Electric Impedance - Science topic

Hi Maam,

It plays an important role to know how the electrode-electrolyte responds toward the wide frequency range

Dear Honest C Makamba,

it doesn't really matter, about "what is the DC potential chosen".

Choose 'any (ruling)', single, V_DC-potential, but always inside the V_window.

A common cyclic voltammogram (CVL) reports about the V-limitations (V_window=V_high - V_low) for your supercapacitor.

The EIS spectra (and the capacitance value) is, usually, the same^[1], inside this V_window, for (common) supercapacitors.

Simão Sampaio its ok. I will try my best to find some extra information, dedicated to your issue. Best regards.

Thanks dears for your valuable answers

It seems from your answers that this kind of impedance combination is rather specific to the electrical engineering field. Am I right or are there applications in other scientific fields, especially in electrochemistry and electrochemical impedance spectroscopy (EIS)?

In general, for this area of land, you must first try to drill at least 10 boreholes. This is so that you can have parametric soundings to calibrate and validate electrical soundings.

Now, and given that the number of drilling is very limited, it seems judicious to me to carry out a grid of 500 m and to carry out a sounding (SEV) with AB/2 of 1000 m in each point of the grid.

The solicited depth of the SEV depends on the increase in the depth of the aquifers (according to geological data). It is therefore necessary to increase the length of electrical soundings in the areas of increase in P and to add SEVs with AB/2 between 3000 and 5000 m (for example).

The establishment of the geo-electrical profiles can be distributed, according to the configuration of the ground, in the following way:

Total number of SEV Number of profile Number of SEV/profile

Zone 1 24 04 06

Zone 2 18 03 06

Zone 3 20 05 04

Best regards

There is information for this Ni-Cr thermocouple alloy on the page:

Dear Orhan Kıbrıslı ,

the temperature and the DC-polarization(s) help to discriminate the (electronic vs ionic) conductivity character. How much your (EIS-)spectra change with the parameter of the DC-polarization, V_DC , value(s) ?

Also say, please, what are

1) your (2 or 4?) electrodes (' materials ?),

and what is

2) the temperature and the DC-polarization(s), V_DC (= ?) in this ('EIS curve.png') EIS study.

Dear Fatemeh Yadollahi,

I see the main issue for the Ohmic resistance coming from the inductivity.

The attached image shows what happens if an inductivity is added to a circuit and how it affects the Ohmic resistance (a few further details in the article).

Best,

Dino

In this case case I would go for a numerical evaluation which is rather easy these days..even if there is a formula somewhere it will be an approximation and not straightforward to solve

It depends baisically on the resistivity contrast between the buried pipe and its surrounding...... The specific characterestics of the pipe itself determine if ERT is useful or no..... The combination of different geophysical methods with their good interpretations provides the optimum detection way.....

You can simulate the obtained EIS experimental points with Zview software using equivalent Randle circuit. The diameter of the semicircle gives the value of Rct.

Dear Henrique Teixeira , I think magnetron sputtering of gold shouldn´t interfere or change your PEDOT:PSS film. Argon plasma is directed towards the gold target, and therefore implantation of argon on your PEDOT:PSS should be negligible and therefore it would mantain its electrical properties.

I wonder if your thin films of Au (just 1nm thick) could cause problems due to holes.

The combination of both PEDOT:PSS and gold sputtering has already been described in publications, for instance:

Thermal evaporation of gold is another option that shouldn´t damage or change the PEDOT:PSS layer:

Hope it helps.

Hey Dr Soleimani,

How did you solve this problem?

Can you explain it to me in Details?

Hi Fahad,

If you apply voltage V across the terminals of a resistance R, then the power absorbed by the resistance is P given by P=V^2/R (This equation can be derived simply from Ohm's law.). To use the same equation in the context of line, the voltage V should be the voltage drop along the line (not the voltage measured at one point on the line), and P is the power loss along the line (not the total power flow along the line). Therefore, you cannot simply use the measured value (which are total power flow (P) and the voltage (V) at one point in the line V) in the above formula to calculate the resistance of the line.

I hope this helps!

Thank you.

see this link https://atrapartodo.blogspot.com/2020/07/magnetoelectric-voltage-coefficient-to.html?m=1

If you can make simple circuit analysis and knows the ideal operational amplifier characteristics. You can simply analyse the transimpedance amplifier very simply.

The ideal op amp has infinite differential gain, infinite input impedance and zero output impedance. So it does not draw currents in its inputs .

Grounding the positive input and injecting the current I in the negative input , it will continue in the feed back reassurance Rf. Since the positive input and negative input have almost the same potential then the negative input will be virtually zero. So, the output voltage V0 = - I Rf. This is the transimpedance amplifier relation The output voltage divided by the input current is equal to the the feedback resistance.

This is the simplest way to analyse and understand the operation of this circuit.

Best wishes

The following analysis shows that the correct unit is the Ohm x cm^2.

Assume that we have two electrodes immersed in electrolyte where the immersed cross sectional area of the twp electrodes are equal of area A. assume that the spacing between the two electrodes is L and the resitivity of the electrolyte is roh, then accordingly one can expels the resistance between the two electrodes as

R= roh L/A,

Rearranging

R XA= roh/L

From this relation it is clear that

When A =1cm^2, then it will give the properties of the electrolyte roh and its path length L.

then the suitable unit is ohm.cm^2.

Best wishes

Dear Franklin,

welcome,

You measure the electrical impedance as you define it. Considering the impedance of LEDS connected in series they have by definition a large signal resistance and small signal impedance as the I-V characteristics of a single diode and a series connections of diodes is nonlinear.

The large signal resistance can be defined by R= V/I, this resistance decreases as the current in the strip increases.

To measure the ac small signal resistance one biases the strip into the DC operating point and measure its impedance as Z = dV/dI, where dV is the small signal voltage and dI is the resulting small signal current. Because of the capacitive behavior, the current dI leads the voltage dV by a phase angle phi.

Z will have an amplitude and phase or a resistive and capacitive reactance.

You can use the method developed in my paper given in the link to make the measurements: https://www.researchgate.net/publication/3062547_A_distributed_SPICE-model_of_a_solar_cell

You can use the method in this paper to measure the impedance of the led strip.

There is also a complete description of the impedance measurement in the paper at the link:

Best Wishes

Chris Delavan To mount the 96well ECIS plate to the reading should not be difficult at all. All you need to do is to use one hand to firmly press the plate onto the reading while shifting the left latch to the right. Then continue to press your plate and shift the right latch to the left. You should feel that your plate sits firmly on the reader. I don't think that expired plates will give you issues with connectivity unless they were kept open and electrodes are corroded. What type of 96 well plate do you use? 20, 10 or 1 electrode?

Depending on the operating conditions, yes.

As Alexei V Ermakov suggests, reducing the ohmic drop caused by the electrolyte can help. Using a probe with a high surface area, or distributed to different points of the fuel cell is a good idea.

Jules

Hi, I happened to consider about this question for a long time since my supervisor expected me to calculate the exact wideness of space charge layer, and I also found that M-S calculation is inproper for my nanowire arrays system, so I think there should be a geometric factor which included in the M-S calculation. Maybe you can try to use the Hall-effect equipment to test the carrier numbers.

Thank you. Could you tell what other values changes during relaxation ? I means the model values which you know

Maybe, HEPES with same conductivity would be helpful.

Denis:

My understanding of the 'exam question' that Farid Hosseinzadeh has set us is:

Given the PCB with GNSS chip installed, what piece of test equipment should be connected to the input connector of the PCB in order to find the characteristic impedance of the track connecting the input connector to the chip?

The picture I have in my head is that the track is in the order of a few cm in length and I am additionally assuming that no modification of the PCB to facilitate the measurement would be welcome.

From the assumption about track length I was then thinking along the lines of section 9.2 in Keysight Technologies, 'Time Domain Analysis Using a Network Analyzer' http://literature.cdn.keysight.com/litweb/pdf/5989-5723EN.pdf, which is saying that the TDR NWA should be operated with wide frequency span to resolve down to disconuity separations in the cm region.

If you could provide details of the measurement you thinking of, which answers the requirement as stated in this post, without using a wideband test pulse or a wide frequency span NWA test signal, I will happily be educated.

I think this "tail" shape come from over potential window, which will cause polarization of electrolyte (accumulation of gases at the interface between electrode and electrolyte). so you must test your electrode below this value (decrease potential window less than this value).

Dear Rajas and colleagues,

I came late to this question but i find it very interesting. My question is do you simulate the loop while you inject an ac current in it and calculate the voltage across its terminal. Then V= I Z,

If you consider both electric and magnetic field resulting from the current in the loop then you have an LCR equivalent circuit. In order to interpret the simulation results one has to calculate Z magnitude as a function of frequency.

The second comment is whit is the dimensions pf metal wire and its material? How large is the simulation space and how the loop is contained in the space?

Best wishes

Dear Eris E Supeni,

if the current is, always, charging^[1] the rechargeable battery, then you might ignore that, the value of the current is changing^[2].

_{1. charging and the average value and RMS value of the current is, always, higher than the self discharge rate of the cell, in storage. Also, this project (or equivalent projects) might help towards prolonging the storage time of some rechargeable batteries.}

Sir, I really not know about impedance spectroscopic analysis. But I am sure in NCL Dr. Gokhale will help you on that

Hi Akhilesh,

Well, it all depends on your operating frequency. SMA is no good above 26.5 GHz, generally. When you said 1-2mm, I assumed you meant that was the wavelength (in free space), corresponding to about 150-300 GHz. If, instead, you mean that the antenna is 1-2mm in size, perhaps half a wavelength or smaller if used on a high-dielectric constant substrate, then it could be below 100 GHz.

Up to 110 GHz, you have the option of using 1mm coax -- but I can tell you from experience that the connectors, adapters, and cal kits for measurement are EXTREMELY expensive, and frankly don't perform very well. (I had to test a part once in 1mm coax where the performance of the part was far better than that of the test adapters, making the test practically meaningless). I wouldn't recommend it.

Really, for anything above 50 GHz, I would use waveguide. Waveguide to printed-circuit launchers can be made, but are typically custom. If you're geometry just wouldn't support a waveguide housing, then the best I can suggest is to test your antenna on a wafer probe station. Mm-wave wafer probes are readily available, but depending on what you want to measure (beam pattern, etc.) the geometry could be awkward.

Matt

Dear friend. i is the average current which can be calculated from CV curves. you can measure maximum peak current from anodic and cathodic parts of the CV. 

Basically, the length and diameter of the wire connected to measure the signal matters a lot. So if the length is quite lengthy try to short it and measure it. Because I have also faced the same problem during measurement of my device.

As the previous two responses stated: impedance that is capacitive is imaginary, but inductive impedance is also imaginary (-90 degrees vs +90 degrees out of phase).  Note also that some real phenomena like diffusion have both real and imaginary components (45 degree phase shift).

dear Aparna, You are right! As it came to aberrations in physics, my motto is NOT: read your… manuals; remake them! That is the name of the game! But it will take time until they do recognize it. much time! 2-dimensional time :))

Fig 3 of the paper, conveys that with rise of temperature, Rxx decreases. Initially fast decrements up to about 100K then slow decrements. This effect is due to more no of free electrons with rise of temp and then towards saturation.

Rxy graph says that on Rxy temperature has fairly no effect. It remains fairly consant (Slightly rises up. This could be slight change in magnetic field over temperature which is assumed as constant).

You have taken ratio, where numerator (Rxx) reducing and Denominator (Rxy) is constant. Hence, ratio is decreasing (green line). Red line is no of free electron, which is increasing with temperature. 

You may say ratio is inversely proportional to temperature

Thank you Ioannis Samaras and Jerry Decker for your suggestions.

My runs are at high temperature, therefore humidity should not be a problem. I´m blowing air on the sample, though, so maybe I should check...

Noise seems to be related to some instability of the signal, because if I increase the excitation voltage amplitude I get cleaner spectra, but at lower voltages noise shows up. The problem with higher excitation voltages is that I get different spectra if I increase the voltage too much, probably due to 2nd order phenomena...

I guess, Ionnis Samaras is absolutely right.

Your impedance magnitude is quite small for the high frequencies. You need a very good setup (potentiostat, wiring,...) to measure up to 1 MHz. Usually, you would expect inductive behaviour at high frequencies, but at very small magnitudes of the impedance and high frequencies, the results often go crazy as in your case.

Maybe you even do not need these very high frequencies for your analysis. Apart from the last, say 10 points, your impedance looks nice and converges nicely to the real axis for high frequencies. The capacitive branch is characteristic for energy storage systems.

I agree with Glen, also now we can find transistors that work for very high frequencies (> 10Ghz) for example:

- RF FET Transistor 10 GHz   "ATF-34143-TR1G"

and also

- "CPH6021" is a NPN Single RF Transistor, 12V, 100mA, fT=10GHz for High-Frequency Low-Noise Amplifier 

Thanks your reponds Michael. Then this is relates to the formation of space charge. I have read that the relaxation time is the time in which one moves from a resistive to a capacitive behavior. But if there is another time of relaxation. What physical or chemical meaning would there be two relaxation times?

Dear Hunter Stevenson,

the EIS data for your "sensor" are measured^[1] using with two or more electrical contacts ?

Also, note, please, the parametric value of the V_DC(= ?) polarization^[2].

You should use ferri-ferrocyanide electrolyte medium for the EIS measurement...you may use some other medium according to your requirements...but the selection of potential and medium is important in EIS measurement.

Please follow the following paper, it may be useful for you.

Best regards,

Piyush Kumar sonkar

I recommend you at first do the calibration and use the reference sample that you know exactly its results. and then check whether there is the same problem within the frequencies you mentioned or not. because some times the impedance instrument is not calibrated well, or sample holder is not clean, or wires have a problem,... If  impedance instrument is working well then your sample preparation may has a problem.

To fit your result you need software, usually each impedance spectrometer has a software. I use WinFit program for Novocontrol impedance spectroscope.

This is a 3D problem and the current density J is a function of position with a maximum at the electrode positions and a minimum at the midpoint between the electrodes.  J(x, y, z) can be obtained by solution of the LaPlace equation in the volume of the disc.  

There are lots of ways to get approximate solutions.  If the disc can be thought of as having zero thickness with a given resistivity/square then the solutions have been worked out (see Van der Pauw in Wikipedia.).  If one needs just the current density at the midpoint between the electrodes, then one could assume a rectangular slab of length D, width L, and thickness T, with contacts covering the ends of the slab.  

At the electrodes, the current must all go through the electrodes and the current density will be approximately  J = I/LS, where I is the current and LS is the area of one of the electrodes.

Look at "active multimeters" in this page: http://meettechniek.info/passive/resistance.html 

You see that the multimeter measures the voltage over a wire, assumes a constant current that it imposes, and calculates the resistance from that (R=V/I, where V is measured and I is 'known'). 

When you connect the wire and current flows through the wire, a voltage drop over the wire will disturb the measurement , because the current I is not only what the multimeter imposes, but also the current that flows through the wire due to your setup. 

Conclusion: never measure resistance while your setup is powered!

dear friend...first make dat file in origin then import it in Z view..it will work..keep all parameters in dat file..

First, the CdS powder grains likely have surface potential barriers so the pellet is somewhat like a polycrystalline CdS solid with grain boundaries.  If one could apply perfectly ohmic contacts  and measure it one would get non-linear I-V characteristics.  These would be symmetrical around the origin with shapes determined by the carrier density in the grains, the grain size, and the nature of inter-grain potential barriers. Qualitatively the shapes would be similar to the negative voltage branch of your curve. The current would be exponentially dependent on temperature.  Second, it is likely that the contacts are not ohmic and not the same. Silver point may react with the CdS if the temperature is elevated during fabrication forming Ag/x/S which is likely to be p-type making the contact more complex.  Doing a forward and reverse sweep is a good idea.  Also you might check for sensitivity to light.  You might read section 9.4, on electrical transport in polycrystalline thin films, and the first part of Ch. 10, on CdS/Cu2S solar cells, of my book "Fundamentals of Solar Cells." 

Share some experimental details.

The values obtained from the equivalent circuit are not matched with the Nyquist plot. Please check.

Hi,

Maybe there is a small change in your original data files you couldn't figure it out. Open a new empty Excell file. Add your file as data not a file. If you click data you will see options: access, web, text, others. When you click text (it is the best fot dat, txt or csv format), you will see a new window such as a kind of editor. If you click next, (2/3) you will see some line between your data lines. You can get moved lines , when you click mouse. If your data or text line is not correct, click the mouse on correct point. Please check next step (3/3) with advanced button for your file decimal system (dot or comma). Good luck.  

Hello David,

Thanks for your response.

I have a very thin (few mm thick) rectangular pellet sample. I am measuring the capacitance using NF ZM2376 LCR meter with four probe measurement. How do I calculate correct A and d?

After getting the Nyquist plots, then follow these procedures

1. open the EC- lab software

2.open the Nyquist plot you wanted to get its equivalent circuit 

3.select the point graph

4.click analysis on the EC-Lab, and select electrochemical impedance spectroscopy, then Z fit.  

5. from there, you can see many types of equivalent circuit, you select one type and click calculate.

6. scroll down and select: method: "randomise and simplex" ; stop randomise iteration: "input the value like 60,000"; "stop fit on: input the value also.

7.select min

8. if the select equivalent circuit is the correct one, then the standard deviation should be less one and x2 value should be 3*10-3

8. if the selected equivalent circuit does not fit with  your data, then standard deviation will not be close to one likewise the x2 value

9.then select another equivalent circuit and try again as before. 

8. the select equivalent circuit is the correct one, then the deviation should be less one and x2 value should 3*10-3

If you use  a resistance then you need 69 ohms in parallel with the antenna (i.e. across the antenna terminals) but over 72% of the power will be lost in the 69 ohm resistor and less than 31% will get to the antenna.  It would be better to leave it unmatched which will reflect 32% of the power back to the generator, if the generator can stand it, and about 68% will go into the antenna.  If you feed it with co-ax then it will probably be unbalanced which will change the impedance and may mess up the radiation too.  A spiral antenna requires a balanced feed which is why a balun (or transformer) is needed if it is fed from co-ax.

As you increase the circuit resistance, electric energy is lost in the form of heat energy. Remember the Ohm's Law:

V = I x R

The Power (P) = I x V = V^2 / R

Hence, as R increases, the power (P) decreases

The specific resistance is measured in Ohms per unit length of the wire. Hence, if you use the specific resistance in P = V^2 / R, then P would be the maximum power.

Hope this helps answer your question.

Professor Yehia Khalil

Yale University

USA

Hello Mustafa,

In order to transfer the maximum amount of power from a power source you have to apply the “Maximum power transfer theorem”.

Please, suppose that your circuit has a power source with its internal impedance connected in series with the load impedance Rl+jXl.

The above mentioned theorem demonstrates that the maximum transferred power is obtained when:

-           Xl=-Xs

-           Rl=Rs.

This means that Zl=Zs* (i.e. the load impedance is the complex conjugate of the source impedance).

Finally, if the reactive part of Zl is constant, the maximum transferred power occurs when Rl=sqrt[Rs^2+(Xs+Xl)^2] which means that Rl is equal to the absolute value of the whole network impedence.

I hope this can help you!

 Regards,

Roberto

@Xolani Thanks for replying. But There must be some reason to Literatures mentioning LG as the most severe fault at alternator terminals. Any idea why ?

The dc side impedance networks provides the unique features which can help boost or buck the voltage as compared to VSI. The filters used on load side are to filter current ripples to make the output pure sine wave. Go through the articles on ZSI, you will get to know.

Dear Ioannis Samaras,

you mean like 4 probe resistance measurement?

measure cathode and electrolyte seperate and then maybe combine them into one pellet to measure again?

Hi Omid, the electrical analogy would be a constant current source loading a C parallel to an R. That would give Vc = R * I * (1 - exp(- t / (R * C))) or with temperature T = Rth * P * (1 - exp(- t / (Rth * Cth))). Since 1 - exp(-1) = 0.632, the pulse width at Rth = 0.632 * Rthmax should be equal to Rth * Cth. Division by Rth will result in Cth. In this case, Rth * Cth = approx. 40 ms. Cth = approx. 0.16 Ws/K. This is just an approximation, of course, based on modelling by lumped elements. Hope this helps.

Hi Pengfei,

Next time, please provide an image in format like png or jpg. The TIF file is so very large and takes long time to download.

To your question:

Almost all electrochemical systems show a transient behavior from the time you close cell switch and put it under potential control. So,in order to reduce the transient behavior, you must perform the EIS AFTER this effect has passed. So, close the cell switch and go to the potential where you want to do your EIS. Wait for 5 min or so. Now do the EIS, You should now expect to see the same curve if you repeat the EIS multiple times.

Observe that in you system 5min waiting might not be enough. I would suggest making an EIS each 30second for 20min with the first one starting directly after the closing of the cell switch. By doing so, you can study how the EIS values evolve by time. You will see that after a certain time, the spectra will not change any more. That time would be you optimized waiting time.

Good luck!

Gustav

In plasma ALD the plasma-on time can be quite small. As a result any variation during the formation period of the plasma can have a significant effect on the result.

In 'impedance matching' you tune the 'matchbox' to the vacuum condition to get highest voltage, and most reliable plasma strike. Here 'most reliable' means most consistent in terms of time. When the plasma strikes the load changes and the matchbox moves physical elements to get to a tune position. This takes some time. And, even with careful algorithms for control the transient between the two conditions may not always follow the same path. This means that there is a transient condition as the matchbox tunes (typically 2-20 seconds!) and that the transient can be different between multiple layers for the ALD process. PID settings that give fast, reliable tuning at one power/pressure setting may not be the right ones for different conditions.

Frequency tuning is quite similar, except instead of changing physical components in the matchbox (capacitors and inductors) the matchbox has fixed values and the generator senses the change in load (without/with plasma) and changes the generator output frequency to shift the matching position [w_resonance ~ 1/(L*C_plasma) ]. This frequency shifting can typically be done much faster than mechanical tuning. Furthermore, these generators are typically configured to operate in delivered-power mode, and don't complain if there is a modest amount of reflected power (they control on P_net=P_forward - P_reflected) which gets the system to a 'matched condition' faster than the mechanical tuning solution. As there is only a single knob (frequency) for tuning, the algorithm is typically stable, but you are dependent on the matchbox design being appropriate, and if there is an issue with an unstable transient this can be very hard to identify and correct for (you are dependent on getting support from the generator supplier.) In addition, as frequency-tuning only allows the matchbox to cover a single-arc across the Real/Imaginary tune-space, these matchboxes are typically designed with multiple 'taps', which are mechanical switches that can be changed (with the rf off, typically) to shift the tuning-arc. Operating the same chamber but with two different tap settings will likely give different strike-variation, and different tuning-times.

Personal opinion: for high-volume-manufacturing, frequency tuning - be careful with the matchbox engineering and the result will be the best for chamber-to-chamber matching/ cost/ maintenance/ etc.

This is a set up problem. Do you have any dummy cell?

This will help you in knowing whether the connection are right enough.As per your instrument specification, I can see there are different current ranges . Try to change the current ranges if it is possible.

Regards,

Ritesh.

impedance matching concept is based on that the load impedance should be the conjugate of the impedance of the source that is the general concept for low power excitation (small signal mode) for some cases the load changes depending upon the excitation (large signal mode). This is phenomena appears clearly on devices. For example the model for the GaAs MESFET device elements behaves linearly as the excitation nearly less than unity (1 Volt) as the excitation exceeds this limit  the capacitors of the model behaves nonlinear and the inter-modulation distortion appears.

Since you are making your measurements on a thin film, the measured resistance will vary with the thickness up to the point where the thickness equals the distance between the two measurement pins.  If you would like to learn about the math behind the measurements, google "four pin Wenner method" to see how this is done in soils where the sample thickness is essentially infinite.

Dear Alireza,

If I have well understood you are asking why we start from zero in the vertical axis of Nyquist plot. The reason is that before zero you can have a signal related to inductance at high frequency. Inductive behavior in the high frequency range is fairly easily explained by instrumental artifacts, or by the inductance of the electrode, or the inductance of the connecting wires. So you don’t know if it is a real inductance.

In most materials dielectric permittivity is frequency dependent - static dielectric permittivity under near DC conditions is different to that at higher frequencies. There is an absorption coefficient for the material which equates to a loss of energy as the frequency increases.  This is well covered in the section of Kaye and Laby 'Tables of Physical and Chemical  Constants' dealing with the the various physical factors which affect a change in permittivity.  .      

Crystal resonator equivalent electrical circuits are  treated  as a series RLC with minimum impedance at  the  resonant frequency  (equivalent  to the mechanical element ) in parallel  with  a capacitance Cs,. This component is the crystal static  dielectric component   which  is independent of motion.   R  represents  any energy  loss element  which electrically would be  resistive  and mechanically  tends to express friction. The series  RLC  circuit characterizes  a minimum impedance (maximum, conductance) at  the resonant  frequency  and although this  reflects  the  mechanical element's natural frequency there are two other critical electri­cal  resonances to consider. .The first of the additional  resonances  lies very close to the primary dynamic resonance  but  is the point where the electrical resonance phase vanishes.  The  second  is characterized as an impedance which  rises  to  a

maximum at a frequency f, here too the phase vanishes. This tuned circuit  appears  from the mechanical series elements  acting  in parallel  with the crystals static capacitive component Cp.  Here Fr  = root(C'+Cp/LC'Cp)  and the impedance is a  maximum.  Above  and below  these   two  principle resonant states  the  impedance  is capacitive,  between  the two the impedance  is  inductive.  The 

difference  in frequency between the two series resonance  condi­tions  is  very small and the separation between the  series  and parallel  resonances  seldom exceeds 2%.  Although  the  parallel resonance is much utilised, the series resonance is preferred. In impedance analyzer microgravimetric analysis and crystal oscillo­metric microbalances the minimal value of R in the series  resonance mode reduces signal voltages and  favours the design of low impedance current derived feedback oscillators.  Both  resonances possess  a  very  sharp  resonant  characteristic  denoting   low resistive loss and a high quality factor Q ( = 1/R root L/C )

 

 

Piezoelectric  sensors are generally  plates or discs.  Operation

is  determined  by  plane of cut(i.e crystal  axis)   in  natural

piezoelectric materials, or by direction of electric polarization

in  synthetic materials such as PZT  piezoceramics.  Industrially

grown quartz has a higher purity than the natural mineral and  in

 

h2X/ Šthese  devices  the temperature coefficient is  lower.   Cleaving

along certain shear planes in the quartz confers improved temper­

ature  coefficients; at approximately 35 and 49 degrees from  the

principle optical axis  [the AT and BT 'cut'] temperature coeffi­

cients  are minimised. Values as low as 8 ppm / deg C are  usual.

Sensors can be classed  by axis ( plane of cut) or  dimensionally

(expander  or  shear i or in terms of wave  propagation  (surface

acoustic  wave  (SAW) or  shear wave(SH).  The  conventional  PZT

sensor   operates  as  an expander, the  whole  crystal  changing

dimensionally (expanding) with its plane of polarization.  Alter­

natively,  the crystal resonates lateral to the  electrode  plane

causing a shear displacement.  This shear mode resonance or Y cut

is usually categorised within  bulk acoustic wave (BAW)  devices.

 

 

We are aware that if the mass loading of a mechanically  resonat­

ing  system changes, so too will the frequency of  resonance.  We

have noted also that, as in the case for ARD,  in a piezoelectric

sensor, mechanical and electrical properties are mutually depend­

ent. Mass variations, therefore, effect the mechanically  depend­

ent  electrical  resonance. By  incorporating  the  piezoelectric

device  into an electronic amplifier and signal  generating  cir­

cuit,  it  is possible (but problematic) for mass changes  to  be

determined  by precision monitoring of changes in the current  at

the  series resonant  frequency. Changing load [mass] forces  the

current  maximum to appear at different frequencies as the  reso­

 

h2X/ Šnance  changes.   However, it is better to introduce  the  device

into a closed oscillatory circuit and allow the sensor to  deter­

mine frequency.

 

 

Unlike the  principle explained in the section dealing with  ARD,

the  oscillatory arrangement requires no separation  between  the

resonator  drive and detector. A piezoceramic resonator forms  an

electrode  connected two terminal device inserted  directly  into

the  amplifier  feedback path [ Figs. 12a & 12b]. With  no  other

dynamic component in the feedback circuit the frequency of oscil­

lation is dominated by the resonator. A very small mass  increase

will effect the base resonant frequency of the crystal, Sauerbrey

(1958) obtained the relationship; 

For ideas on this, visit http://www.sciencedirect.com/science/article/pii/S1933171115007111

The system you describe: electronically conducting particles embedded in dielectric matrix, the whole system supported on a conducting material can be described using a transmission line model. The high frequency resistance shifts because of the relative values of the ionic and electronic conductivities through the system. Please check:

http://dx.doi.org/10.1016/j.jelechem.2014.06.035 

Middlebrook Criterion The Middlebrook Criterion is a graphical method for determining if the input filter of a switching mode power supply will cause instability or degrade performance parameters of a duty-ratio (voltage) programmed dc-to-dc converter switching-mode power supply. As usually applied, the output impedance of the input filter is overlaid on the open-loop input impedance of the switching-mode power supply at the worse-case conditions of low-line and full-load and low-line with shorted output.

If you have bode plot, say Impedance (Z) vs frequency and Phase angle (theta) vs frequency, then you can calculate:

Re(Z) = Z cos(theta)

Im (Z) = Z sin(theta)

Now just plot Im(Z) vs Re(Z). You will get Nyquist plot.  A common practice is to plot |im(Z)| vs Re (Z) in material characterization as the imaginary part because of capacitive contribution is negative.