Major ideas
1. Complex phasor notation is a convenient way to capture amplitude and phase information for sinusoidally varying quantities like current and voltage.
2. Complex impedance expresses a linear relation between current through a system and voltage (potential drop) across the system. The impedance can depend on frequency.
3. Measuring the frequency dependence of the complex impedance of a system under test (a circuit element, a network of circuit elements, or a material) is called "impedance spectroscopy" and can yield insights into the system's composition and physical characteristics.
Major equipment
1. Variable-frequency and adjustable amplitude function generator and a method for limiting and measuring the current that the function generator causes to flow through the system under test.
2. A lock-in amplifier for accurately measuring amplitude and phase of the response potential in the presence of noise.
Tutorials: Stanford Research Instruments and Zurich Instruments
3. A frequency meter.
Alternatives (only choose from these if you have already presented all of the above)
4. Wide-band AC voltmeter
5. Capacitance or LRC meter
6. Oscilloscope
(You should make a clear diagram and list in your lab notebook of all of the equipment, components, and supplies used in the experiment. Any of these is fair game for discussion during your review.)
Data analysis
1. Overlay onto the data a smooth curve plot of the impedance magnitude and phase versus frequency predicted from measured values of the components making up the system under test. State expected limiting behavior at low and high frequency. Discuss deviations between prediction and data.
2. Assume the component values of the system under test are unknown. Find estimates of their values by doing a nonlinear least squares fit of the model to the data. Find some means to estimate the uncertainty in the resulting fit parameters.
3. Develop and discuss a method by which you could quantify the difference between the impedance spectra of two systems under test and thus detect a change if one system had been altered to produce the second system. (This has been investigated as a possible means of discriminating between healthy and cancerous tissues.)
Read and work through the exercises in this link to an attached document.
For a detailed guide to the experiment see the attached document below:
e2_1 Electric Impedance Spectrscopy_latest.pdf.
It is an important part of this experiment that you work the exercises in the guide, writing down results in your lab notebook.
(Note: until further notice, the two major ideas and two major pieces of equipment on this web page supersede the descriptions in the pdf guide. We're working on making all of the documentation consistent. In the meantime, consider that each version includes new things to learn!)
(to be added)