0195136047.pdf

370 SEMICONDUCTOR DEVICES

Also shown in Figure 7.4.3(a) is abreakdown voltage,denoted by BVDGO, at which breakdown in

the drain–gate junction occurs in the channel near the drain. For most JFETs, BVDGOranges from

about 20 to 50 V. The dependence ofiDonvDS, as shown in Figure 7.4.3(b), can be accounted for

by applying a first-order correction to Equation (7.4.1),

iD=IDSS

(

1 +

vGS

VP

) 2 (

1 +

vDS

VA

)

(7.4.2)

A small-signal equivalent circuit (valid at low frequencies where capacitances can be

neglected) can now be developed based on Equation (7.4.2). Denoting the dc values at the operating

point byVGSQ,IDQ, andVDSQ, the small changes that occur can be expressed by

iD=

∂iD

∂vGS

∣ ∣ ∣ ∣ ∣ Q

vGS+

∂iD

∂vDS

∣ ∣ ∣ ∣ ∣ Q

vDS=gmvGS+

1

ro

vDS (7.4.3)

where

gm=

∂iD

∂vGS

∣ ∣ ∣ ∣ ∣ Q

= 2 IDSS

(

1 +

vGS

VP

)(

1 +

vDS

VA

)(

1

VP

)∣∣

∣

∣

∣

Q

=

2 IDSS

VP

[(

IDQ

IDSS

)(

1 +

VDSQ

VA

)] 1 / 2

∼=

(

2

VP

)

(

IDSSIDQ

) 1 / 2

(7.4.4)

and

1

ro

=

∂iD

∂vDS

∣ ∣ ∣ ∣ ∣ Q

=IDSS

(

1 +

vGS

VP

) 2 (

1

VA

)∣∣

∣

∣

∣

Q

=

IDQ/VA

1 +(VDSQ/VA)

∼=IDQ

VA

(7.4.5)

The small-signal equivalent circuit based on Equation (7.4.3) is shown in Figure 7.4.4.

G D

S

+

−

∆vGS gm∆vGS

∆iD

ro

Figure 7.4.4JFET small-signal equiva-

lent circuit for low frequencies.

EXAMPLE 7.4.1

Measurements made on the self-biasedn-channel JFET shown in Figure E7.4.1 areVGS=− 1

V,ID=4 mA;VGS=− 0 .5V,ID= 6 .25 mA; andVDD=15 V.

(a) DetermineVPandIDSS.

(b) FindRDandRSso thatIDQ=4mAandVDS=4V.