Difference between revisions of "Electronics written problems"
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For each of the circuits below, find the voltage at each node and the current through each element. | For each of the circuits below, find the voltage at each node and the current through each element. | ||
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==Equivalent circuits== | ==Equivalent circuits== | ||
Revision as of 18:03, 21 October 2018
This is Part 2 of Assignment 6.
Ideal elements
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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 $.)
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Resistive circuits
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For each of the circuits below, find the voltage at each node and the current through each element. |
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Equivalent circuits
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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. |
Easy Bode plots
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For each of the circuits below, find the transfer function $ H(\omega)=\frac{V_{out}}{V_{in}} $. On a log-log plot, sketch the magnitude of the transfer function versus frequency. Sketch the phase angle of the transfer function versus frequency on a semi-log plot. Suggest a descriptive name for each circuit (e.g. "low-pass filter.") |
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Harder Bode plots
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For each of the circuits below, find the transfer function $ H(\omega)=\frac{V_{out}}{V_{in}} $. Simplify the transfer functions using the following assumptions:
On a log-log plot, sketch the magnitude of the simplified transfer function versus frequency. Label cutoff frequencies. Sketch the phase angle of the transfer function versus frequency on a semi-log plot. Suggest a descriptive name for each circuit. |
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Linear systems
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Assuming R1 = 1 Ω and C1 = 1 μFd, find an equation for $ V_{out}(t) $ for each circuit given the following inputs:
Feel free to make reasonable approximations. You should only get an urge to use a calculator for the first one. |
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Second-order system
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Find the transfer function $ H(\omega)=\frac{V_{out}}{I_{in}} $ for the circuit below. |
Measuring action potentials
The patch clamp is a technique for measuring voltages produced by electrically active cells such as neurons. A circuit model for a neuron 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 and an input capacitance of 20 pFd. A new UROP in the lab attempts to measure the electrical spikes produced by a neuron (called action potentials) by connecting the patch clamp apparatus to the oscilloscope with a cable that has a capacitance of 80 pFd. Action potentials are about 100 mV in amplitude and about 1 ms in duration. The oscilloscope has a noise floor of 10-3 V.
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