Logarithmic converter

The logarithmic converter is implemented with a voltage-to-current converter (OPAM, Ml, and Rs) and a pair of diode-connected, vertical pnp transistors (Qi and Q2). The relation between the differential output voltage (AVeb) and the sample resistance (Rs) is given by the equation  

In the case that Veb = Vs, the sensor signal readout of the logarithmic converter, Eq. (5.2) can be simplified to  

The negative sign is a consequence of the polarity of the differential output voltage Lowering the sensor resistance leads to an increased V s- Equation (5.3) will be used for further discussions of the sensor signal in the section on gas test measurements (Sect. 5.1.9). 

The dc level of the logarithmic converter can be changed with the reference current (/ref) or with the common-mode voltage (Fcm). The bulk-chip temperature sensor can be used to compensate for the temperature dependence of the logarithmic converter. The performance of the logarithmic converter is shown in Fig. 5.6. 

Five calibrated resistors (1% accuracy) with values of 1 kQ, 10 kQ, 100 kQ, 1MQ, and 10 MQ were connected to the input of the logarithmic converter (i.e., the input, to which the metal-oxide-covered electrodes are connected), and the output voltage (A Veb) of the logarithmic converter was measured. The common-mode voltage was 1V, the reference current was 0.1 pA, and the ambient temperature was kept at 25 °C. The offset voltage between the emitter-base voltages was less than 2 mV. The resistance values were estimated from the measurements at 2% resolution. 

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The first monolithic devices have been presented at the same time by a group at NIST and a group at the Physical Electronics Laboratory (PEL) of ETH Zurich [77-81]. The NIST chip hosts an array of microhotplates integrated with transistor switches and a readout amplifier for the sensitive layer. The device presented by PEL includes an analog temperature controller and a logarithmic converter for reading out the sensor values. This was the first monolithic realization of an embedded system architecture with integrated microhotplate. 

Fig. 5.6. Output voltage of the logarithmic converter as a frmction of the sample resistance...

There is another difficulty, however. Additive instrumental noise is also logarithmically converted by the operation. This in turn may affect the validity of the noise assumptions employed in developing certain deconvolution algorithms. When absorptions are very small, we may approximate... 

When the constants are combined and the natural logarithm converted to a common logarithm, the expression for the potential (in volts) at 25°C becomes... 

The antifungal activity and the hydrophobicity are expressed as logarithmically converted reciprocals of MICs (mM) for the fungus E. chevalieri and logarithmically converted retention times from the ODS-HPLC analysis (column, LiChrosorb RP-8 (4.6 i.d. x 250 mm) mobile phase, water-acetonitrile-acetic acid (70 30 1) and detection, at 270 nm) of the compounds, respectively. The symbols denote the compounds grouped into (A), (B), and (C) in Table 5 B, 3-[(a-alkoxy)-a-methoxy]methyl derivatives ((A), alkoxy n-propoxy, n-butoxy, n-pentyloxy, n-hexyloxy, and n-heptyloxy) , 3-[(a-alkoxy)-a-methyl-thio]methyl derivatives ((B), alkoxy n-propoxy and n-butoxy) and A, 3-(alkoxy )methy-lene derivatives ((C), n-propoxy and n-butoxy). 

The linear range of photometric detectors depends firstly on the presence of a logarithmic converter in order to obtain an electrical signal linear in absorbance. 

A very popular descriptor is logP, the logarithm of the partition coefficient, most commonly for the partition between 1-octanol and water (the logarithm converts the... 

In other words, the convolution operation (basically, an integration) in one domain becomes a (much simpler) multiplication in the Fourier domain. Thus, just as logarithms convert multiplication into addition [log(a b) = log(a) + log(b)] in the "log domain", convolu-tion converts integration into multiplication in the Fourier domain. 

The authors wish to thank Mr, A. Bissonnet and R. Ripon for the adaptation of the logarithmic converter and the construction of the electronic device for the specific gravity calculation. 

In double-beam operation the primary signals are amplified and fed directly into logarithmic converters. At the output, the referenee signal is substracted fix)m the sample signal, and the result is fed into an integrator. From there the signal pas.ses to a conventional chart recorder that records the ratio of the two beam signals. 

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