Stray capacitor

In order to reduce the contribution of the linear stray capacitor an inverse current compensation is used which directly reduces the influence of this capacitor [11], The optimized results using this method are shown in Figures 17.13 (c) and (d). Now the ferroelectric switching can be seen clearly. The increase in resolution for the P(V) curve is in the range of a factor of 50. 

Fig. 11.1. Two basic types of current ampliflers. (a) Feedback picoammeter. It consists of two components, an operational amplifier (op-amp) A, and a feedback resistor 1 fb- a typical value of the feedback resistor used in STM is 10 fl. The stray capacitance Cfb is an inevitable parasitic element in the circuit. In a careful design, Cfb 0.5 pF. The input capacitance Cm is also an inevitable parasitic element in the circuit. Those parasitic capacitors, the thermal noise of the feedback resistor, and the characteristics of the op-amp are the limiting factors to the performance of the picoammeter. (b) An electrometer used as a current amplifier (the shunt current amplifier). The voltage at the input resistance is amplified by the circuit, which consists of an op-amp and a pair of resistors R, and R2. The parasitic input capacitance Cm limits the frequency response, and the Johnson noise on Rm is the major source of noise. Also, the input resistance for this arrangement is large.

Capacitivelv coupled noise. Any two objects form a capacitor ( stray capacitance ) which establishes a path for high frequency signals. Noise which is capacitively coupled into a circuit is basically current noise which is converted to voltage by an impedance between the two objects. 

Since the unloaded QCM is an electromechanical transducer, it can be described by the Butterworth-Van Dyke (BVD) equivalent electrical circuit represented in Fig. 12.3 (box) which is formed by a series RLC circuit in parallel with a static capacitance C0. The electrical equivalence to the mechanical model (mass, elastic response and friction losses of the quartz crystal) are represented by the inductance L, the capacitance C and the resistance, R connected in series. The static capacitance in parallel with the series motional RLC arm represents the electrical capacitance of the parallel plate capacitor formed by both metal electrodes that sandwich the thin quartz crystal plus the stray capacitance due to the connectors. However, it is not related with the piezoelectric effect but it influences the QCM resonant frequency. 

A capacitance cell suitable for work with liquids or solutions is shown in Fig. 1 it is made with a small variable-air capacitor of the type formerly in common use in radios and electronic circuits. It should have a maximum capacitance of 50 to 200 pF. This device is more convenient than a fixed-plate capacitor, since with the latter device it is necessary to measure separately the stray capacitance due to electrical leads, etc. In the cell shown, the variable capacitor is used in two positions fully closed (maximum capacitance) and fully open (minimum capacitance) these positions are defined by mechanical stops for the pointer on the knob that rotates the capacitor shaft.f The difference ACbetween the closed (b) and open (a) positions is independent of the stray capacitance. Thus the dielectric constant of the liquid or solution is given by... 

The inductance L is fixed, while the capacitance C is the sum of several separate capacitances that of the conductance cell, Cx, that of a separate variable tank capacitor incorporated in the oscillator, Cj (if present) and stray capacitances due to leads, etc., Q. Also present in some methods is a precision air capacitor Cp graduated directly in capacitance units (generally picofarads), used when the equipment is operated in a null mode. In this mode the precision air capacitor is used to bring the frequency /to the same value in each measurement, and the change in reading of the precision air capacitor is then equal in magnitude to the change in capacitance of the cell. 

The recommended procedure for determining the dielectric constant of an unknown gas with the cell described here depends on the relationship of changes in the capacitance of the cell to changes produced in the effective capacitance in the tank circuit. These are not the same because other capacitances are present besides that of the capacitor contained in the cell, Cceii. These always include the capacitance of the shielded cable connecting the cell to the oscillator and stray capacitances in the oscillator tank these are in parallel with the cell, and lumped together may be called In addition there is in the circuit described... 

If the sample fills the capacitor completely the impedance calculated from eqs 1.3 and 1.5 represents the impedance of the sample alone. But due to the sol-gel process the samples can have pores. In this case the overall impedance of the sample and the pores is determined. The overall impedance constitutes a parallel connection of the impedance of the sample Zs and an ideal, air filled capacitor Ca of the remaining area if stray fields are neglected ... 

The stray fields occur because the real surface charge density on the capacitor plates varies between regions covered by the sample and those without the sample. The approximation of independent capacitors is justified by the small variation of e from one region to the other. This requirement is fulfilled by the highly porous (i.e. low e) aerogels, eq. 3.6 can be solved for the impedance of the sample Zs and separated in real and imaginary parts ... 

The active layer contains the semiconductor. The active layer is typically patterned to avoid leakage currents between transistors, avoid the formation of unintentional parasitic transistors and MOS capacitors, and to avoid unintentional parasitic paths in ungated areas. When the transistor threshold voltage is such that the semiconductor is depleted it is possible in many cases to avoid patterning the active layer. There are also circuit geometries and layout topographies which suppress stray currents and allow the use of unpatterned semiconductor material if that is desirable. These are discussed in further detail in Chapter 5. 

Here, Cg includes the stray capacitance due to the large feedback resistor and a feedback capacitor which is employed for stability of the TIA. Assuming that Rg and Q of Erec are negligible, Xjj(s) can be simplified to Rn/(1 + sC R ). Thus, the gain is rewritten as... 

Figure 6. Experimental setup for two-step excitation of Ba Rydberg states followed by collisional ionization and mass selective detection of the Ba" ions produced. (Taken from Ref. 36.) The parallel plate capacitor served to compensate stray electric fields.

Below 30 MHz, the cathode can be grounded to RF voltages by simply bypassing the filament connections with capacitors, as shown in Fig. 5.69(a). Above 30 MHz, this technique does not work well because of the stray inductance of the filament leads. Notice that in Fig. 5.69(b), the filament leads appear as RF chokes, preventing the cathode from being placed at RF ground potential. This causes negative feedback and reduces the efficiency of the input and output circuits. 

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. 

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