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JFET

The circuit of Figure 123 will be used to study the JFET characteristics. The JFET is a nonlinear device. The voltage sources V_GG and V_DD will be adjusted.

  

Figure 123: n-channel JFET circuit.

A graph of the JFET characteristics, i_D versus v_DS and i_D versus v_GS is shown in Figure 124.

  

Figure 124: n-channel JFET characteristics.

Consider first v_GS=0 V. For small values of v_DS, the drain current i_D increases linearly. For larger values, the increase of i_D is nonlinear until pinch-off occurs when v_DS reaches the value -V_p. After pinch-off, i_D cannot increase further, and stays constant at the value I_DSS.

Now decrease v_GS to a negative value. Then pinch-off occurs at a lower value of v_DS, indicated by the doted line. After pinch-off, in the active or current saturation region, the value of drain current is given (approximately) by the square law  

$$i_{DS} = I_{DSS}(1- \frac{v_{GS}}{V_p} )^2 , \ \ \ (V_{GS} \geq V_p).$$ (110)

A graph of this curve is shown in the left of Figure 124.

If v_GS is reduced to the negative value V_p, then i_D=0 and current flow is cut-off.

Note that, according to (110), i_D is a quadratic function of v_GS. The shape of the i_D versus v_DS characteristic is similar to the i_C versus v_CE curve for a BJT, Figures 97 and 98. However, in the case of the BJT $i_C = \beta i_B$ in the active region, a linear relationship (although

$$i_C \propto \exp ( \frac{V_{BE}}{26{\rm mV}} ) ,$$

a nonlinear relationship.)

An important parameter is the transconductance g_m   defined by

$$g_m = \frac{\partial i_{DS}}{\partial v_{GS}} = -\frac{2 I_{DSS}}{V_p} (1- \frac{v_{GS}}{V_p} )$$ (111)

It gives the slope of the i_D-v_GS curve at the operating point determined by v_GS. This expression is often written as

$$g_{m} = \frac{\partial i_D}{\partial v_{GS}} = g_{m0} (1- \frac{v_{GS}}{V_p} )$$ (112)

where

$$g_{m0} =-\frac{2 I_{DSS}}{V_p}$$

is the transconductance at v_GS=0.

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