Wien bridge

An alternative way of measurement is to incorporate the cell in a bridge circuit as shown in Fig. 16. The configuration of the bridge is identical to the classical Wien bridge [49] except that the a.c. voltage is supplied via the potentiostat so that, simultaneously, the mean d.c. potential E can be controlled as usual [21, 22]. The adjustable series combination of the resistor Rs and the capacitor Cs offers an impedance Zs, given by... 

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. 

Experiments on Wien-bridge oscillators showed such anomalous fluctuations to exhibit a variance proportional — where /3 is the reaction factor and the corresponding threshold value. The relaxation time... 

The time behavior as experimentally detected on a Wien-bridge oscillator has been accounted for by using the theories of Kubo et al. ... 

Horn et al. simulated phase transitions of the first and second kind, and a three-critical point, via a Wien-bridge oscillator. Such behavior is fairly well accounted for by the Landau theory except for very close to the critical point. Furthermore, Horn et al. observed that the phase of their oscillator had a... 

The form of Eqs (5) and (6) has led to the widespread and unfortunate practice of tabulating and plotting measured impedance data in terms of the complex pair (Rs, j/(oCs) even when a Wien bridge has not been used. The impedance notation (Z, jZ") is significantly less ambiguous and will be used here. 

When phase-sensitive null detection is used, the practical low-frequency limit becomes a function of the particular form of bridge chosen. For the Wien bridge, this limit is imposed by the selection of suitably large adjustable capacitance standards at frequencies below about 20Hz. 

Wien bridge An ac bridge used to measure capacitance or inductance. 

Wien bridge oscillator (audio frequency oscillator)... 

The feedback network between the amplifier terminals and the output is a Wien bridge circuit with a series RC network at one arm and a parallel RC network in the next arm. The remaining arms are connected to Ri and Rp. When the bridge is balanced at resonance, the phase shift becomes 0° and a wave is generated at a frequency. 

The differential capacity can be measured primarily with a capacity bridge, as originally proposed by W. Wien (see Section 5.5.3). The first precise experiments with this method were carried out by M. Proskurnin and A. N. Frumkin. D. C. Grahame perfected the apparatus, which employed a dropping mercury electrode located inside a spherical screen of platinized platinum. This platinum electrode has a high capacitance compared to a mercury drop and thus does not affect the meaurement, as the two capacitances are in series. The capacity component is measured for this system. As the flow rate of mercury is known, then the surface of the electrode A (square centimetres) is known at each instant ... 

The ac bridge is based on a classical Wheatstone (or Wien for ac measurements) bridge in which one part is replaced by an electrochemical cell and the other compensating part by a variable, R or C. The dc potential is supplied by a potentiometer in the center and ac by the external source. The double layer capacitance measurements were initially carried out on a dropping mercury electrode (DME), and the bridge compensation had to be carried out always at the same surface area of the DME, that is, after exactly the same time from the beginning of... 

The basic circuit for the determination of an unknown impedance is the bridge network (Fig. 20) named after Wien and Wheatstone [40, 41]. The AC signal is applied to two poles of the network and the AC potentials at points A and B are monitored by a detector. When equal potentials are detected the bridge is balanced and holds Z1/Z2 = Z Z. ... 

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