Computation time is small due to simplicity 1st order frequency-independent loss modelling through resistive circuit elements, similar to what is shown in Figure 2.7 shown later in Section 2.2.1. This simplicity allows easier troubleshooting, and understanding the contribution of each part of the structure to the system dynamics Disadvantages: Not derived from distributed system, so we need confidence in its reliability, especially at high frequencies Only includes resonance points in the model (1st resonance point for Reeves’ model, up to 2nd resonance point for Murgatroyd’s model) Figure 2.1: Basic lumped model for two-conductor integrated passive – commonly used. Figure 2.2: Reeves’ for a two-conductor integrated passive, model from [14] Figure 2.3: Murgatroyd’s for a two-conductor integrated passive, model from [15] The simplest solution method for these models is to implement the model directly in SPICE, which supports all the circuit elements. A potential source of simulation problems is when a higher number of conductors are being modelled: the mutual inductive coupling between every conductor results in a high number of coupling terms needing to be simultaneously solved. This can cause convergence problems. An alternative solution method (for frequency domain) is to take the model into the s-domain, which allows one to obtain the algebraic solution of nodal analysis of the model, including the reactive components. This algebraic solution can be manipulated into an analytical expression for impedance in terms of frequency. This expression is then evaluated in Mathematica.As a case study, the impedance ZA-D is chosen as a point of comparison. The expressions for ZA-D for a load impedance ZL connected between B and C are shown in Equations 2.1 (Reeves) and2.2 (Murgatroyd): As ZL→∞ (i.e. an open-circuit load), we obtain Equations 2.3 and 2.4:
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