Slew rate

In general, in order to be able to achieve high slewing rates, one has to keep the magnet inductance L reasonably low which, on the other hand, means that the current required to achieve a desired value of B is going to be rather large (hence the necessity to find a suitable compromise). 

Such a configuration permits to reach elevated maximum field values Hmax with acceptable slewing rates dBjdt. On the other hand, it presents also a number of design problems and some practical disadvantages. 

Equations (l)-(4) are used here essentially to illustrate the intricate interdependence between the maximum achievable field, the employed electric power, the maximum slewing rate dBjdt and the geometric parameters of the solenoid. A detailed, quantitative treatment (which must necessarily be carried out when designing an actual magnet) is beyond the scope of this review since, for example, the calculation of G and L for a real magnet is quite complex and requires numerical methods. 

The design parameters therefore always represent a compromise between the maximum achievable field and satisfactory slewing rates. The compromise can be resolved once one has defined the maximum available power, the basic geometry of the solenoid (in particular its volume), and any optimization constraints (see the next point). 

On the basis of Eq. (2), it is evident that the lower silver resistivity proportionally reduces the electrical power required to produce a given field. At the same time, it reduces the time constant RjL of the magnet which is an important factor in minimizing the final field-switching times. Section IV C discusses how the magnet time constant RjL and the power supply output voltage affect the maximum achievable slewing rate dBjdt. 

It is evident that, for a given magnet, it is the maximum power supply voltage which determines the maximum field-slewing rates and switching times while, according to Eq. (2), the maximum available power determines the maximum achievable field. 

Fig. 10. Evolution of the current in a switched R, L circuit. When the switch is turned On, the voltage (bottom right) across the magnet jumps from 0 to V, while the current (top right) evolves according to Eq. (5). The starting slope of the I t) curve (the dotted line), corresponding to the maximum field-slewing rate, is given by VIL = (RIL)I, . ...

In subsequent years, the above principle was used and further improved by Koenig and Brown 58,66,78), Kimmich et al. 61,76,77) and Noack et al. 65,75), leading to the realization of magnet/power supply systems with elevated slewing rates. 

During the switching periods, the maximum current-slewing rate dl t)jdt and, consequently, also the maximum field-slewing rate dB t)jdt, are limited. For the current-slewing rate, the limits follow directly from Eqs. (6) and (7) ... 

Here k is the proportionality constant between field and current (B = kI), Vp and Htv are the maximum positive and maximum negative power supply voltage, L and R are the inductance and resistance of the magnet, B is the instantaneous main field value, Su = (kIL)Vp and Sd = (kIL)Vn are the up-going and down-going slewing rates when B = 0, and a = R/kL. 

Table H-2 lists high-voltage op-amps for driving the piezos. The requirements are a high supply voltage range and a high slew rate (SR). The usable current Iq is also an important parameter for high-voltage op-amps. In STM, it is not critical. Most of the useful high-voltage op-amps are manufactured by Apex.

In pulse-power applications, the thyristor is required to supply energy to the load in a very short period of time, which requires that it provide extremely high-current slew rates. During turn-on, excess carrier density increases near the gate area and then spreads throughout the device. As the excess carriers spread, the anode-to-... 

This circuit uses a LF411 op-amp macro model. All op-amp models, except the ideal op-amp model, include bias currents, offset voltages, slew rate limitations, and frequency limitations. Also note that the op-amp model requires DC supplies. The... 

This op-amp circuit is a Schmitt Trigger with trigger points at approximately 7.5 V. A sinusoidal voltage source will be used to swing the input from +14 V to -14 V and from -14 V to +14 V a few times. The frequency of the source is 1 Hz. This low frequency is chosen to eliminate the effects of the op-amp slew rate on the Schmitt Trigger performance. If you... 

The output voltage swing is limited to 15 V and we have added a pole at 30 rad/sec. This is approximately the frequency response of a 741 op-amp. Note that this circuit is still ideal because it does not include many of the other nonideal characteristics of a 741 op-amp such as bias currents, offset voltages, and slew rate. 

PSpice has a model for LM324, but the the UA741 op-amp model was used in its place. The operation amplifier does not play a critical role in this circuit because of its slow response. The limiting parameter of the delay time is the RC time constant and not the slew rate or drive capability of the operational amplifier. The PSpice model response to a step input is shown in Fig. 3.27, and the AC results are shown in Fig. 3.28. 

A simple pulse-shaping modification can be added to the Bessel-Thompson delay filter by using an additional operational amplifier. Resistors are used to divide down the supply voltage to half the output voltage of the delay filter, and its response is then compared with the delay filter s response, which results in a time-delayed square wave. The schematic of this circuit is shown in Fig. 3.31. This simulation also allows us to compare the operational amplifier models that came with each software package. The response of this circuit is driven from rail to rail, providing the saturation voltages of the models. Also, the slew rate of the output should be consistent with the measured and... 

To reduce the switching spike, select an operational amplifier with a larger slew rate. The simulation below (Fig. 6.61 and Table 6.4) compares the output of UA741 to that of LM318. 

There are several other methods of achieving stability in potentiostatic circuits. A capacitor may be added between the counter and reference electrodes to reduce phase shift in the critical frequency region. Some caution must be exercised since a low-resistance reference electrode then becomes the counterelectrode at high frequencies. A particularly interesting method is known as input lead-lag compensation a series RC is connected between the input terminals of the control amplifier, and a second resistor is connected between the noninverting input and common. This form of compensation has minimum effect on the slew rate of the control amplifier. Further details can be found in the book by Stout and Kaufman listed in the bibliography. 

Fig. 6.10 Calculated SFI profile for diabatic ionization of the H like m a 3 states. Top, extreme members of the n = 31, m = 3 Stark manifold. The crosses represent the points at which each m a 3 Stark state achieves an ionization rate of 10 s I. Bottom, calculated SFI profile for diabatic ionization of a mixture containing equal numbers of atoms in each m a 3 Stark level for n = 31 at a slew rate of 109 V/cm s. (from ref. 26).

Fig. 7.6. The criterion for the critical slew rate for the crossings, Sx, may be written...

Fig. 7.12 Ratio of the signal resulting from ionization of m = 2 states (upper curve), and ionization of m = 0 states (lower curve) to the total ionization signal as a function of the slew rate from low to intermediate fields following excitation of the 34dj/2 state via the 3pifl state with o polarization (from ref. 16).

The experimental test and model comparison have been carried out without bleed and hot bypass, but with a cold bypass valve opening of 40%. The use of the cold-air bypass valve (FV-170) allows compressor discharge to be directed into the turbine inlet, bypassing the heat exchangers, air plenum and fuel cell simulator. FV-170 is a nominal 15.4 cm ID Fisher-Rosemont V-150 Vee-Ball control valve with a full range slew rate of 1.5 seconds. 

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