F.M. Colebrook

Bio: F.M. Colebrook is an academic researcher from National Physical Laboratory. The author has contributed to research in topics: Square (algebra) & Sensitivity (control systems). The author has an hindex of 2, co-authored 2 publications receiving 4 citations.

The application of transmission-line theory to closed aerials

Abstract: The paper contains an analysis of the behaviour of frame aerials consisting of a single turn of conductor. It is assumed that the behaviour of such systems, including the mutual interactions of the various elements, can, to a useful degree of approximation, be represented by the differential equations of classical transmission-line theory. Formulae are obtained for the effective induced e. m. f. and the effective impedance (at the tuning point) of frame aerials the dimensions of which are not small compared with the wavelength, both for symmetrical and asymmetrical systems of tuning. It is found that in the case of symmetrically tuned systems the output voltages across the two equal halves of the tuning impedance will not in general be quite equal.It is shown that the “resonance factor” of a frame aerial (i.e. the ratio of output voltage to induced e. m. f.) can be determined by the usual method of reactance-variation at a constant frequency, in spite of the non-uniformity of the current distribution along the length of the conductor, but that the same process carried out by variation of frequency will not, in general, be valid.It is shown that for a given total length of conductor the optimum shape of a rectangular frame aerial, with respect to induced e. m. f., is square. In particular, a square frame with side equal to half a wavelength appears, to have useful practical characteristics in respect of sensitivity and symmetry, both for field-strength measurement and direction-finding.The method of applying the formulae to circular loops by a process of integration is given and illustrated by particular cases. It is found that in the case of small closed aerials the magnitude of the induced e. m. f. is not very sensitive to shape.

An experimental and analytical investigation of earthed receiving aerials

Abstract: The paper is concerned with the behaviour of earthed open- aerial receiving systems. The analysis of such systems is based on the classical transmission-line equations, as modified by Moullin to apply to distributed excitation.Part 1 gives the theoretical formulae so obtained for the case of a plain aerial with uniformly distributed constants, and the detail of the variation with frequency of the resistance and reactance components of the effective impedance of such an aerial.It is shown that successive resonances (i.e. conditions of zero reactance) are given by an equation of the formλ=(4h/n)(1+Ah2)where n is any integer and A is a small factor depending on n and on the attenuation constant of the aerial considered as a transmission line. The corresponding values of the resistance are shown to be Rh/2 (approximately) when n is odd, and a very high value when n is even, R being the total effective resistance per unit length of the aerial.The actual variation of the impedance of a plain uniform aerial as a function of frequency was determined experimentally, and a detailed analysis of the results in relation to the theory is given.The observed variations of resistance and reactance are shown to be in substantial agreement with those deduced from the analysis, but it appears that the actual length of the aerial (h) must be replaced by an effective length h+ e, e being about 5 per cent of h. This is in agreement with a more rigid analysis by Abraham, and with experimental results obtained by Wilmotte. The observed aerial resistance was found to be mainly due to parasitic eddy-current and dielectric losses. It was reduced to less than one-third of its value by using a single-wire “earth screen.”The validity of the fundamental assumptions, to a useful degree of approximation, having been established by measurement, Part 2 of the paper is devoted to obtaining additional information by purely analytical methods. The analysis is mainly based on the case of a plain aerial divided into three parts in each of which a uniformly distributed e.m.f. is assumed to be induced, the intensities being different in the three parts.By an analytical manipulation of this three-part case a line integral formula is found for the effective e.m.f. induced in a uniform aerial by a non-uniform field (Section 7). The variation of the effective e.m.f. induced by a uniform field is considered as a function of frequency and aerial height, and it is shown that no advantage is gained by making h>λ/4 unless certain parts of the aerial are compressed (Section 8).The relative effectiveness of different parts of a receiving aerial is considered in Section (9), and it is found that in an L aerial short compared with the wavelength the addition of a down-lead from the open end nearly to the ground may actually increase the total effective e.m.f. in spite of the reversed e.m.f. induced in the added length.An earthed aerial of this shape with the vertical members of length λ/4 and the horizontal member of length λ/2 is shown to have a figure-of-eight polar diagram with a law of the form cos(½12πcosΘ (Section 10).The effective e.m.f. formulae of the three-element case are applied to the Franklin suppressed half-wave construction and afford means of allowing for the effect of aerial resistance in this system (Section 11).In Section (12) the effective e.m.f. of the present formulation is related to the original conception of “effective height.” It is suggested that the idea of “effective height” is one which has to a great extent outlived its usefulness.The analysis of a receiving aerial considered as a collector of energy from the incident wave is given in Section (13). The figure of merit from this point of view is |e6|2/Re, which is determined as a function of h and λ. It reaches a maximum when h is very approximately λ/4, and thereafter oscillates with rapidly diminishing amplitude. Considered as a collector of energy the suppressed half-wave construction will not apparently give an increase in useful power proportional to the increase in height, owing to the corresponding increase in Re.Current and potential distributions in receiving and transmitting aerials are discussed in Section (14). It is shown that they depend on the distribution of the exciting field, and that the current distribution in a receiving aerial may be totally different from that in a transmitting aerial of the same height. Current nodes in a receiving aerial may be any distance apart from 0 to λ, and are not necessarily separated by half a wavelength as in a transmitting aerial with a point source of excitation

Analysis and Calibration of Loop Probes for use in Measuring Interference Fields

Abstract: : A small shielded loop antenna, to be used as a probe for indicating and measuring radiofrequency interference fields from electronic equipment, has been analyzed. The input impedance is similar to an equivalent shorted two wire, balanced, transmission line. Voltage induced by a field conforms, over the usable frequency range, to that calculated by equations applicable at low frequencies, but the output voltage varies because of the transmission line effect. A number of loop probe designs have been analyzed and found to have undesirable characteristic impedance discontinuities which make calculation of their characteristics almost impossible. A method of calibration, which uses another small shielded loop to establish a radiofrequency field of known characteristics, has been developed, and its accuracy and reliability are proved experimentally. A simplified loop probe design has been found to be the most satisfactory. Loop probes of the approximate dimensions of those analyzed have been shown to be usable for the desired application at frequencies below approximately 400 Mc only, both because of unsatisfactory response characteristics and because of difficulties of calibration at higher frequencies.

An investigation of polarization errors in an H-Adcock direction-finder

Abstract: The polarization-error characteristics of H-type Adcock direction- finders operating in the v.h.f. band and in the upper part of the h.f. band are controlled to a large extent by resonance phenomena. A theoretical and experimental investigation of a rotating system for very high frequencies has demonstrated the feasibility of calculating, from the physical dimensions of the aerial system, the frequencies at which large errors are liable to occur, and also the magnitudes of the maximum errors. The lowest resonant frequency is that for which the product of aerial length and spacing is one-twentieth of a square wavelength. A second resonance occurs when the spacing is half the wavelength and, if the aerial length is approximately equal to the spacing, the third resonance occurs when the spacing is 0.8 times the wavelength.Three major causes of polarization errors are discussed and formulae are given for calculating these errors. The agreement between the calculated and measured errors at the resonant frequencies suggests that the three causes discussed account for nearly all the errors. Various methods of minimizing errors are examined theoretically and experimentally.Although the instrument used for the experimental investigation was designed for very high frequencies, the results have application to a wider band of frequencies and to instruments of both fixed and rotating types.

A review of frictional pressure drop characteristics of single phase microchannels having different shapes of cross sections

Abstract: Abstract This paper theoretically studied pressure drop variation in microchannels having different cross sections (circular, rectangular, square, trapezoidal, triangular, elliptical, parallel plate, co-centric circles, hexagonal, wavy, smoothed or rounded corners cross sections, and rhombus) for single phase Newtonian fluid (gas and liquid) flow. Based on 41 years (approximately) prior literature (1981–till now), 249 articles were studied and number of correlations of pressure drop calculation in microchannels with or without friction factor equation for four cross sections i.e., rectangular, square, circular, trapezoidal, wavy and triangular is collected and also mentioned their limitations at one place. Other than these four cross sections, there is very few experimental/numerical works was present in the literature. A comparable study was performed for laminar as well as turbulent friction factor to calculate the pressure drop with the help of classical theory for gas and liquid flow in microchannels with circular and rectangular cross sections. Results show wonderful outcomes i.e., correlations of laminar pressure drop study can be extendable for transition and turbulent regime in both types (circular and rectangular) of cross sections of microchannels. In different types of flow regime, it is suggested that for each type of cross section (circular and rectangular) we can go for single correlation for gas/liquid system. It is also investigated that the macro channels pressure drop equations can be used for microchannels up to the certain values of Reynolds number. Basically, this paper provides all possible equations of friction factor related to the microchannels that helps to calculate the pressure drop, is collected at one platform also compared their deviation with conventional channels.

Current distributions in short-circuited rectangular loops

Abstract: The current distribution in each arm of a short-circuited rectangular loop placed in a uniform electric field parallel to one side of the loop is evaluated. The effect of switches which bisect the loop and thus modulate the current distribution is analysed, and it is concluded that this forms a useful method, at any given frequency, of measuring magnetic fields in the far zone, irrespective of the ratio of adjacent sides of the loop. The backscattering cross-section of a resonant square short-circuited loop is also evaluated.