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.

Resistive circuits


For each of the circuits below, find the voltage at each node and the current through each element. You do not have to simplify your answer. (You may leave in terms such as R1||R2.) You might be able to dramatically simplify your calculations using equivalent circuits.

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.

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

Bode plots

Make a bode magnitude and phase plot for the circuit below.

LR high pass filter.png