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MASSACHVSETTS INSTITVTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science

6.002 - Circuits and Electronics
Spring 2004

Problem Set 7
Readings and exercises for March 29 through April 4

Issued: 29 March 2004

Reading: This week, read

$\bullet$
From Agarwal and Lang, Chapter 13, through section 13.6

Quiz 2 will be on Friday, April 9, in recitation.

To do and turn in on line before lecture on Monday, April 5

1.1: Step responses for second-order systems

Figure 1: A parallel RLC circuit driven by a current source
\begin{figure}\center{\leavevmode\epsffile{p-rlc.eps}} \end{figure}

This problem deals with two circuits. Each circuit is a parallel RLC circuit driven by a current source, as shown in figure figure 1. The circuits both have $L=0.1$ henrys, but they different values of $C$ and $R$, with the result that one of the circuits has higher Q than the other.

Assume the circuits start in an initial state where the capacitor voltages and the inductor currents are both 0, and suppose we drive both circuits with a unit step in current $i(t)=0$ for $t<0$, $i(t)=1$ for $t \ge 0$. Consider the resulting response of the circuit quantities $i_R$, $i_C$, $i_L$, and $v_C$.

  1. The on-line system will show you eight graphs (also shown on the following page) for these circuit quantities--four for the lower Q circuit and four for the higher Q circuit. Your job is to say which graph corresponds to which quantity for each circuit.

  2. By examining the graphs, you are to estimate the Q for each circuit, and also estimate $R$ and $C$ for each circuit.

Figure 2: Graphs 1-4 for this problem
\begin{figure}\center{\epsfxsize =3in \leavevmode\epsffile{ic-5.ps}\epsfxsize =3... ...ode\epsffile{il-3.ps}\epsfxsize =3in \leavevmode\epsffile{vc-5.ps}} \end{figure}

Figure 3: Graphs 5-8 for this problem
\begin{figure}\center{\epsfxsize =3in \leavevmode\epsffile{ir-3.ps}\epsfxsize =3... ...ode\epsffile{ir-5.ps}\epsfxsize =3in \leavevmode\epsffile{il-5.ps}} \end{figure}

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Hal Abelson 2004-03-19