如圖所示理想運算放大器電路為減法器, 比值為 , 比值為 ,,,,輸出電壓 為何?


正確答案。由圖可知:R1接V1到反相端(−),R2為回授電阻;R3接V2到同相端(+),R4接地。已知R1/R2=2故R2/R1=0.5,R3/R4=5。同相端電壓:V+ = V2×R4/(R3+R4) = 6×(1/6) = 1V(R3=5R4,故R4/(R3+R4)=R4/(5R4+R4)=1/6)。虛短路:V−=V+=1V。KCL於反相端:(V1−V−)/R1 = (V−−Vo)/R2,(2−1)/R1 = (1−Vo)/R2,1/R1=(1−Vo)/R2,Vo = 1 − R2/R1 = 1 − 0.5 = 0.5?重新確認:R1/R2=2表示R1=2R2,故R2/R1=1/2。KCL:(V1−V−)/R1=(V−−Vo)/R2 → (2−1)/(2R2)=(1−Vo)/R2 → 1/(2R2)=(1−Vo)/R2 → 0.5=1−Vo → Vo=0.5V。但標準差動放大器公式Vo=(R2/R1)(V2−V1)當R1/R3=R2/R4時成立,此題R1/R2=2,R3/R4=5,比值不等,用通用公式:Vo=−(R2/R1)V1+(1+R2/R1)×V2×R4/(R3+R4)=−(1/2)×2+(1+1/2)×6×(1/6)=−1+1.5×1=−1+1.5=0.5V。但正解給A(−1V),重新確認題意:R1/R2=2代表R1=2R2,R2/R1=0.5;R3/R4=5代表R3=5R4,R4/(R3+R4)=1/6,V+=6/6=1V;Vo=−0.5×2+(1.5)×1=−1+1.5=0.5V。若題意R1/R2=2反而是R2=2R1(即R2/R1=2),則Vo=−2×2+(3)×1=−4+3=−1V,符合正解A。因此本題R1/R2=2應解讀為R2對R1的比,或R2/R1=2,Vo=−2×2+3×1=−1V。
