Virtual ground measurements

In order to allow the resistance measurement, the current injection is obtained in the circuit represented in fig. 3, by applying a voltage Vo- This current, due to the virtual ground condition determined by the circuit configuration (very high input impedance), will cross the feedback resistor Rf and determine an output voltage. In this example M and Yj (j=l,2,3) are the quantities ... 

With respect to the equivalent circuit in Figure 3.3, an evaluation of the known methods for hysteresis measurements will be given, in view of the effective parasitic capacitance and the influence of reflection. Well known methods to record the hysteresis loop of ferroelectric capacitors by measuring the current response are Sawyer Tower, Virtual Ground, and Shunt measurement as shown in Figure 3.4. 

Figure 3.4 Schematic comparison of (a) Sawyer Tower, (b) Virtual Ground, and (c) Shunt hysteresis measurement method.

The SFM images (Fig. 43) show, that using a d.c. offset of-10.57 V and an excitation voltage of 4.4 V at 1 kHz, high currents in the ilA range can be measured. For this scenario, ceramics are ideal samples, because the low stiffness of the polymers makes it impossible to use excitation frequencies below the bandwidth limit of the constant-force feedback. The much stiffer ceramics permit one to perform measurements without cross-talk effects. Such cross-talk effects occur with soft polymer samples, due to a surface indentation by the tip, which is at virtual ground and so attracted by the back electrode under potential. 

Now, in principle, the angle of contact between a liquid and a solid surface can have a value anywhere between 0° and 180°, the actual value depending on the particular system. In practice 6 is very difficult to determine with accuracy even for a macroscopic system such as a liquid droplet resting on a plate, and for a liquid present in a pore having dimensions in the mesopore range is virtually impossible of direct measurement. In applications of the Kelvin equation, therefore, it is almost invariably assumed, mainly on grounds of simplicity, that 0 = 0 (cos 6 = 1). In view of the arbitrary nature of this assumption it is not surprising that the subject has attracted attention from theoreticians. 

Since the Wenner formula [Eq. (24-41)] was deduced for hemispherical electrodes, measuring errors appear for spike electrodes. To avoid errors in excess of 5%, the depth of penetration must be less than a 5. Soil resistivity increases greatly under frost conditions. While electrodes can be driven through thin layers of frost, soil resistivity measurements deeper than 20 cm in frozen ground are virtually impossible. 

The Control of Substances Hazardous to Health (COSHH) Regulations 1989 covers virtually all substances hazardous to health. Only asbestos, lead, materials producing ionizing radiation and substances below ground in mines (which all have their own legislation) are excluded. The Regulations set out measures that employers must implement. Failure to comply with COSHH, in addition to exposing employees and others to risk, constitutes an offence and is subject to penalties under the Health and Safety at Work Act, etc. 1974. 

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