Difference between revisions of "Electronics written problems"
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==Measuring action potentials== | ==Measuring action potentials== | ||
− | The [https://en.wikipedia.org/wiki/Patch_clamp 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 10<sup>11</sup> Ω. There is an oscilloscope next to the neuron with an ''input impedance'' of 10<sup>6</sup> 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. You can model the noise in the oscilloscope as a random, additive, normally distributed voltage with a standard deviation of 10<sup>-3</sup> V. | + | The [https://en.wikipedia.org/wiki/Patch_clamp patch clamp] is a technique for measuring voltages produced by electrically active cells such as neurons. One potential problem with the patch clamp technique is that it involves physically attaching something to the neuron you want to measure. Attaching a thing to the neuron might change the way it acts. In other words, the patch clamp device itself might ''distort'' the measurement. The problem of the measurement apparatus ''loading'' the system to be measurement is a problem in many kinds of measurements (not just electronic ones). In this problem you will consider a simple model of this kind of distortion as it applies to the patch clamp technique. |
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+ | 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 10<sup>11</sup> Ω. There is an oscilloscope next to the neuron with an ''input impedance'' of 10<sup>6</sup> 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. You can model the noise in the oscilloscope as a random, additive, normally distributed voltage with a standard deviation of 10<sup>-3</sup> V. | ||
[[File:Patch clamp circuit model.png|750px]] | [[File:Patch clamp circuit model.png|750px]] | ||
Revision as of 15:52, 31 March 2019
This is Part 2 of Assignment 6.
Ideal elements
Resistive circuits
For each of the circuits below, find the voltage at each node and the current through each element. |
1 | 2 |
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3 | |
Equivalent circuits
Measuring action potentials
The patch clamp is a technique for measuring voltages produced by electrically active cells such as neurons. One potential problem with the patch clamp technique is that it involves physically attaching something to the neuron you want to measure. Attaching a thing to the neuron might change the way it acts. In other words, the patch clamp device itself might distort the measurement. The problem of the measurement apparatus loading the system to be measurement is a problem in many kinds of measurements (not just electronic ones). In this problem you will consider a simple model of this kind of distortion as it applies to the patch clamp technique.
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. You can model the noise in the oscilloscope as a random, additive, normally distributed voltage with a standard deviation of 10-3 V.
Easy Bode plots
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3 | 4 |
Harder Bode plots
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Linear systems
1 | 2 |
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Second-order system
Find the transfer function $ H(\omega)=\frac{V_{out}}{I_{in}} $ for the circuit below. |
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