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active load with a dc source (such as a
dc machine or an ac adjustable speed drive). Id is the load dc current and is assumed to be
ripple free.
Load
p
n
A B
A B
A
B
iA
Id
50 Hz
Supply
p p
n n
(pure dc)
vd
Fig. 6.1 Single-phase diode bridge rectifier
Fig. 6.2 shows ac line waveforms together with a chart indicating diode conduction
periods. Apo is the instant when A becomes the higher and B the lower of the two
potentials and thus the point in the ac cycle at which diodes Ap and Bn start to conduct.
Similarly, Bpo is the other voltage cross over point. Diagonally opposite diodes Ap, Bn and
Bp, An conduct in sequence for half-cycle intervals. Diodes are named Ap, Bp, An and Bn to
help us visualise the operation of the bridge circuit. Ap is named such because when it
conducts, it connects line A of the ac supply to the positive rail (point p) on the dc side,
and similarly for the other devices.
S6: Static converters
76 EEE8044: Fundamentals
Fig. 6.2 Single-phase diode bridge rectifier waveforms
Fig. 6.2 also shows rectifier voltage and current waveforms. vAB and vBA are the
instantaneous supply line-to-line voltages. vd is the instantaneous dc output voltage
(voltage between point p and n). It is made up of portions of the line-to-line voltages vAB
and vBA depending on which of the ac lines are connected to points p and n by the
conducting diodes.
iA is the instantaneous ac line current waveform. It is made up of positive or negative
pulses of the rectifier dc current Id depending on which diodes conduct. For example, iA=
+ Id for the 180° period in which Ap conducts and iA = - Id for the 180° period in which An
conducts.
A feature of bridge circuits is that the line current waveform is symmetrical ac with no dc
component. The rms line current IL for a single-phase diode bridge rectifier is given by
vAB vBA vAB vBA
AC line
Voltages
Conduction
Periods
DC Output
Voltage v
AC Line
Current iA
d
Top Row
Bottom Row
vAB vBA vAB vBA
Id
Ap
Bn
Ap
An Bn An
Bp Bp
Id
ωt
0 π 2π
3π
4π
π
Apo Bpo Apo Bpo
S6: Static converters
77 EEE8044: Fundamentals
I I d t I L d d = ∫ = 1 2
0 π
ω
π
(6.1)
where Id is the mean dc current of the rectifier.
The instantaneous dc output voltage vd is made up of two identical parts per cycle and is
referred to as a two-pulse waveform. The mean rectifier dc voltage Vd can be obtained by
integrating the instantaneous voltage vd over half a cycle from ωt = 0 to π
V v d t V t d t V V d d L L L = ∫ = ∫ = = 1 1 2
2 2
09
0 0 π
ω
π
ω ω
π
π π
sin . (6.2)
where VL is rms line voltage.
6.1.2 Single-phase thyristor bridge rectifier: voltage & current waveforms
Fig. 6.3 shows a single-phase thyristor bridge rectifier. The bridge input is connected to a
single-phase ac supply with rms line voltage VL. The dc output is connected to a highly
inductive load so that the dc current waveform may be assumed smooth and free from any
ripple.
Load
p
n
A B
A B
A
B
50 Hz
Supply
p p
n n
Id (pure dc)
iA
vd
Fig. 6.3 Single-phase thyristor bridge converter
Fig. 6.4 shows ac line waveforms together with the thyristor conduction periods and
voltage and current waveform for operation with a firing angle α. Apo is the instant when