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Topic 1
Semiconductor valves and their characteristics
Questions
1.1. Explain the nature of valve properties of p-n-junction.
1.2. Explain the amplifying properties of transistor.
1.3. Explain the process of switching on of the thyristor.
1.4. Basic ratios for the transistor circuit with common base.
1.5. Basic ratios for the transistor circuit with common emitter.
1.6. Basic ratios for the transistor circuit with common collector.
1.7. Peculiarities of power uncontrolled valves connected in parallel.
1.8. Peculiarities of power uncontrolled valves connected in series.
1.9. Inductive current dividers principle of operation.
 di 
1.10. Rate of current change   and its influence on power valves operation.
 dt 
 du 
1.11. Rate of voltage change   and its influence on power valves operation.
 dt 
1.12. Give the example of contactless power switches with bidirectional
conductivity.
1.13. Give the basic parameters of power uncontrolled switches.
1.14. Give the basic parameters of power thyristors.
1.15. Give the basic parameters of power transistors.
1.16. What is triac?
1.17. What is photothyristor?
1.18. What parameters of power semiconductor valves influence on their frequency
properties to a great extent?
1.19. What is electronic analog of thyristor, transistor, semiconductor uncontrolled
diode?
1.20. Advantages and drawbacks of power thyristors in comparison with power
transistors.
1.21. What is composite transistor? Give its main features.
1.22. Draw a circuit of composite transistor which consists of three individual
transistors.
1.23. Draw an equivalent circuit of thyristor and explain the positive feedback
action during the process of its switching on.
1.24. What are the peculiarities of a number of thyristors connected in parallel.
1.25. What are the peculiarities of a number of transistors connected in parallel and
in series.
Problems
1.1. Define the average value of rectified current id , RMS values of the
currents in secondary and primary windings in the circuit depicted in Fig. 1.1 if
ktr  1, U1  220 V , Rd  10  . Losses in the transformer and magnetizing currents
are negligible. The valve VD is ideal.
VD
i2
i1
e2
id
Rd
Fig. 1.1.
1.2. Given U1  220 V , f  50 Hz , ktr  1, Rd  10  , Ld  0,01 H . Valve
VD and transformer Tr are ideal. Define the average value of load voltage U d ,
average value of load current id , maximum value of the valve reverse voltage
UVD max . Plot the curve of the load current id and the curve of primary transformer’s
current i1 .
VD
Tr
U1
Rd
e2
Ud
Ld
Fig. 1.2.
1.3. Given U1  220 V , f  50 Hz , ktr  1, Rd  10  , Ld  0,01 H . The
valves VD1, VD2 and the transformer Tr are ideal. Define the average value of
load voltage U d , average value of load current id . Plot the curves: the valve VD1
voltage U VD1 , the load current id , the currents i1 , i2 and iVD 2 .
VD1
Tr
i2
U1 i1
e2
id
VD 2
Rd U d
Ld
Fig. 1.3.
1.4. Define the calculated power of the transformer Tr shown in Fig. 1.4.
The losses are negligible. Given: U1  220 V , U 2  6,3 V , U 3  15 V , U 4  30 V ,
I1  0,2 A , I 2  2 A , I 3  1 A , I 4  0,5 A .
Tr
i2
i3
U1 i1
i4
U2
U3
U4
Fig. 1.4.
1.5. Define the calculated power of the transformer depicted in Fig. 1.5.
Given ktr  1, U1  220 V , Rd  10  . Losses in the transformer and magnetizing
currents are negligible. The valve VD is ideal.
VD
i2
i1
id
e2
Rd
Fig. 1.5.
1.6. Explain the difference between the powers P1 and P2 for the circuit
shown in Fig. 1.6. Why do they exceed the load power Pd  U d  I d . Losses in the
transformer and magnetizing currents are negligible. The valve VD is ideal.
VD
i2
i1
e2
id
Rd
Fig. 1.6.
1.7. Given U1  220 V , ktr  1, Rd  10  . Taking into account that the
valves are ideal and the losses in transformer are negligible, define the constant
component of rectified voltage and current ( U d and I d ). Find RMS value of
transformer’s primary winding current I1 . Plot the curve of reverse voltage of
valve.
VD1
ia1
e2a
Rd
U1 i1
e2b
ia 2 VD 2
Fig. 1.7.
1.8. Given U AB  U BC  U CA  220 V , E2 a  E2b  E2 c  100 V , Rd  10  ,
X d   . The circuit is depicted in Fig. 1.8. Define the RMS value of transformer’s
primary winding current I1 .
A
B
C
i1
e2a
e2b
e2с
Rd
Xd
VD1
VD 2
VD3
Fig. 1.8.
1.9. Given U A  U B  U C  220 V , ktr1 
w11
w
1
, Rd  10  .
 1 , ktr 2  12 
w21
w22
3
Define constant component of rectified voltage U d , RMS value of transformer’s
Tr1 primary winding current I1 . Plot the voltage on the valve VD 4 . The valves and
transformers are considered to be ideal.
A
B
C
О
i1
Tr1
VD1
Fig. 1.9.
VD 2
Tr 2
VD3
VD 4
Rd
1.10. Given U AB  U BC  U CA  220 V . Transformation coefficients for the
transformers Tr1 and Tr 2 are: ktr1  1, ktr 2  2 . Load resistance Rd  10  .
Neglecting the losses in valves and power transformers define the calculated power
of the transformers Tr1 and Tr 2 .
A
B
C
i11
i12
Tr1
Tr 2
i21
i22
Rd
Fig. 1.10.
Topic 2. Commutation processes in uncontrolled rectifiers
2.1. Given: U1  100 V , ktr  1, Rd  10  , X a  5  . For the circuit shown
in Fig. 2.1 define the constant component of the rectified voltage U d and current
id .
Xa
e2a
VD1
Rd
U1 i1
e2b
Xa
VD 2
Fig. 2.1.
2.2. Given: U1  100 V , ktr  1, Rd  10  , X a  5  , X d   . The circuit
under consideration is depicted in Fig. 2.2. Define U d , I d , I1 . Plot the curve of
voltage on the valve VD1.
e2a
Xa
VD1
Rd
Xd
U1 i1
e2b
Xa
Fig. 2.2.
VD 2
2.3. For the circuit in Fig. 2.3 find RMS value of primary winding
transformer’s current if U1  220 V , E2  100 V , Rd  10  , X d   , X a  5  .
Plot the curve of voltage on the valve VD1.
Xa
Tr
U1
VD 4
VD1
VD3
VD 2
Rd
Xd
e2
i2k
Fig. 2.3.
2.4. For the circuit shown in Fig. 2.4 define leakage X a reactance of power
transformer’s windings if U1  220 V , ktr  2,2 , X d   .
Xa
e2a
VD1
Rd
Xd
U1 i1
e2b
Xa
VD 2
Fig. 2.4.
2.5. For the circuit shown in Fig. 2.5 given: U1  220 V , ktr  2,2 . When the
load current changes from I d 1  10 A to I d 1  6 A , rectified voltage U d is changed
by the value 10 V. Find the current I1 in primary transformer’s winding if the load
current is equal to I d  8 A .
Xa
Tr
U1
VD 4
VD1
VD3
VD 2
e2
Rd
Xd
Fig. 2.5.
2.6. Given: E2  100 V , X d   . The circuit is shown in Fig. 2.6. When load
resistance Rd is changed from 10 to 5 Ω, constant component of rectified voltages
is changes by 8 V. Plot the external characteristic of the rectifier Ed  f  I d  .
Calculate X a .
Xa
e2a
VD1
Rd
Xd
U1
e2b
Xa
VD 2
Fig. 2.6.
3.7. For the circuit depicted in Fig. 2.7. given: U1  220 V ,
E2  100 V , Rd  10  , X d   . Commutation angle   15 . What value the
primary current I1 is changed if load resistance Rd is changed from 10 to 5 Ω.
Xa
Tr
U1
VD 4
VD1
VD3
VD 2
e2
Rd
Xd
Fig. 2.7.
2.8. Given U AB  U BC  U CA  U1  220 V , X a   , X d   , E2  100 V ,
Rd  10  . For the circuit shown in Fig. 2.8 find current I1 of the primary
transformer’s winding. Plot the voltage on valve VD1.
A
B
e2a
e2b
C
i1
e2с
Rd
Xa
Xa
Xa
Xd
VD1
Fig. 2.8.
VD 2
VD3
2.9. Given: U AB  U BC  U CA  U1  220 V , E2  100 V , X a  1  , X d   ,
Rd  10  . The circuit under consideration is depicted in Fig. 2.9. Find the current
I1 in the primary transformer’s winding. Plot the valve voltage U VD curve.
A
B
e2a
e2b
e2с
Xa
Xa
Xa
C
i1
VD 4
VD1
VD6
VD3
VD 2
VD5
Rd
Xd
Fig. 2.9.
2.10. Given: U AB  U BC  U CA  U1  220 V , ktr  1,27 , X d   . When
current I d is changed from 10 to 4 A, load voltage is changed by 6 V. Plot the
external characteristic Ed  f  I d  . Calculate X a .
A
B
C
i1
Tr
e2a
ia1
ia 2
Xa
e2b
e2с
Rd
ia 3
Xa
Xa
Xd
VD1
Fig. 2.10.
VD 2
VD3
id
Topic 3. Controlled rectifiers
3.1. Given: U1  220 V , E2  100 V , Rd  10  ,   30 . The circuit is
shown in Fig. 3.1. Define RMS value of primary transformer’s winding current I1 .
Plot the curve of thyristor voltage U T .
T1
e2a
Rd
U1
e2b
T2
Fig. 3.1.
3.2. Given: U1  220 V , E2  100 V , Rd  10  , X d   ,   30 . The
circuit is depicted in Fig. 3.2. Find RMS value of zero valve current I 0 and
primary winding transformer’s current I1 .
T1
VD0
e2a
Rd
Xd
U1
e2b
T2
Fig. 3.2.
3.3. For the circuit in Fig. 3.3 find RMS value of primary winding
transformer’s current I1 if U1  220 V , ktr  1, Rd  10  , X d   ,   30 . Plot
the curve of voltage on the thyristor.
A
U1
B
U1
C
i1
e2a
T1
e2b
e2с
T2
Rd
T3 X
d
Fig. 3.3.
3.4. Given: Rd  10  , X d   ,   30 , E2  100 V . The circuit is shown
in Fig. 3.4. Find i2a .
C
B
A
e2b
i2a
e2a
Rd
Xd
Fig. 3.4.
3.5. Given: X a  1  , Rd  10  , X d   . The circuit is shown in Fig. 3.5.
At   0 Ed  100 V . At what angle  the load current I d equals to 5 A.
Calculate commutation angle  at this value of current. Plot thyristor voltage U T 1 .
A
B
e2a
e2b
e2с
Xa
Xa
Xa
C
T4
T1
T6
T3
T2
T5
Rd
Xd
Fig. 3.5.
3.6. Given: U1  220 V , E2  100 V ,   30  0,523 rad , X a  0,5  ,
Rd  5  , X d   . The circuit is shown in Fig. 3.6. Define constant component of
load current I d , average values of thyristor’s and diode’s currents and RMS value
of primary current I1 . Plot the curve of thyristor voltage.
Xa
Tr
i2
U1
VD 4
T1
VD3
T2
Rd
Xd
e2
VD0
Fig. 3.6.
3.7. Given: U AB  U BC  U CA  380 V , E2  100 V , Rd  10  , X a  1  ,
X d   . Load power Pd  2 kW . Find control angle  . Calculate RMS value of
primary transformer’s winding current I1 , average values of thyristor’s and diode’s
currents.
A
B
e2a
e2b
e2с
Xa
Xa
Xa
C
i1
VD 4
T1
VD6
T3
VD 2
T5
Rd
Xd
Fig. 3.7.
3.8. Given U1  220 V , E2  100 V , E0  70,5 V Rd  10  . The circuit is
depicted in Fig. 3.8. Define RMS value of primary winding transformer’s current
I1 , average value of valves’ current. Plot the curve of thyristor voltage U T if
control angle   90 .
T1
e2a
i1
E0
 
Rd
U1
e2b
T2
Fig. 3.8.
3.9. Given: E2  100 V , X a  1  , X d  10  , Rd  3  , E0  70,5 V . The
circuit under consideration is depicted in Fig. 3.9. Find the control angle 
corresponding to boundary-continuous mode.
Xa
Tr
U1
T4
T1
T3
T2
e2
Rd
Xd
E0
Fig. 3.9.
3.10. Given: U1  220 V , E2  100 V ,   30 X d   , Rd  5  . The
circuit is shown in Fig. 3.10. Find constant component of load current I d , average
values of thyristor’s and diode’s currents, RMS primary current value I1 . Plot the
curve of thyristor’s voltage.
Xa
Tr
i2
i1
U1
Fig. 3.10.
T4
T1
VD3
VD 2
Rd
Xd
e2
Topic 4. Features of switching processes in controlled rectifiers
4.1. The circuit is shown in Fig. 4.1. Given: E2  220 V , Rd  10  ,
X d   , X a  1  ,   60 . Define constant component of load current I d .
Calculate commutation angle  .
Xa
e2a
i1
Rd
T1
Xd
U1
e2b
Xa
T2
Fig. 4.1.
4.2. The circuit is depicted in Fig. 4.2. Given: U1  220 V , E2  100 V ,
Rd  5  , X d   ,   30 . Commutation angle   10 . Find constant component
of load current I d , RMS value of transformer’s primary winding current I1 .
Xa
Tr
i2
i1
U1
Fig. 4.2.
T4
T1
VD3
VD 2
Rd
Xd
e2
4.3. The circuit is shown in Fig. 4.3. Given Rd  10  , X d   , X a  1  .
At control angle   0 , Ed  300 V . At what angle   0 , the load current
I d  10 A . Calculate commutation angle  at given conditions.
A
B
C
i1
Xd
Xa
Xa
Xa
Xa
Xa
Xa
Rd
Fig. 4.3.
4.4. The circuit is depicted in Fig. 4.4. Given: U AB  U BC  U CA  220 V ,
E2  100 V ,
Xa 1 ,
Xd   ,
Rd  10  , control angle
transformer’s primary winding current I1 .
  60 . Find
A
B
C
i1
e2a
e2b
e2с
Rd
Xa
Xa
Xa
Xd
T1
T2
T3
Fig. 4.4.
4.5. The circuit is shown in Fig. 4.5. Given: U1  220 V , E2  100 V ,
Rd  10  , commutation angle   10 , X d   , control angle   30 . Calculate
RMS value of transformer’s primary winding current I1 .
Xa
Tr
i2
i1
U1
Fig. 4.5.
T4
T1
T3
T2
Rd
Xd
e2
4.6. The circuit is shown in Fig. 4.6. Given: U AB  U BC  U CA  U1  220 V ,
E2  100 V , X a  0,5  , X d   , Rd  10  , control angle   30 . Define RMS
value of transformer’s primary winding current I1 .
A
B
e2a
e2b
e2с
Xa
Xa
Xa
C
i1
T4
T1
T6
T3
T2
T5
Xd
Rd
VD0
Fig. 4.6.
4.7. The circuit is depicted in Fig. 4.7. Given: E2  100 V , E0  85 V ,
Rd  2  , Ld  14,6 mH , f  50 Hz ,   60 . Calculate average value of rectified
voltage, constant component of load current I d taking into account that the
transformer and the valves of rectifier are ideal.
T1
i1
e2a
Rd
Ld
U1
e2b
E0
 
T2
Fig. 4.7.
4.8. The circuit is depicted in Fig. 4.8. Given U1  220 V ,
E2 a  E2a  E2b  E2b  100 V , Rd  10  . Control angle of thyristors T 1 and T 2
  30 . Control angle of thyristors T 1 and T 2   90 . Find constant
components of rectified current I d and voltage Ed . Define RMS value of
transformer’s primary winding current I1 . Plot the curve of voltage on thyristors
T 1 and T 1 .
T 1

e2a
T1

e2a
Rd
i1
U1

e2b

e2b
T2
T 2
Fig. 4.8.
4.9. The circuit under consideration is shown in Fig. 4.9. Given U1  220 V ,
E2 a  E2a  E2b  E2b  100 V , Rd  10  , X d   , 1  30 , 1  90 . Find
constant components of rectified current I d and voltage Ed . Define RMS value of
transformer’s primary winding current I1 . Plot the curve of voltage on thyristors
T 1 and T 1 . The transformer and the valves are considered to be ideal.
T 1

e2a
T1

e2a
Xd
Rd
i1
U1
VD0

e2b
T2

e2b
T 2
Fig. 4.9.
U AB
4.10.
The
circuit
 U BC  U CA  U1  380 V ,
is
shown
in
Fig.
4.10.
Given:
E2 a  E2b  E2 a  E2  100 V ,
E0  70,5 V ,
Rd  1  , control angle   60 . Define average value of load current and RMS
value of primary current I1 . Plot the curve of voltage on thyristor.
A
B
C
i1
Fig. 4.10.
T2
e2с
T3

T1
e2b
E0

e2a
Rd
Topic 5. Power indicators of rectifiers
5.1. The circuit is shown in Fig. 5.1. Given: U1  100 V , Rd  10  ,
X a  1  , X d   ,   30 . Calculate total power factor.
T1
Xa
e2a
i1
Rd
Xd
U1
e2b
T2
Xa
Fig. 5.1.
5.2. The circuit is shown in Fig. 5.2. Given: U1  100 V , Rd  10  ,
X a  1  , X d   ,   30 . Calculate total power factor.
T1
VD0
e2a
Rd
Xd
U1
e2b
T2
Fig. 5.2.
5.3. The circuit is shown in Fig. 5.3. Given: U AB  U BC  U CA  U1  220 V ,
E2 a  E2b  E2c  100 V , X d   , Rd  10  , X a  1  , control angle   30 .
Define total power S components: P, Q, T. Possible voltages asymmetry is
negligible.
A
B
e2a
e2b
e2с
Xa
Xa
Xa
C
i1
T4
T1
T6
T3
T2
T5
Rd
Xd
Fig. 5.3.
5.4. The circuit is depicted in Fig. 5.4. Given: U1  220 V ,
E2 a  E2a  E2 b  E2b  100 V , X d   , Rd  10  , Ed  120 V . Find control angle
 . Calculate total power factor and components of total power. Compare these
indicators in the absence of valves VD1 and VD2.
T1

e2a
VD1

e2a
Xd
Rd
i1
U1

e2b
VD 2

e2b
T2
Fig. 5.4.
5.5. The circuit is shown in Fig. 5.5. Given: U1  220 V , E2  100 V ,
Rd  10  , X a  0 , control angle   30 . Calculate total power factor  and total
power components.
Xa
Tr
i2
i1
U1
T4
T1
T3
T2
e2
Rd
Fig. 5.5.
5.6. The circuit is shown in Fig. 5.6. Given: U1  220 V , E2  100 V ,
Rd  10  , X d   , X a  1  . Calculate total power factor  and total power
components of the rectifier.
Xa
Tr
i2
i1
U1
T4
T1
VD3
VD 2
Rd
Xd
e2
Fig. 5.6.
5.7. The circuit is shown in Fig. 5.7. Given: U AB  U BC  U CA  U1  220 V ,
E2 a  E2b  E2c  100 V , X d   , Rd  10  , X a  1  , control angle   60 .
Calculate total power factor  and total power components. Compare the
indicators found for the two cases: with zero valve and without it.
A
B
C
i1
e2a
e2b
e2с
Rd
Xa
Xa
Xa
VD0
Xd
T1
T2
T3
Fig. 5.7.
5.8. The circuit is shown in Fig. 5.8. Given: U AB  U BC  U CA  U1  220 V ,
E2 a  E2b  E2 c  E2  100 V , Rd  10  , control angle   30 . Define total power
consumed by the rectifier from the mains supply and its components.
A
B
e2a
e2b
C
i1
e2с
T4
T1
T6
T3
T2
T5
Rd
Fig. 5.8.
5.9. The circuit is shown in Fig. 5.9. Given: U AB  U BC  U CA  U1  220 V ,
E2 a  E2b  E2 c  E2  100 V , Rd  10  , X d   , control angle   30 . Define
total power consumed by the rectifier from the mains supply, its components and
total power factor  .
A
B
C
e2a
e2b
e2с
i1
T4
T1
T6
T3
T2
T5
Rd
Xd
Fig. 5.9.
U AB
5.10.
The
circuit
is
shown
in
Fig.
5.10.
Given:
 U BC  U CA  U1  220 V , ktr  2 , Rd  10  , X d   , X a  1  , control
angle   90 . Define total power consumed by the rectifier.
A
B
C
i1
e2a
e2b
e2с
Rd
Xa
Xa
Xa
Xd
T1
Fig. 5.10.
T2
T3
Topic 6. Inverters led by mains
6.1. The circuit is shown in Fig. 6.1. Given: U1  220 V , transformation
coefficient of power transformer ktr  1, EMF of DC power supply E0  100 V ,
power consumed from the mains supply Psup  10 kW , converter’s efficiency
  0,9 , internal resistance of DC power supply rint  0,1  . Inductive reactance of
smoothing reactor is infinity. Calculate the currents and voltages of the thyristors,
power factor  , components of total power. Plot the curve of thyristor’s voltage.
T1
Tr
e2a
U1 i1
Id
Xd


E0
e2b
T2
Fig. 6.1.
U AB
6.2. The circuit of inverter led by mains is shown in Fig. 6.2. Given:
 U BC  U CA  380 V , E0  240 V , X d   , internal resistance of DC power
supply rint  0,5  , advance angle   30 , transformation coefficient of power
transformer ktr  1. Define the power consumed from DC power supply, currents
and voltages of power valves.
A
B
C
i1
Xd
e2с
Id
T1
T2
E0

e2b

e2a
T3
Fig. 6.2.
6.3. The circuit is shown in Fig. 6.3. Given: U1  380 V , Psup  10 kW ,
rint  0,5  ,   0,9 , X a  1  , current consumed from the DC power supply
I d  60 A , commutation angle   20 , X d   . Define total power S components:
P, Q, T.
Xa
Tr
U1
T4
T1
T3
T2
e2
Xd


E0
Fig. 6.3.
6.4. The circuit is depicted in Fig. 6.4. Given: U1  380 V , ktr  1 ,
X a  0,1  , frequency of mains supply
f s  50 Hz , X d   , time control
properties recovery of power thyristors trec  100  106 s . Plot the limiting
characteristic of the inverter.
B
A
C
i1
Xd
e2b
e2с
Xa
Xa
Xa

e2a
Id
E0

T1
T2
T3
Fig. 6.4.
6.5. The circuit is shown in Fig. 6.5. Given: U1  380 V , leakage inductance
La  0,001 H , frequency of mains supply f s  50 Hz , ktr  1 , advance angle
  30 , X d   . Find average value of valves’ current I av , maximum vale of
valves’ current I a.max , maximum value of reverse voltage on the valves U a.rev .
Xa
Tr
U1
T4
T1
T3
T2
e2
Xd


E0
Fig. 6.5.
6.6. The circuit is shown in Fig. 6.6. Given: U1  220 V , ktr  1, X d   ,
X a  0,1  ,   30 , commutation voltage drop U x  15 V . Calculate the power
consumed from DC power supply Psup , total power components and total power
factor  .
T1
Tr
e2a
U1 i1
Id
Xd


E0
e2b
T2
Fig. 6.6.
6.7. The circuit is shown in Fig. 6.7. Given: U1  220 V , La  0,001 H ,
E0  100 V ,   30 , f s  50 Hz , X d   . Define commutation angle. Plot the
voltage on thyristor.
A
B
C
e2a
e2b
e2с
i1
T4
T1
T6
T3
T2
T5
Xd
E0
Fig. 6.7.
6.8. The circuit is shown in Fig. 6.8. Given: U AB  U BC  U CA  U1  380 V ,
ktr  1,1, E0  250 V , X d   ,   10 , rint  0,5  , X a  0 . Define RMS value of
primary current I1 , power Psup consumed from DC power supply. Plot the voltage
on thyristor.
A
B
C
i1
Xd
e2b
e2с
Xa
Xa
Xa

e2a
Id
E0

T1
T2
T3
Fig. 6.8.
6.9. The circuit is shown in Fig. 6.9. Given: U1  220 V , ktr  2 , X d   ,
X a  0 , E0  120 V , X d  0 , rint  1  ,   170 . Define the primary current I1 .
Plot the dependence UT  f    .
T

U1 i1
e2
E0

Fig. 6.9.
6.10. The circuit is shown in Fig. 6.10. Given: U AB  U BC  U CA  100 V ,
rint  0,5  , X d   . If E0 changes by the value 10 V, I d changes by the value
20 A. Define control angle   90 . Define I1 if at E0  100 V and   30 ,
I d  50 A . Plot the dependence UT  f    .
A
B
e2a
e2b
e2с
Xa
Xa
Xa
C
i1
T4
T1
T6
T3
T2
T5
Xd
E0
Fig. 6.10.