Fet small signal model

This manuscript addresses the small effect of FET

1. FET: Small Signal Model
Dr. Varun Kumar
Dr. Varun Kumar(IIIT Surat) 1 / 9

2. Outlines
1
Transfer characteristics of FET
2
Small signal model of FET
Dr. Varun Kumar(IIIT Surat) 2 / 9

3. Transfer characteristics of FET
)In an amplier application, the FET is used in the region beyond
pinch-o.
)It is also called asconstant current,pentode, orcurrent saturation
region.
)Let the saturation current isIDSandIDSSis the saturation current at
VGS= 0Vthen
IDS=IDSS

1
VGS
VP

2
)Above relation is called as the
)Relation betweenIDSandVGScan be approximated by the parabola.
Dr. Varun Kumar(IIIT Surat) 3 / 9

4. Cuto
Case 1
)Consider an FET operating at a xed value ofVDSin constant
current region.
)AsVGSincreases (reverse bias), the conducting channel will narrow.
)WhenVGS=VPthen!IDS=IDSS

1
VGS
VP

2
= 0
)With physical device, some small current also ow from drain to
source in n-channel JFET, whenVGS=VP.
)This small leakage current is called asID;OFF, whenjVGSj>jVPj.
)ID;OFForder of nanoamperes for silicon FET.
Case 2
)Gate reverse current also called gate cuto current designated by
IGSS, whenjVGSj>jVPjandVDS= 0
Dr. Varun Kumar(IIIT Surat) 4 / 9

5. FET small signal model
)The linear small signal model is same as the BJT.
)We can formally express as
iD=f(vGS;vDS)
Transconductancegmand Drain Resistancerd
)If bothvGSandvDSboth are variable.
4iD=
@iD
@vGS



vDS
4vGS+
@iD
@vDS



vGS
4vDS
)In small signal model,4iD=id,4vGS=vgs,4vDS=vds
)From above relation,
id=gmvgs+
1
rd
vds
Dr. Varun Kumar(IIIT Surat) 5 / 9

6. Continued{
)gm
@iD
@vGS



vDS

4iD
4vGS



vDS
=
id
vgs



vDS
!Mutual conductance or
transconductance.
)rd
@vDS
@iD



vGS

4vDS
4iD



vGS
=
vds
id



vGS
!Drain resistance
)Reciprocal of drain resistance is drain conductance
1
rd
=gd
Amplication factorof a FET:

@vDS
@vGS



ID
=
4vDS
4vGS



ID
=
vds
vgs



id=0
We can verify that,rd,gmare related by
=gmrd
by settingid= 0
Dr. Varun Kumar(IIIT Surat) 6 / 9

7. Continued{
gm=gmo

1
VGS
VP

=
2
jVPj
(IDSSIDS)
1
2
where,gmo=
2IDSS
VP
)gmois the value ofgmforVGS= 0
)IDSSandVPare of opposite sign,gmois always positive.
)Transconductance varies as the square root of the drain current, or
gm/
p
IDS
Dr. Varun Kumar(IIIT Surat) 7 / 9

8. FET Model
)(a) The low-frequency small-signal FET model.
)(b) The high-frequency model, taking node capacitors into account
Dr. Varun Kumar(IIIT Surat) 8 / 9

9. Continued{
)FET is much more ideal amplier than the conventional transistor
amplier at low frequency.
)Unfortunately, this is not true beyond the audio range (20Hz-20KHz).
)Cgs!Barrier capacitance between gate and source.
)Cgd!Barrier capacitance between gate and drain.
)Cds!Drain to source capacitance of the channel.
)These internal capacitance, feedback exists between input and output
circuits and voltage amplication drops rapidly as frequency is
increased.
Parameter JFET
gm 0.1-10 mA/V
rd 0.1-1M
Cds 0.1-1 pF
Cgs,Cgd 1-10pF
rgs >10
8
rgd >10
8
Dr. Varun Kumar(IIIT Surat) 9 / 9