A number of current-voltage plots are available for the analysis and design of a transistor circuit. The static characteristic curves give information on the value of current flowing into or out of one terminal, for either a given current flowing into or out of another terminal, or a given voltage applied between two terminals. Four sets of characteristics can be plotted for each configuration: (a) the input characteristic, *(b) *the transfer characteristic, (c) the output characteristic and *(d) *the mutual characteristic. In this book, however, the characteristics for the common-base and the common-collector circuits will not be discussed. Two versions of set *(c) *are available.

The method of determining the static characteristics of a transistor is to connect the transistor into a suitable circuit and then to vary the appropriate currents and/or voltages in a number of discrete steps, noting the corresponding values of the other currents at each step. Fig. 10. shows a suitable circuit for the measurement of the static characteristics of an n-p-n transistor in the common-emitter configuration.

The collector and base currents are shown as flowing into the transistor and are therefore, by definition, positive; the emitter current is shown flowing out of the transistor and must be taken as negative. If the static characteristics of a p-n-p transistor were to be measured, the polarities of the two batteries would need to be reversed.

*(a) *Common-emitter Input Characteristic

The *input characteristic *shows the way in which the base current varies with change in the base-emitter voltage, the collector-emitter voltage remaining constant. The input characteristic is measured by maintaining the collector-emitter voltage constant at a convenient value and increasing the base-emitter voltage in a number of discrete steps, noting the base current at each step. This procedure is then repeated for a different but constant value of collector-emitter voltage *V _{CE}, *since any change in this voltage has an effect on the input characteristic. A typical input characteristic is shown in Fig. 11. The input resistance,

*h*of the transistor for a given base-emitter voltage

_{ie },*V*is given by the reciprocal of the slope of the curve at that point. For example, consider the input resistance of the transistor at the point

_{BE }*V _{BE} = *0.7 V.

*h _{ie} = δV_{BE}/δI_{B} *=

*V*constant) (1.13)

_{be}/I_{b}(V_{CE}= 0.02/(22 X 10^{-6}) = 909 Ω

The corresponding p-n-p characteristics would have negative values of *I _{B}, V_{BE} *and

*V*

_{CE}.Since the input characteristic is non-linear, the a.c. input resistance of a transistor will vary with the base current. For example,

when *I _{B} = 2 μA h_{ie} *- 6.7 kΩ

Some manufacturers' data sheets give a graph that shows how *h _{ie }*varies with the collector current.

The d.c. input resistance *h _{IE} *is given by the ratio

*V*At the point of measurement

_{BE}/I_{B}.*h _{IE} *= 0.7/(25xl0

^{-6}) = 28 kΩ

It is evident that a considerable difference may exist between the values of *h _{IE} *and

*h*If the point of measurement is reduced below about

_{ie}.*V*0.68 V, the slope of the input characteristic is much smaller and hence the a.c. input resistance

_{BE}=*h*will be larger so that any difference between

_{IE}*h*and

_{IE}*h*will be much less. For base currents of the order of a few tens of microamps

_{ie}*, h*is typically about 3 kΩ.

_{ie}*(b) *Common-emitter Transfer Characteristic

The *transfer characteristic *shows how the collector current changes with changes in the base current, the collector-emitter voltage being held at a constant value. For this measurement the collector-emitter voltage is kept constant and the base current is increased in a number of discrete steps and at each step the collector current is noted. Finally a plot is made of collector current against base current. Since the transfer characteristic is not independent of the value of the collector-emitter voltage, the procedure can be repeated for a number of different collector-emitter voltages to give a family of curves; Fig. 12. shows a typical n-p-n transistor transfer characteristic.

The slope of the transfer characteristic gives the short-circuit current gain *h _{fe} *of the transistor.

*h _{fe} = δI_{C}/δI_{B} = I_{C}/I_{b} = *(l X 10

^{-3})/(4Xl0

^{-6}) = 250

### (c) Common-emitter Output Characteristic

The *output characteristic *illustrates the changes that occur in collector current with changes in collector-emitter voltage, for constant values of base current. Alternatively, the collector current can be plotted against collector-emitter voltage for constant values of base-emitter voltage. The base current, or the base-emitter voltage, is set to a convenient value and is then maintained constant and the collector-emitter voltage is increased from zero in a number of discrete steps, the collector current being noted at each step. The collector-emitter voltage is then restored to zero and the base current, or the base-emitter voltage, is increased to another convenient value and the procedure repeated. In this way a family of curves (see Figs. 13 and 14) can be obtained. For the corresponding p-n-p characteristic the polarities of *I _{c}*,

*I*and

_{b}*v*should be changed to negative.

_{ce}The slope *δI _{C}/δV_{BE} *of the output characteristic is the

*output admittance, h*of the transistor.

_{oe},The *output resistance *of the transistor is equal to the *reciprocal *of the slope of the output characteristic. From Fig. 13 the output resistance at the point

*V _{CE} = *6 V and

*I*30 μA is

_{B}=*R*_{out}*, **= 1/ h _{oe} *=

*δV*=

_{ce}/δI_{C}*V*constant) (1.14)

_{ce}/I_{c}(I_{B}= 2/0.2xl0^{-3}) = 10 000 Ω

The output admittance *h _{oe}, *and hence the output resistance, varies somewhat with the d.c. collector current. Manufacturers* data sheets may include a graph showing

*h*plotted against

_{oe}*I*

_{c}.When a characteristic is non-linear its slope will vary according to the point of measurement and therefore the point of measurement should always be quoted. It is usual, unless specified otherwise, to measure the slope in the middle of the characteristic. For the greatest accuracy the increments taken either side of the chosen point should be as small as possible although this has not been done in this chapter in order to clarify the diagrams.

The output characteristics of Fig. 13 can also be used to determine the short-circuit current gain *h _{fe} *of the transistor, since, for a given value of collector-emitter voltage

*V*the change in collector current

_{CE},*δI*produced by a change in base current

_{B}*δI*can be obtained by projecting from the appropriate curves. Thus, for

_{B}*V*

_{C}

_{E}*= 4 V a change in the base current from 20 μA to 30 μA*

*will produce a change in the collector current from 2.1 to 2.9 mA. The current gain*

*h*is therefore equal to

_{fe}[(2.9 - 2.1)x 10^{-3}]/[(30-20)xl0^{-6}] = 80

The current gain *h _{fe} *of a transistor is not a constant quantity but varies with the d.c. collector current. Fig. 15 shows a typical graph of

*h*plotted against

_{FE}*I*Manufacture’s data generally quote the collector current at which the maximum value of

_{c}.*h*is obtained, e.g. for me BC 108 the typical

_{fe }*h*is 180 at

_{fe}*I*2 mA. (Both

_{c}=*h*and

_{fe}*h*vary.)

_{FE}It will be seen that Fig. 13 shows a collector current flowing even when the base current is zero. This current is the *common-emitter leakage current, *symbol *I _{CEO}, *which is related to the common-base leakage current

*I*according to the expression

_{CBO}*I _{ceo} *=

*I*1

_{CBO}(*+h*

_{FE}) (1.15)*Example 6*

The collector leakage current *I _{CBO} *of a transistor is 10 nA. If the d.e. current gain of the transistor is

*h*0.995, calculate (

_{fb}=*a*) the collector leakage current when the transistor is connected with common emitter, and (

*b*) the d.c. collector current if a d.c. base current of 10

*μ*A is supplied to the base.

*Solution*

*h _{FE} = *0.995/(1 -0.995) = 199

(*a*) *I _{ceo} *= 10 X 10

^{-9}X 200 = 2 μA

*(Ans.)*

*(b) I _{c} = h_{FE}I_{B} + I_{CEO} = *199 x 10 x 10

^{-6}+ 2 x l0

^{-6}

= 1-992 mA *(Ans.) *

(Clearly the contribution of the collector leakage current is negligibly small.)

The collector leakage current *I _{CBO} *of a common-base transistor is extremely temperature-sensitive and is approximately doubled for every 12°C rise in temperature for silicon transistors and every 8°C rise for germanium transistors. However, the leakage current of a silicon transistor at a given temperature is much less than the leakage current of an equivalent germanium transistor at the same temperature.

Typically, *I _{cbo} *at 20°C may be about 10 μA for a germanium transistor but only about 10 nA for a silicon transistor.

*(d) *Common-emitter Mutual Characteristic

The *mutual characteristics *of a common-emitter connected transistor show the changes in collector current that occur with changes in the base-emitter voltage, with the collector-emitter voltage held constant. Fig. 16 shows a typical mutual characteristic. The slope of the mutual characteristic is the mutual conductance *g _{m} *of the transistor.

Thus, when *V _{BE} *changes from 0.6 V to 0.65 V the resulting change in

*I*is from 1.5 raA to 11.5 mA and so

_{c}*g _{m} = δI_{c}/δV_{BE} *= (10 x 10

^{-3})/0.05 = 200 mS

The mutual conductance can also be determined from the output characteristics of Fig. 14 using a similar method to that employed to obtain *h _{fe} *from Fig. 13. When

*V*= 8 V, a change in

_{CE}*V*from 610 mV to 630 mV causes

_{BE}*I*to vary from 3.3 mA to 6.7 mA. Hence

_{c}*g _{m} = δI_{c}/δV_{BE} = *(3.4 X 10

^{-3})/(20 X 10

^{-3}) = 170 mS

Also *g _{m} = δI_{c}/δV_{BE }(1.16)*

= *(δI _{C}/δI_{B}) *X

*(δ1*

_{B}/δV_{BE})*= h _{fe}/h_{ie }*(3.17)

The mutual conductance *g _{m} *depends only on the d.c. collector current

*I*according to the equation

_{c},*g _{m} = I*

_{C}/26mS (3.18)

where *I _{c} *is in mA.

Thus for the transistor just considered *I _{c} *= (3.3 + 6.7)/2 = 5 mA, and

*g*= 5/26 - 192 mS.

_{m}From equation (3.7), the voltage gain of a transistor is given by *A _{v} *=

*A*This can be written as

_{i}R_{L}/R_{in}.*A*=

_{v}*h*and, using equation (3.16)

_{fe}R_{L}/h_{ie}*A _{v} = g_{m}R_{L} *(3-19)

*Example 7*

An 18 mV peak signal is applied to the base of a common-emitter connected transistor. The resulting change in the collector current is 2 mA. Calculate *(a) *the mutual conductance of the transistor, *(b) *the current gain of the transistor, *(c) *the d.c. collector current, *(d) *the value of collector load resistance that will give a voltage gain of 220 and *(e) *the output voltage. The transistor has an input resistance of 1200 Ω.

*Solution*

*(a) g _{m} = *(2 X 10

^{-3})/(18 x 10

^{-3}) = 111 mS

*(Ans.)*

*(b) h _{fe} *=

*g*= 111 x 10

_{m}h_{ie}^{-3}x 1200 = 133

*(Ans.)*

(c) *I _{c}* =

*26g*- 26 X 111 X 10

_{m}^{-3}= 2.9mA (

*Ans*.)

*(d) *220 = 111 x 10^{-}^{3 }*R _{L}, *therefore

*R*= 1982 ≈ 2000 Ω

_{L}*(Ans.)*

*(e) V _{out} *= 220 x 18 x 10

^{-3}= 3.96V

*(Ans.)*