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An inequality is a statement that quantities are not equal. If two quantities are unequal, the first is either greater than or less than the other. The inequality symbols are: , meaning unequal to; , meaning greater than; and , meaning less than. Thus, 4 3 is read four is unequal to three ; 7 2 is read seven is greater than two ; and 1 5 is read one is less than five. Two inequalities may be of the same order or of opposite order. In inequalities of the same order, the same inequality symbol is used; in inequalities of the opposite order, opposite inequality symbols are used. Thus, 5 3 and 10 7 are inequalities of the same order; 5 3 and 7 10 are inequalities of opposite order. Inequalities of the same order may be combined, as follows. The inequalities x y and y z may be combined into x y z, which states that y is greater than x and less than z. The inequalities a b and b c may be combined into a b c, which states b is less than a and greater than c.

The unit of current, the ampere (A), is de ned as the constant current in two parallel conductors of in nite length and negligible cross section, 1 meter apart in vacuum, which produces a force between the conductors of 2:0 10 7 newtons per meter length. A more useful concept, however, is that current results from charges in motion, and 1 ampere is equivalent to 1 coulomb of charge moving across a xed surface in 1 second. Thus, in time-variable functions, i A dq=dt C/s). The derived unit of charge, the coulomb (C), is equivalent to an ampere-second. The moving charges may be positive or negative. Positive ions, moving to the left in a liquid or plasma suggested in Fig. 1-1(a), produce a current i, also directed to the left. If these ions cross the plane surface S at the rate of one coulomb per second, then the resulting current is 1 ampere. Negative ions moving to the right as shown in Fig. 1-1(b) also produce a current directed to the left.

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Find the input impedance Zin of the circuit of Fig. 3-10(a) in terms of the h parameters, all of which are nonzero.

Table 1-3 Pre x pico nano micro milli centi deci kilo mega giga tera Factor 10 10 9 10 6 10 3 10 2 10 1 103 106 109 1012

Axioms are statements that are accepted as true without proof and are used in the same way as theorems.

The small-signal circuit of Fig. 6-13, with RB R1 R2 = R1 R2 , is applicable if a dependent source hre vce is added in series with hie , as in Fig. 6-1(a). The admittance of the collector circuit is given by G hoe and, by Ohm s law, vce By KVL applied to the input circuit, ib vi hre vce hie 2 hfe ib G 1 1 1 RL RC

CHAP. 1]

AXIOM 1:

In terms of the CB h parameters for the ampli er of Fig. 6-15(a), nd (a) the input impedance Zin , (b) the voltage gain Av , and (c) the current gain Ai .

Fig. 1-1

AXIOM 2:

Of more importance in electric circuit analysis is the current in metallic conductors which takes place through the motion of electrons that occupy the outermost shell of the atomic structure. In copper, for example, one electron in the outermost shell is only loosely bound to the central nucleus and moves freely from one atom to the next in the crystal structure. At normal temperatures there is constant, random motion of these electrons. A reasonably accurate picture of conduction in a copper conductor is that approximately 8:5 1028 conduction electrons per cubic meter are free to move. The electron charge is e 1:602 10 19 C, so that for a current of one ampere approximately 6:24 1018 electrons per second would have to pass a xed cross section of the conductor.

If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.

(a) The h-parameter equivalent circuit is given in Fig. 6-15(b). By Ohm s law, vcb hfb ie hfb ie hob 1=RC 1=RL G vS hrb vcb hib ie 1

EXAMPLE 1.2. A conductor has a constant current of ve amperes. How many electrons pass a xed point on the conductor in one minute 5 A 5 C=s 60 s=min 300 C=min 300 C=min 1:87 1021 electrons=min 1:602 10 19 C=electron

AXIOM 3:

CHAP. 6]

v2

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