Simulations have hundreds of stability analysis techniques to choose from, most focused on one issue and some difficult to apply. A classic method is the Rollett stability factor, or K-factor, which produces valid results for a known-stable network when ideally terminated. Its two-port linear network assumptions degrade at higher frequencies with complex modulation. Tone-based (harmonic balance) frequency domain simulations might falsely converge for some frequencies, leaving instability undetected.

Figure 4

Figure 4 WS-Probes inserted in a simple feedback amplifier circuit.

A broader technique is the Normalized Determinant Function (NDF), which also requires a known-stable network. For normalization, NDF needs access to every source in the network. It creates a passive network by setting all active sources to constant “off” values—removing them from the response. Estimating the off values can be error prone, and black-box models can prevent source access entirely. Large transistor networks make for huge matrices and lengthy simulations. Required frequency sweeps beyond operating ranges add more time and complexity.

Non-invasive impedance probes hold more promise. The S-Probe uses ideal sources for “in-situ” bidirectional S-parameter computation but struggles with feedback around the probe, losing accuracy. Since feedback factors into stability, the S-Probe by itself is ineffective for stability analysis. The WS-Probe (also known as the Winslow Probe, for its inventor Dr. Thomas Winslow) builds on the S-Probe, providing accurate results in the presence of feedback.

WS-Probes enable comprehensive stability analysis techniques. Output processing can generate an admittance matrix for high impedance termination conditions, like NDF. K-factor can also be derived. Figure 4 shows WS-Probes in a simple amplifier-feedback configuration and Figure 5 simulates its loop gain in manual test benches versus WS-Probes—producing exact matches.

Figure 5

Figure 5 Osctest, Middlebrook, Hurst and Tian Bilateral loop gain, comparing test benches with WS-Probe simulations.

One simulation in Figure 5 with the WS-Probe covers the same metrics as 16 different manual test bench simulations. Coverage grows larger with circuit complexity. Figure 6 shows more metrics including Bode’s Return Difference (internal), NDF (external), Driving Point Admittance and Ohtomo loop gain, again with exact matches between manual test benches and WS-Probe results.

Figure 6

Figure 6 Return Difference, NDF, Driving Point Admittance and Ohtomo loop gain, comparing test benches with WS-Probe simulations.

There are two other benefits from simulating with WS-Probes. They can aid in a virtual load-pull, examining load-dependent stability by extending results from Driving Point Admittance with Kurokawa stability criteria. They also apply equally well in both small signal and large signal analysis, avoiding staging difficulties inherent with large signals.

The upshot for densification is more powerful EM-circuit excitation techniques via simulation at the point of design and layout. Using nodal voltages and currents to stimulate an EM structure, circuit plus physical layout attributes, produces a visualization of current density and radiation patterns. Instabilities move around the structure as frequencies vary. Figure 7 shows a simple amplifier structure at three different frequencies, highlighting a bias feedback problem and a ground plane feedback problem.

Figure 7

Figure 7 EM simulation of an amplifier in PathWave RFPro, showing instability locations at several frequencies.

These coupling problems would be near impossible to spot in the lab but are laid open at simulation with non-invasive probes and “in-situ” analysis. Straight-forward layout changes (pushing bias lines apart and adding vias to the ground plane) improve stability across the frequency range. Extend this example to more complex circuits and larger dense structures, and the power of an RF EDA workflow merging design, layout and simulation is evident. Next is a look at this workflow in more detail.


In complex RF systems, frequencies and integration density are rising, and 3D multi-technology assembly is everywhere. Parasitic effects from packaging, physical routing and interconnects and interactions between components degrade system performance. Some symptoms are frequency shifts, resonances, instability, mismatches, power losses and poor isolation from interference. Design integrity faces major risks; an uncaught mistake costs a hardware re-spin, a design win is undone or a market window is missed.

Circuit simulation is familiar territory for most EDA users, it is unthinkable not to take advantage of it. Toss in EM structures and effects, and accurate simulation gets more challenging. As previously shown, there are now innovative and effective EM simulation techniques for densification problems. The question becomes how to fit these techniques into RF design workflows.

One reason teams may be treading carefully is that there are different, disjointed EDA tools for different jobs in the workflow. Becoming proficient with each tool requires a learning curve, and once a tool is in a workflow it is tough to part with it even if it lacks some features. On the plus side, circuit design capture, circuit simulation and physical layout tools have already merged. Most package assembly and EM simulation tools, however, still add extra steps, especially if bad results send teams back to the drawing board.

Those extra steps can chew up weeks at a time. The right side of Figure 8 shows data from 10 years of EDA user interviews. It is the process to get a circuit design into a format ready for EM simulation in a third party tool. Some steps are manual, some scripted. Excess components and structures are stripped, EM simulations extract S-parameters and those are then meticulously reconnected back to the original circuit nodes. In every step, especially the first and last ones, there is a chance for an oversight or error.

Figure 8

Figure 8 In-situ analysis using PathWave RFPro streamlines EM simulation workflow.

The left side of Figure 8 shows “in-situ” 3DEM analysis streamlined with PathWave RFPro. It starts with the original circuit file, extracts and reconnects S-parameters, inserts non-invasive probing automatically and jumps to EM-circuit co-simulation within minutes. Because RFPro reads data through an OpenAccess API, it integrates with Keysight EDA platforms or in a mixed-vendor EDA workflow.

One RFPro customer was able to run only three or four EM simulation runs per week using a third party tool—that customer is now able to do 30. It is more than a productivity improvement, however. Bringing EM-circuit co-simulation into an EDA workflow moves simulation from a limited-use verification sign-off tool to an iterative problem-solving tool at the point of design. Analyzing EM effects becomes routine, like analyzing circuit functionality, and fixes can happen on the spot. Teams can efficiently develop predictable designs with critical EM effects fully assessed before hardware prototyping or deployment. Confidence in design integrity goes up, surprises go down.

These changes point to bigger possibilities in the future for the RF design ecosystem. Vendors design parts, those parts integrate into equipment manufacturer modules and boards, and those fit into larger end-customer systems. Vendor design wins rely on designers at the next level correctly stringing together pieces from different vendors. Aligning data from printed data sheets may produce a fit or it may not.

System-level EM simulation with transportable data and models in simulatable datasheets is the next frontier. Simulatable datasheets for parts will drop into system-level models for virtual performance evaluation. Knowledge about how a part works in an application will flow easily from vendor to customers to customers-of-customers, and back. Teams will not spend time sorting out specifications, but instead will focus on anticipating deployment scenarios at the point of design to achieve design wins.


Densification drives stress for teams, designs and processes and it drives opportunity. EM analysis at the point of the design means that when teams find something, they can do something about it. Three areas were discussed:

1. Information density shows up in far more complex waveforms. Systems demand modulated signals, and so should RF design teams. Seeing, understanding and preserving signal details must be part of the RF design workflow, not an afterthought in verification. RF EDA and measurement science are strongly connected.

2. Physical density, including 3D multi-technology assembly, is spawning more interactions between domains. Interference, crosstalk and parasitic effects can no longer be estimates. Packaging details must be known early. Resonance, thermal and stability concerns need full attention. Finding an issue in hardware is too late and adding EM simulation to workflows is urgent.

3. Shift left will be a competitive advantage. Design in context, in a workflow providing time savings and virtual accuracy using modulated signals and in-situ EM analysis, leads to design wins. If others find issues first, business may be lost. Models and results need to be transportable, ready to connect with other design processes, vendors, customers and environments.

Digital transformation is solving EM densification at the point of design. More versatile analysis engines, behavioral models, tools and IP help designers and their customers create and apply innovative designs in more applications with greater success.


  1. “Accelerate 5G Circuit Designs Using Digitally Modulated Signals,” Keysight, Web,
  2. “Designing for Stability in High Frequency Circuits,” Keysight, Web,
  3. “RFPro in ADS for EM-Circuit Co-Simulation,” Keysight, Web,