Tensor Method of the Analysis of the Amplifier Intermediate Frequencies with the Double-Loop Bandpass Filter

The operation is dedicated to a tensor method of the analysis of an intermediate-frequency amplifier (IFA) of a superheterodyne radio receiver with a frequency-selective load by the way of the double-loop bandpass filter (DBF). The basic purposes of researches, spent for operation, are:

- conclusion of expression for a complex transmission factor (amplification) of voltage of the amplifier;

- deriving relations for IFA basic performances (build-up normalized АFC depending on a parameter value of link);

- estimation of IFA selective properties with DBF of a concrete sample of a communication engineering.

As against a classic method founded on usage of dual circuits, the problem delivered in operation is solved with the help of the tensor methodology with application of models, intrinsic to it. For an introduced key diagram, the primitive web, by the way populations disconnected among themselves of separate "spools" relevant to devices of the key scheme and a simplified "communication" web (of nodal pairs and circuits), taking into account junction and interaction of devices is made. For calculation the nodal method of the analysis is selected, which one guesses a solution of a tensor equation of Ohm's law by the way:

, (1)

where the tensors of conductance and current are known magnitudes, and the components of a stress tensor are necessary for finding.

The solution is yielded according to the dual theorem of Теvenin in the terms of an entering current at security of an idling on an exit of the scheme. With the help of a set of equations, the combining values of voltages in primitive and communication webs, are defined devices of an inverse transposed tensor of transformation. At usage of the known formulas of transformation are retrieved a tensor of conductances and vector of affixed currents in a communication web , .

The solution of a tensor equation of Ohm's law for a current in the communication model is manufactured. Thus with the help of the formulas of reduction, the gear studs are eliminated and the expression for a IFA transmission factor on voltage is obtained:

. (2)

After substitution of devices of the reduced tensor of conductances in expression (2), the formula for a complex transmitting voltage response IFA with DBF completely conterminous with classic is obtained, that confirm realizability of a tendered tensor method of the IFA analysis

. (3)

For a functional test of a method are conducted analytical simulation in a medium Maple 8 and estimate(estimation) of IFA selectivity with DBF of the receiver of a radio set of a gamut МW and DМW, shown practically complete correspondence of calculated parameters to reference data. Thus, on the basis of the tensor methodology, the analysis of a IFA key diagram with DBF was conducted. The expressions for IFA basic parameters and performances are gated out, than the realizability of a tendered method of the analysis confirms. The process of a solution of a tensor equation of Ohm's law for a current at a selected nodal mode of calculation is reduced to shaping a tensor of conductances and holding his transformations, that allows us considerably to spare temporal and hardware operational lifes as contrasted to by classic method of the analysis. And the lowering of volumes of calculations and heightening of their effectiveness specially is obviously exhibited in accordance with magnification of complexity of the schemes. The reliability of obtained outcomes is confirmed by their precise concurrence to classic expressions for IFA with DBF and correspondence of character of associations to a well-known aspect, and also approximated equality of a leading particulars, obtained with their help, to reference data.