which the SCR turns ON, may be controlled either by amplitude triggering or pulse triggering.

40
SCR Half wave Rectifier
Figure(a) shows the circuit of a SCR half-wave rectifier.
In this circuit, the ac supply is connected
to the SCR through a load resistance RL.
The gate current is obtained from the ac supply
through the resistances R and R1 and diode D connected in series.
The diode D is connected in
such a way, so that it blocks the reverse voltage on the gate during the negative half-cycle.
Figure (b), (c) and (d) shows the waveforms of the voltage across SCR (V
SCR
), the load current (I
L
)
and voltage across the load (V
L
) respectively.
The various curves in the waveforms may be
expained as follows:
During the positive half-
cycle, the SCR remains ‘OFF’ till the input voltage
reaches the gate trigger voltage i.e. point A in Fig. (b).
As a result, there is no current through
RL.
Hence load currrent (IL)
and load voltage (V
L
) are zero.
At point A, SCR is fired into
conduction.
It acts like a short and voltage across it drops to zero i.e., curve AB in Fig. (b).
Under this condition, whole of the applied voltage drops across the load resistance.
During the
negative input half cycle, the SCR is reverse biased and hence does not conduct.
As a result, all
the applied voltage appears across SCR and none across the load resistance (RL).
The horizontal distance between the points O and A in Fig. (b) represents the time in the
positive half-cycle, when SCR is not conducting.
This distance in degrees is called the firing
angle, phase angle or delay angle (
α
).
This angle gives us an idea about the position at which
the SCR starts conduction with respect to the origin.
It may may be noted from the figure that
the SCR is coducting between the points B and C.
This angle is called conduction angle (
ɸ
) and
its value is equal to (
π
–
α
).

41
Average Values of Load Voltage and Current
Average load voltage
The equation of a.c. supply voltage is
V
in
= V
m
.sin
ω
t = V
m
.sin
θ
We also know that for a half wave rectifier, the average value of a load voltage is determined by the
relation,
Vdc =
=
=
-----(1)
Now the load voltage is developed only during the period SCR conducts.
This period lies between the
angles
α
and
π
.
Therefore, we must take the average over the limits
α
to
π
instead of 0 to 2
π
in
equation (1)
Vdc =
=
=
α
π
=
=
(1+cos
α
)
-------(2)
Average load current
We know that load current, iL = vL/RL, therefore, the average value of the load current,
Idc =
=
(1 + cos
α
) =
(1 + cos
α
)
------(3)
Where Im is equal to Vm/RL and is the maximum value of the load current. It may be noted that if
the firing angle (
α
) is equal to zero, then the average values of load voltage and current is
obtained from equations (2) and (3)
Therefore
Vdc =
and

42
Idc =
=
=
It may be noted that the above results are the same as obtained for an ordinary diode half-wave
rectifier.
RMS load voltage
The rms voltage across the load is
Vrms = [
2
d(
ω
t)]
0.5
= Vm[
2
ω
td(
ω
t)]
0.5
= Vm[
d(
ω
t)]
0.5
= Vm[
{(
ω
t
–
)}]
0.5
Or Vrms = Vm[
+
]
0.5
RMS load current
And the rms load current is Irms =
90° Variable Half-wave Rectifier (Converter)
The SCR half-wave rectifier circuit shown in the half-wave rectifier is known as 90°
variable half-wave rectifier (or 90° variable phase control circuit).

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