FET Parameter

In a FET, instantaneous drain current i_D is a function of (i) the instantaneous gate voltage V_GS and (ii) instantaneous drain voltage V_DS. Thus,

$i_D = f(V_{GS}, v_{DS})$ ……..(1)

Making use of equation 1, we may define the three FET parameter g_m, r_d and $\mu$ .

Transconductance g_m and Dynamic Drain Resistance r_d

Making Taylor series expansion of equation 1 and considering only the first two terms we get,

$\Delta i_D = \dfrac{\partial i_D}{\partial v_{GS}}|v_{DS} \times \Delta v_{GS} +\dfrac{\partial i_D}{\partial v_{DS}}|v_{GS} \times \Delta v_{DS}$ ……..(2)

Using the conventional small signal notation, $\Delta i_D$ , $\Delta v_{GS}$ and $\Delta v_{DS}$ may be put as,

$i_D = g_m \times v_{gs} + \dfrac{1}{r_d} v_{ds}$ ……..(3)

Where,

$g_m \equiv \dfrac{\delta i_d}{\delta v_{GS}}|v_{DS} \approx \dfrac{\Delta i_{D}}{\Delta v_{GS}}|v_{DS} = \dfrac{i_D}{v_{gs}}|v_{DS}$ …….(4)

And,

$\dfrac{1}{r_d} \equiv \dfrac{\delta i_D}{\delta v_{DS}}|v_{GS} \approx \dfrac{\Delta o_{D}}{\Delta v_{DS}}| v_{GS} = \dfrac{i_D}{v_{DS}}| v_{GS}$ ……..(5)

Parameter g_m is called the mutual conductance or the transconductance of the FET and is expressed in mho (or Seimen) or milli-mho (milli-Seimen).

Parameter r_d is the dynamic drain resistance of the FET and is expressed in ohms. Drain conductance g_d is reciprocal of r_d.

Amplification Factor $\mu$

This is defined as:

$\mu \equiv -\dfrac{\partial v_{DS}}{\partial v_{GS}}|I_{D} \approx \dfrac{\Delta v_{DS}}{\Delta v_{GS}}| I_D = \dfrac{v_{ds}}{v_{gs}}|I_D$ …….(6)

By varying v_ds and v_gs is such a way as to keep i_d = 0, Equation 3 yields:

$O = g_m v_{gs} + \dfrac{1}{r_d}v_{ds}$ ………(7)

Or, $g_m \times r_d = -\dfrac{v_{ds}}{v_{gs}} | i_{d=0}$ ………(8)

Or, $g_m \times r_d = \mu$ ……..(9)

All the three parameters g_m, r_d and $\mu$ vary with gate bias V_GS and ambient temperature. It is found that g_m has negative temperature coefficient. The drain current I_D has the same temperature variation as g_m. Thus, I_d also has negative temperature coefficient. This results basically from the decreased mobility of majority carriers with increased temperature. This is the plus point of FET since with negative temperature coefficient, thermal runaway never results in FET. On the other hand, in BJT, the minority carrier current increases with increases of increases of temperature and these exists a tendency for thermal runaway.

Small Signal Models for FET

Equation 3 gives the incremental drain current i_d in terms of g_m, r_d, v_gs and v_ds. Figure 1 gives a circuit which satisfies equation 3 and hence forms the low frequency small signal model of FET. This model contains one dependent current generator whose current g_m, v_gs is proportional to the time varying gate-to-source voltage v_gs. The constant of proportionality is the transconductance g_m.

In the low frequency model of FET with gate reverse biased, gate current is zero. Hence, the input resistance between gate and source is infinite. Similarly, the resistance between gate and drain is infinite.

Assuming sinusoidal input voltage of rms value v_gs, the model of figure 1 may be redrawn as in figure 2 where v_gs, i_d, v_ds have been replaced respectively by rms value v_gs, I_d, and V_ds.

Comparison of Low Frequency Model of FET and BJT

Let us compare the low frequency model of FET as given in figure 1 and 2 with the h-parameter model of BJT. We find that

Both FET and BJT models have a dependent current generator in the output circuit.
In FET models, the generator current is proportional to the input voltage V_gs whereas in BJT model, the generator current is proportional to the input current.
In FET, there is no feedback from output (drain) to the input (source) whereas in BJT model, there exists feedback through the parameter h_re.
In FET mode, input resistance is very high, theoretically infinity at low frequencies, whereas in common emitter BJT model, the input resistance is low, being only about 1 k-ohm.

We thus conclude that at low frequencies, FET forms a more ideal amplifier than BJT amplifier.

Magnitude of FET Parameters

Table 1 gives the order of magnitude of the parameters in the low frequency model of diffused junction FET. The table also gives the values of the same parameters for typical low frequency MOSFET.

Table 1: Values of parameters of Typical JFET and MOSFET

Parameter

Diffused Junction FET

MOSFET

g_m

r_d

r_gs

0.1 to 10 m-mho

0.1 to 1 M-ohm

> 100 M-ohm

> 10 M-ohm

0.1 to 20 m-mho

1-50 K-ohm

> 10⁴ M-ohm

> 10⁶ M-ohm

FET Parameter

Transconductance gm and Dynamic Drain Resistance rd

Amplification Factor

Small Signal Models for FET

Comparison of Low Frequency Model of FET and BJT

Magnitude of FET Parameters

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Transconductance g_m and Dynamic Drain Resistance r_d

Amplification Factor $\mu$