Shunt Capacitance

Adding shunt capacitors would also reduce Zq but would raise the electrical line length hence it is not considered. Moreover, on EHVs, the charging shunt capacitances, Cq, as such require compensation during light loads or load rejections to limit the voltage rise (regulation) at the far end or the midpoint. Hence no additional shunt compensation is recommended. 

Figure 2. Schematic of a TOF apparatus. R is the current-sensing resistor. C is the total shunt capacitance.

The voltage drop in a cable is due to its series resistance and series inductive reactance. The shunt capacitive reactance is usually too large to be considered for cables installed in a typical plant. However, for long distance high voltage cables, such as submarine cables, the shunt capacitance may need to be included in the calculations of voltage drop. 

Let the series resistance be R ohms, the series inductive reactance be Xi ohms and the total shunt capacitive reactance Xc ohms for a cable of 1 kilometre. Manufacturers usually quote the shunt capacitance data in microfarads/km. 

The method described in sub-section 9.4.3.1 may not always be sufficiently accurate for long cables where the shunt capacitive reactance cannot be neglected. Two more accurate methods can be used in which the cable is treated as an equivalent Tee or an equivalent Pye circuit, see Figures 9.2 and 9.3. 

Z5 is connected in parallel with the left-hand side shunt capacitive reactance, hence this total Zg is,... 

Ddz = lod/ijcoA)- Since u=-jcov and the static or shunt capacitance is Co =... 

Equivalent circuit models have been used to represent piezoelectric material behavior for many years, but are not without limitations. The most common representation for a piezoelectric material, as recommended by the IRE/IEEE standards on piezoelectricity, is the Van Dyke model as described in detail in piezoelectric materials in microfluidics, with a capacitor, resistor, and inductor in series representing a single resonance, or motional component of the piezoelectric element, all set in parallel with a second capacitor, representing the shunt capacitance. Additional resonances may be included by placing additional... 

Choosing a thickness-polarized, thickness-vibrating piezoelectric element as an example, we can define the applied voltage V current i dimensions b, h, and / and the output force and velocity F and u the cross-sectional area bounded by b and I can be defined by A here it is assumed this area is electroded on the top and bottom faces of the element and that b and / are much greater than h. Treating it as a collection of discrete circuit elements as shown in Fig. lb, the Van Dyke circuit allows the analysis of one resonance within the isolated element. Most piezoelectric materials are capacitive insulators, and the shunt capacitance Cs = is the constant capac-... 

Fig. C. 1 The workings of a singe meander-iine polarizer. Top A meander-line sheet acts as a shunt inductance for the vertical components and as a shunt capacitance for the horizontal components of an incident signal. Bottom The vertical componmt of the incident field is reflected with reflection coefficient and transmitted with the transmission coefficient Ty= 1 + Ty as shown in the Smith chart. Similarly, the horizontal component is reflected and transmitted with reflection coefficient T/, and transmission coefficient r/, = 7 + T/, respectively.

The capacitance in Fig. 2(b) is a critical parameter, since for a given bandwidth, B, the higher the capacitance, the lower the value of R, and thus the higher the noise current. Consider a detector operating at a bandwidth of 1 MHz, with a typical combined device and circuit shunt capacitance of 1 pf. The required load resistance, R = l/2-BC = 157,000 ohms and the rms noise current is... 

Figure 2.2.1. Uniform continuous transmission line involving series resistance of 2r per unit length and shunt capacitance of c per unit length, terminated by an impedance Zj-. When Zr=0, Zd = Zj, and when Zr — Zq = Z/xx ...

Sah [1970] introduced the use of networks of electrical elements of infinitesimal size to describe charge carrier motion and generation/recombination in semiconductors. Barker [1975] noted that the Nemst-Planck-Poisson equation system for an unsupported binary electrolyte could be represented by a three-rail transmission line (Figure 2.2.8fl), in which a central conductor with a fixed capacitive reactance per unit length is connected by shunt capacitances to two resistive rails representing the individual ion conductivities. Electrical potentials measured between points on the central rail correspond to electrostatic potential differences between the corresponding points in the cell while potentials computed for the resistive rails correspond to differences in electrochemical potential. This idea was further developed by Brumleve and Buck [1978], and by Franceschetti [1994] who noted that nothing in principle prevents extension of the model to two or three dimensional systems. 

Ri, Li, and C, represent parameters associated with the quartz crystal, whereas Q represents the shunt capacitance of the resonator electrodes in parallel with the container that packages the crystal. 

The waveguide discontinuities shown in Fig. 4.23(a) to Fig. 4.23(f) illustrate most clearly the use of E and H field disturbances to realize capacitive and inductive components. An E-plane discontinuity (Fig. 4.23(a)) can be modeled approximately by a frequency-dependent capacitor. H-plane discontinuities (Fig. 4.23(b) and Fig. 4.23(c)) resemble inductors as does the circular his of Fig. 4.23(d). The resonant waveguide iris of Fig. 4.23(e) disturbs both the E and H fields and can be modeled by a parallel LC resonant circuit near the frequency of resonance. Posts in waveguide are used both as reactive elements (Fig. 4.23(f)) and to mount active devices (Fig. 4.23(g)). The equivalent chcuits of microstrip discontinuities (Fig. 4.23(k) to Fig. 4.23(o)) are again modeled by capacitive elements if the E field is interrupted and by inductive elements if the H field (or current) is interrupted. The stub shown in Fig. 4.23(j) presents a short chcuit to the through transmission line when the length of the stub is A. /4. When the stubs are electrically short ([Pg.331]

Figure 17.2.12 (A) Experimental setup for the current or voltage measurements. (B) Schematic representation of two (electrode/solution) interfaces coupled in series through the solution. Q, doublelayer capacitance Rp faradaic impedance of each interface R, solution resistance voltage source. The electrometer has an input impedance of 2 X 10 " 12 and a shunt capacitance of 2 pE (C) Schematic representation of the experimental setup for the coulostatic experiment. Adapted from reference (22).

Figure 4.11. Two lumped-parameter circuit models for studying the effects of ac electrode polarization in microelectrode systems. simulated biological signal source Cj,Q, contact or source capacitances Cp, electrode polarization capacitance = /(co) shunt capacitance of electrode to electrolyte and reference electrode C, cable leakage capacitance and input capacitance to amplifier system ...

In connection with associated electronic circuitry, fluid-filled microelectrodes behave as low-pass filters, while metal microelectrodes act as high-pass filters (Gesteland et a/., 1959). The reasons for this are simply that glass electrodes exhibit high shunt capacitance and series resistance (Figure 4.10) while electrode polarization impedance associated with metal microelectrodes produces a frequency-dependent RC combination whose series impedance decreases as frequency increases. 

The high-frequency fallofT characteristic of an ac amplifier is produced by the interaction of the shunt capacitances (dotted lines in Figure 7.16) with Kj, Rf and Rj also in RC time-constant relations, but on the parallel rather than the series basis. 

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