fet dc biasing all formula

General Device Equations (Applicable to all FET configurations)

• Gate Current: $I_G\cong 0\text{ A}$
• Drain-Source Current: $I_D=I_S$
• General Terminal Voltages:
  • $V_{DS}=V_D-V_S$
  • $V_{DG}=V_D-V_G$
• JFET and Depletion-Type MOSFET (Shockley’s Equation):
  • $I_D=I_{DSS}{\left(1-\frac{V_{GS}}{V_P}\right)}^2$
  • $V_{GS}=V_P\left(1-\sqrt{\frac{I_D}{I_{DSS}}}\right)$
• Enhancement-Type MOSFET Equation:
  • $I_D=k(V_{GS}-V_{GS(Th)}{)}^2$
  • Device Constant ($k$): $k=\frac{I_{D(on)}}{(V_{GS(on)}-V_{GS(Th)}{)}^2}$

JFET and Depletion-Type MOSFET Biasing Configurations

• Fixed-Bias Configuration:
  • $V_{GSQ}=-V_{GG}$ (for JFET) or $V_{GSQ}=+V_{GG}$ (for Depletion-MOSFET)
  • $V_{DS}=V_{DD}-I_D{R}_D$
• Self-Bias Configuration:
  • $V_{GS}=-I_D{R}_S$
  • $V_{DS}=V_{DD}-I_D(R_D+R_S)$
  • $V_S=I_D{R}_S$
• Voltage-Divider Bias Configuration:
  • $V_G=\frac{R_2{V}_{DD}}{R_1+R_2}$
  • $V_{GS}=V_G-I_D{R}_S$
  • $V_{DS}=V_{DD}-I_D(R_D+R_S)$
• Common-Gate Configuration:
  • $V_{GS}=V_{SS}-I_D{R}_S$
  • $V_{DS}=V_{DD}+V_{SS}-I_D(R_D+R_S)$
  • $V_D=V_{DD}-I_D{R}_D$
  • $V_S=-V_{SS}+I_D{R}_S$
• Special Case ($V_{GSQ}=0\text{ V}$ / $R_S=0\Omega$):
  • $V_{GSQ}=0\text{ V}$
  • $I_{DQ}=I_{DSS}$
  • $V_{DS}=V_{DD}-I_D{R}_D$
  • $V_D=V_{DS}$
  • $V_S=0\text{ V}$

Enhancement-Type MOSFET Biasing Configurations

• Drain-Feedback Biasing Configuration:
  • $V_{DS}=V_{GS}$
  • $V_{GS}=V_{DD}-I_D{R}_D$
• Voltage-Divider Biasing Configuration:
  • $V_G=\frac{R_2{V}_{DD}}{R_1+R_2}$
  • $V_{GS}=V_G-I_D{R}_S$
  • $V_{DS}=V_{DD}-I_D(R_S+R_D)$

Universal JFET Bias Curve Method When using the universal normalized graphs for mathematical or graphical solutions, the following variable scales are used:

• $m=\frac{|V_P|}{I_{DSS}{R}_S}$
• $M=m\times \frac{V_G}{|V_P|}$
• $V_G=\frac{R_2{V}_{DD}}{R_1+R_2}$