Re: [請益] 小信號條件

[deathcustom (Full House)]

※ 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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→ deathcustom: 明確來說，小信號本來就是近似，這個模型帶來的誤差
→ deathcustom: 會造成(放大器)輸出的高次諧波
→ deathcustom: 當你有某個THD需求的時候，本來就需要檢視相應的
→ deathcustom: 輸入限制，不是甚麼"應限制gm在5%以內"，而是(因為實
→ deathcustom: 際電路需求，我的gm誤差必須限制在5%以內"
推 creation: 不好意思 請問為什麼gm_e(%) = sqrt(1-(Vid/2Vov)^2)-1
→ creation: -1  1是"100%"的意思嗎?
→ creation: ~ -(Vid/2Vov)^2/2   是"約等於"-(Vid/2Vov)^2/2  嗎?!
→ creation: 為什麼呢?! ( ~ -(Vid/2Vov)^2/2 )
推 creation: THD是threshold的意思嗎?!
→ samm3320: total harmonic distortion