# prelim2sol07 - ECE 315 2 nd Prelim Exam Solution Fall 2007...

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Unformatted text preview: ECE 315 2 nd Prelim Exam Solution Fall 2007 When you are asked to explain a question briefly, I am only expecting 1-3 short sentences . Any wrong information you put down can be subject to point deduction, whether it is relevant to the question. For a bipolar junction diode, I D = I (exp(V D /V T ) – 1) , with + = D i p p A i n n N n L D N n L D qA I 2 2 and V T = k B T/q . The minority injection level at the edge of the depletion region can be approximated by p n = p n0 × exp( V D /V T ), which is valid for both forward and reverse biases. For nMOSFET with the threshold voltage V th , the drain current I D in the linear and saturation regions above threshold ( V GS > V th ) are: (notice that C ox μ ch = k n ’ ) ( 29 ( 29 ( 29 saturation 2 2 linear 2 2 2 ' 2 2 ' 2 th GS Dsat DS OV n th GS ch ox D th GS Dsat DS DS DS th GS n DS DS th GS ch ox D V V V V V k L W V V C L W I V V V V V V V V k L W V V V V C L W I- = ≥ =- =- = < -- = -- = μ μ And in the saturation region, the quasi-static circuit model can be approximated as: For V GS < V th , if V DS > 3V T , ( 29 ( 29 T th GS th D V V V I I / exp- 2245 κ , where I th is the current at V GS =V th in EKV model. V T is the thermal voltage at 26mV at room temperature. The small signal parameters can be approximated as: g m = κ I D /V T , r o = V A /I D and A vo = κ V A /V T . CS CS with R S CG CD R in ∞ ∞ 1/g m + R L /A vo ∞ R out ( R L load) (r o ||R L ) (r o ||R L )+A vo R S (r o ||R L ) 1/g m || (r o ||R L ) A v ( R L load)- g m (r o ||R L )- g m (r o ||R L )/(1+g m R S ) g m (r o ||R L ) 2245 1 For a CS amplifier with a R L and C L load and an input resistance of R sig , the time constant can be estimated by R sig (C gs + (1+A v )C gd ) + (R L ||r o ) C L . MOSFET Diff pair operation range: OV id OV V v V 2 2 max , < <- , and the small signal transconductance gain at small v id can be evaluated from: = 2 id OVcm d v V I i . For the 5-transistor differential amplifier with a current mirror active load, A vo = g mn (r on ||r op ) , similar to a single-stage CS amplifier. g mn v gs g A vo = g m r o = 2V A /V OV V A is the early voltage. 1 For all problems below, we will use the CMOS parameters as k n ’ = μ n C ox = 0.2mA/V 2 , k p ’ = μ p C ox = 0.1mA/ V 2 , V An =V Ap =10V and V thn =|V thp | = 0.7V. V DD = 5V. 1. (Cascode) For the NMOS cascode amplifier considering the Early effect but ignore the body effect, (a) Assume both transistors are in saturation, draw the small-signal model to derive R out = r o2 + (1+g m2 r o2 )r o1 . (5 pts) (b) Derive the open-circuit small-signal voltage gain v out /v in = - g m1 r o1 (1+g m2 r o2 ) (5 pts) V C v OUT v IN R out v X Q 2 Q 1 v out v x r o2 r o1 g m2 v gs2 g m1 v gs1 1/g m1 1/g m2 i out ( 29 2 2 1 2 1 2 2 1 / o m o o out o out x o x out x m out out out out r g r r R r i v r v v v g i i v R + + = =- +- = = v gs1 =0 here 2 (c) If the large-signal...
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## This note was uploaded on 10/25/2009 for the course ECE 3150 taught by Professor Spencer during the Spring '07 term at Cornell University (Engineering School).

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prelim2sol07 - ECE 315 2 nd Prelim Exam Solution Fall 2007...

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