13.4.

FILTER CIRCUITS

circuits just discussed is not purely dc but also has some ac

The cutput from any of the rectifier
The ripples are maximumin the single phase half-wave rectifier and
components, called ripples, along it.
further with the increase in number of phases. Such
being reduced in full-wave rectifier and being reduced
devices/circuits. Of course, for a circuit such as
supply is not useful for driving sophisticated electronic
nature of supply available from a rectifier is no great detriment as long as
battery charger the pulsating
to radio or tape recorder the
the dc level provided results in charging of battery. But for supply circuits
the operation of the
pulsating dc resuits in 50 (or 100) Hz signal appearing in the output, thereby making
overall circuit poor. For such applications, as well as for many more, the output dc developed will have
to be much steady or smoother than that of the pulsating de obtained directly from half-wave or full-wave
rectifier circuits.
Hence, it becomes essential to reduce the ripples from the pulsating dc supply available from
rectifier circuits to the minimum. This is achieved by using a filter or smoothing circuit which removes
(or filters out) the ac components and allows only the dc component to reach the load. Obviously, a
Tilter circuit should be between the rectifier and the load, as shown in Fig. 13.8.
placed
Atilter circuit is a device that converts pulsating output of a rectifier into a steady dc level. A filter
n tS generally a combination of inductors L and capacitors C. The filtering action of L and C depends
Pon the facts that
network can
an inductor allows de
only and capacitor allows ac only to pass. So a suitable L and
effectively filter out (or remove) the ac components from the rectified output.
 FILTER
TO LOAD
CIRCUIT

RECTIFIED OUTPUT VOLTAGE

OUTPUT vOLTAGE WAVEFORM
OR
INPUT VOLTAGE WAVEFORM

Fig. 13.8

Commonly used filter circuits are (a) series inductor filter (b) shunt capacitor filter (c) choke input
filter (d) capacitor input or t filter and (e) R-C filter. First three will be discussed here in brief

13.4.1. Series Inductor Filter

In this arrangement a high value inductor or
choke L is connected in series with the rec
tifierelement and the load, as illustratedin O00000
L

Fig. 13.9 (a). The filtering action of an LuL

inductor filter depends upon its property of

opposing any change in the current flowing
through it.When the output current of the
rectifier increases above a certain value, energy (a) Circuit Diagram
is stored in it in the form of magnetic field
, WITHOUT WITH CHOKE
and this energy is given up when the output L max FILTER
FILTER
current falls below the average value. Thus
L
by placing a choke coil in series with the
rectifier output and load, any sudden change max

in current that might have occurred in the

circuit without an inductor is smoothed out
by the presence of the inductor L. (b) Output Voltage Wavefoms
The function of the inductor filter may Fig. 13.9 Full- Wave Rectifier With Series Inductor Filter
be viewed in terms of impedances. The choke
offers a high impedance to the ac components but offers almost zero resistance to the desired dc
components Thus ripples are removed to a large extent. Nature of the output voltage without filter and
with choke filter are shown in Fig. 13.9 (6).
For de (zero frequency), the choke resistance Rc in series with the load resistance R forms a voltage
divider and dc voltage across the load is given as

V VacRcR+R I+R
.(13.58)
R
where Vae is dc voltage output from a full-wave rectifier. Usually choke coil resistance R, is much
smaller than R, and, therefore, almost entire of the de voltage is available across the load resistance
R.
Fourier series for the rectified output voltage is given as

= VLmax cos
3Tt
2r-cos 4o ... ..(13.59)
Since the reactance of inductor increases with the increase in frequency, better filtering of the
higher harmonic components takes place, so effect of third and higher harmonic voltages can be
neglected.
As obvious from Eq. (13.58), if choke coil resistance R is negligible in comparison to load resistance

RL, then the entire dc component of rectifier output is available he

across R, and is
equa TLmax
ac voltage partly drops across X; and partly over R,. Since choke and R, are connected in series, the

maximum value of voltage drop across load resistance R, due to second harmonic voltage VLma

Vac max VL max R

R+Xi
RMS value of this ac voltage drop across load resistance R; is given as

VL max
RL
R+Xi
4 Vmax R
Ripple factor, y = Vac m 3t2 R+Xi 2 R
Vde max
3 R +Xi
Since X = 20L
Frequency is doubled in full-wave rectifier

Y
2 ..(13.60)
h4L
R
If 20L >>
R Y 2R
3x 20L 20
RL
320L
...(13.61)
It is seen that ripple decreases with the decrease in R, (or increase in load current I) so inductor
filter is more efficient for high load current or small load resistance R
In case the load resistance is infinite, i.e., the output is an open circuit, then ripple factór from
Eq. (13.60)
Y0,471
This is slightly less than the value of 0.482. The difference being attributable to the omission of
higher harmonics.
13.4.2. Shunt Capacitor Filter
This is the most simple form of the filter circuit and in this arrangement a high value capacitor C is placed
directly across the output terminals, as shown in Fig. 13.10 (a). During the conduction period it gets
charged and stores up energy in the electrostatic field and discharges through the load resistance
delivering energy to it during non-conduction period. Through this process, the time duration R
during which
current flows through the load resistance gets prolonged and ac
components or ripples get
considerably
reduced. It is to be noted here that the capacitor C gets charged to the peak value of
because charging time constant is almost zero. It is so because there is input voltage quickly
no resistance
forward resistance of diode) in the (except the negligible
charging path. But the discharging time is quite large
more than the
charging time depending upon the value of R) because it (roughly 100 times
resistance R. discharge» through load
The function of the capacitor filter
may be viewed in terms of
capacitor C offers a low impedance shunt path to the ac impedances. The large value
components or ripples but offers high
impedance to the de component, Thus ripples get bypassed through capacitor C and only de componen
flows through the load resistance R.
 pacitor filter is very popular because of its
cost,
small size, light weight and good
w
useful for load up to 50 mA
c h

racteristics. It is quite
a r a c t e r i s t i c s .

in
transistor radio, battery eliminators.
1. Half-Wave Rectifier With Shunt Capacitor
Eilter. The waveforms of ac input voltage, rectified
and load current are (a) Circuit Diagram
nd filtered output voltages
and (d) respectively.
hown in Figs. 13.10 (b), (c) smax
During the positive halt cycle of the ac input,

the diode of the (Fig. 13.2) is forward biased rectifier

This quickly charges the capacitor
and so it conducts.
C to peak value
of the supply voltage VS because may -Vsmax
time constant. This is shown
of almost zero charging (b) Input Voltage Waveform To Rectifier
13.10 (c). After being fully charged,
by point b in Fig. ,Vc or VL
the charge till input ac supply to
the capacitor holds VLmex
the negative half
the rectifier goes negative. During
biased and so stops
cycle, the diode gets reverse .
RECTIFIED
conduction. So the capacitor C discharges through OUTPUT
load resistance R and loses charge. Voltage across R TT

(v) or across being equal, decreases C (v), both

(c) Recijied and Fillered Output Voltage Waveforms
exponentially with time constant CR, along the
curve

Because of large
bc, as illustrated in Fig. 13.10 (c).
does not
discharge time constant CR, the capacitor
have sufficient time to discharge appreciably. Due to
this fact the capacitor maintains a sufficiently large
half cycle
voltage across R, even during the negative half
2 3
of the input supply. During the next positive
the capacitor (d) Load Current Waveform
cycle, when the rectified voltage exceeds
in Fig. 13.10 (c), the
voltage vc represented by point c 13.10 Half-Wave Rectifier With Shunt
to Vs maxor Fig.
capacitor C again gets charged quickly Capacitor Filter
d in the figure. This
L max as represented by point
process of charging and discharging
of capacitor C is
It is seen, from the figure, that nearly constant de voltage
repeated for each cycle of input supply voltage. is increased
at all times and also the
dc component of the output voltage
appears across load resistance R,
considerably. the same nature as the waveform
resistive load, the output current waveform is of
purely
In case of a
current is
of output voltage. This is illustrated in Fig.
13.10 (d). During the periods a'b' and c'd the
b'c and de etc. by capacitor C.
supplied by the diode and during periods these
intervals of time ab and cd etc. in Fig. 13.10 (c). During
Diode current flows during short short-
the capacitor (or load) voltage. Hence diode current is
time intervals, diode output voltage exceeds
A small resistor, called the surge limiting resistor is, therefore, always
duration pulses (i.e., surging current).
limit this surge current.
Connected in series with the diode to

The noteworthy points about shunt capacitor

filer are:
time
the load resistance be the discharge
R, larger will
1. For a fixed-value filter capacitance larger hand lower
and more the output voltage. On the other
Constant CR, and therefore, lower the ripples
constant and therefore,
the load resistance (or more the load current), lower will be the discharge time
more the ripples and lower the output voltage.
 2. less charge it can hold and more it will discharge. Thus
Similarly smaller the filter capacitor, the
the peak-to-peak value of the ripple will increase, and the average de level will decrease. Larger the
filter capacitor, the more charge it can hold and the less it will discharge. Hence the peak-to-peak value
of the ripple will be less, and the average dc level will increase. But, the maxImum value of the
capacitance that can be employed is limited by another factor. The larger the capacitance value, the
greater is the current required to charge the capacitor to a given voltage. The maximum current that
can be handled by a diode is limited by the figure quoted by the manufacturer. Thus the maximumn
value of the capacitance, that can be used in the shunt filter capacitor is limited.
Approximate Analysis. Toal change in output voltage is equal to V, the ripple component of outpu
voltage. The average or dc value of output voltage, Vae is almost between the peak value V max and the
minimum value given by points b and c respectively in Fig. 13.10 (c). Thus

Vde VL max ..(13.62)

The total charge lost during non-conduction (or discharge) duration T, through load is given as
dichargeT .(13.63)
This charge is replenished during time interval T1, in which voltage across the capacitor increases
by V, volts. So charge gained by capacitor,
Qcharge CV, .(13.64)
In steady-state, QchargeQdischarge
or CV, =
leT2
or V, = ac2

Assuming T, << T2 T T So V, .(13.65)

Hence from Eq. (13.62) V =
VL max -2c
2fC .(13.66)
From Eq. (13.65) it is revealed that ripple voltage varies directly with the load current I and
inversely with the capacitance C.
Ripple Factor. The rms value of the ripple component of almost triangular wave is independent
of the slope or the length of the almost
straight lines bc and cd but depends only on the peak value
of V The rms value is given as

Vaac rms
23
Hence ripple factor, Y = rms V,
Vae 2v3 Ia R 2/3 Iae R fC .(13.67)
23f CRL
2. Full-Wave Rectifier WithShunt Capacitor
Filter. The filtering action of shunt capacitor filter RECTIFIED
OUTPUT FILTERED
on a full wave rectifier is shown in Fig. 13.11. In OUTPUT
this
Vmax
case capacitance C
discharges twice duringLm VLmin
one cycle. Because both the diodes conduct, non- VAc
conduction period has reduced. The result is that
ripple voltage V, has been reduced to half and V 37t

has been increased relative to half-wave rectifier.

T Fig. 13.11 Rectified and Filtered Output Voltage
In this case
because T2 = =
1/2fs Waveform From Full-Wave Rectifier With Shunt
Filter Capacitor
So v,2C ..(13.68)
 Vde VL max = V,Vmax (13.69)
4fC
VaC rms

So ripple factor, Y = ac Ims

Vde D
23 1acRL .(13.70)
43f CRL
Voltage regulation in this case is better than that in half-wave rectifier.

13.4.3. Choke-Input or L-Section Filter

eimnle series inductor reduces both the peak and effective values of the output current and output
voltage. On the other hand simple shunt capacitor filter reduces the ripple voltage but increases the
Aode current. The diode may get damaged due to large current and at the same time it causes greater
heating of supply transtformer resulting in reduced efficiency.
In an inductor filter, ripple factor increases with the increase in load resistance R, while in a
Capacitor filter it varies inversely with load resistance R
From economical point of view also, neither series inductor nor shunt capacitor type filters are suitable.
Practical filter-circuits are derived by combining the voltage stabilizing action of shunt capacitor
with the current smoothing action of series choke coil. By using combination of inductor and capeitor
ripple factor can be lowered, diode current can be restricted and simultaneously ripple factor can be
made almost independent of load resistance (or load current). Two types of most commonly used
combinations are choke-input or L-section filter and capacitor-input or n-filter. Choke-input filter is
explained below.
Choke-input filter consists of a choke L connected in series with the rectifier and a capacitor C
across the load, as shown in Fig. 13.12 (a). This is
also sometimes called the L-section filter because in this OOO00
arrangement inductor and capacitor are connected, as an
inverted L. In Fig. 13.12 (a) only one filter section
shown, but several identical sections are often employed
to improve the smoothing action. The choke L on the
input side of the filter readily allows de to pass but
opposes the flow of ac components because its dc resist- (a) Circuit Diagram
ance is negligibly small but ac impedance is large. Any FILTEREDD RECTIFIED
fluctuation that remains in the current even after passing L max OUTPUT OUTPUT

the load
through the choke are largely bypassed around -Vac
by the shunt capacitor because X is much smaller than
R. Ripples can be reduced effectively by making X 21 3
greater than X at ripple frequency. However, a small rip-
ple still remains in the filtered output and this is consid-
(b)Rectified and
and)Kecyied and Filtered
Filtered Ouiput
Ouput Voltage Waveform
Voltage Waveform
ered negligible if it is less than 1%. The rectified
Tiltered output voltage waveforms from a full-wave recti-
Full-wave Rectifier With Choke-lnput Filter

Tier with choke-input filter are shown in Fig. 13.12 (b). Fig. 13.12

Regulation. The output voltage of the rectifier is given as

VL max L ma COs 2 ...(13.71) refer to Eq. (13.59)

Considering that the inductor has negligibly small (almost zero) resistance

Va Lmax ..(13.72)
 If R is the choke resistance, then
Vae VL max - Jhe Rc
.(13.73)
in the system
Ripple Factor. The main object of the filter is to suppress the harmonic components
and for this it is necessary that reactance of the choke coil X, is made much greater than combined
of the C and load resistor
capacitor R. The parallel impedance of capacitor C and
parallel impedance
load resistor R, can be made small by making the reactance of capacitor. Xc much smaller than load
resistance R Very little error is caused if it is assumed that the entire alternating current is fowing
through the capacitor and none through the load resistor R,. Under these conditions the net impedance
acros the input terminals of the filter circuit is approximately X = 20L, the reactance of the inductor
at the second harmonic frequency. AC current through the circuit is given as

ac ms max 2 .(13.74) Vae #VL max

37t 2 XL XL
The ac voltage across the load (the ripple voltage) is equal to the voltage across the capacitor so

V.ac rms aCmsXc (13.75)

AL
where Xc = . the reactance of the capacitor at the second harmonic frequency.
20C

Ripple factor, y = Vac 2 Xc (13.76)

20C 20L 6/20 LC
Critical Inductance. During the above discussion it has been assumed that a current flows through
the circuit at all times. In the absence of inductor, current flows through the diode circuit for a small portion
of the cycle, and the capacitor is charged to the peak transformer secondary voltage in each cycle
(neglecting diode forward and transformer resistance). When a small inductance is inserted in the circuit
the diode current will exist for a longer duration but cutout may still occur. With the continuous increase
in inductance, a value is reached for which diode current exists for the whole cycle. This value of
inductance is referred to as the critical inductance Lc.

Current flowing through the load is made up of two components Ic given as and ac component
of peak value L max
3TTX L
For continuous flow of current through diode it is necessary that should always exceed the
negative peak value of ac component so

Na 2 4VL max or
Vde 2L mAL
RL TAL
or RL ..(13.77)
30
The L-C filter was quite popular at one time. Now, it is becoming obsolete in
typical power supplies
because of the size and cost of inductors. For low-voltage power supplies, the L-C filter has been replaced
by IC voltage regulators, active filters that reduce ripple and hold the output dc voltage constant.