Noise compliant macromodel synthesis for RF and Mixed-Signal applications

Abstract

This paper proposes a compact synthesis approach for reduced-order behavioral macromodels of linear circuit blocks for RF and Mixed-Signal design. The proposed approach revitalizes the classical synthesis of lumped linear and timeinvariant multiport networks by reactance extraction, which is here exploited to obtain reduced-order equivalent SPICE netlists that can be used in any type of system-level simulations, including transient and noise analysis. The effectiveness of proposed approach is demonstrated on a real design application.

Thermal Noise Compliant Synthesis of Linear Lumped Macromodels

“…Such a realization enables purely reciprocal synthesis by both resistance and reactance extraction, even addressing additional constraints such as minimality in the number of reactive or resistive elements. It is however unfortunate that all these purely reciprocal techniques require extensive use of ideal transformer networks (or multport transformers), whose size is essentially dictated by the model order n. As a consequence, the number of equivalent elementary (scalar) components that are produced in the synthesis scales as O(n 2 ), as shown in [21]. We can regard this fact as a consequence that internally passive and reciprocal state-space realizations are generally characterized by full matrices.…”

“…We therefore see that any of the classical synthesis methods [17] such as Youla's reactance extraction [18] or Darlington and Belevitch synthesis [19], [20] will do, although these approaches have never been applied for behavioral macromodel synthesis. Two exceptions are [21], where a first attempt based on reactance extraction was documented, and [22], which provides an alternative approach based on classical spectral factorization. These earlier methods do not specifically address the sparsity and the efficiency of the resulting circuit when solved numerically.…”

“…The main contribution of this work is a noise-compliant synthesis process that builds on Darlington's and Belevitch's idea of resistance extraction [12], [17], [20], and differently from [21], produces a sparse equivalent circuit whose complexity scales only linearly with the number of macromodel states n. As a result, the macromodel netlist can be seamlessly used in any type of circuit analysis such as AC, DC, TRAN (Transient), PSS (Periodic Steady State), HB (Harmonic Balance), and for all kinds of noise analysis with high efficiency. Moreover, differently from [22], the proposed method produces a netlist of basic circuit elements, that is compatible with any circuit solver.…”

Sparse noise-compliant synthesis of scattering macromodels via resistance extraction

“…Comparing the proposed synthesis with a direct realization of H(s) via capacitors and dependent sources [1], [4], we gain noise compliance at the price of a slightly increased circuit complexity. In fact, the resistance extraction process forces us to synthesize the lossless subsystem H L (s), which has additional ρ internal ports, which in the worst case can reach ρ = p. The leading complexity scales however only linearly with the number of states n for both approaches, which is a significant advancement with respect to the reactance extraction approach of [14], for which complexity is O(n 2 ).…”

“…We show that, even if such resistors are "artificial" components, the resulting noise analysis performed by SPICE will be correct. With respect to earlier noisecompliant synthesis approaches [14], the proposed technique exploits sparsity to reduce netlist complexity, which scales only linearly with the number of macromodel states. Moreover, there is no need of an explicit additional noise companion synthesis as in [15].…”