_{L} is increased further, the input resistance becomes positive, and gradually decreases to a limiting value of 12,000 ohms. The input resistance of the junction transistor increases from a value of approximately 500 ohms to the limiting value r_{1} = r_{11} = 2,000,000 ohms when the output is open circuited.

* Output Resistance, r _{o}, for the Grounded Collector Connection. *

The

output resistance is defined by eauation 3-21:

In terms of the internal transistor parameters, the output resistance becomes:

The variation of r_{o} with respect to the generator resistance R_{g} is illustrated for both transistors in Figs. 4-12 and 4-13. In the point-contact characteristic, the output resistance is positive over the range of R_{g}, from 0 to approximately 50 ohms. When the generator resistance is increased beyond 50 ohms, r_{o} becomes negative, and gradually approaches a limit-ing value equal to r_{22}(-11,850 ohms) for large values of R_{g}. The out-put resistance of the junction transistor starts at a value of approximately 75 ohms at R_{g}, = 0 and gradually approaches a value equal to r22 (100,050 ohms) for large values of generator resistance.

**Fig. 4-10. Input resistance vs load resistance for typical point-contact transistor
(grounded collector).**

**Fig. 4-11. Input resistance vs load resistance for typical junction transistor (grounded collector).**

**Fig. 4-12. Output resistance vs generator resistance for typical point-contact transistor
(grounded collector).**

**Fig. 4-13. Output resistance vs generator resistance for typical junction transistor.**

As in the case of the grounded emitter, the grounded collector circuit using the point-contact transistor cannot be matched on an basis without external modification, since the stability factor of this circuit is greater than one. However, the grounded collector does exhibit a unique characteristic when external resistance is added in the collector arm. For example, assume that a resistor R_{c} is added to collector arm so that R_{c} + r_{c} = r_{m}. For this modification,

The image matched input and output equations can be applied to the junction transistor since its stability factor is always slightly less than one. A practical method to use in selecting values to be substituted in these equations indicates that r_{1} should be chosen to equal 2 percent of r_{11}, and r_{2} equal to 2 percent of r_{22}. The exact determination of the image matched resistances in the grounded collector circuit is not important, because the power gain is constant over a wide range of load resistances when the signal generator is matched to the input resistance.

In the junction transistor, numerical values for image matched resistances are

**Fig. 4-14. Conditional stability characteristic (grounded collector).**

The grounded collector circuit can be stabilized by adding an external resistance R_{c} in the collector arm. For example, assume that a resistor R_{c}, = 3,100 ohms is placed in series with r_{c}. The open-circuit parameters now become:

can be applied to junction transistors, since the stability factor is not greater than one. In the grounded collector connection, since ∂ is always very near unity, this equation can be simplified as:

**Fig. 4-15 Equivalent "T"
for reverse operation of grounded
collector connection.**

**Fig. 4-16. Transistor collector Ic-Eo characteristic, illustrating maximum limitotions.**

*Reverse Power Gain in the Grounded Collector Circuit.*

The grounded collector connection also has the unique ability to furnish power gain in the reverse direction. This characteristic might be anticipated on the basis of the equivalent circuit, since the internal generator r_{m}i_{e} is common to both the input and output circuits, and the values of

r_{b} and r_{e} are approximately equal. The equivalent circuit for the reverse connection is illustrated in Fig. 4-15. The resulting four-terminal parameters for this connection can be evaluated in terms of the internal transistor parameters as before:

**Comparison of Transistor Connections**

The analyses of the three basic connections and their operating characteristics apply equally to both point-contact and junction transistors. However, due to the difference in comparative values of the internal transistor parameters, r_{e}, r_{b}, r_{c} and r_{m} the performance of the two basic transistor types is considerably different. In practice, the point-contact transistor is unstable, and has negative input and output resistances. On the other hand, the junction type is generally cheaper to produce, has better reliability, better reproducibility, higher available gain, and a lower noise figure than the point-contact type. It is safe to predict the gradual displacement of the point-contact transistor by the junction transistor in all but a few specialized applications, particularly since the frequency range of the junction type is steadily being in-creased by new manufacturing techniques. In view of this, the remainder of the book will deal primarily with the junction transistor, and unless specified, typical junction characteristics will be assumed.

At this point in the book all the basic design formulas have been derived for the three transistor connections. Thus, a comparison between the general characteristics of the three fundamental connections is now in order.

The grounded base connection is similar to the grounded grid cir-cuit in electron tubes. This connection is characterized by low input resistance, high output resistance, and no phase inversion. Although its current gain is less than one, it provides respectable voltage and power gains. It is well suited for d-c coupling arrangements and for preampli-fiers that require a low input and high output impedance match.

The grounded emitter circuit is the transistor equivalent of the grounded cathode connection in the vacuum tube circuit. This transis-tor connection is the most flexible and most efficient of the three basic connections. The grounded emitter connection reverses the phase of the input signal. Its matched input resistance is somewhat higher than that of the grounded base connection; its matched output resistance is considerably lower. The grounded emitter usually provides maximum voltage and power gain for a given transistor type.

The third connection, the grounded collector, is the transistor equi-valent of the grounded-plate vacuum tube. It is characterized by a volt-age gain that is always slightly less than unity. Its current gain is in the same order as that of the grounded emitter. It has a relatively low output resistance, a high input resistance, and does not produce phase reversal. It offers low power gain, but is capable of supplying reverse power gain. The grounded collector circuit is used primarily as a matching or buffer stage.

** Transistor Limitations**

* Maximum Limits. *

To use the transistor in practical circuits, it is necessary to be aware of its limitations. First, the transistor has limited power-handling capabilities. (The maximum power dissipation rating of a transistor is always specified in the manufacturer's rating sheet.) Because the dissipation rating is relatively low, the operating tempera-ture of the transistor is usually kept in the general temperature range of 50°C to 60°C. Relatively low ambient temperatures are also desirable because germanium is temperature sensitive, and behaves erratically at higher temperatures. In addition, the operating range is limited by the maximum allowable collector voltage (a function of the Zener voltage, previously discussed) , and the maximum collector current. (The values of these latter factors are also specified in the manufacturer's rating sheets.)

Figure 4-16 illustrates the three maximum limitations of a typical transistor having the following specified ratings: maximum collector dissipation — 100 milliwatts; maximum collector voltage — 30 volts; and maximum collector current — 15 milliamperes. The useful region of the collector current-voltage characteristics is necessarily limited to the area contained within these boundaries. In circuit application, none of the limiting factors can be ignored; exceeding any of the limits may damage the transistor. For example, assume that the transistor illustra-ted in Fig. 4-16 is operated as follows: collector current I_{c} = 4 milliam-peres, collector voltage E_{c} = 20 volts, load resistance R_{L}= 10,000 ohms. Assume also that the a-c input signal causes a collector current variation of ± 2 milliamperes. Thus, the output signal varies along the load line between the collector current limits of 2 to 6 milliamperes. The collector current never exceeds the maximum limit of 15 milliamperes, and at peak signal the collector dissipation is 40 volts times 2 milliamperes (80 milliwatts) , which is well within the maximum power limits. How-ever, the collector voltage is now 10 volts greater than the allowable limit of 30 volts. The transistor, therefore, would not be suitable for the assumed operation.

*Minimum Limits. *

The minimum limits of the transistor are gen-erally not critical in practical cases. The minimum collector voltage is set by the non-linear portion of the characteristic curve, which is not reached until the collector voltage is reduced to a few tenths of a volt. The minimum collector current must be greater than the saturation current I_{co}, which is considerably less than 100 microamperes in most junction types. The error introduced by assuming the minimum limits to be E_{c} = 0 and I_{c} = 0 is generally negligible.

*Transistor Noise. *

The minimum signal that can be applied to a transistor is limited by the internal noise generated by the transistor. Since the transistor does not require cathode heating (one of the major noise sources in the vacuum tubes) , it is inherently capable of operat-ing at lower noise levels than its vacuum tube brother. At present, the junction transistor is equal to the vacuum tube, insofar as its noise characteristics are concerned. The noise level of the point-contact types is between 15 and 30 db higher.

There is some confusion in the field as to what is meant by the manufacturers' specifications on noise limits. This confusion is caused by the various manners in which the noise level is specified. The noise level, when specified "with reference to thermal noise," tells the most about the transistor, because the reference value is reasonably fixed. The noise factor on this thermal basis is the ratio of the noise power de-livered to a load compared to the power delivered if the only source of noise were the thermal noise of the signal generator. A second method of noise specification is the "signal-to-noise ratio." The noise figure on this basis does not tell as much about the transistor as the first method, because the signal is not at a constant level. Another method is specification of noise in db above one milliwatt (dbm) . This method is least useful since it neither specifies amplifier gain nor bandwidth.

**Fig. 4-17. Effect of noise on equivalent transistor circuit.**

The noise figure of the junction transistor is about 10 db above thermal noise at 1,000 cps; by selection, values as low as 5 db have been found. These noise levels are comparable with those of the best vacuum tubes available. In general, the noise energy in the transistor is concentrated in the lower frequencies and, as might be expected, the noise factor decreases as the operating frequency is increased. The noise factor is affected by the operating point and the signal generator resistance. It appears to be lowest both at low values of collector voltage and when the generator resistance R_{g} is equal to the input resistance r_{1}. In general, transistors with large collector resistance have a low noise level. Figure 4-17 illustrates the equivalent circuit of the grounded base connection, and includes the equivalent voltages E_{1} and E_{2} introduced by transistor noise.

**Testing Transistors**

*Basic Circuits.*

Although the manufacturer's data sheets for transis-tors are very useful in preliminary paper studies of circuits, it is often necessary to make direct transistor measurements. The block diagram of Fig. 3-8 illustrates the basic circuits for measuring the a-c open-circuit parameters r_{11}, r_{12}, r_{21}, and r_{22}. (Methods for measuring a and I are indicated later in this section.) The following general rules aid the experimenter in obtaining reasonably accurate results for all measure-ments.

- Use an accurate meter calibrated for the appropriate operating range. This is required since the transistor operates on comparatively small values of current and voltage.
- Measure the d-c bias voltages with a very high resistance volt-meter, to avoid meter-shunting effects. Shunting errors are particularly noticeable in the collector circuit which may have resistance of several megohms.
- Connect the test signal (usually 1,000 cps) through a step-down transformer that has an impedance ratio in the order of 500:1. This keeps the measurements independent of Rg and, at the same time, per-mits a low signal input without requiring a low oscillator gain control setting.
- Measure all calibrating resistors with an accurate bridge, or use a calibrated resistor decade box for the resistors.
- Check the waveform with an oscilloscope. The waveform quickly indicates reversed bias connections and overloads.

**Fig. 4-18. Equivalent voltage
method of measuring system input
or output resistance.**

*Equal Voltage Method. *

The equal voltage method is a quick way of determining the input or output resistance of a system when the equipment is limited. This connection is illustrated in Fig. 4-18 (A) .

Resistor R is a calibrated decade box or a helipot in series with the effective input resistance of the system under test. Resistor R is adjusted until its voltage drop V is equal to the input voltage V,. Since the arrangement is a simple series circuit, the input resistance r, is then equal to R.

Figure 4-18 (B) illustrates the equal voltage method for measuring a negative resistance. In this case, a calibrated resistor R_{1} having a larger absolute value than that of the negative resistance is connected in series with r_{1}. Again resistor R is adjusted until V = V_{1}, for which R—R_{1} = r_{1}. For example, suppose a point-contact transistor is operat-ing in its negative resistance region. When a resistor R_{1} = 2,000 ohms is placed in series with the input, it brings the circuit into its positive input region (stable operation) . When the connection of Fig. 4-18 (B) is set up, R = 1,225 causes V to equal V_{1}. Then r_{1} = R—R_{1} = 1,225 — 2,000 = —775 ohms.

Notice that this latter arrangement requires that R be greater than the absolute value of r_{1}. If the only calibrated resistors available are low in value, the parallel method illustrated in Fig. 4-18 (C) can be used. The procedure is the same as before except that when V = V_{1}, R is equal to R_{1}, and r_{1} in parallel,

*Transistor Test Sets. *

Several elaborate transistor test sets are available commercially. These testers are useful for large-scale experimental work, since they incorporate means for completely evaluating the char-acteristics of all types of point-contact and junction transistors, and do not require external test equipment and meters. The home experi-menter and the lab technician, however, can get satisfactory results on breadboards, based on the techniques described on the previous pages.

In checking transistors during maintenance and repair, it is not necessary to check all the transistor parameters. A check of two or three of the performance characteristics will determine quickly whether a transistor needs to be replaced.

**Fig. 4-19. Transistor tester for measuring α and I _{co}.**

Figure 4-19 illustrates a transistor check circuit which will measure the current gain and saturation current with reasonable accuracy. The operation procedure and general functional description of the circuits follows:

- With switch SW2 in the calibrate (CAL) position and switch SW1 in the current gain (a) position, adjust the signal gain of the audio oscillator for one volt across resistor R
_{1}. Now throw SW2 to the current gain (a) position. The signal is now connected to the base of the transistor through resistor R_{2}and the d-c blocking capacitor C_{1}. Since resistor R_{2}is 100,000 ohms, the base and emitter resistances of the transistor are negligible; a-c base current i_{b}, 10 microamperes. - The d-c base current bias is controlled by resistors R
_{3}and R_{4}, which permit a variation of from about 1 to 100 microamperes. R_{4}is adjusted until the collector d-c bias current, measured by meter M, is one milliampere. - Practically all of the a-c output appears across the 100 ohm resistor R
_{5}, because of the high impedance of choke coil L (over 60,000 ohms at 1,000 cps) , and the high output resistance of the transistor (usually more than a megohm) . The output voltage across R_{5}is α i_{b}R_{5}, and since i_{b}= 10 microamperes, R_{5}= 100 ohms, this voltage equals .001α. The value of α may vary from 10 to 100. The a-c voltage may, therefore, range from .01 to .1 volt. Thus, the current amplification can be taken directly on a low scale of a good voltmeter.

Due to the comparatively low value of R_{5}, the measured reading closely approximates the maximum current gain α = r_{12} / r_{21}This value of current gain for the grounded emitter connection can be converted into approximately equivalent values for the grounded base and ground-ed collector circuits by means of the following conversion formulas:

where α_{GE} = maximum current gain for grounded emitter connection; α_{GB}= maximum current gain for the grounded base connection; and α_{GC} = maximum current gain for the grounded collector connection. These relationships are derived by neglecting r_{e} and r_{b} in comparison with r_{m}, r_{c} and (r_{c} — r_{e}.) . Error in this approximation is negligible.

For example, assume that a transistor is tested in the circuit of Fig. 4-19 and produces a reading of .022 volt on the a-c output volt-meter connected across R_{5}. The current gain

The saturation current is read directly on the milliammeter M if switch SW1 is now placed in the I_{co} This switch opens the base lead, removing the bias, and also shorts out the inductor L so that the six-volt battery is across the emitter and collector electrodes.

The circuit as shown is only suitable for N-P-N junction transistors, but can be modified easily for the P-N-P type by incorporating a switch to reverse the battery, the meter connections, and the d-c blocking electrolytic capacitors.