Power Electronics Electronic Science

1

Electronic Science Power Electronics

8. Diode Rectifiers

Module 8: Diode Rectifiers

1. Introduction

2. Performance parameters

2.1. Single phase half-wave rectifier (HWR)

2.2. Center tapped full wave rectifier (FWR)

2.3. Bridge rectifier

3. Half-Wave Rectifiers

3.1. HWR to RL load without freewheeling diode

3.2. HWR to RL load with freewheeling

3.3. HWR for Battery Charging

4. Bridge rectifier with RLE load

5. Rectifier Filter Design

5.1. DC filters (load or output side filters)

5.2. AC filters (input side filters)

6. Summary

Learning objectives

1 To know types of Rectifiers

2 To understand Working of Single phase Rectifiers

3 To define and Determine Performance Parameters

4 To study Rectifiers with different Types of Loads

5 To study Rectifier Filters

2


8. Diode Rectifiers

1. Introduction

Diodes are also called as rectifiers and are extensively used as rectifiers in most of the applications.

Rectifier converts bidirectional input voltage in unidirectional voltage. This process is called as

rectification. In short, rectifier circuit is ac to dc converter. The rectifiers can also be categorized

according to type of input or source voltage, for example, single phase rectifier and multiphase rectifier.

Practically, most of the multiphase rectifiers are three phase rectifiers. Rectifiers can be categorized

according to rectifier circuits, for example, half wave and full wave rectifiers. Rectifiers are widely used

in DC Power Supply, SMPS, DC Motor Drives etc. In the subsequent sections various single phase

rectifier circuits are discussed.

2. Performance Parameters

There are different types of rectifiers. The rectifier circuit is selected according to the requirements of a

application. It is necessary to evaluate quality of rectifier quantitatively. Such quantitative evaluation of

rectifier performance is generally on the basis of rectifier parameters as listed below.

a) Average value of the output voltage, Vdc.

b) Average value of the output current, Idc.

c) Output DC Power, Pdc = Vdc Idc,

d) Rms value of the of the output voltage, Vrms,

e) Output ac power, Pac = VrmsIrms.

f) Efficiency, η = Pdc/Pac.

g) Form factor, FF = Vrms/Vdc.

h) Ripple Factor, RF = Vac/Vdc.

i) Transformer Utilization Factor TUF = Pdc/VsIs.

j) Displacement Factor, DF = cos().

k) Harmonic Factor, HF = ((Is2-Is1

2)/Is1

2)

1/2 = [(Is/Is1)

2-1]

1/2.

l) Power Factor, PF = (VsIs1/VsIs) cos = (Is1/Is) cos .

m) Crest Factor, CF = (Is(peak)/Is).

n) Peak inverse voltage (PIV) of a diode.

o) Pulse Number: The ratio of the fundamental frequency of the DC ripple (fripple) to the AC supply

frequency (fs).

3


8. Diode Rectifiers

The simplifying assumptions for the analysis of idealized circuits are as follows.

a) The voltage drop across switching devices is neglected while they are conducting, and the leakage

current is neglected while they are blocking.

b) The turn-on and turn-off times of the switching devices are negligible.

c) The AC line voltage is sinusoidal and there is no stray impedance; for example line impedance,

transformer reactance.

d) DC current constant over each cycle at its average value.

2.1 Single Phase Half-Wave Rectifier (HWR)

A single phase half wave rectifier (HWR) is shown in Figure 1(a). It consists of a transformer, a

diode with resistive load R. During the positive half cycle diode is forward biased and current

flow through diode D and resistor R. Thus the input appears at load resistor. During negative half

cycle, diode is reverse biased and hence it turns off. Therefore no current flows through load and

the load voltage is zero. The output voltage across the resistor is half wave rectified. Hence it is

called as half wave rectifier. Input and output voltages as well as currents are graphically

represented in Figure 1(b).

4


8. Diode Rectifiers

Figure 1 Single phase half wave rectifier with purely resistive load (a) circuit and (b) input and output

waveforms.

The rms and dc values of input and output can be determined from waveforms as follows.

VV

dtwtVT

dttvT

V m

T

m

T

rms 5.02

))sin((1

)(1

2

1

2

0

22

1

0

2

0

R

V

R

VI mrms

rms

5.0

mm

T

m

T

dc VV

dttVT

dttvT

V 318.0)sin(1

)(1 2

000

ωt

vo

Vm

π 2π 0

0 ωt

vo Vm

0 ωt

Vm/R

i0

0 ωt

vD

-Vm

+

-

+ - is

R

vD

vp vs vo

+

- -

+ i0

(a)

D

(b)

5


8. Diode Rectifiers

fT

f 2,1

R

V

R

VI mdc

dc

318.0

R

VPand

R

VP m

acm

dc

225.0318.0

The remaining parameters can be easily calculated as follows.

%45.40ac

dc

P

P

%12121.1157.11 22 FFRF

mm

T

ms VV

dttVV 707.02

sin2

1 2

1

0

2

R

VII m

loads

5.0

286.0

)5.0

)(707.0(

318.02

R

VV

R

V

IV

PTUF

mm

m

ss

dc

It is evident from the output voltage the pulse number is 1. The maximum reverse voltage across diode is

–Vm. hence the diode PIV = Vm.

2.2 Center Tapped Full Wave Rectifier (FWR)

A single phase center tapped full wave rectifier (FWR) is shown in Figure 2(a). It consists of a

transformer, two diodes D1 and D2 with resistive load R. During the positive half cycle diode D1

is forward biased and D2 is reverse biased hence it turns off. The current flows through diode D1

and resistor R. Thus the input positive half cycle appears at load resistor. During negative half

cycle, diode D1 is reverse biased hence it turns off and D2 is forward biased. The current flows

6


8. Diode Rectifiers

through diode D1 and resistor R. Thus the input positive half cycle appears at load resistor. Thus

during both half cycles the positive output voltage appears across the resistor. Hence it is called

as full wave rectifier. Input and output voltages as well as currents are graphically represented in

Figure 2(b).

Figure 2 Single phase center tapped full wave rectifier with purely resistive load (a) circuit, (b) input and

output waveforms and (c) waveforms of secondary current.

The rms and dc values of input and output can be determined from waveforms as follows.

VV

dtwtVT

dttvT

V m

T

m

T

Lrms 5.02

))sin((1

)(1

2

1

2

0

22

1

0

2

vD1 is1

R D1

vp

vs1 vo

+

-

+

-

vs2

is2

D2

+

-

+

-

vD2

+ -

+ -

i0

vs = vs1 = vs2

(a)

0

Vm/R

is1

0

Vm/R

is2

π 2π

(c)

0

vo Vm

ωt

vo

Vm

π 2π 0

0

Vm/R i0

0

vD1

-2Vm

(b)

7


8. Diode Rectifiers

R

V

R

VI mrms

rms

5.0

)12

(cos)sin(1

)(1 2

00

T

T

VdttV

Tdttv

TV m

T

m

T

Ldc

fT

f 2,1

R

V

R

VIV

VV mdc

dcmm

dc

318.0318.0

R

VPand

R

VP m

acm

dc

225.0318.0

%45.40ac

dc

P

P

%12121.1157.11 22 FFRF

mm

T

ms VV

dttVV 707.02

sin2

1 2

1

0

2

R

VII m

loads

5.0

286.0

)5.0

)(707.0(

318.02

R

VV

R

V

IV

PTUF

mm

m

ss

dc


–2Vm. hence the diode PIV = 2Vm.

8


8. Diode Rectifiers

2.3 Bridge rectifier

A single phase bridge type full wave rectifier (FWR) is shown in Figure 3(a). It consists of a

transformer, four diodes D1, D2, D3, and D4 with resistive load R. During the positive half cycle

diode D1 and D2 is forward biased hence turns on and D3 and D4 are reverse biased hence it turns

off. The current flows through diode D1, resistor R and diode D2.. Thus the input positive half

cycle appears at load resistor R. During negative half cycle diode D3 and D4 is forward biased

hence turns on and D1 and D2 are reverse biased hence it turns off. The current flows through

diode D3, resistor R and diode D4.. Thus the input positive half cycle appears at load resistor R.

Thus during both half cycles the positive output voltage appears across the resistor. Hence it is

called as full wave rectifier. Timing waveforms of input and output voltages as well as currents

are shown in Figure 3(b).

Figure 3 Single Phase Bridge Rectifier with purely resistive load (a) circuit, (b) input and output

waveforms and (c) secondary current waveform.

R

D1 D3

D4 D2

i0

iD1

is

v

0

+

-

vs

+

-

vp

+

-

(a) (b)

ωt

vs

Vm

π 2π 0

π 2π 0

io

Vm/R

π

vo

Vm

2π 0

vD1 π 2π

0

-

Vm

(c) is

Vm/R

π 2

π

0

9


8. Diode Rectifiers


–2Vm. hence the diode PIV = 2Vm.

3. Half-Wave Rectifiers

Let us consider the circuit of half wave rectifier with RL load as shown in Figure 4(a). Due to inductive

load the conduction period diode D1 will extend beyond 1800, until current returns to zero at ωt=π+.

The waveforms of current and voltage are as shown in Figure 4(b). The average voltage across the

inductor vL is zero.

3.1 Half-Wave Rectifier to RL load without freewheeling diode

R D1

L

i0 iS

vp

+

- vS

+

-

v0

+

-

vD1 + - (a) (b)

vS

ωt π 2π

Vm

0

i0

Im = Vm/R

0

vR

0

v0

σ

0

vD

0

10


8. Diode Rectifiers

Figure 4 Single phase half wave rectifier with RL load without freewheeling diode, Dm (a) circuit and (b)

input and output waveforms.

The average output voltage is given as

cos1mdc

VV and

the average load current is given as RVI dcdc .

From these equations it can be seen that the average output voltage and hence current are dependent on

value of σ. It clearly shows Vdc is decreased significantly and dependent on the inductor value.

When diode turns off, the inductor back emf creates high voltage transient. It may lead to the destructive

breakdown of a diode if power dissipation is high during turn off.

3.2 Half-Wave Rectifier to RL load with freewheeling diode

From the equations of average output voltage and current, it can be seen that the average output voltage

and hence current can be increased and reach to maximum by adjusting σ = 0. The drawback of the above

circuit of half wave rectifier can be removed with the use of freewheeling diode Dm. this diode is to be

connected across the RL load as shown in the Figure 5(a). This diode is used in reverse bias as shown in

the Figure 5(a) to avoid the negative voltage appearing across the load. This increases the stored magnetic

energy. At time t = t1 = π/ω, the current from D1, is transferred to Dm. This process is called as

commutation of diodes and the corresponding input and output waveforms are as shown in the Figure

5(b) and 5(c). Depending on the load time constant, the load current may be discontinuous. The load

current i0 is discontinuous with resistive load and continuous with very high inductive load. The

continuity of the load current depends on its time constant

11


8. Diode Rectifiers

Figure 5 Single phase half wave rectifier with RL load with freewheeling diode, Dm (a) circuit and (b)

input and output waveforms.

3.3 Half Wave Rectifier for Battery Charging

Figure 6 Single phase half wave rectifier for battery charging (a) circuit and (b) input and output

waveforms.

n:1

R D

E

i0

vs

+

-

vp +

-

(a) vs

ωt

E

0

Vm

π 2π

i0

(Vm-E)/R Im

0

(b)

(b)

R D1

L

i0 iS

vp

+

-

vS

+

-

v0

+

-

vD1 + - (a)

Dm

iD m

vS

ωt π 2π

Vm

0

vR

0

vD

0

v0

0

(c)

iDm

0

i0

0

Im

R

iS

Im

R 0 π 2π

ωt

12


8. Diode Rectifiers

If the output of the diode circuit is connected to a battery, the diode rectifier can be used as a

battery charger. This is shown in the Figure 6.

For vs > E, diode D conducts. The angle when the diode starts conducting can be found from

the condition Vm sin = E.

The diode turns off when vs < E at β = π - . The charging current can be found from the

equation:

tforR

EtV

R

Evi ms sin0 .

4. Bridge rectifier with RLE load

Vm (c)

v0

vS

ωt π 2π

0

Vm E

0

i0

0

is

β 0

0

(b)

vS

ωt π 2π

Vm

v0

0

i0

0

I

is

π+θ θ π/2 0

(a) i0

vp

+

-

vS

+

-

iS R

D1 D3

D4 D2 L

E

v0

+

‒

13


8. Diode Rectifiers

Figure 7 Single Phase Bridge Rectifier with purely resistive load (a) circuit, (b) input and output

waveforms when E=0 and (c) input and output waveforms when E is positive.

5. Rectifier Filter Design

5.1 DC filters (load or output side filters)

It is seen that, the output of a rectifier circuit contains ripple voltage Vr in addition to dc voltage

VDC. It is necessary to include a filter between the rectifier and the load in order to reduce ripple

components. Filter should reduce the ac component. Passive filters are used because it does not

require additional power sources. Mainly the following passive filters are used at the output of

rectifiers.

1. Shunt capacitor filter

2. Series inductor filter

3. Chock input (LC) filter

4. π section filter or CLC filter or capacitor input filter

In the consequent discussion resistive load R is considered for discussion.

Shunt Capacitor filter

It consists of a large value of capacitor, C connected across the load resistor RL as shown in

Figure 8 (a). This capacitor offers a low reactance to the ac components. The reactance of a

capacitor is XC = 1/2πfC. XC should be smaller than load resistance R. The capacitor C gets

charged when the diode/s of the rectifiers conducting and gets discharged when diode/s in the

rectifier are off. When the input voltage, 𝑣 = 𝑉𝑚 sin (𝜔𝑡), is greater than the capacitor voltage, C

gets charged. When the input voltage is less than that of the capacitor voltage, C will discharge

through R. The stored energy in the capacitor maintains the load voltage at a high value for a

long period. The diode conducts only for a short interval of high current. The waveforms are as

shown in Figure 8 (b). Capacitor opposes sudden fluctuations in voltage across it. So the ripple

voltage is minimized.

0

14


8. Diode Rectifiers

Figure 8 FWR with shunt capacitor filter.

The discharging of the capacitor depends upon the time constant τ = RC. As the value of C

increases, the ripple voltage decreases increasing the smoothness of the output. But, as value of

the capacitor increases Crest factor of rectifier increases. This filter is used in circuits with small

load current like transistor radio receivers, calculators, etc.

Series inductor filter

The working of series inductor filter depends on the inherent property of the inductor to oppose

any variation in current intend to take place. Figure 9 (a) shows a series inductor filter connected

at the output of a Full wave rectifier. Here the reactance of the inductor is more for ac

components and it offers more opposition to them. At the same time it provides no impedance

for dc component. Therefore the inductor blocks ac components in the output of the rectifier and

allows only dc component to flow through RL. The action of an inductor depends upon the

current through it and it requires current to flow at all time. Therefore filter circuits consisting

inductors can only be used together with full wave rectifiers. In inductor filter an increase in load

current will improve the filtering action and results in reduced ripple. Series inductor filters are

used in equipments of high load currents. Series inductor filters are used in resistive welding

machines.

+

-

RL C

FW

R

(a) vo

0 t1

t2

T/2

π 2π

vr(PP)

ωt

(b)

15


8. Diode Rectifiers

Figure 9 FWR with series inductor filter

LC filter

It is a combination of inductor and capacitor filter. Here an inductor is connected in series and a

capacitor is connected in parallel to the load as shown in Figure 10 (a). As discussed earlier, a

series inductor filter will reduce the ripple, when increasing the load current. But in case of a

capacitor filter it is reverse that when increasing current the ripple also increases. So a

combination of these two filters would make ripple independent of load current. Since the dc

resistance of the inductor is very low it allows dc current to flow easily through it. The capacitor

appears open for dc and so all dc component passes through it. The capacitor appears open for dc

and so all dc components passes through the load resistor RL.

Figure 10 FWR with LC filter

π – Filter (Capacitor input filter) or CLC filter

This filter is basically a capacitor filter followed by an LC filter as shown in Figure 11 (a). Since

its shape (C-L-C) is like the letter π it is called π – filter. It is also called capacitor input filter

because the rectifier feeds directly into the capacitor C1. Here the first capacitor C1 offers a low

FW

R

(a)

+

-

RL

L

vo C

(b)

vo

0 π 2π

ωt

vr(PP)

FW

R

(a)

+

-

RL

L

vo

(b)

vo

0 π 2π

vr(PP)

ωt

16


8. Diode Rectifiers

reactance to ac component of rectifier output but provide more reactance to dc components.

Therefore most of the ac components will bypass through C1 and the dc component flows

through chock L. The chock offers very high reactance to the ac component. Thus it blocks ac

components while pass the dc The capacitor C2 bypasses any other ac component appears across

the load and we get study dc output as shown below.

Figure 11 Rectifier with CLC filter and waveforms.

Bleeder resistor

For proper operation of a rectifier, the inductor requires a minimum current to flow through, at

all time. When the current falls below the minimum current, the output voltage will increase

sharply. It may generate voltage transient and hence leads to the poor voltage regulation. To keep

up the circuit current above this minimum value, a shunt resistor is permanently connected

across the filtering capacitor. This resistor is called bleeder resistor. Bleeder resistor always

draws a minimum current even if the external load is removed and avoids overcharging of

capacitor. It provides a path for the capacitor to discharge when power supply is turned off.

FW

R

(b) vo

0 π 2π

ωt

RL

L

C1 C2

(a)

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8. Diode Rectifiers

Comparison of DC Filters

Filter

Type

Shunt C Series L Series LC π section (CLC)

Cost Low high high high

Size and

weight

Small Bulky

due to choke

Bulky

due to choke

Bulky

due to choke

DC output

Voltage

Improved DC

output

Lower DC output Lower DC output More output

voltage

Ripple

voltage

Reduced ripples

output

Higher ripple

output

Reduced ripple

output

Ripple less output

Suitability Can be connected

for both Half wave

and Full wave

rectifiers

Can be connected

for HWR with

additional

freewheeling

diode

Can be connected

for HWR with

additional

freewheeling

diode

Suitable to be used

with both HWR

and FWR

In-rush

current

Very high

during power on

Lowest - Limited

due to choke

Lesser than shunt

C filter

Lesser than shunt

C filter

Load

current

Low load current

applications

high load currents

applications

Action is

independent of

load current

high load currents

applications

18


8. Diode Rectifiers

5.2 AC filters (input side filters)

Due to rectification of the input voltage, input current of rectifier contain harmonics. For bridge

rectifier circuit with resistive load, harmonic content is lowest. Due to dc output filters, the input

current largely deviates from sinusoidal nature increasing harmonic content in input current. To

reduce the harmonic content, filters are necessary at input side or ac side. Harmonic contents also

reduce the power factor. Electric utility or electricity supply distribution companies/ boards

restricts the power drawn by the consumers, so as to reduce the harmonic content in the input

current, or make it sinusoidal.

Two methods are used to design the input filter, (a) passive filters and (b) Active filters

(switching type) to make of input line current close to sinusoidal. Here we are presenting passive

filters only. The active filter will be discussed in subsequent sections.

Low pass (L-C) filter circuit on ac side:

Let us consider single phase bridge rectifier with LC filter at output side as shown in Figure 12

(a). Assume the average (dc) load current is without any ripple. In this case, the ac input (source)

current is square wave in nature as shown in Figure 12 (b).

Figure 12 Rectifier with LC filter and waveforms.

Rectifier

+

LC Filter

(a)

+

–

vs

is +

-

v0

i0

RL

(c)

is

Ia

-Ia

0 2 t

(b)

t

i0

Ia

0

19


8. Diode Rectifiers

Figure 13 Rectifier with LC filter and waveforms.

A low pass filter is needed on the input (source) side to reduce the harmonic components in the

input current. Generally LC or T filter is used at the input side as shown in Figure 13 (a) and (b).

The inductors used tend both to improve the power factor and also reduce harmonics. The overall

energy efficiency remains the same, though additional losses occur in the inductors, but

conduction losses in the diodes are reduced.

6. Summary

Rectifiers are used for ac to dc applications with fixed output voltage. The p erformance

parameters are used for the quantitative analysis, Single phase half-wave rectifiers are not used

in high power applications. Center tapped full wave rectifier and bridge rectifier are widely used

on power electronics due to better performance parameters. -Wave Rectifiers In order to increase

the dc contents DC filters (load or output side filters) are must for single phase applications. AC

filters (input side filters) are required for reducing switching noise in the input.

Rec

tifi

er

+

Fil

ter

(a)

+

-

L

C

+

-

vs

is

v0

i0

RL

Recti

fier

+

Fil

ter

(b)

L1 L2

C

+

-

v0

i0

RL

+

-

vs

is

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Power Electronics Electronic Science