Differentiators with Integrated Filters

The next step is to obtain practical differentiators, which involves combining differentiators with filter modules. The latter can be arranged in series or even integrated in the differentiator itself. 

For most practical purposes, these differentiators have too much high-frequency noise in their output - after all, a differentiator is nothing more than a high-pass filter - and therefore the circuit must be modified. One improvement is the addition of a resistor in front of the capacitor (cf.. Fig. 3-14 and Fig. 3-35). The upper cut-off frequency of this differentiator is 

A further step in this direction is to place a capacitor parallel to the resistor R2 (Fig. 3-36). If this differentiator is combined with a low-pass filter and an impedance converter, we have an effective network (Fig. 3-37) with which higher-order derivative devices can also be constructed. 

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A completely wetted filter membrane provides a liquid layer across which, when a differential pressure is applied, the diffusive airflow occurs in accordance with Fick s law of diffusion (Fig. 8). This pressure is called test pressure and commonly specified at 80% of the bubble point pressure. In an experimental elucidation of the factors involved in the process, Reti simplified the integrated form of Fick s law to read as follows ... 

Four different methods used for integrated-path remote gas sensing are discussed here. One of these (tunable diode laser absorption spectroscopy, TOLAS) uses a narrow linewidth source of radiation (usually a laser diode) and the other three methods use broadband sources of radiation. These three analyze the spectrum of the radiation after it has traversed the atmospheric path in different ways both differential optical absorption spectroscopy (DOAS) and Fourier transform infrared (FTIR) spectroscopy analyze the entire spectrum over the spectral region of interest, whilst absorption correlation methods record the spectrum after it has been filtered optically with either an optical filter or a sample of the target gas itself. These four methods use an active source of radiation. It is also possible to carry out integrated-path remote gas sensing using a passive source. 

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