Lumped-capacitance model

Using the thermal resistance and the total heat capacitance, the dynamic equation for a lumped-element model in the linear regime can be written as ... 

The Coupled Lumped Simulink model presented in Section 9.5.1 was extended to analyze for the double layer capacitance behavior using the model given in Section 9.3.3. The Simulink block for calculating the capacitance behavior is shown in Figure 9.21. Results for a load decrease and increase are shown in Figure 9.22. Figure 9.23 shows the same data for the load decrease case but over an expanded timebase to more clearly show the transient behavior due to the electrochemical capacitance. Similar results are found for the load increase case. 

The deforce model of Equation 3.29 can be extended approximately to include low frequency ac fields for an array of semi-insulating particles using lumped capacitance. Colver and Wang, 1994, show approximately that... 

It is assumed that the IPMC is composed of an IP film sandwiched between two perfectly conductive metal electrodes. The linearized PNP model is used to describe the dynamics of the electric potential and the concentration of the mobile counterions within the polymer. In the case of the fiat electrodes, by solving the partial differential equation based on the PNP model, the equivalent circuit, which is composed of the following lumped capacitances - the double-layer capacitance, Cj, the bulk capacitance Q, and the bulk conductance, Si (see Fig. 6a) - can be obtained (Aureli and Porfiri 2012). 

Fig, 6 Equivalent circuits of the IPMC. (a) Lumped capacitance and resistance model, (b) Distributed circuit model that takes into account the roughness of the plated electrodes, (c) A possible distributed circuit model that takes into account the surface resistance of the plated electrodes, (d) A possible circuit model that takes into account the ion transport in the porous electrodes... 

Fig. 7 (a) Lumped circuit model approximation of transport described by the diffusion equation. Such a response can be the result of concentration gradients or combined ionic resistance and distributed capacitance, (b) Example of an equivalent circuit model including a finite diffusion element, a series resistance, and capacitance at the interface between the solution and the polymer... 

The rate of change of volume in the tank can be written as a lumped parameter model, where all the resistance to flow is assumed to be associated with the valve, and all the capacitance of the process is assumed to be associated with the tank. This model is shown in Equations 3.1 and 3.2. The basis of Equation 3.1 is the principle of conservation, mass balance in this case (i.e. what goes in must come out or get accumulated in the system). 

Modeling of High-Speed Interconnections. Modeling the electrical behavior of an interconnection involves two steps. First, the transmission line characteristics, such as the characteristic impedance, propagation constant, capacitance, resistance, dielectric conductance, and coupling parameters, must be calculated from the physical dimensions and material properties of the interconnection. In addition, structures, such as wire bonds, vias, and pins, must be represented by lumped resistance (R), inductance (L), and capacitance (C) elements. 

Fig. 9.22 Coupled lumped model with electrode capacitance.

The network thermodynamics model has been applied to understand the effects of diffusion coupling in the membrane transport of binary flows. In the formalism of network thermodynamics, a membrane is treated as a sequence of discrete elements called lumps, where both dissipation and storage of energy may occur. These lumps are joined in the bond graphs, and have a resistance R, and capacitance (volume) C, which are defined by... 

Fig. 6. Lumped equivalent circuit for a transmission mode spectrometer near a resonance. Kj is the output voltage of the millimeter wave source, Rj is the source resistance, and Cf are the equivalent inductance and capacitance of the resonator, is the resonator resistance, and the load resistance of the detector. The mutual inductances M, and M2 model the coupling into and out of the resonator.

Fig. 6.7. Sschematic models foi C — V measurement of OFETs. (a) shows the connection made to take the characteristic Vos is set to OV and the capacitance is measured between the gate and the shorted source and drain electrodes. In accumulation (b) there are three major contributions to the total capacitance the channel capacitance C oxWL, the gate/source overlap capacitance Cos, and the gate/drain overlap capacitance C gd- In depletion (c), only the overlap capacitance is observed, there is no mobile charge in the channel to contribute to a channel capacitance. The transistor channel is really a distributed RC structure and the lumped R shown is only schematic.

To discuss the results, the sensor is represented as a lossy capacitor, with both the capacitance C and the resistance R depending on frequency (Fig. 4 the frequency dependence of the equivalent-circuit elements is a consequence of the distributed nature of the processes in the sensor, which cannot be modeled appropriately by only two lumped elements with frequency-independent element values.). That simplifies the recognition of even small changes in the impedance, as changes at low frequencies become easily visible in the representation of the resistance R(f) and changes at higher frequencies become even more visible in the representation of the capacitance C(f). 

The problem when trying to make an electrical model of the physical or chemical processes in tissue is often that it is not possible to mimic the electrical behavior with ordinary lumped, physically realisable components such as resistors (R), capacitors (C), inductors, semiconductor components, and batteries. Let us mention three examples 1) The constant phase element (CPE), not realizable with a finite number of ideal resistors and capacitors. 2) The double layer in the electrolyte in contact with a metal surface. Such a layer has capacitive properties, but perhaps with a capacitance that is voltage or frequency dependent. 3) Diffusion-controlled processes (see Section 2.4). Distributed components such as a CPE can be considered composed of an infinite number of lumped components, even if the mathematical expression for a CPE is simple. 

Passive oscillator mode Impedance analysis of the forced oscillation of the quartz plate provides valuable information about the coating even if the active mode is not applicable anymore. For impedance analysis, a frequency generator is used to excite the crystal to a constraint vibration near resonance while monitoring the complex electrical impedance and admittance, respectively, dependent on the applied frequency (Figure 2B). For low load situations near resonance, an equivalent circuit with lumped elements - the so-called Butterworth—van-Dyke (BVD) circuit — can be applied to model the impedance data. The BVD circuit combines a parallel and series (motional branch) resonance circuit. The motional branch consists of an inductance Lq, a capacitance Cq, and a resistance Rq. An additional parallel capacitance Co arises primarily from the presence of the dielectric quartz material between the two surface electrodes (parallel plate capacitor) also containing parasitic contributions of the wiring and the crystal holder (Figure 2B). 

For circuits, interconnection capacitances and fan out (multiple MOSFET loads) will increase response times beyond the device response time, even when parasitics are taken into account. Thus, we are led to consider interconnection delay tint. Although a lumped model suggests, as with Eq. (7.15), that tint ( Gint/ Cg ) Tg. the length of interconnections requires a distributed model. Interconnection delay is then... 

Lumped inductors in series connection are usually described by the n model as shown in Figure 9.59. The shunt capacitors depict the parasitic capacitances of coil windings to ground. Capacitive coupling between windings cause the self-resonance frequency /, as shown in Equation 9.38. Because of increasing effective inductance values in the vicinity of a parallel resonance, the inductors can only be used far below the self-resonance frequency (Figure 9.60). 

Figure 1.62. (a) Diagrammatic view of the correlation circuit for photoconductivity cross-correlation measurement in (CH) on broadband microstrip lines, (b) Corresponding circuit diagram. The switches are modeled using the approximation of lumped elements with a static capacitance Cg and a resistor having a time-dependent conductance G(/) in parallel. Z is the characteristic impedance of the transmission lines. (Reprinted with permission from ref. 149)... 

A lumped model of the pervaporation unit is used to describe the dynamic behavior. Three cells are assumed in each pervaporation module. Since the liquid retentate provides most of the capacitance of the pervaporation unit, the ordinary differential equations describing the dynamic changes compositions and temperature of the retentate in each cell are used. The molar holdup in each cell Mr is assumed constant, so the total molar balance is algebraic. 

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 ...

If the tool that generated the SDF file lumped the transition delay in with the net delay rather than the cell delay (DC assumes that the transition time is by default included in the cell delay), and if you have not back annotated your capacitance information as well, then when DesignTime tries to subtract the transition delay from the net delay it must base the calculations of transition delay on the wire load model. Wl-r vou read the back annotated timing, you should set the two variables if the trans time has been included in the net delay. 

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