ELG4139: and Controlled Rectifiers AC to DC Converters Linear Consist of: • : steps ac up or down. • Rectifier : change ac to “bumpy” dc. • Filter Network: includes and inductors, smooths out the bumps. • : keeps the voltage constant. • Protection: usually a zener circuit. Example: Computer Power Supply

Example: Adjustable Motor Speed Drive

Power Supply Specifics: Half Wave Rectifier

Source: ARRL Half-Wave Rectifier

High 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

  Pdc / Pac Rectification Efficiency

2 2 Vac  Vrms Vdc 푃푎푐 = 푉푟푚푠퐼푟푚푠

FF Vrms /Vdc Form Factor

V V 2 V 2 V 2 RF  ac  rms dc  rms 1  FF 2 1 Ripple factor 2 Vdc Vdc Vdc Example 1: A half-wave rectifier has a pure resistive load of R Determine (a) The efficiency, (b) Form factor (c) Ripple factor.

 1 V V V V V  V sin(t) dt  m (cos  cos(0))  m I  dc  m dc 2  m 2  dc 0 R  R  V 1 V m V  (V sin t)2  m Irms  rms 2  m 2 2 R 0 V V m * m P V * I   R   dc  dc dc   40.53% V V . Pac Vrms * Irms m * m 2 2 R Vm V  FF  rms  2   1.57 Vdc Vm 2  V RF  ac  FF 2 1  1.57 2 1 1.211 Vdc 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 .  2V 1 2Vm m V  V sint dt  190.956 V Idc  12.7324 A dc   m   R 0 1/ 2  1   V V   V sint2 dt  m  212.132 V rms   m 2  0  P V I   dc  dc dc  81.06 % V FF  rms 1.11 Pac Vrms Irms Vdc V V 2 V 2 V 2 RF  ac  rms dc  rms 1  FF 2 1  0.482 2 Vdc Vdc Vdc Real Power V I cos Input power factor =  S S 1 Apperant Power VS I S 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

휋 1 푉푝 푉푑푐 = 푉푝푠푖푛휔푡푑휔푡 = 1 + 푐표푠훼 2휋 훼 2휋

휋 1 2 2 1/2 푉푟푚푠 = 푉푝 푠푖푛 휔푡푑휔푡 2휋 훼

1/2 푉 1 푠푖푛2훼 = 푝 휋 − 훼 + 2 휋 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

휋+훼 2 2푉푝 푉푑푐 = 푉푝푠푖푛휔푡푑휔푡 = 푐표푠훼 2휋 훼 휋

휋+훼 2 2 2 1/2 푉푟푚푠 = 푉푝 푠푖푛 휔푡푑휔푡 2휋 훼

푉 = 푝 = 푉 2 푠

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