AC bridges

Polarography with superimposed AC signal. As examples of chemical analytical importance we shall consider (a) sinusoidal AC, (b) AC bridge, (c) square-wave and (d) Kalousek polarography. 

It is worth noting that we had several constraints in the measurements. First, the minimum temperature of our refrigerator was about 18 mK. Also, the sampling rate of the AC bridge was limited to 2sample/s. Finally, it was impossible to reduce the spurious power below 3 x 10-11W. 

In the low-frequency direction, the capacitative impedance (1/icoC) dominates. It is remarkable how in recent years the capability of commercial ac bridges to measure very low frequencies (10—3 to 10-4 cycles s l) has increased. However, the limit here is not so much in the electronics, but more in the stability of the interlace. A frequency of 10-4 cycles s 1 means a cycle some 3 hr in duration, and it is difficult to maintain a clean and stable solid/solution interface for this length of time. 

The conductivity of a solution is measured using an AC bridge with a two-elec-trode conductance cell on one arm (Fig. 5.40(a)) a balance is sought, manually or automatically, by adjusting the variable resistance and capacitance in another arm of the bridge. Usually AC voltage of a few volts and 1 kHz is applied to the cell. The impedance caused by the double-layer capacity at the electrodes does not affect the measured values of conductivity. In some cases, the conductance is measured with a four-electrode cell, as shown in Fig. 5.40(b). For practical methods of measurement, see the reviews in Ref. [25],... 

Traditionally, the instrument of choice for accurate conductance measurements that are relatively free of capacitance effects has been the ac Wheatstone bridge illustrated in Figure 8.14. The details of operation and the derivation of the balance condition of the ac bridge are presented in considerable detail elsewhere [16,17], The balance condition is exactly analogous to that of the dc bridge except that impedance vectors must be substituted for resistances in the arms of the bridge when reactive circuit elements are present. 

At balance, the points at d and b on the ac bridge must be equal in magnitude as well as in phase. The simplest method for determining when this condition exists is to use an oscilloscope connected as shown in the figure as the null detector. If precautions are taken to ensure that the excitation and the null signal are electronically isolated, the balance condition is easily, albeit slowly, obtained [16]. 

Cells for Conductimetry. Reliable and precise measurements of electrolytic conductance require attention to the design of cells, electrodes, and measuring circuitry. Extraction of an ohmic resistance from AC bridge measurements is not a trivial task, particularly in solutions with high resistance (such as organic solvents) or low resistance (molten salts). Expositions of the principles are provided in monographs that emphasize aqueous solution,54,55 and in a review of conductimetry and high-frequency oscillometry that emphasizes analytical applications.56... 

Figure 6.24 (a) Electrical equivalent circuit for a conductance cell (b) AC bridge with the cell impedance balanced by a series R-C combination (c) AC bridge with the cell impedance balanced by a parallel R-C combination (see Table 6.7). 

AC bridge measurements provide only an absolute impedance and phase shift, so there is no way to distinguish between either a series or parallel R-C combination by use of a pure sinusoidal waveform. Thus the series R-C combination of the cell may be matched by the series combination shown in Figure 6.24b or the parallel combination of the Wien bridge shown in Figure 6.24c. Either an oscilloscope or phase-angle voltmeter100 are recommended as null indicators because they allow both the phase shift and the imbalance potential to be nulled. 

Magnetic thermometry has been developed chiefly to measure temperatures near absolute zero (below -458°F, or -272°C). These measurements are obtained by adiabatic demagnetization of a paramagnetic salt. Inductance can be measured with an AC bridge (as shown in Figure 3.164) whose balance is independent of frequency. The relationship between self-inductance and sus-... 

Fig. 5. Complex-plane plot of impedance spectrum for a polycrystalline diamond film between two ohmic contacts. Frequency/kHz shown on the figure. Solid circles data obtained with ac bridge. Open circles data obtained with phase-sensitive analyzer. Top equivalent circuit [30].

SEC is measured with a conductivity meter, which normally consists of an AC bridge and a conductivity cell or electrodes. The conductance is measured between two electrodes. Two solutions of known conductivity should be used, one to calibrate the metre and the other to check the slope. It is important to correct all data for water temperature, either by calculation or by automatically using the metre s auto-temperature correction mode, since SEC is highly dependent on temperature. SEC increases by about 2% per degree centigrade rise in temperature due principally to an increase in water viscosity. 

Since the reactance can be inductive or capacitive and can be parallel or in series with the resistance, there are many variations of the ac bridge. An arrangement suitable for conductivity measurements is discussed in Exp. 17, and an ac bridge used for capacitance determinations is shown in the following section. A more extensive treatment of ac bridges can be found in Refs. 8-10. 

Note that use of an ac bridge will also eliminate any errors due to thermal voltages, which are dc effects. 

Another type of electrical pressure transducer is a variable-reluctance device. The deflections of a diaphragm of magnetic stainless steel are sensed by two inductance pickup coils. With ac-bridge circuitry, this transducer delivers a full-scale output of 40 mV per volt for a variety of ranges from 0 4 Torr (0- 0.08 PSIA) to 0- 3200 PSIA. 

There is much to think about here. If one wishes to measure the dielectric constant of a liquid, not a conducting ionic solution, one simply uses an alternating current (ac) bridge containing a capacitor in one of the arms. Then the capacitance is measured in the presence of the liquid, the dielectric constant of which is to be measured, and then without it, i.e., in the presence of air. Since the dielectric constant is near to unity in the latter case, this gives rise to knowledge of the dielectric constant of the liquid because the capacitance of the cell in the bridge arm increases as the dielectric constant increases. 

In the more advanced kinetic measurements, which were carried out by using chronopotentiometry [118], chronocoulometry [124, 139], linear [146] and convolution [18, 147] potential sweep voltammetry, or phase-sensitive ac polarography [142, 143], the ohmic drop was either numerically subtracted [118], or compensated [124, 139, 142, 143, 146, 147] with the help of the positive feedback. The feedback adjustment was based either on the assumption that the separation of the current peaks measured by the slow potential sweep voltammetry should reach the value of (59/z)mV [124, 139, 146, 147], or on the value of the solution resistance obtained by an ac bridge technique [142, 143]. However, the former adjustment is not very sensitive, whereas the estimated accuracy of 10 Q [142] in the latter case may not be... 

For ionic solids, measurement of the ionic conductivity, <7 , has long provided a method for studying their atomic diffusion [25, 209, 225, 226] (see also Chapter 3). The measurements are usually made with an alternating current (AC) bridge operating at a fixed frequency, f (typically >1 kHz), to avoid polarization effects. The early studies were restricted to measurements on single crystals, and in this case (7i and the tracer diffusion coefficient were seen to be related by the Nernst-Einstein equation [25] ... 

This technique was the first used to measure double-layer parameters (principally of the dropping mercury electrode) and later to measure electrode impedance in the presence of a faradaic reaction to determine the kinetics of electrode processes. The use of ac bridges provides meas-... 

Operation is based on a low voltage ac bridge noble metal thermopile circuit. A change in... 

For the methods described above, which use a DC power source, two to four balancings are required for each reading, and automation is difficult. The development of AC bridges eliminates the need of current reversal and permits automation in precision thermometry [22, 23],... 

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