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‎final/2012/final_exam.tex

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% -*- latex -*-
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% FILE: "/home/evmik/jobs/wm/2012_spring_Analog_Electronics_252/final_exam/final_exam.tex"
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% LAST MODIFICATION: "Tue, 01 May 2012 11:45:17 -0400 (evmik)"
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% (C) 2009 by Eugeniy Mikhailov, <[email protected]>
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% $Id:$
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\documentclass[letterpaper,addpoints,answers]{exam}
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\usepackage{graphicx}
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\usepackage{hyperref}
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\begin{document}
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%\pagestyle{headandfoot}
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%\lhead{
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%\large\bfseries Physics 107\\
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%Midterm Exam, June 15, 2009
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%}
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%\chead{}
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%\rhead{
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%\large\bfseries Name:\enspace\makebox[2in]{\hrulefill}\\
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%\large\bfseries Signature:\enspace\makebox[2in]{\hrulefill}
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%}
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%\lfoot{}
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%\cfoot[]{Page \thepage}
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%\rfoot{}
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\begin{coverpages}
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\noindent
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\large\bfseries Physics 252
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\vspace{2ex}
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\noindent
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Final Exam, May 2012
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\vspace{5ex}
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\noindent
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\large\bfseries Name:\enspace\makebox[2in]{\hrulefill}\\
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\vspace{5ex}
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\noindent
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\large\bfseries Signature:\enspace\makebox[2in]{\hrulefill}
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\vspace{5ex}
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\noindent
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This test is administered under the rules and regulations of the honor
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system of the College of William \& Mary.
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\vspace{5ex}
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\noindent
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Show your work, circle your answers.
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\vspace{5ex}
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\combinedgradetable[v][questions]
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\end{coverpages}
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\begin{questions}
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\input{questions/filters_multi_choice}
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\input{questions/opamp_vs_transistors_comparison}
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\input{questions/thevenin_parameters_of_a_circuit}
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\input{questions/bjt_amplifier}
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\input{questions/opamp_adder}
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\input{questions/noninverting_amplifier_with_opamp}
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\input{questions/math_with_opamps}
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\input{questions/oscillator}
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\input{questions/output_impedance_of_fancy_opamp_amplifiers}
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\input{questions/matched_njfet_follower}
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\end{questions}
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\end{document}
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% vim: tabstop=2 shiftwidth=2
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‎final/2012/images/exponential_decay.png

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‎final/2012/questions/bjt_amplifier.tex

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% -*- latex -*-
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% FILE: "/home/evmik/jobs/wm/2012_spring_Analog_Electronics_252/final_exam/questions/bjt_amplifier.tex"
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% LAST MODIFICATION: "Tue, 01 May 2012 01:18:46 -0400 (evmik)"
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% (C) 2011 by Eugeniy Mikhailov, <[email protected]>
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% $Id:$
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\question{}
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Consider the circuit shown below \\
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\includegraphics[height=2in]{./schematics/npn_common_emitter_amplifier}\\
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\begin{parts}
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\part[10]
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Derive the expression for the output voltage $V_{out}$, in terms of
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$V_{in}, V_{cc}, R_c, R_e,$ and the base to emitter voltage drop $V_{be}$.
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Assume that $\beta=200$. Also assume that the load resistor ($R_L$) is large enough and does not affect the circuit.
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\vskip 1.5in
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$V_{out}=$
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\part[5]
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What is the small signal gain of this circuit?
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\vskip 0.5in
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$G=$
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\part[5]
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Assume that the load resistor ($R_L$) is large enough and does not affect the circuit.
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If $R_c/R_e=10$, $V_{be}=.6$~V and $V_{cc}=15$~V, what is
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the maximum and minimum DC
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input voltage $V_{in}$ at which this circuit is still not saturated or railing?
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\vskip 1.0in
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$V_{{in}_{min}}=$ \hspace{2in}
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$V_{{in}_{max}}=$
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\bonuspart[5]
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What is the output impedance of this circuit? {\bf Stating it is not
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enough, show the derivation!}
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\vskip 1.0in
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$Z_{out}=$
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\end{parts}
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\pagebreak

‎final/2012/questions/filters_multi_choice.tex

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% -*- latex -*-
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% FILE: "/home/evmik/jobs/wm/2012_spring_Analog_Electronics_252/final_exam/questions/filters_multi_choice.tex"
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% LAST MODIFICATION: "Mon, 30 Apr 2012 23:14:28 -0400 (evmik)"
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% (C) 2011 by Eugeniy Mikhailov, <[email protected]>
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% $Id:$
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\question{}
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For circuits shown below specify if it a low-pass, high-pass, band-pass
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or band-reject filter. {\bf Hint:} It may be useful to think about
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transfer function at high and low frequencies.
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\begin{parts}
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\part[2]
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\includegraphics[height=0.7in]{./schematics/rc_low_pass}
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\part[2]
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\includegraphics[height=0.7in]{./schematics/rc_high_pass}
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\part[2]
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\includegraphics[height=0.7in]{./schematics/rl_high_pass}
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\part[2]
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\includegraphics[height=0.7in]{./schematics/rl_low_pass}
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\part[2]
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\includegraphics[height=0.7in]{./schematics/rlcnotch}
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\part[2]
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\includegraphics[height=0.7in]{./schematics/rlc_band_pass}
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\part[2]
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\includegraphics[height=0.7in]{./schematics/band_pass_filter}
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\part[2]
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Sketch the transfer function of the last filter (g) in log-log
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scale.
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\vskip 1in
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\part
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Under what conditions the last filter (g) has a transfer
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function close to unity at least in some frequency region?
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\begin{subparts}
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\subpart[2]
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Express one condition in terms of $3_{dB}$ points of the
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low-pass and high-pass filters constituting combined
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filter (g).
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\vskip 0.5in
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\subpart[2]
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What must be true about $R_1$ and $R_2$?
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\end{subparts}
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\end{parts}
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\pagebreak
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‎final/2012/questions/matched_njfet_follower.tex

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% -*- latex -*-
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% FILE: "/home/evmik/jobs/wm/2011_spring_Analog_Electronics_252/final_exam/questions/matched_njfet_follower.tex"
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% LAST MODIFICATION: "Thu, 05 May 2011 10:50:43 -0400 (evmik)"
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% (C) 2011 by Eugeniy Mikhailov, <[email protected]>
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% $Id:$
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\question{}
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Consider the circuit shown below. \\
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\includegraphics[height=2in]{./schematics/njfet_matched_follower}\\
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NJFETs in this circuit are {\bf matched}.
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Presume that $V_{dd}$ is large enough for transistors to be in saturation.
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\begin{parts}
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\part[5]
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First consider only bottom part (below $V_{out}$ terminal). It can be
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thought as a constant current source with current $I_d$ (assume that it
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is somehow known to you).
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Write the {\bf symbolical} expression for the $V_{GS}$ of the bottom transistor.
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\vskip .5in
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$V_{GS}=$
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\part[15]
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Using above information. Derive the {\bf symbolical} expression for the output
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voltage $V_{out}$ in terms of the input voltage, $V_{GS}$, $I_d$, and
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$R_s$. {\bf Hint:} you might not need all of them at the very end.
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\vskip 1.8in
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$V_{out}=$
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\part
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The transistors parameters are the following: the pinch off voltage
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$V_p=-2$~V, the coefficient $k=2\times10^{-3}$~A/(V$^2$). Supply
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voltage $V_{dd}=20$~V, $R_s=500$~$\Omega$.
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\begin{subparts}
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\subpart[5]
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Find the quiescent current supplied by the power supply.
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\vskip 1in
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$I_{d}=$
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\subpart[5]
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Find the quiescent power dissipated by this circuit
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\vskip .5in
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$P_{q}=$
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\end{subparts}
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\end{parts}
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\pagebreak

‎final/2012/questions/math_with_opamps.tex

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% -*- latex -*-
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% FILE: "/home/evmik/jobs/wm/2012_spring_Analog_Electronics_252/final_exam/questions/math_with_opamps.tex"
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% LAST MODIFICATION: "Tue, 01 May 2012 01:11:51 -0400 (evmik)"
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% (C) 2011 by Eugeniy Mikhailov, <[email protected]>
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% $Id:$
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\question{}
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\begin{parts}
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\part[20]
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Design (use as many Op-Amps as needed)
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and sketch a circuit which output is governed by the following
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expression.
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\begin{equation}
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V_{out}=-5(V_1+ V_2) + 10 V_3
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\end{equation}
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Explain your design.
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Specify all relevant components values, assume that you are using
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ideal Op-Amps (open loop gain $A=\infty$).
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\bonuspart[5]
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{\bf Note:} You will get it if you use only one Op-Amp.
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\vskip 2.5in
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\end{parts}
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\pagebreak
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‎final/2012/questions/noninverting_amplifier_with_opamp.tex

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% -*- latex -*-
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% FILE: "/home/evmik/jobs/wm/2012_spring_Analog_Electronics_252/final_exam/questions/noninverting_amplifier_with_opamp.tex"
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% LAST MODIFICATION: "Tue, 01 May 2012 01:08:13 -0400 (evmik)"
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% (C) 2011 by Eugeniy Mikhailov, <[email protected]>
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% $Id:$
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\question{}
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Consider the non inverting amplifier shown below \\
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\includegraphics[height=1in]{./schematics/noninv_ampl}\\
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\begin{parts}
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\part[10]
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Find the expression for the output voltage in terms of $V_{in}$,
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$R_1$, $R_2$, and $A$. Do not assume that $A$ is infinite.
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\vskip 2.5in
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$V_{out}=$
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\part
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If the gain bandwidth product $A(f) \times f = 10$~MHz.
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$R_2/R_1=10$.
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\begin{subparts}
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\subpart[5]
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What is the gain of the system at 10~Hz
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\vskip 0.5in
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$G(10~Hz)=$
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\subpart[5]
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What is the gain of the system at 10~MHz
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\vskip 0.5in
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$G(10~MHz)=$
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\end{subparts}
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\part[5]
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Consider the practical limitations now.
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If $R_2/R_1=99$, $V_{in}=0.01$~V, and $A=\infty$,
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but maximum output current of the
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Op-amp is 2~mA. What is the minimal possible load resistor which you
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can hook to the output without overloading the Op-amp?
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Assume that $R_2 \gg R_L$.
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\vskip 0.5in
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$R_{L_{min}}=$
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\bonuspart[5]
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What is the output impedance of this amplifier at low
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frequencies?
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{\bf Why} do you think so?
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Assume $A=\infty$.
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\vskip 0.4in
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$Z_{out}=$
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\end{parts}
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\pagebreak
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‎final/2012/questions/opamp_adder.tex

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% -*- latex -*-
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% FILE: "/home/evmik/jobs/wm/2012_spring_Analog_Electronics_252/final_exam/questions/opamp_adder.tex"
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% LAST MODIFICATION: "Mon, 30 Apr 2012 15:45:04 -0400 (evmik)"
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% (C) 2011 by Eugeniy Mikhailov, <[email protected]>
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% $Id:$
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\question{}
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Consider the circuit shown below \\
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\includegraphics[height=1in]{./schematics/summing_inv_ampl}\\
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The open loop gain $A=\infty$.
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\begin{parts}
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\part[10]
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Derive the expression for the output voltage $V_{out}$, in terms of
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$V_{in1}$, $V_{in2}$, $R_1$, $R_2$, and $R_f$. Note that $R_1 \neq R_2$.
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\vskip 2.5in
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$V_{out}=$
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\part[3]
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If a power supply provides $\pm15$~V to the amplifier, and $R_f/R_1=2$,
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$R_f/R_2=3$, $V_{in1}=V_{in2}=4$~V. What is the
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output voltage?
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\vskip 2.0in
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$V_{out}=$
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\part[2]
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Same as above but $V_{in1}=1$~V, $V_{in2}=-1$~V.
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\vskip 1.0in
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$V_{out}=$
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\end{parts}
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\pagebreak
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‎final/2012/questions/opamp_vs_transistors_comparison.tex

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% -*- latex -*-
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% FILE: "/home/evmik/jobs/wm/2011_spring_Analog_Electronics_252/final_exam/questions/opamp_vs_transistors_comparison.tex"
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% LAST MODIFICATION: "Thu, 05 May 2011 10:01:49 -0400 (evmik)"
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% (C) 2011 by Eugeniy Mikhailov, <[email protected]>
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% $Id:$
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\question{}
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\begin{parts}
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\part[4]
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List advantages of Op-amps when they are compared to transistors
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\vskip 3in
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\part[3]
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List situations when you would use a transistor instead of a generic Op-amp
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\vskip 3in
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\part[3]
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What is so good about FETs when they are compared to BJTs.
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\vskip 3in
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\end{parts}
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\pagebreak
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‎final/2012/questions/oscillator.tex

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% -*- latex -*-
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% FILE: "/home/evmik/jobs/wm/2012_spring_Analog_Electronics_252/final_exam/questions/oscillator.tex"
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% LAST MODIFICATION: "Tue, 01 May 2012 14:21:05 -0400 (evmik)"
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% (C) 2011 by Eugeniy Mikhailov, <[email protected]>
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% $Id:$
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\question{}
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Consider the relaxation oscillator base on the open collector
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comparator shown below with the following parameters:\\
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$R_1=100$~k$\Omega$, $R_2=100$~k$\Omega$, $R_f=100$~k$\Omega$, and
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$R_{{p.up}}$=1~k$\Omega$.
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\begin{parts}
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\part[2]
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Disregarding $R_{{p.up}}$.
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What is the voltage at non-inverting input when output is
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high?
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\\
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\includegraphics[height=2in]{./schematics/oscillator}
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$V_{+}=$
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\part[2]
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Disregarding $R_{{p.up}}$.
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What is the voltage at non-inverting input when output is
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low?
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\vskip 1.0in
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$V_{+}=$
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\part[4]
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If $R=1$~M$\Omega$, what is the value of the capacitor to
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get period of oscillation T=$1$~mS?
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\vskip 1.0in
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$C=$
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\part[2]
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Can we completely get rid of $R_{p.up}$? Why?
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\vskip 1.0in
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\bonuspart[5]
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When we built a blinker, we learn that hooking an LED
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directly to the output is bad idea die to large output
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impedance in comparison to the small input impedance of the
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LED. What is the output impedance of this circuit? {\bf
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Show} your reasons.
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\vskip 1.0in
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$Z_{out}=$
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\end{parts}
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\pagebreak
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