## Extracting Useful Information from Impedances

I've recently found myself conducting large numbers of tests on nanoscale devices in a liquid. The device themselves are an insulated silicon wire, with an electrochemically active tip. The circuit in which they are placed can be described as follows, though my notation is most likely incorrect:

Control electronics ---> internal resistance ---> capacitor ----> liquid resistance ---> ground

where I define the internal resistance is the resistance of the silicon material itself and the external resistance is that from the solution through with current should pass. My control electronics are able to apply currents or voltages to the device and measure the responses (for any who are interested, the control electronics is a Axon Multiclamp 700B, a lovely and flexible tool used by electrophysiologists to test electrical properties of living cells).

I have great flexibility over the experiments I can perform on these systems. One important value I worked to collect is the total impedance of the device. I applied a voltage waveform varying between 0 and -25 mV at a number of frequencies, and measured the current response. Using matlab, I fit both waveforms, extracted amplitudes and phase shift, and then determined the real and imaginary impedance of the devices.

My questions:
1. To fit my voltage waveform, I removed the -12.5 mV DC offset arbitrarily, and never put it back in. My peak voltage measured is thus different than that actually applied. However, taking Vpeak / Z = Ipeak; where the peak values are the amplitudes of the voltage and current sinusoids. So on the surface it seems to be fine to remove the dc offset, but this worries me, because I worry about things like that.

2. Things written about phase angles and phase shifts use a variety of notations-- phi, theta, etcetera. I always worry about radians vs degrees for these things. My calculated phase shift is in radians. From the equation

cos theta = R/Z I should thus be able to extract the total resistance of the system, given my calculated and checked total impedance. Just take the cosine of the value in radians (a typical value being 0.5) and multiply by impedance to give total resistance?

3. Assuming the imaginary component of the impedance is all capacitive, that value should thus be the capacitive reactance, so from Xc = 1/2∏fC I should be able to calculate the total capacitance?

4. I can measure the RC time constants by applying step voltages... but it is easy to saturate my recordings, so I miss the peak values of many devices. I go ahead and fit to I = io(1-e^-t/RC), so whatever value I determine from RC in questions 2 and 3 should match that determined from this DC measurement?

Thank you all for taking the time to read my list of stuff here. I went out and got a physics book today to assist me in some of this, but the chapter on the topic constitutes about four total pages. Sadness. Still helpful though.

Also, if theres any suggestions for other helpful values or details that I might consider extracting from my dataset, I am fully open to doing so!

Best,
Thiosk
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 What you are doing sounds interesting. Probably I can't help, but am curious. Why do you believe that your measurements of time constant using DC and your measurements of impedance using AC should agree?
 This belief is certainly not grounded in theory. I had suspected that they were two different ways to arrive at the same value, but if not, then I am not sure the best way to present the calculated values.

## Extracting Useful Information from Impedances

I only have a BSEE and shouldn't be suggesting anything to you, but what the heck.
Why convert the measured data to impedances? Why not leave the data as measured values?
If you would like more data on capacitors, you can Google “dielectric absorption” or for my favorite author, Google “dielectric absorption Bob Pease”

Good Luck
Carl Pugh

 Tags capacitance, impedance, reactance, sinusoid