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The Complex Art Of Handling S-Parameters

The importance of extraction and fitting to circuit simulation involving S-parameters.

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By Pradeep Thiagarajan and Youssef Abdelkader

IC design is transforming at an accelerated pace along with fabrication technology. The need to incorporate more functionality has led to denser dies, multi-die chips, stacked 3D ICs, and advanced packaging. Furthermore, the increasing demand for enhanced connectivity with more and faster access to data continues to drive technology towards higher data rates and increased functional capabilities. We now must deal with much more power and ground signals and their distribution. The same goes for clocks and other signals routes on die, between dies, on package, and on board. To boost performance in SoCs, frequencies continue to reach new heights for high-speed serial link and memory protocol standards, and so do CPU frequencies. Signal transmission and reflection needs to be well understood to properly design for signal integrity in various signal conduits. Furthermore, custom passive structures such as inductors, T-coils, capacitors, and resistors are being innovated in each technology progression in order to meet design challenges and specifications related to frequency synthesis, noise filtering, and bandwidth extension. S-Parameters (Scattering Parameters) play a crucial part in IC design, and in this article, we focus on their importance for accurate design considerations.

What are S-parameters?

Signals operating in the radio frequency (RF) realm between 3 kHz to 300 GHz are an inherent part of processing by circuit components within and outside an IC. Linear characteristics of RF circuits can be well represented by S-parameters, by which important characteristics such as impedance, gain, loss, and voltage standing wave ratio (VSWR) can be calculated. The term scattering implies how voltages and currents in a transmission line are affected due to a discontinuity of an inserted network into it. As shown in figure 1, the two-dimensional S-matrix for an electrical component is a frequency specific data that provides a relationship between the incident, reflected, and transmitted waves at each port over a range of frequencies. It provides an amplitude-phase feel in frequency domain rather than transient voltages and currents.

Fig. 1: S-parameter fundamentals.

S-parameters describe linear time-invariant (LTI) systems in frequency domain. By linear, we mean commutative, associative, and distributive mechanisms that do not include clipping or mixing and only involves amplitude and delay variations. Time invariant means a certain input will give the same output regardless of when the input was applied to the system wherein Y(n)=H(x(n)) is equivalent to Y(n-t)=H(x(n-t)). LTI systems further imply causality and passivity of a bounded input to a bounded output system. Causality means that an output is a reaction to present and past events but not future input, where a model only responds after being excited. Passivity is a measure for stability and a passive system does not generate energy across all frequencies.

There are many benefits of S-parameters. For starters, they can be easily converted to Y, Z, H, or T parameters for a circuit analysis. And then, S-parameters are more reliable. While S-parameters require matched loads, the other listed types require open and short circuit terminations that are difficult to maintain at RF frequencies. Furthermore, the portability of S-parameters with standard file formats such as Touchstone and Citi enables compatibility with most simulators. S-parameter files can be easily included in a testbench with other circuit blocks with appropriate connectivity to simulate that cross section with necessary stimuli.

Industry EM field solvers can generate S-parameters. In the lab, Vector Network Analyzers (VNAs) can be used to measure them. Since S-parameters change with frequency, the frequency specification is a necessity in addition to characteristic impedance. In essence, they should be viewed as a black box abstraction of the electrical system (simple or complicated) with frequency characterized parameters for input-output port relationships.

S-parameters are mostly used to model passive systems such as inductors, capacitors, T-lines, cables, packages, bond wires, microwave distributed circuits, etc. LC VCO designers specifically indulge in experimenting various inductor architecture types modeled with S-parameters for easy inclusion into VCO analysis before attempting physical layout. S-parameters are also used to model high-speed digital interconnects and channels including PCB traces, vias, connectors, and packages to characterize the effects of impedance mismatches, reflections, losses, dispersion, and crosstalk. SerDes designers also put them to heavy use in early design stages for formulating budgets for power, gain, and noise where it is crucial to know frequency-induced effects and impedance mismatch effects. Low noise amplifier (LNA) designers find the S-parameter value to design input and output matching systems to optimize the tradeoff between gain uplift and noise figure minimization.

There are different types of S-parameters. The most common is the small-signal S-parameters where signals have only small linear effects on the network where gain compression or other non-linear effects are not prevalent. This is the case for passive networks. Large signal S-parameters differ in that they will vary based on input signal strength. And then there are mixed mode S-parameters for analyzing the response of balanced circuits using common mode and differential stimulus signals. Signal integrity engineers are often required to compare mixed-mode SP against industry-standard measures. Pulsed S-parameters are another variant that represent the system before it heats up, mostly applicable to power devices.

Aspects of S-parameter handling

Extracting S-parameters

The more the frequency points, the better the accuracy of raw data, and this applies to low and high frequency areas, especially if the points are well placed to capture the model’s dynamic behavior across frequency. Not having a dc value (frequency=0) can be problematic where simulators will have it extrapolated with assumptions that can be prone to inaccuracies in low frequencies. Sometimes they could be manually overridden by the user; that may be discontinuous to data trajectory on low frequency, or badly extracted by extractor (such as having an imaginary part).

For higher frequencies, it is best to extract up to at least the fifth harmonic, or one decade higher than the fundamental frequency. Choosing adaptive sampling in extractor settings is the best option where the EM solver would inject frequency points around the regions of high activity such as resonances. Logarithmic sampling with typically 100 points/dec has proven to be sufficient across the board.

For a well-behaved S-parameter model, the real parts must undergo zero slope at DC, i.e., the real parts have the characteristics of an even function. Contrarily, the imaginary parts must have a zero value at DC but can have a non-zero slope, i.e., the imaginary parts have the characteristics of an odd function.

Fitting

Fitting is a common term in the S-parameter world. Discrete raw data in frequency domain needs to be fitted to get a continuous representation across frequency, and in return, facilitates time domain simulations. S-parameters generated from industry field solvers will need to be “fitted” by the simulator with rational functions like Laplace transfer functions to create an equivalent circuit representation of the black box that needs to work at any frequency. This is used for calculating equivalent pole-residue representations.

However, the rational function created in the process can be non-passive, i.e., it creates energy (like unintended extreme voltage or current spikes at nodes) and won’t converge. Conversion to passive nature is required; however, it can cause damage to the model and hence loss of accuracy. Consequently, the need for an efficient passivation algorithm arises, one that can guarantee a passive behavior up to infinity while causing minimum perturbations to the vector fitted data. Non-passive data will impose complications on time domain analysis and will eventually lead to “time step too small” issues.

Vector fitting also aids in enforcing causality and creating reduced order models. Fitted data is causal by construct. Non-causality can arise from sparse data samples, noisy measurements, stitching files together, or inaccuracies on the EM solver side, even if the system is causal. A causal system, when analyzed on a polar plot, will follow a clockwise trajectory which is a property of real physical systems where only a positive delay can be induced.

Fig. 2: Causality illustration.

Rational function model

Alternatively, the fitting process can be avoided if the EM extractor has the ability to create a rational function model (RFM) that the simulator can directly use without doing any sort of fit, essentially taking all of the guessing out of the equation. This paves the way for an equivalent baseline among different circuit simulators. RFMs are passive and causal by construct. The poles and residues for each port pair are already pre-calculated, so no fitting or passivity enforcement is required, saving prep time for simulations.

Analog FastSPICE platform

Siemens EDA’s Analog FastSPICE platform (AFS) is a simulation technology that provides nm-accurate circuit simulation, mixed-signal simulation, and full-spectrum device noise analysis. AFS is foundry-certified by the world’s leading foundries delivering SPICE accuracy. AFS is a single executable platform that supports high capacity and functionality with high performance. It supports industry-standard netlist syntax and is seamlessly integrated into industry EDA design environments. The AFS RF engine supports Shooting Newton and Harmonic Balance analyses with recent innovations. For silicon-accurate characterization, the AFS platform includes a comprehensive full-spectrum device noise analysis and integrates with Solido Variation Designer to deliver full variation-aware design coverage in orders-of-magnitude fewer simulations, but with the accuracy of brute force techniques.

Analog FastSPICE eXTreme (AFS XT) technology further enhances performance for large post-layout netlists. There is no additional cost to existing and new customers. AFS XT can handle over 300 million element transient capacity and delivers fast mixed-signal simulation with Symphony Mixed-Signal platform.

S-parameter investments into AFS

Recent investments by Siemens EDA into S-parameter handling for enhanced useability and performance is showcased in figure 3 below.

Fig. 3: S-Parameter focus areas in AFS.

RFM support: Provides the ability to read an RFM model and use as an alternative to touchstone, citi, or spectre format S-parameter files.

Passivity enforcement: AFS now incorporates a new method for a modified vector fit as well as a new passivity enforcement technique. The result is high accuracy with guaranteed passivity at any frequency using a novel DC weighted enforcement scheme to maintain high DC precision.

Backend optimization: Applies to converting rational function to circuit elements using proprietary devices for better convergence and memory footprint.

Causality checks: Applies to detecting causality for band limited data based on heuristics. When the designer is notified about data being non-causal, it can help them re-extract the S-parameters with more accuracy.

Delay line handling: Applies to electrical delay lines that have a high order I/O transfer function that need a complex fitting process where AFS now operates in a sweet spot on the accuracy-performance tradeoff continuum.

Touchstone 2 support: Applies for single-ended network parameter data, an extension of Touchstone 1.

Mixed mode support: Extends S-parameter analysis capabilities to calculate differential and common mode S-parameters.

Nport compression: Applies for shorted ports, open ports, and ports with pure resistors that match the model’s characteristic impedance. These are implemented in a way with focus on S-parameter accuracy, improved fitting performance, reduced backend element conversion overhead and avoids DC leakage from dangling ports.

Performance: Applies to speed up on fitting algorithms.

The passivity aspect of AFS is illustrated in figure 4 below. AFS iteratively perturbs the data in order to enforce passivity across the whole frequency spectrum in compliance with the original band limited data. The end goal would be, at any given point in frequency, the passivity norm should be <=1 as highlighted below.

Fig. 4: Passivity illustration.

Figure 5 below illustrates the importance of a well-fitted S-parameter model as well as the direct RFM alternative. A 24.5GHz VCO with a multi-port S-parameter for the inductor was simulated for four scenarios: 1) RFM model with AFS; 2) Well extracted S-parameter model with AFS fitting; 3) Well extracted S-parameter model with bad fitting; and 4) Poorly extracted S-parameter model. Scenarios 1 and 2 yield matching and highly accurate results, unlike scenarios 3 and 4. The large discrepancy in scenario 4 is an inevitable side effect to extracting models without DC, and/or without low or high frequency data, and/or sparse datapoints in frequency bands of interest.

Fig. 5: Example of high frequency clock with varying extraction quality, fitting, and RFM alternative.

Figure 6 below illustrates a sample of AFS fitting speedup over the past year across many S-parameter models of varying port sizes and frequency band complexity.

Fig. 6: AFS fitting performance.

Furthermore, as S-parameter usage becomes more and more complex in IC development, technical support for guidance on proper S-parameter handling as well as debug for anomalies becomes equally important, and Siemens EDA is committed to prompt support.

Summary

For circuit simulation involving S-parameter files, choose your simulation engine wisely, since its expected frequency behavior cannot be compromised. Siemens EDA’s Analog FastSPICE platform (AFS) provides nm-accurate circuit simulation, mixed-signal simulation, and full-spectrum device noise analysis and is foundry-certified by the world’s leading foundries delivering SPICE accuracy. Take advantage of the latest AFS offering that provides S-parameter handling performance and accuracy along with the many features it supports including RFM support, enhanced fitting, backend optimization, mixed mode support, delay handling, causality checks, and N-port compression. Furthermore, you will benefit from the multi-threaded capability AFS offers for additional speedup for designs needing extensive sweeps, corners, and statistical analysis.

References

[1] https://eda.sw.siemens.com/en-US/ic/analog-fastspice/



1 comments

Raj Raghuram says:

Thanks for the excellent article. Though it has its own problems, convolution may be a better solution in some cases. Increasingly, we see a large number of ports and sometimes only a few of the elements are critical or needed. Fitting in itself can take a long time while convolution can avoid the fitting overhead

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