Worst-case model of spurious resonances appearing in radio-frequency cables and degrading electromagnetic compatibility characteristics of wireless equipment at out-of-band frequencies

A worst-case model of spurious resonances which can occur in electromagnetic system consisting of an antenna, cable and transmitter output filter (or receiver input filter) is proposed. These resonances may cause significant increase in power of spurious emissions for transmitting equipment and the decrease in out-of-band radiated susceptibility levels for receiving equipment. Three amplitude-frequency characteristics (AFCs) are the initial data for the model synthesis: AFC of the cable attenuation, AFC of the transmitter output port impedance (or AFC of the receiver input port impedance), and AFC of the antenna input impedance. It is assumed in the model that the cable length and phases of the impedances are unknown, therefore, at each frequency, the maximum possible increase in power of spurious emissions or the decrease in radiated susceptibility levels is estimated. Validation of the developed model is performed by numerical computation of an equivalent circuit containing a circuit-level model of the transmitter output filter, two-port network described by scattering matrix of the cable and one-port network characterized by the antenna input impedance. Measured AFC of the input impedance for antenna S65-8262-2, calculated AFC of the attenuation in radio-frequency cable RG58, and parameters of the transmitter output filter (pass band, attenuations in pass band and stop band, shape factor) are used as initial data for the validation. As a result of the numerical modeling, the influence of the cable is estimated: the AFC maximum for ratio of spurious emission power accepted by the antenna to the power of this emission accepted by the 50 ohm load is 7.7 dB; the AFC maximum for ratio of spurious emission powers accepted by the antenna using 2 m cable and without the cable is 29 dB. The validation demonstrates the worst-case behavior of the developed model.