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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.301 Solid State Circuits Final Exam December 15, 2008 180 minutes 1. This examination consists of four problems. Work all problems. 2. This examination is closed book. 3. Please summarize your solutions in the spaces provide in this examination packet. Draw all sketches neatly and clearly where requested. Remember to label ALL important features of any sketches. 4. All problems have equal weight. 5. Make sure that your name is on this packet and on each examination booklet. Good luck. General equations, worst case OCT: R2Ο R3 R1 rπ va gmva R1Ο R2 R10 � � (R1 + R2 ) = rπ � � 1 + gm R2 R20 = R1 �[rπ + (β + 1)R2 ] +R3 + � �� � R� 2 gm rπ R� R3 rπ +(β+1)R2 Problem 1 OCT’s and transfer functions Consider the following ampliﬁer: Q4 VB ro/2 Vout Q3 ro/2 Co Vcasc Q2 Q1 Cin iin • β→∞ • Cπ = 0 • Cµ = 100fF • Co = Cin = 1pF • Assume Ic1 = Ic2 = Ic3 = Ic4 • Do not ignore the Early eﬀect. (a) Solve for the following transfer functions • vout iin • vf vout • vin (vf , iin ) (b) Approximate the 3dB frequency (f3dB ) using the method of open circuit time constants. Make reason­ able approximations. 3 Problem 2 Op amps A three-stage BJT op-amp is shown below. Assume VBE,on = 0.7V, β = 100, VA = 2.5V, Q9 100�A Vi- Q2 Q1 = 25mV. Q11 Q 10 Vi+ kT q Q3 Q4 Q5 Q6 st 1 stage Vo C1 Q7 Q8 7k� 2 nd stage rd 3 stage (a) Calculate all collector currents (b) Calculate the low-frequency gain of each stage. Include rπ ’s and ro ’s in your calculation. (c) Explain the function of the 2nd stage. (d) The dynamics of the ampliﬁer are dominated by C1 . Estimate the location of the lowest frequency pole in terms of C1 and quantities involved in part (b). 4 Problem 3 Op Amp applications Note: For parts (a) and (b) you may assume the op amps and diodes are ideal. (a) Derive the voltage vo as a function of vI and vA in the following circuit R/2 R vA vI + R vO (b) Derive vA as a function of vI in the following circuit when: 1. vI > 0 2. vI < 0 R R + vI vA (c) What function is implemented by the following circuit? Give both a qualitative and quantitative ( vvoI ) answer. R R R + vI R/2 + vO R (d) Now consider the diodes to be nonideal (i.e., they have a forward drop of 0.6V when conducting). What is the output voltage vA of the circuit in part (b) under this condition? R R vI + 5 vA Problem 4 Charge Control An inverter circuit is shown below +10V SW2 SW1 R 100� vO ic vI 20pF The transistor has negligible space-charge layer capacitances. In this case, the charge control equations are iC = iB = iE = � 1 qF 1 � dqR − qR + − τF τR τBR dt qF dqF qR dqR + + + τBF dt τBR dt � 1 qF 1 � dqF − qF + − τBF τF τBF dt When the transistor is in saturation iB − iBo = qS dqS + τS dt The transistor parameters are τF = 1ns βF = 100 τBF = 100ns τR = 2ns βR = 5 τBR = 10ns τS = 15.1ns (a) The circuit is initially conﬁgured with switch 1 open and switch 2 closed. Input voltage vI (t) is a 10.7 volt step and the initial value of the capacitor voltage is zero. Find iC (t) valid for all time slightly greater than zero. (b) Switch 1 is now closed. Other conditions remain the same as for part (a). Find the value of R that makes iC a constant for all time slightly greater than zero. (c) Switches 1 and 2 are now both opened. With vI (t) a 10.7V step and zero initial capacitor voltage, the voltage vo (t) is given by the following graph 6 fa st 10V vO(t) 10V τ1 t TD What are the values of delay time TD and τ1 ? You may express TD in terms of logarithms if you wish. (d) The circuit is now operated with switch 1 closed and switch 2 open, R = 2.5kΩ, and vI a constant 10.7 volts. After equilibrium is reached switch 2 is closed. What is the value of iC slightly after the switch is closed? What is the ﬁnal value of iC ? 7 MIT OpenCourseWare http://ocw.mit.edu 6.301 Solid-State Circuits Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.