Created it, 05/10/15
Update it, 06/01/16
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SEMICONDUCTORS 6 “12th PART”
FOOT-NOTE :
The curves characteristic of a transistor represent the static values which can be given for any point of operation of this transistor.
They are essential because they make it possible to have a general sight on the behavior of the transistor; in particular, they are very useful to find the point of operation which is appropriate best and thus to determine the circuit of polarization. Once the point of fixed operation, it is often interesting to know the properties of the transistor while being limited to this point and while operating on numbers instead of continuing to use the characteristic curves.
The properties of a transistor relating to a point of particular operation can be defined by means of a certain number of values called parameters.
The coefficient of performance in D.C. current (
and 
according to the type of assembly) is a typical parameter, but this one is not
enough to give a complete indication of the properties of a transistor. Indeed,
two transistors for example, one of very low power and the other of higher
power, can have the same value of coefficient of performance while showing very
different characteristics in addition.
To entirely determine the properties of a transistor, it is thus necessary to call upon several parameters ; more precisely, one needs of them four for a transistor used low frequency, and six when it is about a transistor used in high frequency.
There are various systems of parameters, i.e. the properties of a transistor can be represented according to various systems of four parameters. The choice of one or other system depends only on the type of calculation which one must carry out.
In this theory, the various systems will not be entirely analyzed; one will only take into account more used for the transistors low frequencies, i.e. the system consisted the parameters in h.
Moreover, some data will be provided on another system, also very employed, formed by the parameters in r and also relating to the transistor low frequency.
Lastly, it will be given some indications on the parameters used in high frequency.
Before examining the significance of the parameters out of h, it is first of all advisable to define the resistance of entry and the resistance of exit of a transistor.
1. - RESISTANCE
OF ENTRY AND EXIT IN D.C. CURRENT
Let us consider the circuit of polarization represented figure 1. This circuit makes it possible to regulate the tension of the collector by means of potentiometer PC and the basic current by the variable resistor RB ; it is thus possible to make function the transistor in any point of its characteristics.
Moreover, millivoltmeter VE and microammeter IE make it possible to measure the tension and the basic current (sizes of entry) while the voltmeter VS and milliammeter IS measure the tension and the collector current (output variables).
We fix a point of operation determined by a certain tension VCE and a certain current IB. Under these conditions, it circulates in the circuit of collector a current IC indicated by IS and there exists between the base and the transmitter a tension VBE indicated by VE.
One then calls resistance of entry relating to the point of operation considered and indicated by Re, the value obtained by submitting the relationship between the tension and the current of entry, is :
By measuring tension VBE into mV (this tension is very weak and it is thus advisable to express it in millivolts) and current IB in µA, the Re value will be expressed in kW.
Same manner, one defines the resistance of exit as being the relationship between the tension and the current output, is :
Since the tension of collector is measured in volts and the current in milliamperes, the resistance of exit will be also expressed in kW.
Resistances Re and Rs thus defined are indeed the resistances presented by the transistor ; Re is the resistance which has the basic circuit at the passage of current IB and in the same way, Rs is resistance that the circuit of the collector presents at the passage of current IC, when the transistor functions in a given point of its characteristics.
Since these resistances relate to the behavior of the transistor, when only continuous tensions of polarization are applied on its terminals, these resistances are called static resistances (of entry and exit) or resistance in D.C. current.
The terms “resistance static” indicate that, in the circuit used, no signal to be amplified was applied to the control electrode (the base, in the case of the common transmitting assembly). The transistor is thus in condition of “rest”, i.e. in “statics”.
The values of static resistances of entry and exit can be obtained starting from the characteristics of the transistor instead of taking measurements with the circuit of figure 1.
The complete characteristics relating to a transistor assembled out of common transmitter, are represented figure 2.
To determine the Re values and Rs while being useful of those, it is first of all necessary to set a point of operation.
Let us suppose that it is characterized by the following values : VCE = 4,5 V ; IB = 50 µA, it are located figure 2 by a point A on one of the characteristics of the quadrant numbered I.
Let us plot a horizontal straight line passing by point A and cutting the vertical semi-axis. One reads on this last the value of the collector current relating to the point of operation : IC = 2,8 mA.
It then becomes possible to calculate the Rs resistance which is equal to :
1,6 kWFor the calculation of the resistance of entry, it is necessary to determine tension VBE relating to the point of operation considered.
To obtain this value, the vertical should first of all be traced passing by point A until meeting the characteristic of quadrant IV having like parameter the value of IB relating to the point of operation.
In our example, since IB = 50 µA, the curve which interests us are that which has as a parameter 50 µA ; point D. thus is determined.
Let us trace the horizontal one now passing by the point D and cutting the vertical axis (point C) ; one can read on this one the value of the tension VBE which is 162 mV.
The Re value is thus equal to :
The point D in quadrant IV and point A in quadrant I account for both the point of operation considered ; the only difference is that in quadrant I, one reads on the axes the values of the tension and the collector current, while in quadrant IV, one also reads the tension of collector on the horizontal axis, but on the vertical axis it is the basic tension which is read instead of the collector current.
The same point of operation can also be represented in quadrants II and III respectively by the point B and C. Indeed, these points are both located on the vertical passing by the value IB = 50 µA read on the left semi-axis horizontal, which means that the transistor has a current of basic polarization of 50 µA ; these points moreover are located on the characteristics having like parameter the value VCE = 4,5 V, which means that the transistor functions with a tension of collector of 4,5 V.
These values (VCE = 4,5 V and IB = 50 µA) are not other than those of the point of operation considered in our example. The point of operation of the transistor being fixed, one can thus conclude that this one can be represented by four distinct points, one in each quadrant.
These points (A, B, C, D on figure 2) are always laid out on the tops of the angles of a rectangle whose sides (in dotted on the figure) cut the four semi-axes according to values' of the four electric quantities (VCE, IC, VBE, IB) characterizing the point of operation considered.
It should be noted that, of the four points mentioned those the most adapted to determine resistances of exit and entry are respectively point A and the point C. Indeed, Si one traces point A, the horizontal line and the vertical line up to the points of meeting with the axes, one obtains the values VCE and IC which will be used to us to determine Rs.
In the same way, if one plots starting from the point C the horizontal straight line and the vertical line up to the points of meeting with the axes, one obtains the values of VBE and IB which we will use to determine Re.
Until now, only the common transmitting circuit was taken into account ; it is however obvious that one can use the same reasoning for the assembly bases common and in this case also, one can determine a resistance of entry and a resistance of exit.
Since for the assembly bases common, the sizes of entry are tension VEB and the current of transmitter IE while the output variables are the tension collector bases VCB and current IC, one will have obviously:
These resistances can be given starting from the characteristics of the transistor which must be now those of the assembly bases common. The procedure to be followed is identical to that used for the common transmitting assembly.
2. - RESISTANCE OF ENTRY AND EXIT
IN AC CURRENT
Let us consider again the circuit of figure 1.
Let us suppose that one regulated RB and PC so as to make function the transistor in a certain point of his characteristics and that V'BE, I'B, V'EC and I'C are the values of the tensions and the currents indicated by the apparatuses.
Now let us act on RB in order to increase the basic current I'B up to value I"B ; consequently, the tension base-transmitter will also increase and voltmeter VE will indicate either the value V'BE but a larger value, V"BE.
In other words, one increases the basic current
of I"B - I'B which one notes 
IB
and one note a corresponding increase in the tension base-transmitter V"BE
- V'BE noted VBE.
One thus defines the dynamic resistance of entry
or resistance of entry into alternate which
one indicates by re ; its value is :
VBE /
IBIt can happen that the increase of IC which is obligatorily caused by the increase in IB involves a reduction in tension VCE. If that occurs, for reading the values of I"B and V"BE, it is necessary to bring back VCE to its initial value while operating PC.
Indeed, the dynamic resistance of entry must be calculated by maintaining constant the value of the tension of collector VCE, and this for the simple reason that this tension always has a certain influence on the values of the current and the basic tension.
In a way similar to that used previously, one now
operates PC in order to increase the tension
of collector of a value VCE
while carrying it of the value V'EC to the
value V"EC ; an increase in the
collector current and basic current are thus obtained.
If it is wanted that the increase in the collector current is not due partly to that of the basic current, one must act on RB in order to bring back the basic current to his initial value I'B.
One can then read on milliammeter IS
new value I"C and the increase in the
collector current thus equal to I"
- I'C is C noted IC.
One then defines the dynamic resistance (or in AC current) of exit which one indicates by rs, its value is :
VCE
/ ICThe name of “resistance in AC current” or “dynamic resistance” given to resistances of entry and exit which have just been defined, is due to the fact that these values are those which the transistor present at the passage of the AC current (superimposed with the D.C. current of polarization) constituting the signal to be amplified applied to the entry of the transistor or that amplified taken at the exit.
It is interesting to note that the transistor behaves in a very different way with respect to the alternative D.C. current of polarization and that constituting the signal.
Also, the values of resistances in D.C. current and AC current are in general very different one from the other.
To have an idea of the existing difference between these values, it is advisable to calculate re and rs for the point of operation considered in the preceding example.
For the re determination, it is necessary to cause an increase in IB and to see which increase in tension VBE results from this (by maintaining of course constant the value of the tension of collector).
While referring to the characteristic of entry (quadrant III) of figure 2, one can see that the point of operation C must move on the curve having for parameter 4,5 V (since it is the value of the tension of collector relating to the point of operation considered).
Let us suppose that one increases the basic current by 50 µA with 70 µA: the point of operation passes from C in C' as indicated figure 3. So tension VBE increases, passing by 162 mV to 177 mV.
The re value relating to the point of operation C is thus equal to :
VBE
/ IB
= (177 - 162) / (70 - 50) = 15 mV / 20 µA = 0,75kWIn a similar way, one can determine the dynamic resistance of exit starting from the characteristics indicated to quadrant I deferred figure 4 below.
Let us suppose that one increases the tension of collector of 4,5 V with 6,5 V by maintaining constant the value of the current basic ; the point of operation of the transistor passes then from A in A'. The A' point is also on the characteristic having like parameter IB = 50 µA (see figure 4 below).
This increase in VCE runs the collector current of 2,8 mA to 3,1 mA as one can read it on the vertical scale of figure 4. One thus deduces the value from it from the dynamic resistance of exit :
VCE
/ IC
= (6,5 - 4,5) / (3,1 - 2,8) = 2 V / 0,3 mA
6,67 kW
As one can notice it by comparing the results obtained with those of the preceding example, the transistor, although functioning at the same point of its characteristics, presents values of resistance of entry and exit at the D.C. current very different from those presented at the AC current.
Indeed, the resistance of entry is higher in the first case (3,24 kW against 0,75 kW) while in the second case the resistance of exit increases appreciably (of 1,6 kW).
In the assembly bases common, one can in the same manner of defining a dynamic resistance of entry and exit.
One can graphically determine their value using the characteristics of the transistor in assembly bases common or in experiments by measuring the increases in current and tension on the circuit bases common.
In a circuit of this type, the sizes of entry are represented by the tension transmitter-bases VEB and the current of transmitter IE while the output variables are given by the tension collector-bases VCB and current IC.
One deduces the following formulas from them :
VEB
/ IE
; Rs = VCB / IC ; rs = VCB
/ IC
3. - HYBRID PARAMETERS
The hybrid parameters (symbolized by the letter “h”) are four for the transistors used low frequency.
To distinguish these parameters, indices with two digits are used. The four parameters are then located in the following way : h11, h12, h21, h22.
The hybrid parameters correspond to the type of assembly used. Thus, one distinguishes those relating to the common transmitting assembly, those relating to the assembly bases common and those relating to the common collecting assembly. It is thus necessary to provide to differentiate them to know to which type of assembly they refer.
For this reason, the index is supplemented by the letter “e” in the case of the common transmitting assembly, by the letter “b” in the case of the assembly bases common and by the letter “c” in the case of the common collecting assembly, from where symbols :
The definition of each parameter and the way of deducing the values from them are identical for the three types of assembly. To simplify, we will limit ourselves to the case of the common transmitting assembly.
Let us return to the diagram of figure 1 above and regulate RB and PC at the point of operation for which the value of the hybrid parameters is required.
Let us make undergo a small increase with current
IB by making sure that the value of the
tension collector remains constant (by improving PC,
if necessary). Let us call IB
the
value of this increase. In the same way, let us indicate by VBE
the corresponding increase in the basic tension and by
the IC increase in the
collector current. These notations are indicated figure 5.
The parameters h11e and h21e are defined by the following formulas :
VBE
/ IB
with constant VCEIC
/
IB with constant VCEOne can immediately see what these parameters indicate or more precisely which is their physical significance ?
The parameter h11e is not other than the resistance of entry in AC current. Indeed, its value is given by the relationship between the increase in VBE and the increase in IB to constant tension of collector ; it is defined in the same way that was to it the resistance of entry in the preceding paragraph. The value of h11e is thus expressed in W (or in kW) since it is about a resistance.
The parameter h21e
on the other hand, represents the relationship between the rush of the current
of collector and the increase in the basic current with constant tension of
collector. It is thus the coefficient of performance in AC current. As
the characteristics represented in quadrant II
are comparable to lines passing by the origin, it is considered that the
coefficient of performance in D.C. current
and that the coefficient of performance in AC current h21e
are equal.
To determine the other parameters h, let us consider again the diagram of figure 1. Let us make grow the tension of collector while operating PC, without forgetting to improve RB to bring back IB to its initial value.
One indicates respectively by VCE,
IC
and VBE,
the increase in the tension of collector and the increases which
result from this for the collector current and the tension basic, as indicated
figure 6.
The values of h22e and 12th are given by the following formulas :
IC
/ VCE
with constant IBVBE
/ VCE
with constant IBOne notices that the parameter h22e is the relationship between the increase in the collector current and the increase in the tension of collector with constant basic current, i.e. the reverse of the resistance of exit in AC current.
The reverse of resistance being defined by the conductance, the parameter h22e thus represents the conductance of exit into alternate of the transistor ; its value is expressed in units of conductance, i.e. in mho (S) or millisiemens (mS) or in microsiemens (µS), but one generally gives it in mA / V (milliampere per volt), unit equivalent to the millisiemens or in µA / V (equivalent with the µS).
Lastly, the parameter h12e is given by the relationship between the increase in the basic tension and that of the tension of collector which caused it (with constant basic current). This parameter is called coefficient of reaction in tension, since it expresses the influence of the output voltage on the tension of entry.
Generally, the tension of entry only is little influenced by the output voltage, i.e. the increase in VBE is always much weaker than that of VCE. Consequently, h12e is always very small, about a few thousandths or less.
By taking again the same reasoning, but this time
for a circuit bases common, one can define the hybrid parameters h11b,
h21b, h12b, h22b. Here however, the parameter h21b
is appreciably equal to the coefficient 
.
In conclusion, let us see the definition which it is possible to give to the various parameters :
It is important to recall that the first two parameters must be measured by maintaining the output voltage constant, while the two others must be measured with constant current of entry.
It should be noted that the symbol h (initial of the English term hybrid) allotted to these parameters is due to the fact that they are not homogeneous with regard to their measuring units. Indeed, while two of them (h21 and h12) are pure numbers thus without dimension, the first (h11) is a resistance and the last (h22) a conductance.
By observing the formulas which define the various hybrid parameters, one notices that figure 1 refers to the entry and figure 2 to the exit. Thus, h11 indicates the parameter obtained by the ratio of two sizes of entry. Of the same way, h21, h12 and h22 respectively indicate the parameters obtained by the relationship of an output variable with a size of entry, of a size of entry with an output variable and finally between two output variables.
There also exists of other terms to define the indices of the parameters. Indeed, h11 is sometimes indicated by hi because it represents the resistance of entry (“I” being the initial one of input = entered).
The parameter h21 is also indicated by hf because it represents direct amplification, i.e. the amplification which a current undergoes “while going from the entry towards the exit” (“f” being the initial one of forward = direct).
The parameter h12 can be replaced by hr, because it expresses a reaction in “opposite” direction (“r” being the initial one of reverse = opposite), i.e. between the entry and output voltages.
Lastly, the parameter h22 can be replaced by ho because it represents the conductance of “exit” (“o” being the initial one of output = left).
4. - VALUES
OF THE PARAMETERS ACCORDING TO THE POINT OF OPERATION
The properties of a transistor depend in a more or less large way of its point of operation.
It is thus obvious that the hybrid parameters will also depend on the point of operation, i.e. they will vary when one moves this one on the characteristic.
For this reason, when one indicates the values of the parameters h, it is necessary to specify with which point of operation they are referred.
In the case of transistor BC 108B for example, the parameters h given for a common transmitting assembly (not of operation : VCE = 5 V and IC = 2 mA at the frequency of 1 kHz and the temperature of 25° C) are as follows :
To know the values of the hybrid parameters relating to points of operation different from that for which the values were given, it is necessary to use suitable diagrams that one finds in the handbooks of the manufacturers. An example of these graphs is represented figure 7 ; they relate to transistor BC 108B and are used for to pass from the point characterized by VCE = 5 V and IC = 2 mA at an unspecified point located in the allowed zone of the characteristics of the transistor in question.
The diagram of the figure 7-a below takes account of current IC of the new point of operation, while that of the figure 7-b relates to tension VCE.
Let us suppose that one wants to calculate the parameters h of transistor BC 108B for the point of operation characterized by VCE = 9 V and IC = 7 mA. The curve hie of the figure 7-a gives us for IC = 7 mA the value KI = 0,36 while that of the figure 7-b gives for VCE = 9 V the value KV = 1,05.
The value h'ie relating to the level of the point of operation is obtained by the following formula in which hie is the value relating to the point of initial operation :
h'ie = hie x KI x KV = 4,8 x 0,36 x 1,05 = 1,81 kW
While proceeding in the same way for the other parameters, one finds the values following :
For hfe : KI = 1,1 ; KV = 1,05 thus h'fe = 330 x 1,1 x 1,05 = 381
For hre : KI =
1,15 ; KV = 0,87 thus h're = 0,0002 x 1,15 x
0,87
0,00020
For hoe : KI = 4,6 ; KV = 0,79 thus h'oe = 30 x 4,6 x 0,79 = 109 µA / V
Although the diagrams of figure 7 relate to transistor BC 108B, they can nevertheless give an idea of the variation of the hybrid parameters relating to the common transmitting assembly for any type of transistor of low power used low frequency, when the current and the tension of collector vary.
By observing the diagram of the figure 7-a, one can say that, when IC increase, the resistance of entry of the transistor (tamper) decreases appreciably; the conductance of exit (hoe) grows on the other hand considerably and as the conductance is the reverse of resistance, one deduces from it that the resistance of exit strongly decreases when the collector current increases. The coefficient of performance while running hfe remains, as for him, practically constant.
In the same way, by observing the diagram of the figure 7-b, one can say that the resistance of entry (tamper) and the coefficient (hfe) remain appreciably constant when the tension of collector increases, while the conductance of exit decreases slightly, which means that the resistance of exit increases slightly.
5. - INFLUENCE
OF THE TEMPERATURE ON THE VALUE OF THE HYBRID PARAMETERS
The hybrid parameters, like the characteristics, vary when the temperature to which the transistor is (or better its junctions) varies. The values indicated in the handbooks relate, in general, to the temperature of 25° C.
To know the new values which take the hybrid parameters when the temperature changes, one can refer on the figure 8 which represents a diagram similar to those of figure 7. This one provides the coefficient KT by which one must multiply the values of the parameters h, relating to the temperature of 25° C, to pass to those relating to another temperature ranging between - 60° C and + 80° C, for transistors of low power used low frequency.
The diagram of figure 8 makes it possible to note that above 25° C, all the parameters increase with the temperature, the resistance of entry and increasing coefficient of performance the less quickly than the conductance of exit and the coefficient of reaction.
While carrying, for example, the temperature of 25° C to 70° C, the conductance of exit becomes four times and half larger, which means that the resistance of exit becomes four times and weaker half, while the coefficient hfe becomes on the other hand only 1,1 times larger.
In lower part of 25° C, the resistance of entry and the coefficient of performance decrease gradually with the temperature, while the conductance of exit and the coefficient of reaction recover to grow. The coefficient hfe, for example, is tiny room of 22 % at the temperature of - 25° C.
6. - DETERMINATION
OF THE PARAMETERS “h” FROM THE CHARACTERISTICS
The value of the parameters h can be given starting from the families of characteristics of the transistor by obviously considering the point of operation which interests us.
To calculate the value of the parameter hie, the procedure to be followed is the same one as that indicated figure 3 since, as one saw, this parameter coincides with the resistance of entry in AC current.
To determine the parameter hoe, one proceeds in a way similar to that indicated figure 4 to the difference that it will be necessary to submit the relationship between the increase in the collector current and that of the tension of collector, since this parameter coincides with the reverse of the resistance of exit.
The parameter hfe is given starting from the characteristics of quadrant II. It is enough to take an increase in the collector current in correspondence with the increase in the basic current when the tension of collector remains constant.
Lastly, there remains the calculation of the parameter hre. On this subject, it should be observed that this parameter is determined very with difficulty on the characteristics of quadrant IV because of its generally low value.
End of this first lesson and to finish this one, we will continue on another page entitled “Semiconductor 6 - 2nd part”. (Paragraph 17.1. See summary electronics fundamental).
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