Difference between revisions of "Electronics written problems"

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

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 Ω. There is an oscilloscope next to the neuron with an input impedance of 10⁶ Ω. A circuit model for the oscilloscope is a 10⁶ Ω 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. Suggest a descriptive name for each (e.g. "low-pass filter" or "Phil the Powerful High-Phrequency Destroyer.")

Properties of linear systems

• For the given input signal $ x(t) $, what is the output signal $ y(t) $ in each of the circuits below?