有一如圖之空乏型 MOSFET 電路,若 = 2.5 V , = 1.5 V ,(W/L)= ,當流過偏壓電阻 、 之電流為 ,則 、 約為何?


計算流程:P通道MOSFET源極接RS(2kΩ)後連至+5V。VS=+5V−ID×RS。VSG=VS−VG,VSD=2.5V故VD=VS−2.5V。空乏型P通道工作於飽和區,ID=(1/2)μpCox(W/L)(VSG−|Vtp|)²=(0.5)(1mA/V²)(VSG−1.5)²。由VSD=2.5V且飽和條件VSD≥VSG−|Vtp|,設VSG=2V(使VSG−|Vtp|=0.5V),則ID=0.5×1×(0.5)²=0.125mA。VS=5−0.125×2=4.75V,VG=VS−VSG=4.75−2=2.75V。偏壓電流=0.1ID=0.0125mA,電源為+5V到−5V共10V,總電阻=(R1+R2)=10V/0.0125mA=800kΩ。VG=−5+(R2/(R1+R2))×10=2.75V,故R2/800=7.75/10,R2≈620kΩ…需重新核算:實際以VSG讓飽和區成立,取VSG−|Vtp|使VSD(=2.5V)≥VSG−1.5。嘗試VSG=2.5V:ID=0.5×1×(1)²=0.5mA;VS=5−0.5×2=4V;VG=4−2.5=1.5V;偏壓電流=0.05mA;R1+R2=10/0.05=200kΩ;VG=−5+(R2/200)×10=1.5→R2/200=6.5/10→R2=130kΩ,R1=70kΩ,與選項不符。再試VSG=1.9V:ID=0.5×(0.4)²=0.08mA;VS=5−0.08×2=4.84V;VG=4.84−1.9=2.94V;偏壓電流=0.008mA;R1+R2=10/0.008=1250kΩ;VG=−5+(R2/1250)×10=2.94→R2=(7.94/10)×1250=992.5kΩ,R1=257.5kΩ,仍不符。就選項B(R1=20.6kΩ,R2=59.4kΩ):R1+R2=80kΩ,偏壓電流=10/80k=0.125mA;VG=−5+(59.4/80)×10=−5+7.425=2.425V;ID=偏壓電流/0.1=1.25mA;VS=5−1.25×2=2.5V;VSG=2.5−2.425=0.075V,此值使|VSG|<|Vtp|,MOSFET不導通,矛盾。重新考量:P通道空乏型可在VSG<|Vtp|仍導通(空乏模式)。VG=2.425V,VS=2.5V,VSG=0.075V;ID=0.5×1×(0.075−(−1.5))²…空乏型Vtp=−1.5V時:ID=0.5×1×(VSG−Vtp)²=0.5×(0.075+1.5)²=0.5×2.480=1.24mA≈1.25mA ✓;偏壓電流=0.1×1.25=0.125mA;R1+R2=80kΩ✓;R2=59.4kΩ、R1=20.6kΩ完全吻合,答案B正確。
