This document discusses various types of filters used in power electronics, including L, C, and LC filters. It also discusses capacitor filters and how they smooth the DC output voltage of a rectifier. Finally, it discusses firing circuits for thyristors, including resistance and RC firing circuits, and provides equations for calculating voltage and current in half-wave converter circuits with resistive and RL loads.

1. Rama Kishore Bonthu
Associate Professor
Email: ramkishore.bonthu@gmail.com
POWER ELECTRONICS - II
FILTERS:
A filter provides an output voltage as smooth as possible. If the filter is connected across rectifier input side, it is called ac
filters. If the filter is connected across rectifier output side, it is called dc filters. The more common ac & dc filters are of L,
C and LC type as shown in figures (a), (b),(c) and (d).
An inductor L in series with load R, Fig(a), reduces the ac
component, or ac ripples. It is because L in series with R offers
high impedance to ac component but very low resistance to dc.
Thus ac component gets attenuated. A capacitor C across load
R. Fig (b), offers direct short circuit to ac component, these are
therefore not allowed to reach the load. However, dc gets
stored in the form of energy in C and this allows the
maintenance of almost constant dc output voltage across the
load.
CAPACITOR FILTER (C-FILTER):
This diagram represents the diode bridge rectifier with R-load. A
capacitor C directly connected across the load, serves to smoothen out the
dc output wave. Source voltage vs = Vm sin wt is sketched in below
Fig.(a). Load voltage Vo is shown in Fig. (b). In this figure, from wt = 0
to wt =θ, source voltage Vs is less than capacitor discharges through load
resistance R. At wt = θ, V0 = Vc = V2 as shown in Fig. (b). Soon after wt = θ,

2. Rama Kishore Bonthu
Associate Professor
Email: ramkishore.bonthu@gmail.com
source voltage Vs exceeds Vo (= Vc), diodes D1, D2 get forward biased and begin to conduct. As a result, source voltage charges
capacitor from V2 to Vm at wt = π/2, as shown Fig.(b). Soon after wt = π/2, source voltage Vs begins to decrease faster
than the capacitor voltage Vc. it is because capacitor discharges gradually through R. Therefore, after wt = π/2, diodes Dl, D2
are reverse biased and capacitor discharges through R. The capacitor voltage falls exponentially, shown in Fig. (b).In the next
half cycle, Vc = V0= V2 at wt = (π + θ). Just after wt = (π + θ), Vs> Vc, diodes D3, D4 get forward biased and begin to
conduct. The capacitor voltage rises from V2 to Vm at wt = 3π/2. It is seen from figure (b) that voltage drop from maximum to
minimum is Vm -V2, or peak to peak ripple voltage, Vrp =Vm - V2.
In Fig. (c) is drawn the profile of ripple voltage with the help of Fig. (b). A horizontal line at a height 1/2(Vm + V2), from
reference line wt in Fig. (b) is now taken as the
reference line in Fig. (c) for plotting voltage profile Vr. Ripple voltage is seen to be almost triangular in shape.
From the Fig. (c), Peak to peak ripple voltage is Vrpp= Vm - V2
Peak ripple voltage Vrp = 1/2(Vm - V2)
ChargingofCapacitor:
From wt =θ to π/2, capacitor charges from V2 to Vm . The equivalent circuit for capacitor
charging, shown below, gives the charging current is as under :
The charging current ic at wt = π/2 is ic= wcvmcos 900
= 0, but Vc =Vs= Vmsin900
= Vm.
Therefore, energy stored in C at wt = π/2 is 1/2(CVm
2
)
Discharging of capacitor:
KVL for the circuit model of below figure, for capacitor discharging gives
Charging time is usually small, therefore it can be neglected. As a result t1+t2 = t2 = T/2. But T = 1/f, therefore t2 = 1/2f

3. Rama Kishore Bonthu
Associate Professor
Email: ramkishore.bonthu@gmail.com
FIRING CIRCUITS FOR THYRISTORS:
SCR can be switched from off-state to on-state in several ways. Those are forward voltage
triggering, dv/dt triggering, temperature triggering, light triggering and gate triggering. The instant of the turning on the SCR
cannot be controlled by the first four methods listed above. However, gate triggering method turns-on the SCR accurately at
the desired instant. In addition gate triggering is reliable and efficient. In this method gate must be fired by using firing
circuits at a particular angle or instant.
RESISTANCE FIRING CIRCUITS:
Resistance trigger or firing circuits are the simplest and
most economical. They however, suffer from a limited range of
firing angle control (0°
to 90°).In this circuit,R2 is the variable
resistance, R is the stabilizing resistance. In case R2 is zero, gate
current may flow from source, through load, R1, D and gate to
cathode. The function of R1 is to limit the gate current to a safe value as
R2 is varied. Resistance R should have such a value that maximum
voltage drop across it does not exceed maximum possible gate voltage
Vgm. As resistances R1, R2 are large, gate trigger circuit draws a
small current. Diode D allows the flow of current during Positive
half cycle only, i.e. gate voltage Vg is half-wave dc pulse.
The amplitude of this dc pulse can be controlled by varying R2.
The potentiometer setting R, determines the gate voltage amplitude. When R2 is large, current i is small and
the voltage across R, i.e. Vg = i . R is also small as shown in Fig.(a). As Vgp (peak of gate voltage vg) is less than

4. Rama Kishore Bonthu
Associate Professor
Email: ramkishore.bonthu@gmail.com
Vgt (gate trigger voltage), SCR will not turn on. Therefore, load voltage Vo = 0, io = 0 and supply voltage Vs
appears as VT across SCR as shown Fig. (a).
In Fig.(b), R, is adjusted such that Vgp = Vgt. This gives the value of firing angle as 900
.
In Fig. (c), Vgp > Vgt. As soon as vg becomes equal to Vgt for the first time SCR is turned on. Increasing Vg above
Vgt turns on the SCR at firing angles less than 90°. When vg reaches Vgt for the first time, SCR fires, gate loses control
and Vg is reduced to almost zero (about 1 V) value as shown.
From the above analysis Where α = firing angle of SCR
In this method, the resistance triggering cannot give firing angle beyond 90°.
RESISTANCE-CAPACITANCE (RC) FIRING CIRCUITS:
The limited range of firing angle control by resistance firing circuit can be overcome by RC firing
circuit. There are several variations of RC trigger circuits. Two of them are (i) RC half wave trigger circuit (ii) RC full
wave circuit
(i) RC half-wave trigger circui:
By varying the value of R, firing angle can be controlled from 0° to 180°. In the negative half cycle, capacitor C
charges through D2. After wt = -900
, source voltage vs decreases from -Vm at wt = - 900
to zero at wt = 0°. During this
period, capacitor voltage Vc may fall from –Vm at wt = - 90° to some lower value - oa at wt = 0° as shown in below figure.
Now, as the SCR anode voltage passes through zero and becomes positive, C begins to charge through variable
resistance R from the initial voltage -oa. When capacitor charges to positive voltage equal to gate trigger voltage Vgt,
SCR is fired.
Diode D1is used to prevent the breakdown of cathode to gate junction through D2 during the negative half cycle.
In figure (a), R is more, the time taken for C to charge from -oa to Vgt is more, firing angle is more and therefore
average output voltage is low. In figure (b), R is less, the time taken for C to charge from -oa to Vgt is less, firing angle
is less and therefore average output voltage is more.
(ii) RC full wave circuit:
Diodes D1—D4 form a full-wave diode bridge. In this circuit, the initial voltage from which the capacitor C
charges is almost zero. When capacitor charges to a voltage equal to Vgt, SCR triggers and rectified voltage vd
appears across load as vo. In Fig. (a), for high value of R, firing angle α is more than 90° and in Fig. (b) for low value
of R ,α< 90°.

5. Rama Kishore Bonthu
Associate Professor
Email: ramkishore.bonthu@gmail.com
SINGLE PHASE HALFWAVE CONVERTER (RECTIFIER) WITH R-LOAD:
thyristor conducts from (wt = α to π, 2π+α to 3π and so
on. Over the firing angle delay α, load voltage Vo = 0 but
during conduction angle (π-α), Vo = Vs. As firing angle is
increased from zero to π the average load voltage
decreases from the largest value to zero.
Average voltage Vo across load R, for the single-phase
half-wave circuit in terms of firing angle a is given by

6. Rama Kishore Bonthu
Associate Professor
Email: ramkishore.bonthu@gmail.com
SINGLE PHASE HALFWAVE CONVERTER (RECTIFIER) WITH RL-LOAD:
A single-phase half-wave thyristor circuit with RL
load is shown in Fig. Line voltage Vs is sketched in
the top of Fig. At wt = α, thyristor is turned on by
gating signal. Then The load voltage V0 becomes
equal to source voltage Vs as shown. But the
inductance L forces the load current i0 to rise
gradually. After some time, i0 reaches maximum
value and then begins to decrease. At wt =π, V0 is
zero but i0 is not zero because of the load inductance
L. After wt = π, SCR is subjected to reverse anode
voltage but it will not be turned off as load current i0
is not less than the holding current. At some angle β,
i0 reduces to zero and SCR is turned of as it is
already reverse biased. After wt = β, V0, = 0 and i0 =
0. At wt = 2π + α, SCR is triggered again, Vo is applied
to the load and load current develops as before. Angle β is
called the extinction angle and β – α = γ is called the
conduction angle.
The Voltage equation for the above circuit, when SCR is ON
The load current i0 consists of two components, one steady-state component is and the other transient component it.
Therefore i0 = is + it
The transient component it can be obtained from force-free equation:
Constant A can be obtained from the boundary condition at wt = α, At this time t = α/w, i0=0
β can be determined by using the condition, when wt=β, t= β/w, i0=0
This transcendental equation can be solved to obtain the
value of extinction angle β, if β is known, the average
voltage is given by

7. Rama Kishore Bonthu
Associate Professor
Email: ramkishore.bonthu@gmail.com
Single-phase Half-wave Circuit with RL Load and Freewheeling Diode :
The waveform of load current io in RL load circuit can
be improved by connecting a freewheeling (or
flywheeling) diode across load as shown in above
circuit, A freewheeling diode is also called by-pass or
commutating diode. At wt= 0, source voltage is
becoming positive. At some delay angle α, forward
biased SCR is triggered and source voltage
appears across load as At wt = π, source voltage Vs,
is zero and just after this instant, Vs tends to reverse,
freewheeling diode FD is forward biased through
the conducting SCR. As a result, load current i0 is
immediately transferred from SCR to FD asVs
tends to reverse. At the same time. SCR is
subjected to reverse voltage and zero current. it
is therefore turned off at wt = π. It is assumed
that during freewheeling period. load current does
not decay to zero until the SCR is triggered again at
wt=2π+α. Voltage drop across FD is taken as almost zero
the load voltage Vo is zero during the freewheeling
period.
The voltage variation across SCR is shown as VT in above waveform. It is seen from this waveform that SCR is
reverse biased from wt= π to wt = 2π.
Operation of the above circuit can he explained in two modes. In the first mode, called conduction mode, SCR conducts from
wt=α to π, to 2π + α to 3π and so on and FD is reverse biased. The second mode, called freewheeling mode, extends from π to
2π + α, 3π to 4π + α and so on. In this mode, SCR is reverse biased from π to 2π, 3π to 4π and so on.
conduction mode:
The load current i0 consists of two components, one steady-state component is and the other transient component it.
therefore i0 = is + it

8. Rama Kishore Bonthu
Associate Professor
Email: ramkishore.bonthu@gmail.com
Constant A can be obtained from the boundary condition at wt = α, At this time t = α/w, i0=I0
freewheeling mode:
SINGLE-PHASE HALF-WAVE CIRCUIT WITH R-L-E LOAD:
A single-phase half-wave controlled converter
with RLE load is shown above. The counter
emf E in the load may be due to a battery or a
dc motor. The minimum value of firing angle
is obtained from the relation Vm sin wt = E.
This is shown to occur at an angle θ1 in
waveform. Where θ1 = sin-1
(E/Vm).
In case thyristor T is fired at an angle w < θ1,
then E > V, SCR is reverse biased and therefore
it will not turn on. Similarly, maximum value
of firing angle is θ2 = π – θ1 shown in above
waveform. During the interval load current i0 is
zero, load voltage Vo = E and during the time
is is not zero, Vo follows Vs curve.

9. Rama Kishore Bonthu
Associate Professor
Email: ramkishore.bonthu@gmail.com
The solution of this equation is made up of two components, namely steady-state current component is, and
the transient current component it. For convenience, is, the sum of is1 and is2, where is1 is the steady state
current due to ac source voltage acting alone and is2, is that due to dc counter emf E acting alone (according to
superposition theorem).