Capacitance stray

Accurate control of potential, stability, frequency response and uniform current distribution required the following low resistance of the cell and reference electrode small stray capacitances small working electrode area small solution resistance between specimen and point at which potential is measured and a symmetrical electrode arrangement. Their design appears to have eliminated the need for the usual Luggin capillary probe. 

In contrast to the ionizing electrode method, the dynamic condenser method is based on a well-understood theory and fulfills the condition of thermodynamic equilibrium. Its practical precision is limited by noise, stray capacitances, and variation of surface potential of the air-electrode surface, i.e., the vibrating plate. At present, the precision of the dynamic condenser method may be limited severely by the nature of the surfaces of the electrode and investigated system. In common use are adsorption-... 

Stray capacitance-resistance paths from electrode leads and other sources should be minimized. 

The measurement electrodes can be wrapped around, threaded onto, or painted over a standard capillary. The use of a grounded shield in between the measurement electrodes greatly reduces stray capacitance. (B) Simplified circuit diagram for a contactless conductivity detector. includes double layer capacitance Cjj as well as the capacitance across the capillary wall. 

The tunneling current occurring in STM is very small, typically from 0.01 to 50 nA. The current amplifier is thus an essential element of an STM, which amplifies the tiny tunneling current and converts it into a voltage." The performance of the current amplifier, to a great extent, influences the performance of the STM. There are natural limits for the overall performance of current amplifiers, as determined by the thermal noise, stray capacitance, and the characteristics of the electronic components. In this section, we will present these issues by analyzing several typical current amplifier circuits, which can be easily made and used in actual STMs. 

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.

There are several factors which impose natural limits for the performance of that current amplifier, such as the stray capacitance parallel to the feedback resistance, the stray capacitance parallel to the input terminals, which will be discussed in the following subsections. 

In reducing Johnson noise, to incorporate all the amplification in one single stage is the best choice. However, a stray capacitance Cfb is always present. In this case, the relation between the input current and the output voltage is determined by the differential equation... 

The existence of the stray capacitance results in a time delay RmCvn- The frequency response of the amplifier is reduced. In a practical design, a compromise between bandwidth and noise is often to be made, as explained in the following subsection. 

First, we analyze the effect of the stray capacitance in parallel with the feedback resistance. Consider a sinusoidal input current with frequency /. From Fig. 11.1, the magnitude of the output voltage is... 

Even if a very careful layout design is made, a stray capacitance of Cfb = 0.5 pF is common. With = 100 Mfl, using Eq. (11.10), the -3 dB cutoff frequency is estimated to be / 3 kHz. For most applications in STM, a gain of IV/lnA is desirable. A one-stage current amplifier requires a feedback resistance of IGO. The -3 dB cutoff frequency would be about 0.3 kHz, which is too low. 

If / iCi = R2C2, then there is no phase difference between /,n and Vout- The optimum value of C2 can be determined by trial and error. Taking / i = 100 Mfi and / 2 = 1 Mfl, the typical value of C2 is 10 20 pF. The compensation is never perfect, because there are other stray capacitances in the circuit, which are not compensated by this simple RC network. Nevertheless, a bandwidth of 100 kHz is attainable. 

The heaters commonly consist of a resistive wire or a coaxial heating cable with an insulated heating wire inside bendable metal tubing. These are usually powered by DC supplies. Electrical leads and feedthroughs are designed for minimal leakage currents and stray capacitances. 

A few comments are in order on the probable validity of conclusions based on this equivalent circuit to real cells. Quite simply stated, real cells that are properly designed will have the same properties as dummy cells of the same values of Rs, Ru, and Cdl. Important design features of a cell are (1) equal resistance between all points on the surface of the working electrode and the auxiliary electrode (2) low-impedance reference electrode and (3) low stray capacitance between electrodes, between leads, and to shields. Spherical symmetry is a good, but somewhat inconvenient, method of meeting the first requirement a parallel arrangement also works with planar electrodes. At the very... 

Time-domain response of feedback amplifiers has been regularly correlated with frequency-domain behavior, and vice versa. Examples have usually been restricted to those situations in which only the amplifier contributes phase shift (single pole) or where a second source of phase was included (two-pole), such as from nonideal amplifier design or from the effects of stray capacitance at the input terminal. The system of interest in electrochemistry is more complicated than a two-pole system because there is also a decreasing phase shift caused by... 

P. Kuban and P.C. Hauser, Effects of the cell geometry and operating parameters on the performance of an external contactless conductivity detector for microchip electrophoresis, Lab Chip, 5 (2005) 407-415. J.G.A. Brito-Neto, J.A.F. da Silva, L. Blanes and C.L. do Lago, Understanding capacitively coupled contactless conductivity detection in capillary and microchip electrophoresis. Part 2. Peak shape, stray capacitance, noise, and actual electronics, Electroanalysis, 17 (2005) 1207-1214. 

P. Kuban and P.C. Hauser, Fundamental aspects of contactless conductivity detection for capillary electrophoresis. Part II Signal-to-noise ratio and stray capacitance, Electrophoresis, 25 (2004) 3398-3407. 

A contactless conductivity detector was also constructed using 10-p.m A1 foil strips fixed on a 125-p.m-thick PMMA chip with epoxy. Here, the PMMA plate was the dielectric layer. The electrodes were arranged in an antiparallel fashion to minimize stray capacitance between them [772]. 

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