MOSFET Small Signal Analysis

JFET SMALL-SIGNAL MODEL

• The gate-to-source voltage controls the drain-to-source (channel) current of a JFET.
• Gate-to-source voltage controls the level of dc drain current through a relationship known as Shockley’s equation: I_D = I_DSS (1 – (V_GS/V_P))²
• The change in drain current that will result from a change in Gate-to-source voltage can be determined using the transconductance factor g_m in the following manner: ΔI_D = g_m ΔV_GS
• g_m=ΔI_D/ΔV_GS

Mathematical Definition of g_m:

where |V_P| denotes magnitude only, to ensure a positive value for g_m .

• slope of the transfer curve is a maximum at VGS = 0 V.

• The control of I_d by V_gs is included as a current source g_mV_gs connected from drain to source as shown in Fig.
• The current source has its arrow pointing from drain to source to establish a 180° phase shift between output and input voltages as will occur in actual operation.

• The input impedance is represented by the open circuit at the input terminals and the output impedance by the resistor r_d from drain to source.
• Note that the gate-to-source voltage is now represented by Vgs (lowercase subscripts) to distinguish it from dc levels.
• In addition, note that the source is common to both input and output circuits, whereas the gate and drain terminals are only in “touch” through the controlled current source g_mVgs.

E-MOSFET Small signal analysis

• The ac small-signal equivalent circuit is shown in Fig. , revealing an open-circuit between gate and drain–source channel and a current source from drain to source having a magnitude dependent on the gate-to-source voltage.
• There is an output impedance from drain to source r_d , which is usually provided on specification sheets as a conductance g_os or admittance y_os.
• The device transconductance g_m is provided on specification sheets as the forward transfer admittance y_fs .
• In our analysis of JFETs, an equation for g_m was derived from Shockley’s equation.
• For E-MOSFETs, the relationship between output current and controlling voltage is defined by: I_D = k(V_GS – V_GS(Th))²
• since g_m=ΔI_D/ΔV_GS

E-MOSFET DRAIN-FEEDBACK CONFIGURATION

• R_G could be replaced by a short-circuit equivalent since I_G = 0 A and therefore V_RG = 0 V.
• However, for ac situations it provides an important high impedance between Vo and Vi .
• Otherwise, the input and output terminals would be connected directly and Vo = Vi.

• R_F is not within the shaded area defining the equivalent model of the device, but does provide a direct connection between input and output circuits.

• The negative sign for Av reveals that Vo and Vi are out of phase by 180°.

E-MOSFET VOLTAGE-DIVIDER CONFIGURATION