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APPLICATION NOTE
MAINS RECTIFICATION FOR THE GS100T300-x
The GS100T300-x is a family of DC-DC converters with different output voltages (x), that can deliver an output power of 100 Watt when an unregulated DC voltage source of 300 V typical is available. The key data for GS100T300-x are: Po = Output power = 100 Watt Vo = Output voltage = from 3.3 to 48 VDC = Efficiency = 80 % min. Vin = Input voltage = 200 to 400 VDC IinRMS = Input RMS current = 0.88 ARMS The following note describes how to obtain an unregulated DC input voltage from the mains. Four examples are considered: the Europe and Usa mains, and, for each of them, with and without the hold-on characteristic. The hold-on characteristic is the ability of the input voltage source to mantain a DC voltage higher than the minimum input voltage of the DC-DC converter, even in case of a mains interruption of 1 cycle. 1. European mains without the hold on characteristic. The European mains characteristics are: Vinac = 230 VRMS 15 % 240 VRMS 10 % f = 50 Hz The minimum AC voltage is, therefore, 195 VRMS while the maximum AC voltage is 264 VRMS. A bridge rectifier as shown in fig. 1 can be used to obtain the required unregulated DC voltage.
Figure 1: AC-DC converter for Europe Mains.
AC mains C
Unregulated DC voltage
AN645/0594
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MAINS RECTIFICATION AND FILTERING
The typical waweform for this type of rectifier is shown in fig. 2 where: Vc = Voltage across capacitor C. Vpk = peak value of the input AC voltage. Vmin = minimum voltage across capacitor C. tch = charging time of the capacitor C tdch = discharging time of the capacitor C ich = peak charge current for the capacitor C Idc = average input current T = total time for one complete cycle The total energy Win to be supplied by the capacitor C during one full cycle of the mains is: In this case: W in Pin Po = = f *f (1) 2 Vpk = * VinRMSmin - 4 = 1.41* 195 - 4 = 271 V Where 4 V is a good assumption for the voltage drop across the rectifying diodes and the input filter. According to the GS100T300-x data, Vmin=200 V. Therefore, from equation (3): C= During each half cycle, the capacitor has to deliver 1/2 Win and its voltage will drop from Vpk to Vmin. The following equation applies:
1 1 Win = C (V 2 - V 2 ) PK min 2 2
therefore C= Win V
2 pk
(2)
- V2
(3)
min
where Pin is the input power in Watt of the GS100T300-x and f is the mains frequency in Hz. In this case: Win = 100
0.8 * 50
= 2.5 W * s
2.5
271 - 2002
2
= 75 F
Figure 2. Typical waveform for the circuit of fig. 1
mains_2
Vc
Vpk
Vmin
t
Ich
tch tdch
T/2
ich
Idc t
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MAINS RECTIFICATION AND FILTERING
The nearest available value is 82F. By using this value, the new Vmin is given by: Vmin = and so: Vmin = The average value of the input current is given by: Iin(AVG) = ich
*
V2 pk
(10)
Win - C
(4)
From equations (8), (9) and (10): = 2 * 2.23
*
10-3
-3
2712 - 2.5 -6
82* 10
Vripple = Vpk - Vmin
= 207 V
20 * 10
= 0.223
Iin(RMS) = 2.35 = 1.11 ARMS 0.223 Iin(AVG) = 2.35 * 0.223 = 0.524 ADC (5) The RMS current across the capacitor is the difference between the input RMS current and the input average current that is not flowing through the capacitor:
2 I2 Icap(RMS) = in(RMS) - Iin(AVG)
The ripple voltage across the capacitor is:
Vripple = 271 - 207 = 64 Vp-p The maximum voltage across C is obtained when the AC input voltage is at its maximum and the DC-DC converter does not deliver power. In this case the voltage drop across the diodes and the filter is about 2 V so that the maximum voltage is: 2 VPKmax = = 1.41
* *
(11)
VinRMSmax - 2 =
2 1.112 - 0.524 Icap(RMS) = = 0.978 ARMS
264 - 2 = 370 V
From fig. 2, it may be assumed that the charging current is flowing during the time tch and with a rectangular shape with a peak value of ich. The charging time is given by: tch = tch = 20 * 10 T cos-1 Vmin Vpk = 2.23 ms (6)
The equation (11) is valid if the circuit of fig. 1 is connected to a DC load. The GS100T300-x is a switch mode DC-DC converter so that also the input RMS current of the converter (0,88 ARMS) is flowing through the capacitor. Therefore
2 2 Icap(RMS) + IDC-DC(RMS) IcapTOT(RMS) =
(12)
2
-3
2
cos-1
207
0.9782 + 0.88 IcapTOT(RMS) = 2 = 1.31 ARMS
2. European mains with hold-on characteristics In this case the capacitor C must be able to deliver the whole energy during one complete mains cyclefailure. The input waveform is shown in fig. 3, where: Vpf = Voltage across the capacitor after one cycle of power fail. The worst case is when the mains interruption happens when the capacitor voltage is already at Vmin; the following equation applies: Win = 1 C (V2 - V2 ) min pf 2 (13)
271
The charging peak current is given by: ich = C therefore: ich = 82 * 10-6 271 - 207 2.23 * 10-3 = 2.35 Ap Vpk - Vmin tch (7)
The RMS value of the input current is given by: Iin(RMS) = ich (8)
where is the duty cycle i.e. the diodes conduction time (tch) divided by T/2: 2 tch = T (9)
Equation (2) is still valid. By combining equation (2) and (13) V2 - V2 = 1 (V2 - V2 ) min pf 2
PK
min
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MAINS RECTIFICATION AND FILTERING
therefore Vmin = from equation (13) C= 2Win V
2
min
Vpf =
1 (2 * V2 + Vpf 2 ) pk
3
2712 - 3 * 2.5 -6
270 * 10
= 214 V
(14) Vmin = (15) 3
1 (2 * 2712 + 214 2)
= 254 V
VRipple = Vpk - Vmin = 271 - 254 = 17 Vp - p tch = 20 * 10-3 254 cos-1 = 1.14 ms 271 2
*
-
V2 pf
By combining eq. (14) and eq. (15) C= 3Win V2 - V2
pk pf
(16)
ich = 270 * 10-6 Iin(RMS) = 4.03
271 - 254 1.14 * 10-3
= 4.03 Ap
By assuming Vpk = 271 V and Vpf = 200 V C= 3 * 2.5 = 224 F 2712 - 2002
1.14
10
*
= 1.36 ARMS
Iin(AVG) = 4.03
1.14 = 0.46ADC 10
The nearest higher value is 270 F. By adopting this value Vpf =
2 Icap(RMS) = = 1.28 ARMS 1.362 - 0.46
V2 - 3W in pk
C
(17)
IcapTOT(RMS) = 2 = 1.55 ARMS 1.282 + 0.88
Figure 3. Typical waveform with one cycle of power failure
mains_3
Vc
Vpk
Vmin
Vpf
t
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MAINS RECTIFICATION AND FILTERING
The key results are summarized in the following table: European mains: Vinac=195VRMS min; f=50Hz
Without hold-on 82 207 64 370 2,35 2,23 1,11 0,524 1,32
230 VRMS typ; 264 VRMS max Win = 2.5 W x Sec.
With hold-on 270 254 214 17 370 4,03 1,14 1,36 0,46 1,55 Unit F V V Vp-p V Ap ms ARMS ADC ARMS
Parameter C Vmin Vpf VRipple Vmax ich tch Iin(RMS) Iin(AVG) IcapTOT(RMS)
3. Usa mains without the hold-on characteristics The USA mains characteristics are: VINAC =117 VRMS 15 % 60 Hz
To reach the minimum input voltage required by the GS100T300-x, a voltage doubler configuration is required as shown in fig. 4. Figure 4. AC-DC converter for USA mains.
C1 and C2 are alternatively charged to peak line voltage minus the voltage drop across the input filter and one diode of the rectifying bridge so that a voltage drop of 2V may be assumed. The waveforms are shown on fig. 5. By assuming a linear discharge of the capacitors, when the capacitor C1 reaches its minimum (Vc1min), the voltage of the capacitor C2 is half way between Vpk and Vc2min.
AC mains C Unregulated DC voltage
C
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MAINS RECTIFICATION AND FILTERING
Therefore: Vmin = VC1min + If C1=C2=C Vmin = 3 VCmin + VPK 2 (18) VPK + VC2min 2 In the case of the USA mains: 2 VPK = * 117 * 0.85 - 2 = 138 Vp Win = Pin P0 100 = = = 2.08 W f * f 0.8 * 60
*
s
By imposing Vmin = 200V, from equation (20) VCmin =
2 * 200 - 138
3
Each capacitor has to supply one half of the energy required by the GS100T300-x for an entire line cycle. Therefore: 1 1 Win = C (V2 - V2 ) PK Cmin 2 2 C= Win V2
PK
= 87 V
and from equation (19) C= 2.08 = 181 F 1382 - 872
(19)
Cmin
- V2
The nearest higher value is C=220F. By adopting this value, from equation (19) VCmin =
From equation (18) VCmin = 2 Vmin - VPK 3 (20) VCmin =
V2 - W in pk
C 220 * 10 = 98 V
(21)
1382 - 2.08 -6
Figure 5. Waveform for the voltage doubler configuration
Vc Vpk Vmin Vmax
mains_5
t
Vc1 Vpk
VC2min
t
Vc2 Vpk
VC1min
t
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MAINS RECTIFICATION AND FILTERING
and from equation (18) Vmin = From fig. 5 Vmax = VPK + VPK + VCmin 138 + 98 = 138 + = 256V 2 2 3 * 98 + 138 = 216 V 2 By supposing that the power fail occurs when the total voltage is VMIN, the voltage at the end of 1 cycle failure (Vpf) is obtained by Win = where: Ceq = 1 Ceq 2
*
( V2
min
- V2 )
pf
(22)
1 C 2 C= 4 Win V
2
min
VRipple = Vmax - Vmin = 256 - 216 = 40 V p-p Equations (6),(7),(8),(9),(10),(11),(12) are still valid. However, since the capacitors are charged every other half cycle, the duty cycle is given by: = tch = tch T
- V2
pf
Equation (18), (21) and (23) must be valid at the same time. After some straightforward calculations the value of C is 406 F. The nearest higher value is 470 F. From equation (21) VCmin =
1 98 cos-1 = 2.07 ms 138 2 * * 60 138 - 98 2.07 * 10-3
-3 *
1382 - 2.08 -6
470 * 10 3 * 120.9 + 138
= 120.9 V
ich = 220 * 10-6 *
= 4.25 Ap
From equation (18) Vmin = = 250.36 V
= 2.07 * 10
60 = 0.124
2
IinRMS = 4.25 = 1.49 ARMS 0.124 IinAVG = 4.25
*
The voltage after 1 cycle of power fail is given by Vpf = Vpf =
0.124 = 0.53 ADC
V2 - 4 W in min
C 470 * 10
(24)
IcapRMS = 2 = 1.39 ARMS 1.492 - 0.53 Icap totRMS = 1.39 + 0.88
2 2
= 1.64 ARMS
250.362 - 4 * 2.08 -6
= 212 V
When the AC mains is at its maximum (134 VRMS) Vpk = 2 VCmin =
*
By applying equations (6), (7), (8), (9), (10), (11) and (12) the following values are obtained: tch =
134 - 2 = 187 V = 160 V
1872 - 2.08 -6
220 * 10 3 * 160 + 187
120.9 1 cos-1 = 1.33 ms 138 2 * * 60
138 - 120.9 1.33
* *
ich = 470 * 10-6 *
10-3
= 6.02 Ap
Vmin = Vmax
2
= 333 V
= 1.33 * 10-3
60 = 0.08
187 + 160 = 187 + = 360.5 V 2
IinRMS = 6.02 * = 1.7 ARMS 0.08 IinAVG = 6.02 * 0.08 = 0.48 ADC
VRipple = 360.5 - 333 = 27.5 Vp - p 4. USA mains with hold-on characteristics From fig. 5, during a mains failure of one cycle, the two capacitors in series must provide all the energy required by the GS100T300-x for the same period.
1.72 - 0.48 IcapRMS = 2 = 1.63 ARMS 1.632 + 0.88 IcapTOT (RMS) = 2 = 1.85 ARMS
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MAINS RECTIFICATION AND FILTERING
138 + 120.9 = 267.4 V 2 3
*
Vmax = 138 +
Vmin =
175 + 187 = 355.6 V 2 187 + 175 = 368 V 2
VRipple = 267.4 - 250.4 = 17 V p-p When the AC main is at its maximum (134VRMS) 2 Vpk = VCmin =
*
Vmax = 187 +
134 - 2 = 187 V
VRipple = 368 - 355.6 = 12.4 V p-p
1872 - 2.08 -6
470 * 10 VinAC=99 VRMSmin; f=60 Hz
= 175 V
The key results are summarized in the following table: USA Mains 117 VRMStyp; 134 VRMSmax; Win=2.08 W x Sec.
The following values are calculated for VinAC=99VRMS exception made for Vmax that is calculated for VinAC = 134VRMS
Parameter C Vmin Vpf VRipple Vmax ich tch Iin(RMS) Iin(AVG) IcapTOT(RMS) Without hold-on 220 216 40 360.5 4.25 2.07 1.49 0.53 1.64 With hold-on 470 250.36 212 17 368 6.02 1.33 1.7 0.48 1.85 Unit F V V Vp-p V Ap ms ARMS ADC ARMS
The four configurations are shown in fig. 6a and 6b Figure 6a. Different AC-DC converter configurations (European versions)
European mains
Without HOLD-ON With HOLD-ON
220 Vrms 82 F 400 V
220 Vrms C 270 F 400 V
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MAINS RECTIFICATION AND FILTERING
Figure 6b. Different AC-DC converter configurations (USA versions)
USA Mains
Without HOLD-ON With HOLD-ON
117 Vrms 220 F 200 V 220 F 200 V
117 Vrms 470 F 200 V 470 F 200 V
5. Ripple current of the filtering capacitor The previous calculations don't take into account that the capacitance value and the maximum ripple current are not independent. In other words available capacitors of a given capacitance may not meet the requirements for ripple current. For example, in the case of the European Mains without hold-on, the minimum required capacitance is 82 F and the maximum ripple current is 1.32 ARMS. While the calculation is correct, such a capacitor doesn' t exist: available capacitors of 82 F / 400 V have a ripple current capability that is 1/3 of the required value at the best. The designer has to repeat the calculation according to the available capacitors that meet the ripple current requirement, the allowed value for a given application, the cost, etc. An example is reported in the following. An available series of capacitors has the following data:
C (F) 47 68 100 150 220 330 Ripple Current - ARMS @ 85 C 0.71 0.84 1.04 1.23 1.50 1.80
calculated values are modified as follows. Vmin =
V2 - W 2712 - 2.5 in = -6 = 235 V PK C
136 * 10 1 Vmin = VPK
VRipple = VPK - Vmin = 271 - 235 = 36 Vp-p tch =
2f
cos-1
1 235 cos-1 = 1.66 ms 271 2 50 ich = C VPK - Vmin = tch 271 - 235
= 136 * 10-6 * =
1.66 * 10-3
= 2,94 Ap
2 tch 2 * 1.66 = = 0.166 T 20
IinRMS = ich * = 2.95 * = 1.20 ARMS 0.166 IinAVG = ich
*
= 2.95
inRMS
*
0.166 = 0.490 ADC
inDC-DCRMS
Icap totRMS = = I2 - I2 +I
inAVG
From the table, the increase in ripple current capability is not proportional to the increase of capacitance. For the two extreme values, the increase of capacitance is 330 / 47 = 7.02 while the increase in ripple current capability is 180 / 0.71 = 2.53. Therefore it is more convenient to use smaller capacitors in parallel rather than one single capacitor at high value of capacitance. For this example, 2 capacitors of 68 F are used in parallel, therefore C = 2 x 68 F = 136 F. The
= = 1.40 ARMS 1.20 - 0.49 + 0.88
2
2 2
The parallel of 2 capacitors has a current capability of 2 x 0.84 = 1.68 ARMS so that the capacitors are not overstressed. The impedance of the two capacitors in parallel is about 0.1 Ohms at f = 100 kHz. The designer can repeat the calculations according to the application (European/USA mains, with or without hold-on) to different size and cost targets, etc.
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MAINS RECTIFICATION AND FILTERING
Information furnished is believed to be accurate and reliable. However, SGS-THOMSON Microelectronics assumes no responsibility for the consequences of use of such information nor for any infringement of patents or other rights of third parties which may result from its use. No license is granted by implication or otherwise under any patent or patent rights of SGS-THOMSON Microelectronics. Specification mentioned in this publication are subject to change without notice. This publication supersedes and replaces all information previously supplied. SGS-THOMSON Microelectronics products are not authorized for use as critical components in life support devices or systems without express written approval of SGS-THOMSON Microelectronics. (c) 1994 SGS-THOMSON Microelectronics - All Rights Reserved SGS-THOMSON Microelectronics GROUP OF COMPANIES Australia - Brazil - China - France - Germany - Hong Kong - Italy - Japan - Korea - Malaysia - Malta - Morocco - The Netherlands Singapore - Spain - Sweden - Switzerland - Taiwan - Thailand - United Kingdom - U.S.A.
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