Spring 2020 Assignment 6

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20.309: Biological Instrumentation and Measurement

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This is Part 2 of Assignment 6.

Ideal elements


For each of the ideal, two-terminal elements listed below, show the symbol, label the terminals, indicate the direction of current flow, write the constitutive equation, and find an expression for the impedance, $ Z(\omega)=\frac{V}{I} $. (To find the impedance, substitute $ V=Ae^{j\omega t} $ into the constitutive equation and solve for $ \frac{V}{I} $ as a function of $ \omega $.)

  • Resistor
  • Capacitor
  • Inductor
  • Voltage source
  • Current source

Resistive circuits


For each of the circuits below, find the voltage at each node and the current through each element.

1 2
Voltage divider.png Current divider.png
Ladder circuit.png

Equivalent circuits


For each of the circuits in the previous problem, find two equivalent circuits — the first one consisting of a single voltage source and a single resistor, and the second one consisting of one current source and one resistor. In both equivalent circuits, the I-V curve at the Vout the port should be identical to the original circuit.