Mathematical Analysis
Analysis by hand is based on the assumption that the load inductance is sufficiently
large to keep the load current ripple-free. Programs written for computer
simulation are not based on this assumption and they simulate the operation
based on the parameter keyed-in.
When the load current is continuous, the average value of the output voltage
is obtained as follows. Let the supply voltage be vs = E*Sin (q
), where q varies from 0 to 2p
radians. Since the output waveform repeats itself for every half-cycle, the
average output voltage is expressed in equation (1) as a function of a,
the firing angle.
If the load current is continuous, the r.m.s. value of output voltage is
obtained as shown in equation (2).
The maximum average output voltage occurs at a firing angle of 0o.
Let it be Vom. Then the ripple factor RF(a) is defined as shown
in equation (3). Equations (4) and (5) apply when the conduction is discontinuous.
The variation of average output voltage, r.m.s. output voltage and the ripple
factor with the firing angle have been shown below, based on the assumption
that the load inductance is large. The plots shown below have been normalized
with respect to Vom. For example, when the firing angle is 60o,
the average output is shown to be 0.5. It means that the actual average output
voltage is 0.5Vom. It can also be seen that when the firing angle
is 0o, the r.m.s. output voltage is about 1.1Vom and
the ripple factor is about 0.48. The ripple factor increases as the firing
angle increases.
click here to open the applet
If the firing angle is highly retarded or if the load inductance is not sufficiently
large, conduction of load current is not continuous. Let us consider the positive
half-cycle. When q equals the firing angle, the
SCRs S1 and S3 are triggered. Let the load current start
from zero at q = a and let the load current fall
to zero when q = p + b , before the next pair of
SCRs is triggered. It means that b < a
. Then the average output voltage is computed as shown in equation (4), whereas
the r.m.s. output voltage is computed as shown in equation (5).
The value of b can be found out by iteration,
as shown in earlier pages. For the case when the conduction is discontinuous,
the plots of the average output voltage, the r.m.s. output voltage and the
ripple factor are illustrated below. Key-in the ratio of wL/R, where L is
the load inductance, R is the load resistance and w is the angular frequency
of the source. In practice this ratio can vary from a low value to about 5.
The load angle can be defined to be tan-1(wL/R). When the firing
angle is less than the load angle, the conduction is continuous. As explained
below, the load current is discontinuous if the firing angle is greater than
the load angle.
click here to open the applet
TO THE TOP |
