Inductor networks

Equally important as tape casting in the fabrication of multilayer ceramics is thick film processing. Thick film technology is widely used in microelectronics for resistor networks, hybrid integrated circuitry, and discrete components, such as capacitors and inductors along with metallization of MLC capacitors and packages as mentioned above. 

If there are many large or small consumers that a distribution line is feeding, it is possible that the voltage of the network may be distorted beyond acceptable limits. In this case it is advisable to suppress these harmonics from the system before they damage the loads connected in the system. Preferable locations where the series inductor or the filter-circuits can be installed are ... 

Similarities with classical waves are considered. In particular we propose that the networks of electric resonance RLC circuits may be used to study wave chaos. However, being different from quantum billiards there is a resistance from the inductors which gives rise to heat power and decoherence. 

Dayhoff [50] suggested that one might measure a rest mass of photon by designing a low-frequency oscillator from an inductor-capacitor (LC) network. The expected frequency can be calculated from Maxwell s equations, and this may be used to give an effective wavelength for photons of that frequency. He claimed that one would have a measure of the dispersion relationship at low frequencies. Williams [51] calculated the effective capacitance of a spherical capacitor using Proca equations. This calculation can then be generalized to any capacitor with the result that a capacitor has an additional term that is quadratic in the area of the plates of the capacitor. However, this term is not exactly the one that Dayhoff referred to. But it seems to be a very close description of it. One can add two identical capacitors C in parallel and obtain the result... 

Immittance — In alternating current (AC) measurements, the term immittance denotes the electric -> impedance and/or the electric admittance of any network of passive and active elements such as the resistors, capacitors, inductors, constant phase elements, transistors, etc. In electrochemical impedance spectroscopy, which utilizes equivalent electrical circuits to simulate the frequency dependence of a given elec-trodic process or electrical double-layer charging, the immittance analysis is applied. 

The a.c. impedance technique [33,34] is used to study the response of the specimen electrode to perturbations in potential. Electrochemical processes occur at finite rates and may thus be out of phase with the oscillating voltage. The frequency response of the electrode may then be represented by an equivalent electrical circuit consisting of capacitances, resistances, and inductors arranged in series and parallel. A simplified circuit is shown in Fig. 16 together with a Nyquist plot which expresses the impedance of the system as a vector quantity. The pattern of such plots indicates the type and magnitude of the components in the equivalent electrical network [35]. 

Impedance-matching network (passive) An interconnected arrangement of components, the most important of which is an inductor (often tunable), that matches the impedance of a device (e.g., one transducer of an AW sensor) to the impedance of the instrumentation (e.g., an amplifier) to which it is to be connected. This maximizes the power that can be transferred. 

If we have a circuit (or network) constituted only of resistors, the voltage at any point in it is uniquely defined by the applied voltage. If the input varies, so does this voltage — instantly, and proportionally so. In other words, there is no lag (delay) or lead (advance) between the two. Time is not a consideration. However, when we include reactive components (capacitors and/or inductors) in any network, it becomes necessary to start looking at how the situation changes over time in response to an applied stimulus. This is called time domain analysis. ... 

Figure 15.7.1 A low-current transducer for insertion between the working electrode and the current follower (CF) of a potentiostat. Depending on which feedback resistor is chosen in the first stage, the ampUfication factor in this system is 10, 10, or 10. The capacitors in the feedback loops provide some filtering (time constant, 100 fjLs). An inductor-capacitor network was inserted in each power supply connection to minimize noise coupling. [Reprinted with permission from H.-J. Huang, P. He, and L. R. Faulkner, Anal. Chem., 58, 2889 (1986). Copyright 1986, American Chemical Society.]...

We see that such a A./4 network is easier to implement at the lower frequencies where we already noted that such networks would be more useful. At the higher frequencies we get out of range of the traditional (multiturn) variable inductors, especially for small characteristic impedance Z. 

You can make a A/4 network from scratch with commercially available variable inductors and capacitors from sources... 

In order to simplify the physical construction, we have made a A/4 network as described in this section by modifying a commercial antenna tuner. Use the type containing a high voltage variable inductor and modify the capacitors so that you end up with two equal sections on the same shaft. (Some manufacturers will sell you the capacitor plates and spacers so that you can make up any size capacitor you wish, limited only by the shaft length and breakdown voltage.)... 

While the crystal oscillator amplification ensures there is no freqnency drift, the system still requires the use of the matching network, consisting of an inductor and capacitor that antomatically and continuously maintain the impedance of 50 O seen by the generator. 

The electric analogy is one of the most extensively used methods for flow and species transport modeling in channel-based microfluidic systems. A microfluidic network is equivalent to an electric circuit, of which each component can be individually described by resistors, ccmductors, and inductors. Equations 1 and 2 show the RLC circuit models in electric and fluidic domain ... 

Electrochemical systems are in general nonlinear which often makes analytical treatment of their kinetics prohibitively complex. Fortunately, in many cases where small voltage changes are involved, a linear approximation, equivalent to representing the electrochemical system as an electric network made of ideal resistors, capacitors and inductors, can be employed. The voltage response of resistances is not only linear but also time independent, and it follows Ohms law, i = V/R, where R is not only independent of i and E but also independent of time. However, the current/voltage dependence of such elements as capacitors and inductors is time dependent and expressed by differential equations... 

Similarly, for an inductor Z(s) = s L. It can be seen that Eq. (3) has the same form as Ohm s law and the quantity Z(s) plays the same role as resistance in Ohm s law. That allows us to treat the voltage/current relationship for any network of capacitors, resistors and inductors in the Laplace domain as if they all were resistors, only substimting the quantity Z s) instead of resistance for each element. For example the Laplace current for a serially connected resistor R and a capacitor C will be I(s) = V(s)l Zis) + R) which can be rearranged as... 

An electrical drctiit or electrical network is an array of interconnected elements wired so as to be capable of conducting current. The fundamental two-terminal elements of an electrical circuit are the resistor, the capacitor, the inductor, the voltage source, and the current source. The circuit schematic symbols of these elements, together with the algebraic symbols used to denote their respective general values, appear in Fig. 2.1(a) through Fig. 2.1(e). 

Conventional two-terminal resistors, capacitors, and inductors are passive elements. It follows that networks formed of interconnected two-terminal resistors, capacitors, and inductors are passive networks. Two-terminal voltage and current sources generally behave as active elements. However, when more than one source of externally applied energy is present in an electrical network, it is possible for one or more of these sources to behave as passive structures. Comments similar to those made in conjunction with two-terminal voltage and current sources apply equally well to each of the four possible dependent generators. Accordingly, multiterminal configurations, whose models exploit dependent sources, can behave as either passive or active networks. 

A filter is a multiport network designed specifically to respond differently to signals of different frequency. This definition excludes networks which behave as filters incidentally, sometimes to the detriment of then-main purpose. Passive filters are constructed exclusively with passive elements (i.e., resistors, inductors, and capacitors). 

The next step in designing an LP prototype filter network is to select inductors and capacitors so that the admittance parameters 21 and 722 are as specified in Table 4.10. The procedure is demonstrated for a representative fourth-order filter (Chebyshev with 3-dB ripple), and the results are given in Table 4.11 for... 

Franco, 1988). This discussion has assumed that the feedback around the op-amp is purely resistive and has ignored stray capacitance that might be associated with a load on the op-amp. If the feedback network around the op-amp is not purely resistive and/or there are capacitors (or inductors) in the load, then an analysis must be performed to determine whether the amplifier is stable or not. The one-pole model developed here can be used for this analysis. 

Ladder simulations can be classed into two groups operational simulations and element simulations. In other words, one class of simulations is focussed on the equations of the passive network, and the other class concentrates on the elements, especially the inductors. 

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