Transconductance
We h:I\’C seen that one of the important p.u amctcrs used in the truusistor models uf the last section the emitter resistance r., depends on the de bias current by way of the relation
In fact. all small-signal parameters depend on dc operating conditions, some to a greater extent than others. Our goal now is to develop a transistor model that reflects that dependency better than the models of the previous section. One of the advantages of the model is that it permits liS to perform (approximate) small signal analysis based entirely on a knowledge of the dc characteristics of a transistor.
We begin with a discussion of a new small-signal parameter, 11’lI1l.\·CO/Il/IIc/lIl1(,l!, whose approximate value can be found using only de quantities. Transconductance is another derived parameter that is widely used in the analysis of electronic devices of all kinds, It is designated g”, and is defined as the ratio of a small-signal output current to a small-signal input voltage, with de output voltage held constant:
Output Resistance
The out rut resistance of a CE’ transistor can also he determined values. I{ccall that
Instcad of output resistance. the output is used in many transistor models:
The Transconductance Model
Figure 5-44 shows a CE transistor model based on the parameters we have discussed’ in this section. Note that the current source representing collector current is now labeled g”‘U, .•.. From tcquation 5-73. we have i, = gmu’ ••.• so the current source. is correctly labeled. Because the model utilizes gll” it is often calk-d transconductunce .
Example 5-11
The results of the preceding example show that the voltage gain of the amplifier
We see that there is good agreement between the calculations. 5-5
SMALL SIGNAL PARAMETER EQUIVALENTS: h PARAMETERS
In Chapter <) we will study the theory and application of a set of jerived parameters called It PIIJ'(JII/(‘/(‘J’s. These arc used as the basis for constructing liybrid models of electronic devices of many different kinds. Transistor data sheets often (1’ ovide values for small-signal II parameters instead of or in addition to the physical parameters we have discussed so far. For that reason, and because some electronic devices courses do not have time to cover II parameters in depth, Table 5-1 shows a list of upproxirnatc parameter equivalents and conversions. In h-parameter notation, the second subscript attached to the letter h identifies the parameter as a CB. CC, or CE parameter: b = CO; c = CC; and e = CEo For example, h;,., h”., hI'” and h,•. are common-emitter parameters, while hj”, II”.. “I)” and h”” are common-base parameters.
Example 5-12
Use the It-parameter specifications given in Figure 5-47 to find the quantities listed, in connection with the circuit shown in Figure 5-48. (Assume a “low gain” device having (3oc = 100.)
1. the small-signal {3of the transistor
2. the transconductance of the transistor
3. the emitter resistance r,
4. the output resistance of the amplifier stage
5. the voltage gain U,/US
Solution
We first find the collector bias current, so we can determine the smalf signal parameters from the graphs given in the specifications:
Using the graphs showing h parameters versus collector current we find the following approximate values when lc = 1 mA in a low-gain device:
1. From Table 5-1, the small-signal {3 = hi’ == 100.
2. From Table 5-1,
3. From Table 5-1,
4. From Table 5-1,
