Re: [理工] 【電子學】MOS差動對
看板Electronics作者deathcustom (litron-intl)時間13年前 (2012/04/04 12:35)推噓1(1推 0噓 1→)留言2則, 2人參與討論串2/2 (看更多)
※ 引述《kela12340 (Avanlandis)》之銘言：
: ※ [本文轉錄自 Grad-ProbAsk 看板 #1FUlidle ]
: 作者: kela12340 (Avanlandis) 看板: Grad-ProbAsk
: 標題: [理工] 【電子學】MOS差動對
: 時間: Tue Apr 3 21:29:07 2012
: 題目:
: In this example we consider the design of the current source that
: supplies the bias current of a MOS differential amplifier.Let it be
: required to achieve a CMRR of 100dB and assume that the only source
: of mismatch between Q1 and Q2 is a 2% mismatch in their W/L ratios.
: Let I = 200uA and assume that all transistors are to be operated at
: Vov = 0.2V. For the 0.18-um CMOS fabrication process available.
: VA'=5 V/um.
: (1)If a simple current source is utilized for I,what is the
: required value of "channel length"?
: (2)If a cascode current source is utilized,what's the channel length
: of the two transistors in the cascode?
: ---------------
: (1)小題書上的算法求gm時: gm = 2ID/Vov = 2 x (I/2) /Vov = 2 x 0.1 /0.2
: = 1m A/V，
I = 200uA
Vov = 0.2V
Id = 0.1mA
gm = 2Id/Vov = I/Vov = 1mA/V
CMRR = 2gmRss/(dgm/gm)
100dB = 10^5 = 2*1mA/V*Rss/0.02 = 100*1mA/V*Rss = 0.1A/V*Rss
Rss = 1M-ohm = Va/I = Va/200uA
Va = 1M*200u = 200V
Va'*L = Va = 200
L = 200/Va' = 40um
: 但(2)小題時 gm = 2I/Vov = 2 x 0.2 / 0.2 = 2m A/V ，
: 想請問為何current source的構造從單一MOS變成CASCODE的形式時，流過的I
: 卻變為兩倍?
: 目前的想法解讀是:因為cascode兩顆MOS串聯，所以Leq = 2L，所以電流將會是
: 使用一個MOS的0.5倍..，但是這...只會讓電流變小阿= ="(今天上課老師
: 剛好有提到這個，但不是電子學的課..)
: 感謝各位!!
現在我們知道Rss = 1M
而且cascode裡面Rss = Ro = ro1 + ro2 + gm2ro2ro1
這裡的gm, ro都是指"current source"的gm跟ro，所以跟第一題裡面用到的
2gmRss/(dgm/gm)不同，因為左式的gm指的是input differential pair Q1, Q2的gm
所有gm, ro都一樣，所以等於 Ro = (gm*ro+2)ro
gm = 2I/Vov = 2*0.2mA/0.2V = 2mA/V
Ro = (0.002ro+2)ro = 0.002ro^2 + 2ro = 1M
ro = -2 + sqrt(4 +8000)/0.004 = 21.866k ~ 22k
(如果用簡單的方式，Ro = gmro^2 = 1M，則ro^2 = 1M/2m = 0.5G = 500M
算出來的ro = 22.36k ~ 22.5k，其實大概就這樣算)
ro = Va/I = Va/0.2mA
Va = ro*I = 22k*0.2mA = 4.4V = Va'*L = 5V/um*L
L = 0.88(或者簡化算法算出來0.9)um#
--
第一小題看到的gm是"差動對自己的gm"
所以用gm = 2Id/Vov = I/Vov #
第二小題看到的gm是"cascode current source"自己的gm
所以用gm = 2Id/Vov = 2I/Vov #
這樣有明白嗎?
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