Frequency-dependent parameters

Hence, coefficient K is not simply a numerical factor as considered previously, but a frequency-dependent parameter since ep varies with frequency. 

This process of setting a window to limit the range of frequencies admitted to the receiving system is called narrowbanding and can be accomplished in several ways. For fixed frequency operation, it is easy to construct a narrow-band amplifier with a window centered at the desired carrier frequency. This is frequently done, even in commercial spectrometers, and is sufficient if either no other nuclei need to be examined at that field intensity or if no frequency dependent parameters need to be measured. On the other hand, a variable frequency operation can be implemented in several ways. The first is to make (or buy) as many fixed frequency units as needed. This is a simple solution if there is no need for a continuous frequency range and if only a few discrete frequencies are adequate for one s needs. Another is to make the spectrometer tunable, but to keep it a narrow band device. This means that each transmitter and receiver section has to be made tunable, and it is a fairly complicated operation. (The third way is to make it tunable but by a technique known as heterodyning discussed a bit later.)... 

Another problem is that the transmission line is modeled in time domain, so some important frequency-dependent parameters can t be exactly represented. These parameters can only be approximated and idealized in order to simplify the simulation process. These approximations lead to critical errors due to divergence of the parameter extraction. Consequently, the measurement system is not efficient and don t realize a sufficient accuracy. Furthermore, the impulse response is derived from the scattering parameter SI 1, which is measured in the frequency domain and transformed to the time-domain. This is critical for the resolution and computational time. In [23] only the wire faults with open circuits and some special impedance changes are estimated. 

The main geometrical parameters of a coplanar spiral inductor are the strip width (W), the spacing between adjacent turns (S), the internal radius (Rmt), the number of turns (Nt), the spacing to the surrounding coplanar ground plane (Sg), and the metal thickness (VetaO- A relevant frequency-dependent parameter to measure the overall electrical quality of an inductor is the Q factor obtained when one port is shorted the higher the Q factor is, the better the device electrically behaves. The second parameter, often measured to evaluate inductors, is the self-resonance frequency. A selfresonance occurs when the inductive reactance of the device is equal to the parasitic capacitive reactance between the inductor and the substrate, i.e., if Q = 0. 

Barsali S, Ceraolo M, Marracci M, Tellini B (2010) Frequency dependent parameter model of supercapacitor. Measurement 43 1683-1689... 

However, in the real world, circuit elements exhibit much more complex behavior the simple concept of resistance cannot be used and in its place, impedance, a more general circuit parameter, is used. Like resistance, imp ance is the ability of the system to impede the flow of electrical current through it. Though it is similar to resistance, impedance is not time independent it is a time- or frequency-dependent parameter. Similar to resistance, impedance is defined as the ratio of the time-dependent current to the time-dependent potential. 

Snelson, J. K. 1972. Propagation of traveling waves on transmission lines—Frequency dependent parameters. IEEE Trans. Power Appl. Syst. 91 85-90. 

Ametani, A. 1974. Stratified effects on wave propagation—Frequency-dependent parameters. IEEE Trans. Power App. Syst. 93(5) 1233-1239. 

Frequency-Dependent Parameters 1.5.2.1 Frequency-Dependent Effect... 

Using Eq. 1-2 for resistance R and Eq. 1-3 for capacitance C, which are frequency-dependent parameters when analyzed over a broad frequency range, a general impedance equation (Eq. 1-10) can be developed as a function of the frequency-dependent characteristic electrical properties of the analyzed material or system. This expression takes into account the frequency-dependent values of relative permittivity e((o) and resistivity p(co) or its inverse, electrical conductivity a(co), combined with the geometry factors of the electrode surface area (/4) and the sample s thickness between the bounding electrodes (d) ... 

Attenuation coefficient is a frequency-dependent parameter. It increases with increasing frequency (low-pass filter effect). As a first approximation, there is a proportiOTiality aoc/. Berzon (1977) gives the following mean values ... 

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