Electronics written problems

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20.309: Biological Instrumentation and Measurement

This is Part 2 of Assignment 6.

Ideal elements

• Draw the symbol for one of the two terminal, ideal elements. Label the terminals and indicate the direction of current flow. Show the constitutive equation for the element you chose.

Conservation laws

• Find the voltage at each node and the current through each element in these circuits consisting of resistors and ideal sources.

Equivalent circuits

• Create a simplified version of each circuit. The simplified circuit should contain one source and one resistor. The I-V curve of the port should be the same as the original circuit.

Measuring voltage

A circuit model for a neuron in culture connected to a patch clamp apparatus consists of a time-varying voltage source in series with an output impedance of 1011 &Omega. There is an oscilloscope next to the neuron with an input impedance of 106 &Omega. A circuit model for the oscilloscope is a 106 &Omega resistor to ground. A new UROP in the lab attempts to measure the electrical spikes produced by the neuron (called action potentials) using the oscilloscope. The oscilloscope has a noise floor of 10-3 V.

• What is the magnitude of the action potential signal after the student connects the oscilloscope?
• Does the student succeed? Why or why not?
• What is the signal to noise power ratio?
• How many times does the student curse during the measurement attempt?
• What is the minimum input impedance that a measurement device must have in order to make a high-fidelity measurement of an action potential.

Bode plots

• Draw a Bode plot for each of the circuits: