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SPICE methods o er a frequency sweep option that allows a small-signal, sinusoidal steady-state analysis of a circuit. The frequency sweep is invoked by a control statement of the following format: .AC DEC points start freq end freq
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Node voltages and device currents are inherently complex number values. The magnitudes and phase angles of calculated quantities can be retrieved by the Probe feature of PSpice by appending a p and n, respectively, to the variable. For example, magnitude and phase angle of the voltage between nodes 2 and 3 are speci ed by Vm(2,3) and Vp(2,3).
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Example 8.9. For the BJT ampli er circuit of Fig. 3-10, assume CC ! 1. The small-signal equivalent circuit is given by Fig. 8-4 where RB R1 kR2 . Let hoe hre 0, hfe 90, R1 1 k, R2 16 k, RE 500 , CE 330 F, RC 1 k, and RL 10 k. Use SPICE methods to determine the low-frequency cuto point.
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CHAP. 8]
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The netlist code that follows describes the circuit:
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Ex8_9.CIR vi 1 0 AC 0.250V R1 1 0 1kohm R2 1 0 16kohm Vsen 1 2 DC 0V Rhie 2 3 200ohm Fhfe 3 4 Vsen 90 RE 3 0 500ohm CE 3 0 330uF RC 4 0 1kohm RL 4 0 10kohm .AC DEC 25 10Hz 10kHz .PROBE .END
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Execute hEx8_9.CIRi and use the Probe feature of PSpice to yield the plots of Fig. 8-13. From the marked points, it is seen that the low-frequency cuto is fL 214:4 Hz, where the voltage gain has a value of AvL 289:7:
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Fig. 8-13
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The above example utilized the small-signal equivalent circuit. Small-signal analysis frequency sensitivity can also be implemented using the SPICE model of the transistor directly.
Example 8.10. For the BJT ampli er of Fig. 3-10, let Ri RE 0, RC 3 k, R1 1 k, R2 15 k, CC1 CC2 1 F, and VCC 15 V. The transistor can be modeled by the parameters of Example 3.4, except Rb 10 , Rc 100 , and Cje 100 pF. Use SPICE methods to graphically show the voltage gain magnitude and phase angle over the frequency range of 100 Hz to 1 GHz and to determine the low- and high-frequency cuto points where fL depends on the value of the bypass capacitor CE and fH depends on the BJT junction capacitance values.
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[CHAP. 8
The following netlist code describes the circuit:
Ex8_10.CIR vi 2 0 AC 0.250V Cc1 2 3 1uF R2 6 3 15kohm R1 3 0 1kohm VCC 6 0 15V RC 6 4 3kohm Cc2 4 7 1uF RL 7 0 5kohm Q 4 3 0 QPNPG .MODEL QPNPG PNP(Is=10fA Ikf=150mA Ise=10fA Bf=150 +Br=3 Rb=10ohm Rc=100ohm Va=30V Cjc=10pF Cje=100pF) .AC DEC 100 100Hz 1GHz .PROBE .END
Execution of hEx8_10.CIRi and use of the Probe feature of PSpice results in the plots of Fig. 8-14 where it is seen that the midfrequency range extends from fL 197:3 Hz to fH 238:3 MHz.
Fig. 8-14
Solved Problems
8.1 Calculate and tabulate the di erence between the asymptotic and exact plots of Fig. 8-2, for use in correcting asymptotic plots to exact plots.
The di erence " may be found by subtraction. For 0 ! 1 :  For the Mdb plot, (1)
"Mdb 0 f 10 log 1 ! 2 g 10 log 1 ! 2
CHAP. 8] 1 For ! > :  and for the  plot, For 0 For ! 0:1 : 
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"Mdb 10 log ! 2 10 log 1 ! 2 10 log 1 1= ! 2
" 0 tan 1 ! tan 1 ! " 458 log 10! tan 1 ! " 908 tan 1 ! tan 1 ! 908
(3) (4) (5)
0:1 10 <!< :   10 : 
For ! !
Application of (1) to (5) yields Table 8-1.
Table 8-1 ! 0.1/ 0.5/ 0.76/ 1/ 1.32/ 2/ 10/
Bode-Plot Corrections "Mdb 0.04 1 2 3 2 1 0.04 " 5.78 4:98 2:48 08 2.48 4.98 5:78
The s-domain transfer function for a system can be written in the form T s Kb z1 s 1 z2 s 1 sn p1 s 1 p2 s 1 1
where n may be positive, negative, or zero. Show that the Bode plot (for Mdb only) may be generated as a composite of individual Bode plots for three basic types of terms.
The frequency transfer function corresponding to (1) is T j! From de nition 3 of Section 8.2,  Mdb 20 log jT j! j 20 log which may be written as Mdb 20 log Kb 20 log j1 j!z1 j 20 log j1 j!z2 j 20n log j j!j 20 log j1 j!p1 j 20 log j1 j!p2 j  Kb j1 j!z1 jj1 j!z2 j j j! n jj1 j!p1 jj1 j!p2 j 3 Kb 1 j!z1 1 j!z2 j! n 1 j!p1 1 j!p2 2
It is apparent from (4) that the Bode plot of T j! can be formed by point-by-point addition of the plots of three types of terms: 1. A frequency-invariant or gain-constant term Kb whose Bode plot is a horizontal line at Mdb 20 log Kb .
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