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Unformatted text preview: 232 CHAPTER 6 8. Find the Thévenin equivalent seen at A—B for the circuit
of ﬁgure P6.8. Him: For this type of problem, the more natural
solution technique is source transformations; why? V3
_ 7.
9. Find the Thevenin equivalent seen at AﬂB for the circuit
of ﬁgure P69. Hint: Find Rth ﬁrst; then identify the appropriate
supernode and use nodal analysis to ﬁnd V00. Figure P69 ANSWER: Rth : 8 k9, VOC = 4.5 V. 10.. Find the Thévenin equivalent of the circuit of ﬁgure P6.10
enclosed in the dashed box. Then compute IL and the power
absorbed by the Z—k $2 resistor. Hint: There is some extraneous
information. tﬁgure P610 ANSWERS: 52 V, 24 kg, 2 mA. ii. (a) Find the Thévenin equivalent circuit for the two—
terminal non—series~parallel network of ﬁgure P6.11. Use
MATLAB to solve the equations. (in) If a load resistance R L is connected to terminals A—B,
use MATLAB to calculate and plot the power absorbed by
the load for 10 5 RL 5 200 S2 in 5—9 steps. 100 (2 1009 Figure P611
ANSWERS: (a) 12°C 2 2VS/3, Rth : 100 S2. THEVENIN, NORTON, AND MAXIMUM POWER TRANSFER THEOREMS Thévenin and Norton Equivalents for Active
Circuits 12. Find the Thévenin equivalent of the circuit of ﬁgure P6.12
as a function of Cl. Figure £36.12 2.5 ._+_OL 9
1.5 13. Find the value of gm so that the Thévenin equivalent resis
tance of the circuit of ﬁgure P613 is —40() k9. ANSWER: U00 2 O, Rth 2 Figure PGJE 3 ANSWER: gm 2 10 its.
M. For the circuit of ﬁgure P6.14, ﬁnd the Norton equivalent
Circuit. 200 S2 300 S2 Figure R814 ANSWER: —600 32, [SC 2 0.
15. Use loop analysis to compute the Thévenin equivalent for
the circuit of ﬁgure P6.15. What is the Norton equivalent? Figure mi 5 ANSWER: V0C = 0, Rm = 100 $2. Figure P6.’ :7. (3) Find the Norton and Thévenin equivalents of the circuit of ﬁgure P6.17.
(b) If a load resistor R L is attached across the output termi— nals,plot the power absorbedby the load for 1 g R L 5 24 S2
using MATLAB or equivalent. For what value of R L does
the load absorb maximum power? 41'] Figure 136.17 ‘_SWERS: v00 2 18 V, Rth = 12 52,1’SC = 1.5 A, 12 £2.
. Find the Thévenin equivalent of the circuit in ﬁgure P6.18. I Figure P619 (‘1) 5/6 V, 95/6 9, 1/19 A; (b) —1/3, 20 52. 233 20. For the circuit of ﬁgure P620, ﬁnd the Thévenin equivalent. 300 o 100 9
WV Figure P620 ANSWERS: Rth = 400 52, V00 2 0. (Note that the value of VS makes no difference to V09. Why?)
21.. (a) Find the Thévenin equivalent for the network of ﬁg ure P621.
(1)) If the value of each independent source is cut in half, what is the new V06? 100 v [Figure 96.21 ANSWERS: (a) 1.6 k9, —260 V; (b) V00 2 —130 V. Find the Norton equivalent for the circuit of ﬁgure P622. Figure P622 ANSWERS: isc = 150 mA downward, —100 £2. In ﬁgure P623, replace the circuit to the left of nodes A
and B with its Thévenin equivalent and ﬁnd i and the power consumed by the 609 resistor. Figure P623 CHECK: voc = 18 V, Rth = 15 £2. < 3 24. Find the Thévenin and Norton equivalents of the circuit of ﬁgure P624 as follows: l r g 234 CHAPTER 6 THEVENIN, NORTON, AND MAXIMUM POWER TRANSFER THEOREMs
l .. N... . .. v.2“ ..,.",..,.,.....d..._. ,,,.,..,.....,, .2. H. W... , A ,
l a (a) Redraw the circuit, add an external variable indepen—
dent voltage source vs, and indicate the loop currents on the
diagram. Label the two unknown loop currents as 11 and [2,
with [1 associated with the external source vs. Note that us
is not considered an unknown. (in) Add the voltage variable v to your circuit diagram
across the appropriate (internal) source, according to the
method of modiﬁed loop analysis. (c) Write three independent equations in the three un— knowns 11, [2, and 1).
(ti) Write these equations in matrix form as follows: 11 .
12 = 7 03+
1) ‘7 (e) Solve using MATLAB. In particular ﬁnd 11 in terms of Us and a constant.
(1") Find ISC and Rth. Hint: Review equation 6.11. (3) Find Voc
(b) Sketch the Thévenin and Norton equivalent circuits. 552 20 mA ﬁgure 96.24 ANSWERS: VOC = 12.5 V, Rm = 650 $2.
' Find the Thévenin equivalent seen at A—B for the circuit of
ﬁgure P625 as follows:
(a) Excite terminals A—B with an external independent
current source is, following the development of equa tion 6.10.
(5)») Write nodal equations with unknowns VA, VC, VD, and VE.
(c) Express the equations in matrix form as follows: ???‘7VA ? ?
???‘7VC_?+?
???9VD“?‘S?
‘2??va 7 ? (ti) Use MATLAB to solve the equations. In particular, ex
press VA in terms Of i s and a constant. Compare with equa— tion 6.10 tO determine Rth and voc.
(e) If the l—mA source becomes an 8mA source, ﬁnd the new values of Rth and voc. A stz lmA Figure P625 ANSWERS: (d) Rth = 5.8182 ko, voc = 3.8182. Op Amp Circuits 26. Find the Thévenin equivalent seen at terminals A~B for the
Op amp circuit of ﬁgure P626. Figure P626 ANSWERS: 1200 = 4VS, Rth = 20 S2. 27. (a) Find the Thevenin equivalent seen at terminals A—B for
the op amp circuit of ﬁgure P627.
(b) If a 1629 load resistor is attached across terminals A—B, ﬁnd the resulting voltage gain VA 3 / V5. 10052 +
C W M
200
w»
IZkSZ 1809;
OB Figure E3627 ANSWERS: (a) voc = 3.6VS, Rth : 18 52; (b) 3.24. 28., (35) Find the Thévenin equivalent to the right Of terminals
A~B for the (ideal) op amp circuit of ﬁgure P628.
(b) If the practical source indicated in the ﬁgure is attached
to A—B, ﬁnd the current I s in terms of VS. 15m
A W»
————— no +
10m ’
WV
4m; 12k§2
..... __o__.
B ___ Figure P628
ANSWERS: (a) VCC = 0, Rth = —5 k9; (b) 0.2 x 10—3Vs 6—9 CEﬂmﬁ“ (Qu'la Ulcj=0 é—F—n—F b/L: Fecha Asunto: — p r s . Hoja de Hoja d? Hoja de Fecha Hoja de
#—> .
Asunto: Fecha . _ . Hoja de
———> _
Asunto: .. . _ Hoja de Fecha Hoja de
p—II'.> .
Asunto: . .. 7 7 <S+l§ﬁz)\/x= gVoC,
L§+L§Q~ L§+stVocj 3Voc, §+trﬂz=qm+83 Vac, \
=  11.
Vac, 0 ME §+ I: o 3
IJfW/l/l/I’ [AgUK & 4 V’E. :
Jr '5 3 3' alrm‘i/ll 3‘ Hoja de JADEm,“
‘ l 70””; w 41m.. BomA= Vtﬂrw Vﬂm =55“
V1= 36w.46'b/I' = v [CC/L W1”): <5"%ro = 0.03 + o.o(o[c1.4)+ ISL
 Igc= 0.044—033— 0.14.4. o. 2.. 3+30W ﬁlSV wv/wsa ...
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 Spring '08
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