作者deathcustom (Full House)
看板Electronics
標題Re: [請益] 小信號條件
時間Mon Jan 3 14:38:28 2022
※ 引述《creation (cc)》之銘言：
: https://imgur.com/a/YisHGLx
: (9.117 & 9.118式 置於 圖3)
: 請問一下，圖1的最後一行 & 圖2的第一行：
: 為什麼 "限制gm誤差在5%以內，明確的小信號條件是9.129式" ?!
what we said for gm is:
gm = dI/dVi
therefore, in a linear model, we have
Id = Id_0 + gm*Vid/2
Here, gm = 2Id/Vov = I_tail/Vov (or I/Vov in brief)
from 9.117, you can see that the real Id is expressed as:
Id = Id_0 + gm*Vid/2*sqrt(1-(Vid/2Vov)^2)
the error could be expressed as:
gm_e(%) = sqrt(1-(Vid/2Vov)^2)-1 ~ -(Vid/2Vov)^2/2
we want to have this no more than 5% (1/20)
so we have:
(Vid/2Vov)^2/2 < 1/20
Vid/2Vov< sqrt(1/10)
Vid < Vov*2*sqrt(1/10) = 0.632Vov#
the wording here is not precise enough, what should be written is:
"若我們希望gm誤差在5%以內，則...Vid應該限制在Vov的0.632倍以內"
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1F：→ deathcustom: 明確來說，小信號本來就是近似，這個模型帶來的誤差 01/03 14:39
2F：→ deathcustom: 會造成(放大器)輸出的高次諧波 01/03 14:40
3F：→ deathcustom: 當你有某個THD需求的時候，本來就需要檢視相應的 01/03 14:40
4F：→ deathcustom: 輸入限制，不是甚麼"應限制gm在5%以內"，而是(因為實 01/03 14:41
5F：→ deathcustom: 際電路需求，我的gm誤差必須限制在5%以內" 01/03 14:42
6F：推 creation: 不好意思 請問為什麼gm_e(%) = sqrt(1-(Vid/2Vov)^2)-1 01/03 16:14
7F：→ creation: -1 1是"100%"的意思嗎? 01/03 16:16
8F：→ creation: ~ -(Vid/2Vov)^2/2 是"約等於"-(Vid/2Vov)^2/2 嗎?! 01/03 16:18
9F：→ creation: 為什麼呢?! ( ~ -(Vid/2Vov)^2/2 ) 01/03 16:20
10F：推 creation: THD是threshold的意思嗎?! 01/03 16:23
11F：→ samm3320: total harmonic distortion 01/03 16:35