Passive Intermodulation in Finite Lengths of Printed Microstrip Lines

Characterisation of passive intermodulation in passive RF devices with X-parameters

“…The decaying periodic undulations of the reverse PIM3 level in Fig. 2(b) are also in full agreement with the qualitative analytical model of distributed PIM generation [6].…”

“…Thishas been realised with the following circuit parameters: L 0 = 0.3 nH, G = 3*10 -5 S, C 0 = 0.127 pF. The nonlinear capacitance C 2 = 2.11*10 -11 pF/V 2 has been retrieved from the experimental data reported in [6,7]. The equivalent circuit model of uniform NTL has been validated by simulations of the characteristic features of distributed PIM3 generation, such as a cumulative growth of the PIM3 level at the NTL output ("forward PIM") and periodic undulations of the PIM3 level at the input ("reversed PIM") with the line length.…”

Passive Intermodulation Due to Self-Heating in Printed Transmission Lines

“…From the closed-form expressions obtained, we observe that the third-order intermodulation distortion generation process might also be described, for a specific separation between tones, by a phenomenological model of a quadratic current-dependent distributed resistance of the form (27) Several authors have suggested the use of (27) to explain the relation between losses and intermodulation [16]. However, this phenomenological model is incorrect, and predicts a nonexistent third harmonic.…”

“…By substituting (12) into (15), we obtain (16) with . If we combine the telegrapher equations (17) which can be rewritten as (18) where refers to frequencies and with (19) and (20) We now substitute (16) in (18) to get (21) where the subscript refers to frequency . Equation (21) can be solved for the nonlinear current along the line (22) with (23) Equation (22) can be approximated to (24) Thus, if we assume , the power delivered to a matched load is (25) with (26)…”

“…The approach found in the -method [15] is a rigorous procedure to extract thermal material properties by measuring the third-harmonic generated by self-heating in metallic strips at audio frequencies. The existing nonlinear transmission line models [16] do not address these underlying mechanisms of passive intermodulation generation in printed transmission lines and are based strictly on phenomenological approaches. Only [17] and [18] analyze the thermal heating contribution to intermodulation in coaxial waveguides and transmission lines, respectively.…”