Lect. 13: High-Frequency Model of MOSFET (4.8)

Lect. 13: High-Frequency Model of MOSFETC GDL ov,1L ov,2L ov= L ov,1 +L ov,2C GSIn saturation,C GS= 2/3 WLC ox+ WL ovC ovC GD=WL ovC ov (about 2fF for L=1.0µm)C GS> C GD(about 20fF for L=1.0µm)Electronic Circuits 1High-Speed Circuits and Systems Laboratory

Lect. 13: High-Frequency Model of MOSFETHow does a capacitor affect frequency response of a circuit?Consider an RC circuitvi() t − vo() t dvo()t= it () = CRdtdvo() t vo() t vi()t+ =dt RC RCIf v ( t) = V exp( jωt), v ( t) = V exp( jωt) (why?)Voi i o o= ?What is V O(t)/V i(t)?Electronic Circuits 1Voexp( jωt) Viexp( jωt)jω⋅ Voexp( jωt)+ =RC RC1 1Vo( jω+ ) = ViRC RC11RC jωCVo = Vi = Vi1 1jω+ R+RC jωC1Voltage divider with capacitor impedance of !jωCHigh-Speed Circuits and Systems Laboratory

Lect. 13: High-Frequency Model of MOSFETFor any circuit having capacitors and inductors,1 1use Z= (or ) for capacitor impedance and Z= jωL(or sL) for inductor impedance.jωCsCVo( ω) Vo( s)(or ) = ?; Frequency response, System function, Transfer functionV( ω) V( s)ii1Vo( ω) jωC1 1 1= = = ( ω0= )V ( ) 1iωR1 j RC ω++ ω1+jRCjωCωV ( ω) 1 V ( ω)−1ω= , ∠ =−tanV ω ω ωoo( )2i 1+ω Vi( )ω2000Electronic Circuits 1High-Speed Circuits and Systems Laboratory

Lect. 13: High-Frequency Model of MOSFETHow fast can a MOSFET transistor operate?C GDC GSUnit-Gain Frequency (f t):Frequency at which magnitude of the short-circuit current gain of CS configuration becomes 1Or Mag(I o(ω)/I i(ω)) = 1Why V gs, not v gs? Frequency-domain analysisElectronic Circuits 1High-Speed Circuits and Systems Laboratory

Lect. 13: High-Frequency Model of MOSFETHow fast can a MOSFET transistor operate?VgsI0= gmVgs − = gmVgs − jωCgdVgs gmVgs ( ∵gm >> ωCgd)1jωC⎛ 1 1 ⎞ 1Vgs = Ii ⋅ || = Ii⋅⎜ jωCgd jωC ⎟⎝gS ⎠ jω( Cgd + Cgs)I g( )0m∴ =Ii jωCgd + Cgs0mFor 1, ωIi Cgd + CgsgmOr fT=(Unit-gain Frequency)2 π ( Cgd+ Cgs)How to make MOSFET faster?Which is faster NMOS or PMOS?Current state-of-the-art NMOS has f Tapproaching 100 GHz.I= =gdgElectronic Circuits 1High-Speed Circuits and Systems Laboratory

Lect. 13: High-Frequency Model of MOSFETHow fast can a MOSFET transistor operate?VgsI0= gmVgs − = gmVgs − jωCgdVgs gmVgs ( ∵gm >> ωCgd)1sC⎛ 1 1 ⎞ 1Vgs = Ii ⋅ || = Ii⋅⎜ jωCgd jωC ⎟⎝gS ⎠ jω( Cgd + Cgs)I g( )0m∴ =Ii jωCgd + Cgs0mFor 1,Ii Cgd + CgsgmOr fT=(Unit-gain Frequency)2 π ( Cgd+ Cgs)How to make MOSFET faster?Which is faster NMOS or PMOS?Current state-of-the-art NMOS has f Tapproaching 100 GHz.I= ω =gdgElectronic Circuits 1High-Speed Circuits and Systems Laboratory

Lect. 13: High-Frequency Model of MOSFETHomework: (Due before Tutorial on 10/17)For the circuit given below,1. Determine the transfer function V i(ω)/V s(ω).2. Plot magnitude and phase of Vi(w)/Vs(w) in dB scale (Bode plot).3. What is the 3-dB frequency?20KΩ80KΩ5pFElectronic Circuits 1High-Speed Circuits and Systems Laboratory