ELG4139: Rectifiers and Controlled Rectifiers AC to DC Converters

Linear Rectifier Consist of:

• Transformer: steps ac voltage up or down.

• Rectifier Diodes: change ac to “bumpy” dc.

• Filter Network: includes capacitors and inductors, smooths out the bumps.

• Voltage Regulator: keeps the voltage constant.

• Protection: usually a zener diode circuit.

Example: Computer Power Supply

Example: Adjustable Motor Speed Drive

Power Supply Specifics: Half Wave Rectifier

Source: ARRL

Half-Wave Rectifier

High ripple factor.

Low rectification efficiency.

Low transformer utilization factor.

Power Supply Specifics Full Wave Center-Tapped Rectifier

Source: ARRL

Power Supply: Full Wave Bridge Rectifier

Source: ARRL

Filtering Capacitors are used in power supply filter networks. The

capacitors smooth out the rippled AC to DC.

Source: ARRL

Rectifier Performance Parameters

22dcrmsac VVV

acdc PP / Rectification Efficiency

dcrms VVFF /

11 2

2

222

FFV

V

V

VV

V

VRF

dc

rms

dc

dcrms

dc

ac

Form Factor

Ripple factor

𝑃𝑎𝑐 = 𝑉𝑟𝑚𝑠𝐼𝑟𝑚𝑠

Example 1: A half-wave rectifier has a pure resistive load of R Determine (a) The efficiency, (b) Form factor (c) Ripple factor.

mm

mdc

VVtdtVV ))0cos(cos(

2)sin(

2

1

0 R

V

R

VI mdc

dc

2)sin(

2

1

0

2 mmrms

VtVV

R

VI m

rms2

%53.40

2*

2

*

*

*

R

VV

R

VV

IV

IV

P

P

mm

mm

rmsrms

dcdc

ac

dc

57.12

2

m

m

dc

rms

V

V

V

VFF

211.1157.11 22 FFV

VRF

dc

ac

.

Three-Phase Diode Bridge Rectifier

Waveforms and Conduction Times of Three-Phase Bridge Rectifier

Three-Phase Full-Wave Rectifier

Example 2: A single-phase diode bridge rectifier has a purely resistive load of R=15 ohms and, VS=300 sin 314 t and unity transformer ratio. Determine (a) The efficiency, (b) Form factor, (c) Ripple factor, (d) and, (d) Input power factor.

VV

tdtVV mmdc 956.190

2sin

1

0

AR

VI m

dc 7324.122

VV

tdtVV mmrms 132.212

2sin

12/1

0

2

%06.81rmsrms

dcdc

ac

dc

IV

IV

P

P

11.1dc

rms

V

VFF

482.011 2

2

222

FFV

V

V

VV

V

VRF

dc

rms

dc

dcrms

dc

ac

Input power factor = 1cosPowerReal

SS

SS

IV

IV

PowerApperant

Alternative! Controlled Switching Mode

• By using linear regulator, the AC to DC converter is not efficient and of large size and weight!

• Using Switching-Mode

• High efficiency

• Small size and light weight

• For high power (density) applications.

• Use Power Electronics!

Thyristors and Controlled Rectifiers

Controlled Rectifier Circuit

𝑉𝑑𝑐 =1

2𝜋 𝑉𝑝𝑠𝑖𝑛𝜔𝑡𝑑𝜔𝑡 =

𝑉𝑝2𝜋

𝜋

𝛼

1 + 𝑐𝑜𝑠𝛼

𝑉𝑟𝑚𝑠 =1

2𝜋 𝜋

𝛼

𝑉𝑝2𝑠𝑖𝑛2𝜔𝑡𝑑𝜔𝑡

1/2

=𝑉𝑝

2

1

𝜋𝜋 − 𝛼 +

𝑠𝑖𝑛2𝛼

2

1/2

Example: Consider the following SCR-based variable voltage supply. For RL=240 Ohm, derive the RMS value of the load voltage as a function of the firing angle, and then calculate the load power

when the firing angle is 0, /2, and .

Full-Wave Rectifiers Using SCR

𝑉𝑑𝑐 =2

2𝜋 𝑉𝑝𝑠𝑖𝑛𝜔𝑡𝑑𝜔𝑡 =

2𝑉𝑝𝜋

𝜋+𝛼

𝛼

𝑐𝑜𝑠𝛼

𝑉𝑟𝑚𝑠 =2

2𝜋 𝜋+𝛼

𝛼

𝑉𝑝2𝑠𝑖𝑛2𝜔𝑡𝑑𝜔𝑡

1/2

=𝑉𝑝

2 = 𝑉𝑠

With a purely resistive load, SCRs S1 and S2 can conduct from to , and SCRs S3 and S4 can conduct from + to 2.