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 amplifier application, the FET is used in the region beyond
pinch-off.
⇒ It is also called as constant current, pentode, or current saturation
region.
⇒ Let the saturation current is IDS and IDSS is the saturation current at
VGS = 0V then
IDS = IDSS
1 −
VGS
VP
2
⇒ Above relation is called as the transfer characteristics.
⇒ Relation between IDS and VGS can be approximated by the parabola.
Dr. Varun Kumar (IIIT Surat) 3 / 9

4. Cutoff
Case 1
⇒ Consider an FET operating at a fixed value of VDS in constant
current region.
⇒ As −VGS increases (reverse bias), the conducting channel will narrow.
⇒ When VGS = VP then → IDS = IDSS
1 − VGS
VP
2
= 0
⇒ With physical device, some small current also flow from drain to
source in n-channel JFET, when VGS = VP.
⇒ This small leakage current is called as ID,OFF , when |VGS | |VP|.
⇒ ID,OFF ∼ order of nanoamperes for silicon FET.
Case 2
⇒ Gate reverse current also called gate cutoff current designated by
IGSS , when |VGS | |VP| and VDS = 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 )
Transconductance gm and Drain Resistance rd
⇒ If both vGS and vDS both are variable.
4iD =
∂iD
∂vGS

8. vDS
4vGS +
∂iD
∂vDS

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

12. Continued–
⇒ gm ≡ ∂iD
∂vGS

15. vDS
≈ 4iD
4vGS

18. vDS
= id
vgs

21. vDS
→ Mutual conductance or
transconductance.
⇒ rd ≡ ∂vDS
∂iD

24. vGS
≈ 4vDS
4iD

27. vGS
= vds
id

30. vGS
→ Drain resistance
⇒ Reciprocal of drain resistance is drain conductance 1
rd
= gd
Amplification factor µ of a FET:
µ ≡ −
∂vDS
∂vGS

33. ID
= −
4vDS
4vGS

36. ID
= −
vds
vgs

39. id =0
We can verify that µ, rd , gm are related by
µ = gmrd
by setting id = 0
Dr. Varun Kumar (IIIT Surat) 6 / 9

40. Continued–
gm = gmo
1 −
VGS
VP
=
2
|VP|
(IDSS IDS )
1
2
where, gmo = −2IDSS
VP
⇒ gmo is the value of gm for VGS = 0
⇒ IDSS and VP are of opposite sign, gmo is always positive.
⇒ Transconductance varies as the square root of the drain current, or
gm ∝
√
IDS
Dr. Varun Kumar (IIIT Surat) 7 / 9

41. 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

42. Continued–
⇒ FET is much more ideal amplifier than the conventional transistor
amplifier 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 amplification drops rapidly as frequency is
increased.
Parameter JFET
gm 0.1-10 mA/V
rd 0.1-1M Ω
Cds 0.1-1 pF
Cgs,Cgd 1-10pF
rgs 108
rgd 108
Dr. Varun Kumar (IIIT Surat) 9 / 9