GENERAL PROPERTIES OF FREQUENCY-CONVERTING NETWORKS *)
S. Duinker · Research Repository (Delft University of Technology) · 1957
Summary Some general properties of frequency-converting networks (i.e., networks used for the purpose of modulation, mixing, detection, etc.) are analyzed. These networks generally contain nonlinear elements. After an introductory chapter, conditions are derived in chap. IJ for nonlinear two-pole and. coupling elements (sets of coupled coils, insulated conductors and conducting bodies) which satisfy the property of local passivity. The introduetion of nonlinear coupling elements is necessary since they are shown to be not generallyequivalent to combinations of two-pole elements and ideal transformers. After giving the mesh and nodal equations for a general nonlinear network, it is assumed that a certain high-level voltage and current distribution (the so-called' fundamental state) results from the presence of energy sources. In chap. rn, the first-order perturbational equations are derived that result if the fundamental state is subjected to a small disturbance. These linear differential equations, with timedependent coefficients which satisfy the reciprocity condition, define the so-called perturbational state. In, chap. IV, for a periodic fundamental state (fund. freq. p), the equations, describing the perturbational state that results from harmonic small-signal sources (freq. q), are represented in matrix form, after the introduetion of complex quantities in the trigonometrical expressions for the signal currents and voltages, and in the Fourier expressions for the periodic coefficients. These matrices generally contain an infinite number of elements owing to the occurrence of an infinite nuruber .of signal frequencies q + mp (m = ... , -1, 0, + 1, ~..). In chap. V, the effect on the matrix equations is investigated of the shifting of the time origin, of the interchanging of the role of the frequency q and a frequency generated by conversion, of 'a symmetric fundamental state and of the presence of linear impedances. Further, reasons are indicated which permit the matrix equations to be reduced to finite systems in practical cases. The problem of representing a conversion network by an equivalent circuit, by introducing the notions of fictitious meshes or terminal pairs that pertain to the various frequencies of a physical mesh and terminal pair, is considered in chap. VI. It is found that generally the equivalent circuit includes network elements that are not physically realizable and even may he active if the network contains nonlinear reactances. Based on this latter conclusion, an energy theorem for purely reactive conversion networks is derived in chap. VII. The possibility ofinstabilities (so-called Hardey effect), the conversion gain and loss, and the condition for the absence of reaction on the signal source are discussed. In chap. VIII, the simplification of the matrix equations is discussed for conversion networks that contain a balanced, configuration of elements of exclusively the same kind. The cases that are treated, viz., a magnetic, a dielectric and a diode modulator (Graetz), are special cases of the balanced poly-phase networks of which one example (the poly-phase magnetic modulator) is worked out in some detail.