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Table 3-2 Parameter Is Ikf Isc Bf Br Rb Rc Va Cjc Cje Description saturation current high current roll-o base-collector leakage forward current gain reverse current gain base resistance collector resistance forward Early voltage base-collector capacitance base-emitter capacitance Major Impact " Is, # VBEQ # Ikf, # IC " Isc, " IC " Bf, " IC " Br, " rev. IC " Rb, # diB /dvBE " Rc, " VCEsat # Va, " diC =dt high freq. response high freq. response Default 1 10 1 0 100 1 0 0 1 0 0

Example 3.2. Use SPICE methods to generate the CE collector characteristics for an npn transistor characterized by (a) the default parameter values and (b) a reasonable set of values for the parameters appearing in Table 3-2. (a) Figure 3-5(a) shows a connection method to obtain data for the collector characteristics. The netlist code that follows will generate the desired data for default parameter values.

CHAP. 10]

Ex3_2.CIR Ib 0 1 0uA Q 2 1 0 QNPN *Q 2 1 0 QNPNG VC 2 0 0V .MODEL QNPN NPN() ; Default BJT *.MODEL QNPNG NPN(Is=10fA Ikf=150mA Isc=10fA Bf=150 *+ Br=3 Rb=1ohm Rc=1ohm Va=30V Cjc=10pF Cje=15pF) .DC VC 0V 15V 1V Ib 0uA 150uA 25uA .PROBE .END

Execute hEx3_2.CIRi and use the Probe feature of PSpice to produce the collector characteristics for the default BJT model (QNPN or QPNP) shown by Fig. 3-5(b).

(c) The function f such that f (x) = [x] for all x is discontinuous at each integer, because condition (i) is not satis ed (see Fig. 7-12). The discontinuities show up as jumps in the graph of the function. (d) The function f such that f (x) = |x|/x for all x = 0 is discontinuous at 0 [see Fig. 8-1(b)]. lim f (x) does not exist and f (0) is not de ned. Notice that there is a jump in the graph at x = 0.

($28,000 $4,000) / 32,000 hours = 0.75 times 7,200 hours = $5,400 Solved Problem 15.4 Equipment costing $9,600, with an estimated scrap value of $1,600, was bought on July, 1, 1999. The equipment is to be depreciated by the straight-line method for a period of 10 years. The company s scal year is January through December. Show the journal en try to record the equipment s cost on the balance sheet for December 1999. Solution: Equipment Less: Accumulated Depreciation $9,600 400

Fig. 3-5

CHAP. 3]

If a function f is not continuous at a, then f is said to have a removable discontinuity at a if a suitable change in the de nition of f at a can make the resulting function continuous at a. EXAMPLES In example (a) above, the discontinuity at x = 0 is removable, since if we rede ned f so that f (0) = 1, then the resulting function would be continuous at x = 0. The discontinuities of the functions in examples (c) and (d) above are not removable. A discontinuity of a function f at a is removable if and only if lim f (x) exists. In that case, the value of the

(b) Edit hEx3_2.CIRi to move the leading asterisks up one position on both the transistor speci cation statement and the .MODEL statements. Execute the revised hEx3_2.CIRi and use the Probe feature of PSpice to produce the collector characteristics for the generic BJT model (QNPNG or QPNPG) as displayed by Fig. 3-5(c). Example 3.3. Apply SPICE methods to determine the CE transfer characteristics for the generic npn transistor (QNPNG). Figure 3-6(a) presents the connection method chosen for determination of the transfer characteristics. The associated netlist code follows:

Fig. 3-6

function at a can be changed to lim f (x).

Ex3_3.CIR Vbe 1 0 0V Q 2 1 0 QNPNG Vc 2 0 1V .MODEL QNPNG NPN(Is=10fA Ikf=150mA Isc=10fA Bf=150 + Br=3 Rb=1ohm Rc=1ohm Va=30V Cjc=10pF Cje=15pF) .DC Vbe 0V 2V 0.01V Vc 0V 2V 0.2V .PROBE .END

$9,200

Execution of hEx3_3.CIRi and use of the Probe feature of PSpice yields the desired transfer characteristics displayed by Fig. 3-6(b). Example 3.4. Using SPICE methods, determine the CB collector characteristics for the generic pnp transistor (QPNPG). Figure 3-7(a) shows the circuit for use in the determination. The netlist code below describes that circuit.

A function f is said to be continuous on a set A if f is continuous at each element of A. If f is continuous at every number of its domain, then we simply say that f is continuous or that f is a continuous function. EXAMPLES

Fig. 3-7