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(Saturated) MOSFET Small-Signal Model …

EE 105 fall 1998 Lecture 11( saturated ) MOSFET Small-Signal ModelnConcept: find an equivalent circuit which interrelates the incremental changes in iD, vGS, vDS, etc. for the MOSFET in saturationvGS = VGS + vgs , iD = ID + id -- we want to find id = (?) vgsWe have the functional dependence of the total drain current in saturation:iD = n Cox (W/2L) (vGS - VTn )2 (1 + nvDS) = iD(vGS, vDS)Solution: do a Taylor expansion around the DC operating point (also called the quiescent point or Q point) defined by the DC voltages Q(VGS, VDS):If the Small-Signal voltage is really small , then we can neglect all everything past the linear term --where the partial derivative is defined as the transconductance, iDQvgs()12---vGS22 iDQvgs() +++=iDIDvGS iDQvgs()+IDgmvgs+==11EE 105 fall 1998 Lecture 11 TransconductanceThe Small-Signal dra

EE 105 Fall 1998 Lecture 11 (Saturated) MOSFET Small-Signal Model Concept: find an equivalent circuit which interrelates the incremental changes in iD, vGS, vDS, etc. for the MOSFET in saturation

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Transcription of (Saturated) MOSFET Small-Signal Model …

1 EE 105 fall 1998 Lecture 11( saturated ) MOSFET Small-Signal ModelnConcept: find an equivalent circuit which interrelates the incremental changes in iD, vGS, vDS, etc. for the MOSFET in saturationvGS = VGS + vgs , iD = ID + id -- we want to find id = (?) vgsWe have the functional dependence of the total drain current in saturation:iD = n Cox (W/2L) (vGS - VTn )2 (1 + nvDS) = iD(vGS, vDS)Solution: do a Taylor expansion around the DC operating point (also called the quiescent point or Q point) defined by the DC voltages Q(VGS, VDS):If the Small-Signal voltage is really small , then we can neglect all everything past the linear term --where the partial derivative is defined as the transconductance, iDQvgs()12---vGS22 iDQvgs() +++=iDIDvGS iDQvgs()+IDgmvgs+==11EE 105 fall 1998 Lecture 11 TransconductanceThe Small-Signal drain current due to vgs is therefore given byid = gm +_BVDS = 4 V+_12345100200300400500600iD( A)VDS (V)

2 6vGS = VGS = 3 VVGS = 3 V+_vgsiD = ID + idvGS = VGS + vgsQidgm = id / vgsEE 105 fall 1998 Lecture 11 Another View of gm* Plot the drain current as a function of the gate-source voltage, so that the slope can be identified with the transconductance:DSG+_BVDS = 4 V+_12345100200300400500600iD( A)vGS (V)6vGS = VGS = 3 VVGS = 3 V+_vgsiD = ID + idvGS = VGS + vgsQidgm = id / vgsiD(vGS, VDS = 4 V)EE 105 fall 1998 Lecture 11 Transconductance (cont.)nEvaluating the partial derivative:nIn order to find a simple expression that highlights the dependence of gm on the DC drain current, we neglect the (usually) small error in writing:For typical values (W/L) = 10, ID = 100 A, and nCox = 50 AV-2 we find thatgm = 320 AV-1 = mSgm nCoxWL----- VGSVTn ()1 nVDS+()=gm2 nCoxWL----- ID2 IDVGSVTn --------------------------==EE 105 fall 1998 Lecture 11(Partial) Small-Signal Circuit ModelnHow do we make a circuit which expresses id = gm vgs ?

3 Since the current is not across its controlling voltage, we need a voltage-controlled current source:gmvgsgatesourcedrain+_vgs_idEE 105 fall 1998 Lecture 11 Output Conductance/ResistancenWe can also find the change in drain current due to an increment in the drain-source voltage:The output resistance is the inverse of the output conductanceThe (partial) Small-Signal circuit Model with ro added looks like:goiD vDS ------------Q nCoxW2L------ VGSVTn ()2 n nID ==ro1go-----1 nID------------==gmvgsrogatesourcedrain+ _vgsid+_vdsid = gm vgs + (1/ro)vdsEE 105 fall 1998 Lecture 11 MOSFET Capacitances in SaturationIn saturation, the gate-source capacitance contains two terms, one due to the channel charge s dependence on vGS [(2/3)WLCox] and one due to the overlap of gate and source (WCov, where Cov is the overlap capacitance in fF per m of gate width)

4 In addition, there is the small but very important gate-drain capacitance (just the overlap capacitance Cgd = Cov) There are depletion capacitances between the drain and bulk (Cdb) and between source and bulk (Csb). Finally, the extension of the gate over the field oxide leads to a small gate-bulk capacitance Cgb. gatedrainsourcen+n+qN(vGS)overlap LD overlap LD fringe electric field linesCsbCdbdepletionregionCgs23---WLCoxW Cov+=EE 105 fall 1998 Lecture 11 Complete Small-Signal ModelnAll these capacitances are patched onto the Small-Signal circuit schematic containing gm and ro.

5 Gmb is open-circuited for EECS 105 since vbs = 0 ++bulkEE 105 fall 1998 Lecture 11p-channel MOSFETsnStructure is complementary to the n-channel MOSFETnIn a CMOS technology, one or the other type of MOSFET is built into a well -- a deep diffused region -- so that there are electrically isolated bulk regions in the same substraten+ sourcep+ sourcen+ drainp+ drainp+ n+ p-type substrateisolated bulk contact withp-channel MOSFET shorted to source common bulk contact forall n-channel mosfets (to ground or to the supply)n well n-channel MOSFETp-channelMOSFET (a)(b) AA EE 105 fall 1998 Lecture 11p-channel MOSFET ModelsnDC drain current in the three operating regions: -ID > 0nThe threshold voltage with backgate effect is given by:Numerical values: pCox is a measured parameter.

6 Typical value: pCox = 25 AV-2 VTp = to V, which should be approximately -VTn for a well-controlled CMOS processI D0 AV(SGV T) =I D pCoxWL ()VSGVTpVSD2 () +[]1 pVSD+()VSD=V(SGV TpVSDVSGVTp)+ , I D pCoxW2L() ()VSGVTp+()21 pVSD+()=V(SGV TpVSDVSGVTp)+ , VTpVTOp pV SB2 n+()2 n () = mV1 L-------------------------- EE 105 fall 1998 Lecture 11p-channel MOSFET Small-Signal modelnthe source is the highest potential and is located at the top of the schematicgmvsggmbvsbrogatedrainbulk+_vsg CgsCsbCdbCgdCgb_source id vsb


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