Damped capacitance

Temptation has been strong, and not always resisted, to approach total compensation by damping the oscillations out with an appropriately placed capacitance so as to reach the ideal situation of total compensation with unconditional stability. In fact, the cure is worse than the disease. The additional response time accompanying introduction of the damping capacitance will indeed distort the Faradaic current in a more severe and undecipherable manner than does ohmic drop. 

GRAPH 11.46 Two steps in the transformation of the Formal Graph of a spatially damped oscillator, (a) Split of the damping capacitance (diagonal link) and (b) apparent variables and operators are chosen for obtaining a circular graph. 

In a typical case, where ksi = 0.3, the antiresonance state varies from the previously mentioned mode and becomes closer to the resonance mode. The low-coupling material exhibits an antiresonance mode where capacitance change due to the size change is compensated completely by the current required to charge up the static capacitance (called damped capacitance). Thus, the antiresonance frequency/a will approach the resonance frequency/r. 

One of the most interesting observations during the measurements of the time dependence of the differential capacitance in saturated adenine solutions was the appearance of damped capacitance oscillations [67]. The oscillations appear after the potential jump near the negative edge of the capacitance pit. The oscillations were observed with adenine, but not with thymine. 

Electrostatic capacitances help to tame and damp the arriving surge... 

Electrostriction dominates the voltage dependence of membrane capacitance. However, at low tensions ( 4 x 10 N/m) the contribution of undulations is also important. The latter is in good agreement with the results of [78] if the same membrane parameters are chosen. At higher tension undulations are damped and their role becomes less significant. 

The constants Kp, Kt, and Kd are settings of the instrument. When the controller is hooked up to the process, the settings appropriate to a desired quality of control depend on the inertia (capacitance) and various response times of the system, and they can be determined by field tests. The method of Ziegler and Nichols used in Example 3.1 is based on step response of a damped system and provides at least approximate values of instrument settings which can be further fine-tuned in the field. 

There is an equivalence between the differential equations describing a mechanical system which oscillates with damped simple harmonic motion and driven by a sinusoidal force, and the series L, C, R arm of the circuit driven by a sinusoidal e.m.f. The inductance Li is equivalent to the mass (inertia) of the mechanical system, the capacitance C to the mechanical stiffness and the resistance Ri accounts for the energy losses Cc is the electrical capacitance of the specimen. Fig. 6.3(b) is the equivalent series circuit representing the impedance of the parallel circuit. 

An electrical measuring instrument contains electrical circuits incorporating capacitance, inductance, and resistance. In the absence of resistance, a circuit tends to oscillate with a definite frequency /when disturbed. For optimum performance an amount of resistance is incorporated that is barely sufficient to damp the oscillations resulting from transient inputs the circuit is then said to be critically damped. For a critically damped circuit it can be shown that the root-mean-square (rms) fluctuations in voltage V and in current /are given by... 

The relative permittivity of a medium, K=Kr-iKi, is in general a complex quantity whose real part k, (also known as the dielectric constant) is associated with the increase in capacitance due to the introduction of a dielectric. The imaginary component tq is associated with mechanisms that contribute to the energy dissipation in the system, due to viscous damping of the rotational motion of the molecules in alternating fields this effect is frequency dependent. The experimental setup consisted of a parallel plate capacitor of... 

This section deals with a physical problem in which both homoclinic and infinite-period bifurcations arise. The problem was introduced back in Sections 4.4 and 4.6. At that time we were studying the dynamics of a damped pendulum driven by a constant torque, or equivalently, its high-tech analog, a superconducting Josephson junction driven by a constant current. Because we weren t ready for two-dimensional systems, we reduced both problems to vector fields on the circle by looking at the heavily overdamped limit of negligible mass (for the pendulum) or negligible capacitance (for the Josephson junction). 

The control signal calculated by the PID algorithm (see Note 3) is translated into a heating profile by way of pulse width modulation. The heater receives a pulse train (frequency of 0.5 Hz) with variable on time. During the on segment of each 0.5 s pulse, the heater is on at lull power. The integrated power over the lull pulse is controlled to achieve the desired temperature. The thermal capacitance of the capillaries and the heater itself is sufficient to damp out any temperature fluctuations such that the temperature measured inside the capillaries is steady (does not show any 0.5 Hz ripple). 

And the skeptics some are still convinced that the small anode-cathode zener capacitance can combine with the input capacitance of the FET and the lead and trace inductances to form a high-Q pi type of tank circuit (C-L-C). So they recommend a small resistor of about 10 ohms placed between the zener and the gate lead, to damp out any oscillations. 

We can clearly see one major problem already. That is, what if the tube does not fire This is a real-world possibility, since the seals at the ends of the tube may leak, thus affecting the vacuum inside the tube over a period of time. In this situation, we are expecting to replace the tube, not the ballast But in a virtually undamped LC circuit, the oscillations will build up every cycle, and eventually the transistors, which see the same current when they turn on, will be destroyed. This is what leads to the deactivated tube test. The tube does not fire and the filaments at the end of the tube are typically of such low resistance, that they really can t damp out the steadily escalating oscillations. Some engineers therefore try to place an additional resistor in series with the small starter capacitance, but this certainly affects the ability to start the tube, especially at lower mains input voltages. 

Abstract Oscillators are the standard interface circuits for quartz crystal resonator sensors. When applying these sensors in gases a large set of circuits is available, which can be adapted to particular applications. In liquid applications viscous damping accompanied by a significant loss in the Q factor of the resonator requires specific solutions. We summarize major design rules and discuss approved solutions. We especially address the series resonance frequency and motional resistance determination and parallel capacitance compensation. We furthermore introduce recent developments in network analysis and impulse excitation technique for more sophisticated applications. Impedance analysis especially allows a more complete characterization of the sensor and can nowadays be... 

As shown in the previous section, the mechanical properties of a quartz crystal close to resonance frequency can be expressed by means of a motional impedance. To complete the equivalent circuit of a quartz crystal, the capacitance, Co, must be added in parallel to the motional impedance. It results in the Butterworth-Van Dyke (BVD) equivalent circuit of a quartz crystal, as shown again in Fig. 8 for an unloaded quartz crystal [32]. In this notation common in electronic Hterature, Is is the dynamic inductance and is imder-stood here as a representation of the oscillating mass of the quartz crystal. Cs is the dynamic capacitance and reflects the elasticity of the oscillating body. Rs is the dynamic resistance and returns friction of the quartz slice as well as all kinds of acoustic damping. 

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