1ECE 315 Final Exam Solution Fall 2006 Name: ___________________________________ Student net ID: _______________________ •When you are asked to explain a question briefly, use only 1-3 short sentences. Any wrong information you put down can be subject to point deduction, whether it is relevant to the question. •The default temperature is 300K, and the default semiconductor is silicon with the bandgap of 1.1eV. •The Debye length is defined as DBsiDNqTkL20εε=, and the minority diffusion length as: nnnDLτ=, where Dnis the diffusivity, τnis the minority recombination lifetime, kBthe Boltzmann constant, and Tthe temperature. •Diode equations: Wd= xn+ xp biDAsiVNNq⎟⎟⎠⎞⎜⎜⎝⎛+=1120εε, NAxp= NDxn,2iDAbinNNqkTV=,ID= I0(exp(VD/VT) – 1), with ⎟⎟⎠⎞⎜⎜⎝⎛+=DippAinnNnLDNnLDqAI220and VT= kBT/q. The minority injection level at the edge of the depletion region can be approximated by pn= pn0×exp(VD/VT), which is valid for both forward and reverse biases. •For nMOSFET with the threshold voltage Vth, the drain current IDin the linear and saturation regions above threshold (VGS> Vth) are: (notice that Coxμch= kn’) ()()()saturation22linear222'22'2thGSDsatDSOVnthGSchoxDthGSDsatDSDSDSthGSnDSDSthGSchoxDVVVVVkLWVVCLWIVVVVVVVVkLWVVVVCLWI−=≥=−=−=<⎟⎟⎠⎞⎜⎜⎝⎛−−=⎟⎟⎠⎞⎜⎜⎝⎛−−=μμ•And in the above-Vthsaturation region, the quasi-static small-signal model can be approximated as: •For VGS< Vth, ()()TthGSthDVVVII/exp−≅κ, where Ithis the current at VGS=Vthin EKV.•The single-stage amplifiers with the MOSFET in the saturation region or BJT in the active region: CS CS with RSCG CD Rin∞∞1/gm + RL/Avo∞Rout (RLload)(ro||RL) (ro||RL)+AvoRS(ro||RL)1/gm || (ro||RL)Av (RLload)−gm(ro||RL)−gm(ro||RL)/(1+gmRS) gm(ro||RL)≅1 •MOSFET Diff pair operation range: OVidOVVvV22max,<<−, and the small signal transconductance gain at small vidcan be evaluated from: ⎟⎠⎞⎜⎝⎛=2idOVcmdvVIi. gmnvgsDAoOVDOVchoxmIVrVIVCLWg===2μVAis the early voltage.
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