Positive feedback compensation

A strategy for handling the ohmic drop problem that combines satisfactory accuracy with minimal tedium therefore consists of using the positive feedback compensation as much as possible and, when necessary, correcting the residual ohmic drop by the approximate procedures discussed above. A more general and more rigorous treatment of ohmic drop may be devised with the help of convolutive treatments of the current-potential data, discussed in the next section. 

TABLE 6.2. Positive Feedback Compensation of Ohmic Drop Equations of the Forward and Reverse Traces for Oscillatory and Nonoscillatory Behaviors0... 

One must keep in mind that modern electrochemical instrumentation compensates for the potential drop i (Rn + Rnc) through the use of appropriate circuitry (positive feedback compensation). This adds a supplementary potential to the input potential of the potentiostat (equal to the ohmic drop of the potential), which is generated by taking a fraction of the faradaic current that passes through the electrochemical cell, such that in favourable cases there will be no error in the control of the potential. However, such circuitry can give rise to problems of reliability in the electrochemical response on occasions when an overcompensation is produced. 

Garreau, D. Hapiot, P. Saveant, J.M. (1990). Fast cyclic voltammetry at ultramicroelectrodes Current measurement and ohmic drop positive positive feedback compensation by means of current feedback operational amplifiers. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, 281,73-83. 

At small values of voltage sweep rate, typically below 1 mV/s, the capacity effects are small and in most cases can be ignored. At greater values of sweep rate, a correction needs to be applied to interpretations of ip, as described by Nicholson and Shain. With regard to the correction for ohmic drop in solution, typically this can he handled adequately by careful cell design and positive feedback compensation circuitry in the electronic instrumentation. 

The second experimental quantity to be dealt with is the electrolyte resistance. The electrode potential measnred vs. the reference electrode includes the contribution IReiectr The most common way of handling this is to employ positive feedback compensation. This involves routing an adjustable fraction of the current follower output of the potentiostat back to the signal generator input which adds a voltage, proportional to the current, to the input wave form. For more details we refer to Reference 10. 

As shown in Fig. 24, the mechanism of the instability is elucidated as follows At the portion where dissolution is accidentally accelerated and is accompanied by an increase in the concentration of dissolved metal ions, pit formation proceeds. If the specific adsorption is strong, the electric potential at the OHP of the recessed part decreases. Because of the local equilibrium of reaction, the fluctuation of the electrochemical potential must be kept at zero. As a result, the concentration component of the fluctuation must increase to compensate for the decrease in the potential component. This means that local dissolution is promoted more at the recessed portion. Thus these processes form a kind of positive feedback cycle. After several cycles, pits develop on the surface macroscopically through initial fluctuations. 

The ohmic potential drop can be compensated by means of positive feedback of the potentiostat or by algebraic subtraction under potentiostatic or galvanostatic conditions, respectively. 

The electrode potential was controlled with an EG G Princeton Applied Research (PAR) model 173 potentiostat/galvanostat and is referenced to a saturated calomel electrode (SCE). A PAR model 276 current-to-voltage converter allowed monitoring of current during the ORC and SERS experiments and it also provided for positive feedback iR compensation for accurate potential control. 

There are two ways of handling the ohmic drop effect. One consists of equipping the instrument with a positive feedback loop that subtracts from E a tension, Rei, proportional to the current, thus eliminating, at least partially, the effect of the ohmic drop.14 One may even get the impression that total compensation, or even more, overcompensation, could be achieved. In fact, before total compensation is reached, oscillations appear as a result of the bandpass limitations of the operation amplifiers. The entire instrument can indeed be represented by a self-inductance, La, that is a... 

Although, strictly speaking, total compensation cannot be achieved, partial compensation may well lead to a negligible residual ohmic drop, although the presence of damped oscillations does not yet prevent detection of the Faradaic current. Such a situation is typically reached for ARu = 417 in the system shown in Figure 1.8. This figure illustrates how the positive feedback ohmic drop compensation should be carried out in practice. The procedure may be summarized as follows ... 

Feedback loop A set of geochemical processes that influence each other. In a negative feedback, an alteration in the rate of one process is at least partially compensated for by changes in the rates of the other interconnected processes. In a positive feedback, an alteration in the rate of one process is amplified by accompanying changes in the rates of the other interconnected processes. 

Fig. 5.45 Circuit for a three-electrode polarograph. The bold lines are for positive feedback iR-drop compensation. Q is a capacitor to decrease the current fluctuation.

Positive feedback iR compensation in three-electrode measurements As described in Section 5.3, the influence of iR-drop is serious in two-electrode polarography or voltammetry. The influence is eliminated considerably with three-electrode instruments, if the tip of the reference electrode is placed near the surface of the indicator electrode. However, there still remains some iR-drop, which occurs by the residual resistance at... 

Accepting these results for an idealized system confirms the intuitive notion that the use of positive feedback from the current follower is identical to physically moving the reference electrode closer to the working electrode. There are no additional concepts to cope with in relating response to physical parameters. It will become evident that this situation allows a rather simple assessment of loop gain and a clear view of corrective measures that will lead to stability with Ru compensation. 

Relative value of voltage drop, Rui(s), to be compensated by positive feedback ... 

E. R. Brown, H. L. Hung, T.G. McCord, D. E. Smith, and G. L. Booman, A Study of Operational Amplifier Potentiostats Employing Positive Feedback for iR Compensation II. Application to AC Polarography, Anal. Chem. 40 1411 (1968). 

In order to avoid the distortion caused by these two effects, the usual approach is to compensate the resistance Ru by a positive feedback loop (this is imperative in systems like plasticized membranes for which the uncompensated resistance can be of the order of megaohms [32-34]). Another possibility is to use microelectrodes, for which a decrease in the measured current is obtained which minimizes the ohmic drop and charging current distortion (see Sects. 2.7 and 5.4.1). 

Four-electrode system — Figure. Electronic circuit of a four-electrode potentiostat (X, potential input Y, current output RE1 and RE2, reference electrodes CE1 and CE2, counter electrodes PF, positive feedback circuit for IR drop compensation)... 

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