ECE3243 (Chapt 2)
Diode circuit problems
Vers 2.2
Defaults: All resistances in kΩ and currents in mA unless otherwise specified
2-1. For the circuis shown, find the values of the voltages and currents indicated using the ideal rectifier model.
+5V
(A)
(B)
(C)
I2
10
V2
V1
I1
(D)
10
10
I4
I3
V3
20
40
V4
+2.0V
40
GND
2-2. For the circuits of problem 2-1, find the values of voltage and currents indicated using the constant-voltage-drop (0.7V)
model.
2-3. For the diode circuit shown find the values of voltage and
current indicated for
(a) the ideal rectifier model and
(b) the constant-voltage-drop (0.7V) model
+10V
10
I1
V1
(HINT: Use nodal analysis)
20
20
GND
2-4. For the diode circuit shown find the values of voltage and
current indicated for
(a) the ideal rectifier model and
+50V
10
(b) the constant-voltage-drop (CVD) (0.7V) model.
I2
40
V2
(c) for part (b) find the power dissipated in the diode.
(HINT: Use nodal analysis)
20
40
GND
2-5. For the diode circuit shown find the values of voltage and
current indicated for the constant-voltage-drop (CVD)) (0.7V)
model. And find the power dissipated in the diode string.
(HINT: Apply nodal analysis at nodes V3 and V4.
+10V
10
I2
25
V4
V3
Answers: {7.29V, 5.89V, .0889mA}
40
25
GND
2-6 (a) Identify all permissible options for the diode circuit shown when the resistances R1, R2, R3, R4 are not specified. Use
“1” to indicate that the diode is conducting and “0” to indicate that the diode is non-conducting. (b) Solve for ID1, ID2, ID3,
ID4 assuming that all diodes = “on” (one of the possible options) and R1 = 40kΩ, R2 = 25 kΩ, R3 = 20 kΩ, R4 = 50 kΩ. Use the
CVD model (VD = 0.7V ).
D4 D3 D2 D1
+10
R2
R4
D2
D1
D4
D3
R3
R1
-10.7
2-7 (a) Identify all permissible options for the diode circuit shown when the resistances R1, R2, R3, R4 are not specified. Use
“1” to indicate that the diode is conducting and “0” to indicate that the diode is non-conducting. (b) Solve for ID1, ID2, ID3,
ID4 assuming that all diodes = “on” (one of the possible options) and R1 = 20kΩ, R2 = 50 kΩ, R3 = 25 kΩ, R4 = 25 kΩ. Use the
CVD model (VD = 0.7V ).
D4 D3 D2 D1
+11.4
R3
R1
D3
D1
D2
R2
R4
-8.6
D4
2-8. A 1.0A power diode (i.e. 1.0A at 0.7V) is used in series with a resistance of value 20Ω and a voltage source of value
10.68 VDC. The current through the diode is 0.5A. What is the effect on the power dissipated in the diode if an identical
diode is placed in parallel with this diode? Assume the ideal diode model with emission coefficient n = 1.
2-9. A voltage regulator which uses a 6.8V Zener in series with a 100Ω resistance, intended for operation with a 9.0V supply
is accidentally connected to a 15V supply. Assume that the Zener resistance rZ = 10Ω
(a) Determine the current IZ and the power dissispated in (1) the Zener diode and (2) the resistance, for the intended
power supply of 9V.
(b) Determine the current IZ and the power dissispated in (1) the Zener diode and (2) the resistance, for the unintended
power supply of 15V.
Answers: {(a) 20mA, 0.14W, .04W (b) 74mA, 0.562W, 0.555W }
2-10. Assume a zener diode for which VZ = 6.2V, rZ = 100Ω
+12V
(a) for RL = 6 kΩ and IZ = 0.5 mA, find VO, and the value
of R1 necessary to achieve these levels.
(b) Assume R1 = 3 kΩ and find VO and IZ when
RL = 10 kΩ.
R1
VO
(HINT: Make use of nodal analysis at VO ).
RL
GND
2-11. The circuit shown represents a voltage-reduction circuit
designed for use for plug-in of a 9-V cellphone into an automotive
environment. Automobile batteries range from 12.0 to 13.6V,
depending on their condition and on other loads. The cellphone
requires a maximum of 0.5W power at full volume. The maximum
power that can be dissipated by the 9V Zener diode is 1W.
RS
+
-
(a) Choose resistance RS such that the Zener diode always remains in
reverse breakdown (maintains regulation) with current of a minimum
of 1.0 mA.
(b) Determine the power dissipated in the Zener under worst-case
conditions and the minimum power rating of resistance RS.
Answers: { 53Ω, 0.78W, 0.4W }
VBAT
Cellphone
2-12. A simple half-wave AC-DC converter, as shown, is used to
provide a rough DC source for a 400 Hz, 40Vrms aircraft system. If
itis desired that the ripple VR be less than 2.4V, determine
(a)
(b)
(c)
(d)
VP and VL(avg)
The minimum value of C that will be required.
PIV rating for the diode (Max reverse voltage + 50%)
ID(avg)
ID
+
VL
C
40Vrms
RL = 50Ω
Neglect the voltage drop across the diode.
2-13. Design an AC-DC converter using a full-wave bridge that provides an average DC outout voltage of +15V with maximum ripple 0.6V when supplying a 50Ω load. The converter is supplied by a 120VAC (rms) line source through a transformer, with turns ratio to be determined. Assume that the diodes are approximately ideal rectifiers.
(a) What is the maximum AC (rms) voltage that must be applied across the rectifier bridge, and the turns ratio necessary
for the transformer?
(b) What is the mimimum size of filter capacitance needed?
(c) What is the required PIV rating of the diodes (Max reverse voltage + 50%)?
(d) What is the average current through the diodes during conduction and the power dissipated in the diodes?
Answers: { (a) VS = 10.82V, n1/n2 = 11.09, (b) C = 4330 µF, (c) PIV = 45.9V, (d) ID(av) = 3.74A, PD = 2.67W }
2-14. The circuit shown is the basic form of an AC voltmeter. Note
that the diodes form a full-wave bridge. Assume that the meter has
internal resistance rM = 100 W and requires 0.4 mA for full-scale
reading. Using time average of the rectified input signal, determine
the value of R necessary for full-scale reading to correspond to an
input of 20Vrms at Vin. What maximum VA will occur at the output
of the opamp?
Vin
VA
meter
rM
R
AC Voltmeter
2-15. Construct the transfer curve for -10V < VI < +10V. Indicate
plainly all corners and slopes.
+10V
VO
4kΩ
VI
2kΩ
4kΩ
2-16. For the circuit shown determine the transfer curve ( VO vs VI )
for -5.0< VI < +5.0
+10V
10
Hint: Identify which diodes remain ON when VI > 4.65 V
VO
VI
10
10
-10V
2-17. Assume that each Zener diode has rZ = 50Ω, VZ = 3.3V, and
that each junction diode has internal resistance 50Ω and VD = 0.7V.
Construct the transfer curve for -15V < VI < +15V. Indicate plainly
all corners and slopes.
+
+
Answer: {slope1 = 1.0, Vbrk = 8.0V, slope2 = .091}
VI
VO
-
-
2.0kΩ
2-18. Assume ideal rectifier model, and construct the transfer curve
for -10V < VI < +10V. Indicate plainly all corners and slopes.
Hint: Assume that the diode state is (ON, OFF) according to polarity
and apply nodal analysis. And make use of symmetry.
+
VI
VO
-
2kΩ
2kΩ
2kΩ
2-19. For a square-wave input VI of amplitude + 4.5V to -4.5 and frequency 5 kHz, determine the steady-state response of
each of the circuits shown. Assume C = 10 µF and R = 1 kΩ.
C
(A)
C
(B)
VI
VI
VO
VI
VO
R
VO
R
GND
(D)
C
(C)
R
GND
(E)
C
VI
VO
GND
(F)
C
VI
VO
C
VI
VO
2R
R
R
GND
2-20. For the Zener-regulated FWB battery-eliminator
shown, we desire to choose component values so that
+9VDC is produced from a 240V 50Hz European
power line. The maximum current to be required is
approximately 100 mA.
(a) Choose the transformer turns ratio n such that the
peak capacitance voltage is greater than 9V. Note that
VP =
2 Vrms .
R
R
GND
GND
R1
VA
VL = 9 VDC
Radio
240VAC
50Hz
C1
VZ
n
(b) Choose an appropriate value for VZ such that VL
will be approximately 9V
(c) Now choose values for R1 and C1 such that the ripple component VR is less that 5% x VP under full-load conditions.
(d) Evaluate circuit to determine the maximum power dissipated in each component. If the power exceeds 1.0W in any
component (including resistance R1) revise choices of R1 and C1 .
2-21. The alternator of an automobile can be represented by the circuit shown. The alternator consists of
three coils, energized sequentially at phase angles that
are 120o with respect to each other by the rotating electromagnet . The three phases are rectified by diodes
D1, D2, and D3. The charging voltage applied to the
battery is sampled by a control circuit which adjusts the
strength of the electromagnet rotor by means of a
dependent source.
D1
D2
R1
+
-
gVx
The resistance R1 = wiring resistance = 0.1Ω
CTRL
(a) Consider the case in which VB = 11.6V and determine VP such that the charging current will be 50 A.
(b) Determine the ripple in VP that results
(c) Determine the mechanical power in HP necessary
to provide this current. (note: 746W = 1 hp)
D3
Answers: { VP = 17.4, VR = 2.33, PM = 1.11HP }
2-22. For the square-wave input shown, and using the
assumption that the diodes are ideal rectifiers (VD = 0),
show that, at equilibrium
V1
C
2V P
V 2 = -----------------------------( 1 + R1 ⁄ R2 )
Assume that τ1 = R1C >> T/2 and τ1 = R2C >> T/2,
where T = period of waveform.
Hint: At equilibrium I1 = I2
R1
VI
2V P
= -----------------------------( 1 + R2 ⁄ R1 )
R2
GND
VI
VI
+VP
+V1
-VP
-V2
VO
VB