This document discusses different types of uncontrolled diode rectifiers. It begins by classifying rectifiers as controlled, half-controlled, or uncontrolled based on whether they use thyristors, thyristors and diodes, or only diodes, respectively. The document then describes various single-phase and three-phase uncontrolled rectifier circuits including half-wave, full-wave center-tap, full-wave bridge, and multiphase designs. Key parameters like efficiency, voltage, current, ripple, and frequency are defined for each rectifier type. Circuit diagrams and operating principles are provided to explain how the different rectifiers function.

1. Diode (Uncontrolled) Rectifiers
ER. FARUK BIN POYEN
ASST. PROFESSOR
DEPT. OF AEIE, UIT, BU
FARUK.POYEN@GMAIL.COM

2. Contents:
 Classification of Rectifiers
 Performance Parameters of Rectifiers
 1 – φ Half Wave Rectifier
 1 – φ Full Wave Rectifier – Centre Tapped
 1 – φ Full Wave Bridge Rectifier
 3 – φ Uncontrolled Rectifier Classification
 3 – φ Half Wave Rectifier
 3 – φ Full Wave 6 Pulse Mid – Point Rectifier
 3 – φ Full Wave Bridge Rectifier
 3 – φ Full Wave 12 Pulse Rectifier
2

3. Classification of Rectifiers based on Control:
 The converter circuit which converts AC to DC is called a Rectifier.
 The rectifier circuit using diodes only is called an Uncontrolled rectifier circuit.
 All rectifiers are broadly categorized into three sections.
1. Controlled Rectifier - It has only thyristors. NO diodes
2. Half Controlled Rectifier - It has thyristor + diodes
3. Uncontrolled Rectifier - Only diodes
 Control here means controlling when to start rectification and when to stop.
3

4. Classification of Uncontrolled Rectifiers:
 Single Phase Half Wave Uncontrolled Rectifier (with R load, RL load and RL with FD)
 Single Phase Full Wave Uncontrolled Rectifier.
1. Centre Tapped (Mid Point) Rectifier
2. Bridge Rectifier
 Three Phase Full Wave Uncontrolled Rectifier.
1. 3 – φ Half Wave Rectifier
2. 3 – φ Mid Point 6 Pulse Rectifier
3. 3 – φ Bridge Rectifier
4. 3 – φ 12 Pulse Rectifier
4

5. Uncontrolled Rectifiers Parameter Comparison:
Parameters Half-wave
Centre tapped
Full-wave
Bridge
No of Diodes 1 2 4
Max. Efficiency 40.6% 81.2% 81.2%
Peak Inverse Voltage VM 2VM VM
Average Current/Diode Idc Idc/2 Idc/2
Vdc (no load) Vm/π 2Vm/π 2Vm/π
Output Frequency f 2f 2f
Transformer Utilisation Factor 0.287 0.693 0.812
Ripple Factor 1.21 0.48 0.48
Form Factor 1.57 1.11 1.11
Peak Factor 2 √2 √2
5

6. Single Phase Half Wave Rectifier:
 During each “positive” half cycle of the AC sine wave, the diode is forward biased as the
anode is positive with respect to the cathode resulting in current flowing through the
diode.
 Since the DC load is resistive (resistor, R), the current flowing in the load resistor is
therefore proportional to the voltage (Ohm´s Law), and the voltage across the load resistor
will therefore be the same as the supply voltage, V s (minus V f), that is the “DC” voltage
across the load is sinusoidal for the first half cycle only so V out = V s.
 During each “negative” half cycle of the AC sinusoidal input waveform, the diode is
reverse biased as the anode is negative with respect to the cathode.
6

7. Single Phase Half Wave Rectifier:
 Therefore, NO current flows through the diode or circuit. Then in the negative half cycle
of the supply, no current flows in the load resistor as no voltage appears across it so
therefore, V out = 0
7

8. Single Phase Half Wave Rectifier (R Load): 8
 𝐴𝑣. 𝑜𝑢𝑡𝑝𝑢𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉0 =
1
2𝜋 0
𝜋
𝑉 𝑚 𝑠𝑖𝑛𝜔𝑡𝑑(𝜔𝑡) =
𝑉 𝑚
2𝜋
−𝑐𝑜𝑠𝜔𝑡 0
𝜋
=
𝑉 𝑚
𝜋
 𝑅𝑀𝑆 𝑂𝑢𝑡𝑝𝑢𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉 𝑟𝑚𝑠 =
1
2𝜋 0
𝜋
𝑉 𝑚
2
𝑠𝑖𝑛2
𝜔𝑡𝑑(𝜔𝑡)
1
2
=
𝑉 𝑚
2𝜋 0
𝜋 1−𝑐𝑜𝑠2𝜔𝑡
2
𝑑(𝜔𝑡)
1
2
=
𝑉 𝑚
2
 𝐴𝑣. 𝐿𝑜𝑎𝑑 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐼0 =
𝑉0
𝑅
=
𝑉 𝑚
𝜋𝑅
 𝑅𝑀𝑆 𝐿𝑜𝑎𝑑 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐼 𝑟𝑚𝑠 =
𝑉 𝑟𝑚𝑠
𝑅
=
𝑉 𝑚
2𝑅
 𝐼𝑛𝑝𝑢𝑡 𝑃𝑜𝑤𝑒𝑟 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝑉 𝑟𝑚𝑠∗𝐼 𝑟𝑚𝑠
𝑉 𝑠∗𝐼 𝑟𝑚𝑠
=
2𝑉 𝑠
2𝑉 𝑠
= 0.707 𝑙𝑎𝑔

9. Single Phase Half Wave Rectifier (RL Load):
 Current I 0 continues to flow even after source voltage V S is negative because of the
presence of inductance L in load.
 After + ve half cycle, diode remains ON, so – ve half cycle appears across load current
until I 0 decays to zero at ωt = β.
 When I 0 = 0 at ωt = β; V L = 0, V R = 0 and V S appears as reverse bias across diode D.
 At β, diode voltage V D jumps from 0 to V M sin β where β > π.
 Here β = γ is the conduction angle of the diode.
9

10. Single Phase Half Wave Rectifier (RL Load):
 𝐴𝑣. 𝑜𝑢𝑡𝑝𝑢𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉0 =
1
2𝜋 0
𝛽
𝑉 𝑚 sin 𝜔𝑡 𝑑 𝜔𝑡 =
𝑉 𝑚
2𝜋
1 − cos 𝛽
 𝐴𝑣. 𝑂𝑢𝑡𝑝𝑢𝑡 𝐶𝑢𝑟𝑟𝑟𝑒𝑛𝑡 𝐼0 =
𝑉0
𝑅
=
𝑉 𝑚
2𝜋𝑅
1 − cos 𝛽
10

11. Single Phase Half Wave Rectifier (RL with FD):
 Performance is improved by connecting FD across the load.
 FD prevents o/p voltage from becoming –ve.
 The load current waveform is more smooth and load performance is better.
 System efficiency is improved as energy from L is transferred to R through FD.
 𝐴𝑣. 𝑜𝑢𝑡𝑝𝑢𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉0 =
1
2𝜋 0
𝜋
𝑉 𝑚 sin 𝜔𝑡 𝑑 𝜔𝑡 =
𝑉 𝑚
𝜋
; 𝐴𝑣. 𝐿𝑜𝑎𝑑 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐼0 =
𝑉 𝑚
𝜋𝑅
11

12. 1 – φ Full Wave Rectifier – Centre Tapped
 Also called Mid – point rectifier.
 The turns ration from each secondary to primary is taken as unity for simplicity.
 When “A” is +ve w.r.t mid – point O, D1 conducts for π radians.
 When “B” is +ve w.r.t mid – point O in the next half cycle, D2 conducts for the other π
radians.
 Peak Inverse Voltage (PIV) for both D1 and D2 is 2 V S and hence it is called 1 – φ 2 –
pulse diode rectifier.
12

13. 1 – φ Full Wave Rectifier – Centre Tapped
 𝐴𝑣. 𝑂𝑢𝑡𝑝𝑢𝑡 𝑃𝑜𝑤𝑒𝑟 𝑉0 =
1
𝜋 0
𝜋
𝑉 𝑚 sin 𝜔𝑡 𝑑 𝜔𝑡 =
2𝑉 𝑚
𝑅
 𝐴𝑣. 𝑂𝑢𝑡𝑝𝑢𝑡 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐼0 =
𝑉0
𝑅
=
2𝑉 𝑚
𝜋𝑅
 𝑅𝑀𝑆 𝑂𝑢𝑡𝑝𝑢𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉 𝑟𝑚𝑠 =
1
𝜋 0
𝜋
𝑉 𝑚
2
𝑠𝑖𝑛2
𝜔𝑡𝑑(𝜔𝑡)
1
2
=
𝑉 𝑚
2
= 𝑉 𝑆
 𝑅𝑀𝑆 𝑂𝑢𝑡𝑝𝑢𝑡 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐼 𝑟𝑚𝑠 =
𝑉 𝑟𝑚𝑠
𝑅
=
𝑉 𝑠
𝑅
 𝑃𝑜𝑤𝑒𝑟 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑒𝑑 𝑡𝑜 𝑙𝑜𝑎𝑑 = 𝑉 𝑟𝑚𝑠 ∗ 𝐼 𝑟𝑚𝑠 = 𝐼 𝑟𝑚𝑠
2
𝑅
 𝑃𝑜𝑤𝑒𝑟 𝐹𝑎𝑐𝑡𝑜𝑟 𝑝𝑓 =
𝑉 𝑟𝑚𝑠.𝐼 𝑟𝑚𝑠
𝑉 𝑆.𝐼 𝑟𝑚𝑠
= 1
13

14. 1 – φ Full Wave Bridge Rectifier
 On the positive half cycle of transformer secondary supply voltage, diodes D1 and D2
conduct, supplying this voltage to the load.
 On the negative half cycle of supply voltage, diodes D3 and D4 conduct supplying this
voltage to the load.
 It can be seen from the waveforms that the peak inverse voltage of the diodes is only V m
 The average output voltage is the same as that for the centre - tapped transformer full-
wave rectifier.
 𝑃𝑒𝑎𝑘 𝑅𝑒𝑝𝑒𝑡𝑖𝑡𝑖𝑣𝑒 𝐷𝑖𝑜𝑑𝑒 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐼 𝑚 =
𝑉 𝑚
𝑅
 𝐴𝑣. 𝑂𝑢𝑡𝑝𝑢𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉0 =
2𝑉 𝑚
𝜋
; 𝑅𝑀𝑆 𝑂𝑢𝑡𝑝𝑢𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉 𝑟𝑚𝑠 = 2𝑉 𝑠
14

15. 1 – φ Full Wave Bridge Rectifier
 𝐴𝑣. 𝐷𝑖𝑜𝑑𝑒 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐼 𝐷𝐴 =
1
2𝜋 0
𝜋
𝐼 𝑚 sin 𝜔𝑡 𝑑 𝜔𝑡 =
𝐼 𝑚
𝜋
;
 𝑅𝑀𝑆 𝑂𝑢𝑡𝑝𝑢𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉 𝑟𝑚𝑠 = 2𝑉 𝑆
 𝑅𝑀𝑆 𝐷𝑖𝑜𝑑𝑒 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐼 𝐷𝑟𝑚𝑠 =
1
2𝜋 0
𝜋
𝐼 𝑚
2
sin2
𝜔𝑡 𝑑 𝜔𝑡
1
2
=
𝐼 𝑚
2
15

16. 3 – φ Uncontrolled Rectifier
 3 – φ Rectifier offers the following advantages:
1. Higher o/p voltage for a given i/p voltage.
2. Lower amplitude ripples i.e. output voltage is smoother.
3. Higher frequency ripples simplifying filtering.
4. Higher overall efficiency.
16

17. 3 – φ Uncontrolled Rectifier: Classification
 They are generally of four types.
1. 3 – φ Half – wave rectifier.
2. 3 – φ Mid – point 6 Pulse rectifier.
3. 3 – φ Bridge rectifier.
4. 3 – φ 12 Pulse rectifier.
17

18. 3 – φ Half – Wave Rectifier:
 It uses a 3 – φ transformer with primary in delta and secondary in star connection.
 D1, D2 and D3 have common connected cathode to common load R and all diodes are
oriented in different phases and therefore called as Common – Cathode Circuit.
18

19. 3 – φ Half – Wave Rectifier:
 The rectifier element connected to the line at the highest +ve instantaneous voltage can
only conduct and pulsates between V max and 0.5 V max.
 It is called 3 – φ 3 pulse rectifier as the o/p is repeated thrice in every cycle of V s.
 The ripple frequency (f r) of the o/p voltage is
𝑓 𝑟
= 𝑛𝑓 𝑠
; 𝑛 = 𝑛𝑜. 𝑜𝑓 𝑑𝑖𝑜𝑑𝑒𝑠, 𝑓 𝑠
= 𝐴𝐶 𝑠𝑢𝑝𝑝𝑙𝑦 𝑓𝑟𝑒𝑞.
 The ON diode connects its most +ve source terminal to the other two diode cathodes
keeping the other diodes OFF.
 The sudden switchover from one diode to another is called “commutation”.
 Each diode conducts for 120 º intervals.
 Delta connection provides path for triplen (odd multiples of the 3rd harmonic) harmonic
currents stabilizing the voltage on star secondary.
19

20. 3 – φ Half – Wave Rectifier:
𝑉0(𝑎𝑣𝑔.) =
𝑛
𝜋
𝑉𝑚 sin
𝜋
𝑛
= 0.827 ∗ 𝑉𝑚= 0.477 ∗ 𝑉𝐿; 𝑛 = 3;
𝐼0(𝑎𝑣𝑔.) =
𝑛
𝜋
𝐼 𝑚 sin
𝜋
𝑛
= 0.827 ∗ 𝐼 𝑚; 𝐼 𝐷(𝑎𝑣𝑔.) =
𝐼0(𝑎𝑣𝑔.)
𝑛
 RMS value of load current
𝐼 𝑂(𝑅𝑀𝑆) = 𝐼 𝑚
1
2𝜋
𝜋
𝑛
+
1
2
sin
2𝜋
𝑛
1
2
= 0.408 ∗ 𝐼 𝑚; 𝑛 = 3
 𝑅𝑖𝑝𝑝𝑙𝑒 𝐹𝑎𝑐𝑡𝑜𝑟 𝑅𝐹 =
2
𝑛2−1
=
2
32
−1
= 0.177
 𝐹𝑜𝑟𝑚 𝐹𝑎𝑐𝑡𝑜𝑟 = 𝑛 = 3 = 1.732
20

21. 3 – φ Mid – Point 6 Pulse Rectifier:
 A rectifier with more number of pulses will provide a smoothed out curve giving
improved performance and lesser ripples.
 Delta – primary, Star – secondary transformer is used here.
 The secondary of each pulse is in two halves.
 The mid – point of all the secondary's are connected to form the neutral (n).
 Six phase supplies are a1, c2, b1, a2, c1 and b2 terminals.
 Phase voltages are 120 º apart from V a1, V b1 and V c1 and likewise for others.
 V a1 – V a2, V b1 – V b2, V c1 – V c2 are 180 º apart.
 Adjacent voltages are 60 º apart.
 Diode that senses the highest +ve anode voltage conducts with a periodicity of 60 º .
21

22. 3 – φ Mid – Point 6 Pulse Rectifier: 22

23. 3 – φ Mid – Point 6 Pulse Rectifier:
 𝐴𝑣. 𝑂𝑢𝑡𝑝𝑢𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉 𝑂 =
1
𝜋 3 𝜋 3
2𝜋 3
𝑉 𝑚 sin 𝜔𝑡𝑑 𝜔𝑡 =
3𝑉 𝑚
𝜋
 𝑉 𝑟𝑚𝑠 =
1
𝜋 3 𝜋 3
2𝜋 3
𝑉 𝑚
2
𝑠𝑖𝑛2
𝜔𝑡𝑑(𝜔𝑡)
1
2
=
3𝑉 𝑚
2𝜋
𝜋
3
−
sin 240°−sin 120°
2
1
2
= 0.9558 ∗ 𝑉 𝑚
 𝑉 𝑟𝑖𝑝𝑝𝑙𝑒 = 𝑉 𝑟 = 𝑉 𝑟𝑚𝑠
2
− 𝑉0
2
= 𝑉 𝑚 0.9558 2 −
3
𝜋
2 1 2
= 0.0408 ∗ 𝑉 𝑚
 𝑉𝑅𝐹 =
𝑉 𝑟
𝑉0
=
0.0408∗𝜋
3
= 4.3%
 𝐹𝑜𝑟𝑚 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝑉 𝑟𝑚𝑠
𝑉0
=
0.9558∗𝜋
3
= 1.009
 𝑅𝑒𝑐𝑡𝑖𝑓𝑖𝑒𝑟 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 =
𝑉 𝑟𝑚𝑠
𝑉0
=
3
𝜋
2
∗
1
(0.9558)2 = 99.82%
23

24. 3 – φ Bridge Rectifier:
 Two series diodes are always conducting while four diodes are blocking.
 One of the conducting diodes is odd numbered while the other is even numbered.
 Each diode conducts for 120 º.
 Current flows out from the most +ve source terminal through an odd numbered diode
through the load followed by the even numbered diode and then back to the most –ve
source terminal.
 Output has less ripples and the diodes are numbered in accordance to their conductance.
 The bridge uses both the +ve and –ve halves of the i/p voltage.
 Ripple frequency is 6*f.
 Upper set of diodes constitutes the +ve group while the lower set constitutes the –ve.
 Transformer Primary – Secondary is in Delta – Star configuration.
24

25. 3 – φ Bridge Rectifier:
 The diode with the most +ve voltage will be conducting.
 B is chosen as reference.
 During 0º - 30º, the voltage at C is highest (arbitrarily). Hence D5 is conducting as it is
the most +ve.
 Between 30º and 150º, A becomes the most +ve and hence conducting.
 During 150º - 270º, B being most +ve conducts.
 The cycle repeats itself.
 Each diode conducts for 120º.
 𝑂𝑢𝑡𝑝𝑢𝑡 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉𝑂 =
1
𝜋 3 𝜋 3
2𝜋 3
𝑉𝑚 sin 𝜔𝑡𝑑 𝜔𝑡 =
3𝑉 𝑚
𝜋
= 0.955 ∗ 𝑉𝑚
 𝑅𝑀𝑆 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉𝑟𝑚𝑠 =
1
𝜋 3 𝜋 3
2𝜋 3
𝑉𝑚
2 𝑠𝑖𝑛2 𝜔𝑡𝑑(𝜔𝑡)
1
2
=
3𝑉 𝑚
𝜋
= 0.9558 ∗ 𝑉𝑚
25

26. 3 – φ Bridge Rectifier: 26

27. 3 – φ Bridge Rectifier:
 𝐼0 =
𝑉0
𝑅
= 0.9558 ∗ 𝐼 𝑚; 𝐼 𝐷(𝑎𝑣𝑔.) = 𝐼0(𝑎𝑣𝑔.)/3
 𝑅𝑖𝑝𝑝𝑙𝑒 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = 6 ∗ 𝑓 𝑠
; 𝐷𝑖𝑜𝑑𝑒 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 =
2𝜋
3
= 120°
 𝑅𝑖𝑝𝑝𝑙𝑒 𝐹𝑎𝑐𝑡𝑜𝑟 𝑅𝐹 =
2
𝑛2−1
= 0.404
 𝑅𝑒𝑐𝑡𝑖𝑓𝑖𝑒𝑟 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 =
3
𝜋
2
∗
1
0.9558
= 99.82%
 𝑅𝑀𝑆 𝑙𝑖𝑛𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝐼 𝑠 =
2
𝜋 𝜋 3
2𝜋 3
𝐼 𝑚
2
𝑠𝑖𝑛2
𝜔𝑡𝑑(𝜔𝑡)
1 2
= 0.7804 ∗ 𝐼 𝑚
 𝑇𝑈𝐹 =
𝑃 𝑑𝑐
𝑉𝐴 𝑟𝑎𝑡𝑖𝑛𝑔
=
3
𝜋
2
∗
6
3∗0.7804
= 0.9541
 𝑇𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚𝑒𝑟 𝑉𝐴 𝑟𝑎𝑡𝑖𝑛𝑔 = 3 ∗ 𝑉 𝑠 𝐼 𝑠 = 3 ∗
𝑉 𝑚
6
∗ 0.7804 ∗ 𝐼 𝑚
27

28. 3 – φ 12 Pulse Rectifier:
 With 12 pulses per cycle, the o/p waveform quality is much improved with high ripple
frequency.
 12 pulse is constructed by connecting 2 6 – pulse rectifiers in series.
 3 – φ AC source supplying to these two bridges are shifted by 30º w.r.t. each other and
this is achieved by using 2 3 – φ transformers, one is Y connection and other in Δ
connection, on the secondary side.
 The two bridges are series connected having a summation of upper and lower rectifiers.
 The secondary voltage of the Δ transformer is lesser by a factor of 3 to the Y transformer.
 The problem is solved by having a √3 turn’s ration for Y – Δ transformer.
 Ripple frequency is 12 times the source frequency.
 𝑉0(𝑎𝑣𝑔.) =
𝑉 𝑚∗6 2
𝜋 3+1
= 0.989 ∗ 𝑉 𝑚; 𝑃𝐼𝑉 ≥ 3 ∗ 𝑉 𝑠
𝑉0 = 𝑉01 + 𝑉02
28

29. 3 – φ 12 Pulse Rectifier: 29

30. References
 http://www.eng.uwi.tt/depts/elec/staff/rdefour/ee33d
 Power Electronics, P S Bimbhra.
 https://www.slideshare.net/nitishkumar54943600/3-phase-diode-rectifierspower-
electronics
 http://www.ee.co.za/article/rectifier-transformers-technology-update.html
30