From the figure 1, the critical frequency is the highest point on the curve and from the figure 2 it is the point where the conductivity of the system changes from frequency independent phase (DC conductivity) to frequency dependent phase (AC conductivity). I just want to understand the meaning of critical frequency on the basis of these two graphs.
As per my understanding if I start with the figure 2 then it is quite easier to understand the meaning of critical frequency. According to this, the highlighted portion of the graph consists of very low frequency which is analogous to DC current (zero frequency).
Now if we replicate this concept to the figure 1 then while reaching the highest point of the curve (highlighted portion) we have to increase the frequency by many folds and which I guess will NOT definitely be analogous to DC current (zero frequency). I can support to my assumption on the basis of the fact that while reaching to the highest point of the curve there is always some capacitance generated in the system and a capacitance cannot be due to DC current.
Therefore I think that the critical frequency on the figure 1 should be far below as shown by figure 3.
I know, I am understanding something wrong. Can anyone help me to understand the basic theoretical knowledge in this regard?
Please reply me in simple plain words and not circumlocutory.
Dear Dr. Makhdoon:
There is a small number of answer on the RG system, in which I had participate, some of them linked below..
https://www.researchgate.net/post/How_can_I_analyze_grain_and_grain_boundary_resistance_from_impedance_data
https://www.researchgate.net/post/why_there_is_a_term_complex_number_in_the_impedance
https://www.researchgate.net/post/How_can_I_analyze_the_impedance_spectrum_of_ceramic
https://www.researchgate.net/post/How_do_I_interpret_my_impedance_spectroscopy_results
https://www.researchgate.net/post/Is_a_new_type_of_dielectric_spectroscopy_for_liquids_possible2
https://www.researchgate.net/post/When_does_peak_position_of_e_coincide_with_the_loss_tangent_tand_peak
https://www.researchgate.net/post/I_m_looking_for_dielectric_properties_of_frozen_sugar_solutions_Can_anyone_give_me_some_references
https://www.researchgate.net/post/What_is_the_reason_behind_high_loss_modulus_in_a_dielectric_measurement
https://www.researchgate.net/post/What_is_the_purpose_of_using_frequency_window_1_kHz_to_1_MHz_while_measuring_the_dielectric_constant_of_any_material2
https://www.researchgate.net/post/Why_does_dielectric_constant_increases_or_decrease_with_temperature
https://www.researchgate.net/post/How_can_I_analyze_grain_and_grain_boundary_resistance_from_impedance_data
https://www.researchgate.net/post/What_is_the_physical_interpretation_of_ac_and_dc_conductivity_in_relation_to_the_dielectric_constant
In specific, with relation to question, it is possible to reach some insight if further attention is payed to the origin of function-of-Impedance selected to analysis. One or other question has been ascribed to the representation of function Impedance, which can be transformed in another function as: Electric Modulus M, Admmitance Y and complex permittivity E, all function are complex numbers. Below in attachment is the Transformation Table adapted of Macdonald, 1987.
Table Impedance Function Transformation
A priori the transformation allows further “vision of properties since, some transformation involves the reciprocal of a previous function that change the magnitude of values. Furthermore, from basic mathematics, imaginary part of previous function is transformed in real part of new function giving new opportunity windows to analyses the electrical and dielectrical phenomena.
Seems that the parameter called of critical frequency is in fact the most frequent relaxation frequency that in ideal Z’ versus Z”” plot is defined at highest value of Z” (imaginary part of Impedance function). In a Impedance diagram the frequency of measurement is lowest at right side of diagram. In the Admittance plot showed, the line showing positive slope present highest frequencies values, 10^3 or 10^4 up to 10^6 Hz. In this way, long range conductivity (dc conductivity) based on shifting of carrier at long distances is view in lowest domain frequency, left side of plot.
Best regards
Marcos Nobre
Dr Makhdoom - a semicircular (Nyquist) plot in the complex plane is the classic frequency response of a single pole low pass filter. The critical frequency Fc on the Nyquist plot occurs at the peak of the semicircle, corresponding to a phase lag of 45 degrees. I don't see why you feel that it should be lower down. Check the references Dr Nobre has given, I'm sure you will find a more thorough explanation there! Best wishes with your research.
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