近期電源常見術語及結構說明 - 3C
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By Zora
at 2017-09-24T12:39
at 2017-09-24T12:39
Table of Contents
最近市場上電源有幾個常見術語及結構,這篇文章在下提供簡單的解釋
1.雙DC-DC
DC-DC電路的全名是直流轉直流電源電路,以往在主機板/顯示卡上最為常見(轉換CPU/GPU
的核心電壓、記憶體及週邊電路零件所需電壓等),另一個比較常聽到的是VRM(Voltage
Regulator Module電壓調節模組),主要是進行不同電壓的轉換,在電源中使用的DC-DC就
是將12V轉換成3.3V、5V、-12V等電壓,因為DC-DC電路多採交換式(Switching)結構,比
起傳統電源採用的磁放大(Magnetic Amplifier)電路有更高的效率,另外經12V轉換出
3.3V/5V,彼此輸出電流不平均下的影響可以降到最低,對於現今使用12V為主的電腦系統
,可避免因為3.3V/5V負載量影響12V的輸出,所以目前比較好的電源,尤其是高效率機種
,都會採用雙DC-DC甚至三DC-DC的架構
2.交叉調整率Cross-Regulation
Cross-Regulation又被稱作交叉調整率,因為電腦用電源供應器屬於多輸出電源,同時輸
出3.3V/5V/12V/-12V,傳統電源上,只要3.3V/5V/12V其中一組輸出的電流發生變動,其
他組的輸出電壓就會受到影響。以目前電腦系統配置來說,CPU/GPU主要用電都集中在12V
上,3.3V/5V消耗量已不如以往,採單主變壓器並使用單組磁放大電路穩定3.3V的傳統電
源在12V負載加重時,電源供應器為了避免3.3V/5V電壓受到影響(超壓),此時12V電壓會
被”牽制住”而產生壓降。為了解決這種問題,電源開始採用雙磁放大電路,也就是同時
使用磁放大電路穩定3.3V/5V,不過單磁放大與雙磁放大都會因為電壓調整範圍不夠,而
無法同時滿足電源輸出輕載與重載下的條件,尤其Intel在Haswell平台開始,要求在節能
模式下12V必須要能輸出最低0.05A電流的要求,對於傳統單磁/雙磁放大的電源,12V輕載
下的3.3V/5V輸出也會受到其影響,當時為了這個問題,部分高瓦數電源採用3.3V/5V一組
功率級、12V一組功率級的設計,不過因為體積占用過大,後續就由雙DC-DC電路去取代,
以目前電源來說,採用雙DC-DC是目前改善交叉調整率的一個主要方法
3.無橋式APFC
80PLUS認證中的鈦金(Titanium)認證,115V輸入下其輸出百分比及轉換效率要求分別為
10%輸出90%效率、20%輸出92%效率、50%輸出94%效率、100%輸出90%效率,除了
20%/50%/100%輸出下的轉換效率必須要提升外,還多要求一個10%下的輕載轉換效率,大
部分高效率電源在輕載時會採用調降APFC電壓、進入跳週期模式(Skipped Mode)來降低功
耗,但是為了改善整體轉換效率,鈦金高效率電源開始採用Bridgeless APFC(無橋式主動
功因修正),顧名思義就是把APFC電路中,用來處理所有交流轉直流電源功率的橋式整流
器,使用原本APFC終就會使用的高速MOSFET及碳化矽蕭特基(SiC Schottky)高壓二極體來
取代,因為MOSFET有低導通阻抗的特性,比起傳統橋式整流器存在1.4V(全波整流下每周
期會經過兩顆二極體0.7V*2)的順向偏壓損失,要有更低的功率消耗,整體APFC電路可因
此減少5~8%的效率損失。依照結構,有分為Bridgeless(無橋)、Dual-Boost(雙升壓)、
Semi-Bridgeless(半無橋)、PSSB(Phase-Shift Semi-Bridgeless移相半無橋)、
Totem-Pole Bridgeless(圖騰柱無橋)
4.諧振轉換器Resonant Converter
電源中轉換器(Converter)的主要功用就是負責將APFC輸出的高壓直流轉換成低壓直流12V
,也常被稱功率級(Power Stage),相較於傳統電源使用的PWM(脈寬調變)轉換器,80PLUS
金牌/白金牌效率電源大多採用諧振轉換器(Resonant Converter),透過諧振電感與諧振
電容組合的諧振槽(Resonant Tank),以頻率調變(FM)方式來控制輸出的功率。電腦電源
中最常見的是LLC諧振槽電路,經由諧振槽的激磁電流,能讓一次側MOSFET寄生電容能量
消除,使其運作在ZVS(零電壓切換)區間,可讓MOSFET降低開關應力,部分廠商在LLC諧振
電路上也有一些改良款,使其有更寬的最佳轉換效率區間及更小的頻率調變區間,讓電源
有更好的效能。電腦用電源設計上常見的有HB LLC(半橋式LLC)、FB LLC(全橋式LLC),半
橋式使用的MOSFET數量為全橋式的一半,其驅動電路也比較簡單,不過在大功率電源上,
仍以全橋電路設計採用較多
5.同步整流Synchronous Rectifier
主功率級經過變壓器轉換後,二次側需要經過整流才會從高頻交流變成直流電,傳統電源
使用蕭特基障壁二極體(Schottky Barrier Diode,SBD)來進行整流,因為其帶有
0.3~0.5V的順向偏壓損失,雖比起矽二極體的0.7V要低,但仍會造成損失,隨著輸出電流
增加,其損失的功率也就越高(損失功率=順向偏壓X流過電流),即使並聯多顆SBD,也只
是降低每一顆所負擔的功率損失,避免單顆集中過高功耗導致過熱燒毀,整體功率損失仍
不會改變。而MOSFET傳輸損耗是由其RDS(ON)乘上平方電流來決定,所以採用更低RDS(ON)
的MOSFET,可降低其傳輸損耗,若是並聯更多的MOSFET,電流分配到多顆MOSFET上時,產
生的傳輸損耗會更小。例如分擔到兩顆MOSFET,每個元件損耗可以減少1/4(1/2平方為
1/4),整體損耗就可下降一半,所以在高效率電源上,二次側大量採用同步整流,大功率
電源還會並聯多顆MOSFET,以降低二次側所產生的損耗,也可降低產生的熱量及提高轉換
效率。同步整流中另一個主角是同步整流控制器(SR Controller),須具備高切換頻率、
大電流MOSFET驅動能力,也需要保護電路,避免高端(High-side)與低端(Low-side)的同
步整流MOSFET被同時啟動導致短路造成損壞
報告完畢,謝謝收看
--
1.雙DC-DC
DC-DC電路的全名是直流轉直流電源電路,以往在主機板/顯示卡上最為常見(轉換CPU/GPU
的核心電壓、記憶體及週邊電路零件所需電壓等),另一個比較常聽到的是VRM(Voltage
Regulator Module電壓調節模組),主要是進行不同電壓的轉換,在電源中使用的DC-DC就
是將12V轉換成3.3V、5V、-12V等電壓,因為DC-DC電路多採交換式(Switching)結構,比
起傳統電源採用的磁放大(Magnetic Amplifier)電路有更高的效率,另外經12V轉換出
3.3V/5V,彼此輸出電流不平均下的影響可以降到最低,對於現今使用12V為主的電腦系統
,可避免因為3.3V/5V負載量影響12V的輸出,所以目前比較好的電源,尤其是高效率機種
,都會採用雙DC-DC甚至三DC-DC的架構
2.交叉調整率Cross-Regulation
Cross-Regulation又被稱作交叉調整率,因為電腦用電源供應器屬於多輸出電源,同時輸
出3.3V/5V/12V/-12V,傳統電源上,只要3.3V/5V/12V其中一組輸出的電流發生變動,其
他組的輸出電壓就會受到影響。以目前電腦系統配置來說,CPU/GPU主要用電都集中在12V
上,3.3V/5V消耗量已不如以往,採單主變壓器並使用單組磁放大電路穩定3.3V的傳統電
源在12V負載加重時,電源供應器為了避免3.3V/5V電壓受到影響(超壓),此時12V電壓會
被”牽制住”而產生壓降。為了解決這種問題,電源開始採用雙磁放大電路,也就是同時
使用磁放大電路穩定3.3V/5V,不過單磁放大與雙磁放大都會因為電壓調整範圍不夠,而
無法同時滿足電源輸出輕載與重載下的條件,尤其Intel在Haswell平台開始,要求在節能
模式下12V必須要能輸出最低0.05A電流的要求,對於傳統單磁/雙磁放大的電源,12V輕載
下的3.3V/5V輸出也會受到其影響,當時為了這個問題,部分高瓦數電源採用3.3V/5V一組
功率級、12V一組功率級的設計,不過因為體積占用過大,後續就由雙DC-DC電路去取代,
以目前電源來說,採用雙DC-DC是目前改善交叉調整率的一個主要方法
3.無橋式APFC
80PLUS認證中的鈦金(Titanium)認證,115V輸入下其輸出百分比及轉換效率要求分別為
10%輸出90%效率、20%輸出92%效率、50%輸出94%效率、100%輸出90%效率,除了
20%/50%/100%輸出下的轉換效率必須要提升外,還多要求一個10%下的輕載轉換效率,大
部分高效率電源在輕載時會採用調降APFC電壓、進入跳週期模式(Skipped Mode)來降低功
耗,但是為了改善整體轉換效率,鈦金高效率電源開始採用Bridgeless APFC(無橋式主動
功因修正),顧名思義就是把APFC電路中,用來處理所有交流轉直流電源功率的橋式整流
器,使用原本APFC終就會使用的高速MOSFET及碳化矽蕭特基(SiC Schottky)高壓二極體來
取代,因為MOSFET有低導通阻抗的特性,比起傳統橋式整流器存在1.4V(全波整流下每周
期會經過兩顆二極體0.7V*2)的順向偏壓損失,要有更低的功率消耗,整體APFC電路可因
此減少5~8%的效率損失。依照結構,有分為Bridgeless(無橋)、Dual-Boost(雙升壓)、
Semi-Bridgeless(半無橋)、PSSB(Phase-Shift Semi-Bridgeless移相半無橋)、
Totem-Pole Bridgeless(圖騰柱無橋)
4.諧振轉換器Resonant Converter
電源中轉換器(Converter)的主要功用就是負責將APFC輸出的高壓直流轉換成低壓直流12V
,也常被稱功率級(Power Stage),相較於傳統電源使用的PWM(脈寬調變)轉換器,80PLUS
金牌/白金牌效率電源大多採用諧振轉換器(Resonant Converter),透過諧振電感與諧振
電容組合的諧振槽(Resonant Tank),以頻率調變(FM)方式來控制輸出的功率。電腦電源
中最常見的是LLC諧振槽電路,經由諧振槽的激磁電流,能讓一次側MOSFET寄生電容能量
消除,使其運作在ZVS(零電壓切換)區間,可讓MOSFET降低開關應力,部分廠商在LLC諧振
電路上也有一些改良款,使其有更寬的最佳轉換效率區間及更小的頻率調變區間,讓電源
有更好的效能。電腦用電源設計上常見的有HB LLC(半橋式LLC)、FB LLC(全橋式LLC),半
橋式使用的MOSFET數量為全橋式的一半,其驅動電路也比較簡單,不過在大功率電源上,
仍以全橋電路設計採用較多
5.同步整流Synchronous Rectifier
主功率級經過變壓器轉換後,二次側需要經過整流才會從高頻交流變成直流電,傳統電源
使用蕭特基障壁二極體(Schottky Barrier Diode,SBD)來進行整流,因為其帶有
0.3~0.5V的順向偏壓損失,雖比起矽二極體的0.7V要低,但仍會造成損失,隨著輸出電流
增加,其損失的功率也就越高(損失功率=順向偏壓X流過電流),即使並聯多顆SBD,也只
是降低每一顆所負擔的功率損失,避免單顆集中過高功耗導致過熱燒毀,整體功率損失仍
不會改變。而MOSFET傳輸損耗是由其RDS(ON)乘上平方電流來決定,所以採用更低RDS(ON)
的MOSFET,可降低其傳輸損耗,若是並聯更多的MOSFET,電流分配到多顆MOSFET上時,產
生的傳輸損耗會更小。例如分擔到兩顆MOSFET,每個元件損耗可以減少1/4(1/2平方為
1/4),整體損耗就可下降一半,所以在高效率電源上,二次側大量採用同步整流,大功率
電源還會並聯多顆MOSFET,以降低二次側所產生的損耗,也可降低產生的熱量及提高轉換
效率。同步整流中另一個主角是同步整流控制器(SR Controller),須具備高切換頻率、
大電流MOSFET驅動能力,也需要保護電路,避免高端(High-side)與低端(Low-side)的同
步整流MOSFET被同時啟動導致短路造成損壞
報告完畢,謝謝收看
--
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
By Anonymous
at 2017-11-10T07:35
at 2017-11-10T07:35

By Skylar Davis
at 2017-11-11T00:06
at 2017-11-11T00:06

By Ula
at 2017-11-11T15:23
at 2017-11-11T15:23

By Bennie
at 2017-11-13T23:39
at 2017-11-13T23:39

By Daph Bay
at 2017-11-18T17:21
at 2017-11-18T17:21

By William
at 2017-11-23T01:07
at 2017-11-23T01:07

By Dora
at 2017-11-26T12:43
at 2017-11-26T12:43

By Franklin
at 2017-12-01T08:12
at 2017-12-01T08:12

By Dorothy
at 2017-12-02T16:25
at 2017-12-02T16:25

By Zanna
at 2017-12-04T15:30
at 2017-12-04T15:30

By Catherine
at 2017-12-06T17:34
at 2017-12-06T17:34

By Blanche
at 2017-12-10T11:36
at 2017-12-10T11:36

By Heather
at 2017-12-11T14:15
at 2017-12-11T14:15

By Caitlin
at 2017-12-14T22:32
at 2017-12-14T22:32

By Kelly
at 2017-12-15T01:20
at 2017-12-15T01:20

By Daph Bay
at 2017-12-15T08:31
at 2017-12-15T08:31

By Todd Johnson
at 2017-12-19T01:26
at 2017-12-19T01:26

By Hedy
at 2017-12-19T06:00
at 2017-12-19T06:00

By Mia
at 2017-12-21T19:06
at 2017-12-21T19:06

By Caitlin
at 2017-12-26T10:32
at 2017-12-26T10:32

By Queena
at 2017-12-29T00:08
at 2017-12-29T00:08

By Rae
at 2018-01-02T20:18
at 2018-01-02T20:18

By Joseph
at 2018-01-05T07:29
at 2018-01-05T07:29

By Ida
at 2018-01-06T19:20
at 2018-01-06T19:20

By Christine
at 2018-01-10T18:56
at 2018-01-10T18:56

By Daniel
at 2018-01-13T23:51
at 2018-01-13T23:51

By Lucy
at 2018-01-15T09:29
at 2018-01-15T09:29

By Lauren
at 2018-01-18T13:22
at 2018-01-18T13:22

By Madame
at 2018-01-20T09:24
at 2018-01-20T09:24

By Olive
at 2018-01-24T15:56
at 2018-01-24T15:56

By Hedwig
at 2018-01-26T06:14
at 2018-01-26T06:14

By Faithe
at 2018-01-27T10:06
at 2018-01-27T10:06

By Eartha
at 2018-01-31T15:30
at 2018-01-31T15:30

By Carolina Franco
at 2018-02-04T00:01
at 2018-02-04T00:01

By Agatha
at 2018-02-07T02:26
at 2018-02-07T02:26

By Olivia
at 2018-02-09T01:27
at 2018-02-09T01:27

By Ethan
at 2018-02-13T06:44
at 2018-02-13T06:44

By Selena
at 2018-02-15T22:12
at 2018-02-15T22:12

By Quintina
at 2018-02-16T10:04
at 2018-02-16T10:04

By Frederic
at 2018-02-17T17:54
at 2018-02-17T17:54

By Catherine
at 2018-02-22T08:22
at 2018-02-22T08:22

By Olivia
at 2018-02-22T22:27
at 2018-02-22T22:27

By Joseph
at 2018-02-26T00:09
at 2018-02-26T00:09

By Callum
at 2018-02-26T02:54
at 2018-02-26T02:54

By Adele
at 2018-02-27T03:12
at 2018-02-27T03:12

By James
at 2018-02-28T13:37
at 2018-02-28T13:37

By Isla
at 2018-02-28T21:15
at 2018-02-28T21:15

By Olga
at 2018-03-03T09:21
at 2018-03-03T09:21

By Callum
at 2018-03-05T11:20
at 2018-03-05T11:20

By Todd Johnson
at 2018-03-09T20:44
at 2018-03-09T20:44

By Brianna
at 2018-03-11T18:48
at 2018-03-11T18:48

By Edith
at 2018-03-15T10:05
at 2018-03-15T10:05

By Andrew
at 2018-03-19T19:27
at 2018-03-19T19:27

By Franklin
at 2018-03-21T05:08
at 2018-03-21T05:08

By Edith
at 2018-03-24T17:57
at 2018-03-24T17:57

By Emily
at 2018-03-28T13:35
at 2018-03-28T13:35

By Bennie
at 2018-03-31T06:27
at 2018-03-31T06:27

By Mary
at 2018-03-31T23:44
at 2018-03-31T23:44

By Kama
at 2018-04-05T01:55
at 2018-04-05T01:55

By Lily
at 2018-04-09T23:36
at 2018-04-09T23:36

By Mary
at 2018-04-14T03:13
at 2018-04-14T03:13

By Jake
at 2018-04-15T13:12
at 2018-04-15T13:12

By Sarah
at 2018-04-16T10:13
at 2018-04-16T10:13

By Elvira
at 2018-04-19T14:28
at 2018-04-19T14:28

By Mary
at 2018-04-24T12:10
at 2018-04-24T12:10

By Lucy
at 2018-04-29T05:58
at 2018-04-29T05:58

By Tom
at 2018-05-01T11:54
at 2018-05-01T11:54

By Emma
at 2018-05-05T10:20
at 2018-05-05T10:20

By Catherine
at 2018-05-08T21:42
at 2018-05-08T21:42

By Adele
at 2018-05-10T09:09
at 2018-05-10T09:09

By Emma
at 2018-05-11T08:39
at 2018-05-11T08:39

By Daph Bay
at 2018-05-14T14:45
at 2018-05-14T14:45

By George
at 2018-05-15T06:30
at 2018-05-15T06:30

By Necoo
at 2018-05-17T23:03
at 2018-05-17T23:03

By Callum
at 2018-05-22T10:18
at 2018-05-22T10:18

By Lauren
at 2018-05-23T06:22
at 2018-05-23T06:22

By Ida
at 2018-05-24T05:05
at 2018-05-24T05:05

By Odelette
at 2018-05-28T13:51
at 2018-05-28T13:51

By Heather
at 2018-05-31T02:27
at 2018-05-31T02:27

By Tracy
at 2018-06-04T17:29
at 2018-06-04T17:29

By Zanna
at 2018-06-06T15:14
at 2018-06-06T15:14

By Megan
at 2018-06-09T12:09
at 2018-06-09T12:09

By Megan
at 2018-06-13T07:28
at 2018-06-13T07:28

By Eden
at 2018-06-13T16:04
at 2018-06-13T16:04

By Sarah
at 2018-06-18T04:09
at 2018-06-18T04:09

By Hardy
at 2018-06-21T12:25
at 2018-06-21T12:25

By Andrew
at 2018-06-22T06:57
at 2018-06-22T06:57

By Sarah
at 2018-06-24T07:23
at 2018-06-24T07:23
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By Yuri
at 2018-06-28T16:04
at 2018-06-28T16:04
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By Rebecca
at 2018-06-29T17:39
at 2018-06-29T17:39
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By Frederic
at 2018-06-29T20:15
at 2018-06-29T20:15
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By Zora
at 2018-07-04T07:28
at 2018-07-04T07:28
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By Connor
at 2018-07-04T22:13
at 2018-07-04T22:13
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By Charlotte
at 2018-07-06T21:48
at 2018-07-06T21:48
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By Ivy
at 2018-07-08T01:39
at 2018-07-08T01:39
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By John
at 2018-07-09T03:00
at 2018-07-09T03:00
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By Isabella
at 2018-07-13T18:01
at 2018-07-13T18:01
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By Ingrid
at 2018-07-13T22:04
at 2018-07-13T22:04
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By Irma
at 2018-07-18T02:20
at 2018-07-18T02:20

By Emma
at 2018-07-20T04:17
at 2018-07-20T04:17
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By Selena
at 2018-07-24T08:21
at 2018-07-24T08:21
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By Hedwig
at 2018-07-27T11:32
at 2018-07-27T11:32
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By Madame
at 2018-07-29T09:01
at 2018-07-29T09:01

By Una
at 2018-07-31T16:46
at 2018-07-31T16:46
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By Quanna
at 2018-08-02T01:43
at 2018-08-02T01:43
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By Ida
at 2018-08-06T09:04
at 2018-08-06T09:04

By Liam
at 2018-08-11T07:24
at 2018-08-11T07:24

By Donna
at 2018-08-13T05:23
at 2018-08-13T05:23

By Oliver
at 2018-08-16T10:01
at 2018-08-16T10:01

By Steve
at 2018-08-20T14:31
at 2018-08-20T14:31
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By Kumar
at 2018-08-23T14:03
at 2018-08-23T14:03
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By Audriana
at 2018-08-26T07:27
at 2018-08-26T07:27
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By Belly
at 2018-08-27T04:42
at 2018-08-27T04:42

By Caroline
at 2018-08-28T18:43
at 2018-08-28T18:43
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By Heather
at 2018-08-30T01:55
at 2018-08-30T01:55
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By Quanna
at 2018-08-30T15:07
at 2018-08-30T15:07
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By Xanthe
at 2018-09-02T20:49
at 2018-09-02T20:49
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By Dinah
at 2018-09-07T15:11
at 2018-09-07T15:11

By Yuri
at 2018-09-10T03:49
at 2018-09-10T03:49
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By Valerie
at 2018-09-10T18:56
at 2018-09-10T18:56

By Aaliyah
at 2018-09-13T16:49
at 2018-09-13T16:49
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By Jacob
at 2018-09-16T11:06
at 2018-09-16T11:06
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By Gary
at 2018-09-17T11:35
at 2018-09-17T11:35
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By Bethany
at 2018-09-19T00:19
at 2018-09-19T00:19

By Olive
at 2018-09-22T16:37
at 2018-09-22T16:37

By Zora
at 2018-09-26T11:25
at 2018-09-26T11:25

By Cara
at 2018-09-29T05:00
at 2018-09-29T05:00

By Linda
at 2018-09-29T23:18
at 2018-09-29T23:18
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By Faithe
at 2018-10-01T03:38
at 2018-10-01T03:38
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By Rachel
at 2018-10-06T02:19
at 2018-10-06T02:19

By Margaret
at 2018-10-10T21:55
at 2018-10-10T21:55

By Caroline
at 2018-10-11T16:21
at 2018-10-11T16:21

By Anthony
at 2018-10-13T01:52
at 2018-10-13T01:52
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By Hedda
at 2018-10-14T01:19
at 2018-10-14T01:19

By Blanche
at 2018-10-14T23:27
at 2018-10-14T23:27

By Oscar
at 2018-10-16T08:32
at 2018-10-16T08:32

By Joe
at 2018-10-18T11:58
at 2018-10-18T11:58

By John
at 2018-10-22T19:40
at 2018-10-22T19:40

By Sandy
at 2018-10-24T23:05
at 2018-10-24T23:05

By Zanna
at 2018-10-26T04:19
at 2018-10-26T04:19

By Yuri
at 2018-10-26T09:38
at 2018-10-26T09:38

By Anthony
at 2018-10-29T02:44
at 2018-10-29T02:44

By David
at 2018-11-02T15:11
at 2018-11-02T15:11

By Kyle
at 2018-11-06T13:22
at 2018-11-06T13:22

By Emma
at 2018-11-09T11:39
at 2018-11-09T11:39
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By Leila
at 2018-11-13T00:08
at 2018-11-13T00:08
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By Zenobia
at 2018-11-16T23:15
at 2018-11-16T23:15
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By Delia
at 2018-11-19T11:47
at 2018-11-19T11:47

By Yuri
at 2018-11-23T09:45
at 2018-11-23T09:45
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By Hardy
at 2018-11-26T22:58
at 2018-11-26T22:58
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By Yuri
at 2018-11-29T12:41
at 2018-11-29T12:41

By Thomas
at 2018-11-30T10:50
at 2018-11-30T10:50

By Gilbert
at 2018-12-01T14:12
at 2018-12-01T14:12
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By Odelette
at 2018-12-03T21:19
at 2018-12-03T21:19
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By Dora
at 2018-12-04T13:55
at 2018-12-04T13:55
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By Eartha
at 2018-12-08T09:21
at 2018-12-08T09:21
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By Bennie
at 2018-12-12T21:29
at 2018-12-12T21:29

By Christine
at 2018-12-13T08:29
at 2018-12-13T08:29
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By Hamiltion
at 2018-12-13T20:31
at 2018-12-13T20:31
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By Iris
at 2018-12-15T12:59
at 2018-12-15T12:59
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By Todd Johnson
at 2018-12-15T23:34
at 2018-12-15T23:34

By Lily
at 2018-12-19T10:46
at 2018-12-19T10:46
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By Vanessa
at 2018-12-21T11:05
at 2018-12-21T11:05

By Frederica
at 2018-12-24T00:59
at 2018-12-24T00:59
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