Fet small signal model

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

Fet small signal model

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Fet small signal model