top of page

Power Integrity Unleashed: Navigating State-Space Average VRM Models for Robust Simulation Designs in Keysight ADS

Updated: 7 days ago

Power Supplies and voltage regulator modules (VRMs) are the unsung heroes of modern electronic systems. They provide stable and regulated voltage supplies to power-hungry components like CPUs, GPUs, and FPGAs. VRMs are commonly found on computer motherboards, graphics cards, and other high-performance devices. This blog will explore the fascinating world of VRM state-space average models (SSAMs) and how they are revolutionizing the field of power integrity.

The Challenge of End-to-end Power Integrity Simulation

In the world of power electronics, the focus is on the power supply, and the load is modeled as a simple resistor. In the world of power integrity, the focus is on the decoupling capacitors required for the digital load and the power supply is modeled as a simple resistor in series with an inductor. In the real world, neither assumption solves the problem of simulating the power delivery ecosystem with switching power supply control loops, gigabit switching digital loads, and a PCB network of filtering and decoupling components. The challenge is how to simulate the power integrity ecosystem and include the feedback loop and switching noise of a switch mode power supply (SMPS) without waiting days for the simulation results [1]. Traditional modeling approaches struggle to capture the dynamic behavior of these complex systems.

Introduction to State-Space Average Models for Efficient Power Supply Simulations

State-space average models offer an elegant solution. These models, first introduced in the 1970s, focus on the average behavior of switching power supplies. Here’s how they work:

  1. Switching Behavior Averaging: In a switching power supply, the voltage across the inductor and output capacitor varies due to the switching action. SSAMs take the average of the two states for the switches, effectively smoothing out the switching behavior. This allows us to focus on the small signal AC behavior of the control loop in the frequency domain.

  2. Fast Simulation: State-space average models enable rapid simulation without waiting days for results. By using control loop theory state-space equations, we create a behavioral model of the switch mode power supply (SMPS). This model includes the feedback loop and switching noise, making it suitable for stability assessment, noise ripple analysis, and power supply rejection ratio calculations.

  3. Dynamic Control Loop Behavior: The fidelity of SSAMs allows us to include the dynamic control loop behavior. Engineers can assess stability, phase margin, and other critical parameters without sacrificing simulation speed.

Insights Into the Sandler State-Space Average Model (SSAM)

One notable SSAM is the Sandler State-Space Average Model, developed by Steve Sandler. This model has been widely adopted in the industry. The Sandler State-Space Average Model (SSAM) uses control loop theory state space equations to create a behavioral model of an SMPS that allows for fast simulation. This SSAM, which was previously published [2], has the fidelity to include the dynamic control loop behavior for stability assessment, large signal and small signal noise ripple, and power supply rejection ratio. The model also works with the Non-Invasive Stability Measurement (NISM) method to assess the control loop phase margin from output impedance data.

It provides accurate predictions for VRM performance, including stability, noise, and other key metrics. The SSAM also works seamlessly with the Non-Invasive Stability Measurement method, allowing assessment of the control loop phase margin from simple output impedance data. The SSAM, with its ability to quickly simulate both small signal AC response and large signal switching noise, makes it ideal for optimizing the end-to-end power integrity ecosystem. A model that will even work with the latest challenges in designing high current, low voltage multi-phase power delivery networks for high-speed digital loads.

Readout of a VOUT - voltage ripple with DC load with PCB effects

Figure 1 - MPM3698 and MPM3699 - 2000Amp VRM and PDN Large Signal Output Voltage Ripple with 11 different output phases [4]

Diagram of a 2000 amp VRM and PDN VOUT vs load current with load line

Figure 2 - MPM3698 and MPM3699 - 2000Amp VRM and PDN Voltage Response with Load Line [4]

Diagram of a steady state voltage ripple with forced 91 kHz load current

Figure 3 - MPM3698 and MPM3699 - 2000Amp VRM and PDN Output Voltage Ripple with Forced Response [4]

Why a Sandler State-Space Average Model in Keysight ADS is the Better Solution

  • Ideal Vsource has the wrong output impedance

  • R-L model only models output impedance and not with good accuracy

  • RLC models only output impedance without information on switching noise, PSRR, stability, etc.

  • As shown in Figure 4, the State-space average model predicts performance over process variations.

  • The state-space Average Model does it all, and it is measure-based and verified for the application.

Table 1 -  Comparison of VRM models. The ideal voltage source does not work for higher frequency behavior, the L-R is not as good as the L-R-L-R model, and only the Sandler SSAM behavioral model provides all of the VRM 2-port behavior. [1]

VRM model comparison table

Higher fidelity SSAM for the VRM makes it easy to find component sensitivities, optimize their values, and assess tolerances to meet design margins

Figure 4 - Higher fidelity SSAM for the VRM makes it easy to find component sensitivities, optimize their values, and assess tolerances to meet design margins [1]

Other simulation tools, like HSPICE, only support small signal voltage regulator (VR) or VRM models, board (PCB) PDN, package PDN, and die models. Tools like SIMPLIS only support small signal VRM modeling and struggle with importing the PCB, package, and complex die models. In contrast, in Keysight ADS, all these components can be modeled together seamlessly to provide a true end-to-end power integrity simulation.

What can the Sandler State-Space Average Model be used to Simulate?

The Sandler State-Space Average VRM model (SSAM) can be used for both frequency and time domain analyses:

  • These models are designed to support true end-to-end power integrity simulation and modeling using Keysight ADS.

  • VRM models provide small signal load ripple and large signal VRM switching ripple.

  • Large signal analysis, including assessing large signal effects

  • Small signal analysis

  • Harmonic balance simulation

  • Transient analysis

  • AC analysis

  • Phase noise analysis

  • EMI Analysis

  • Monte Carlo or worst-case circuit analysis

  • Voltage ripple noise analysis

  • VRM and power supply efficiency modeling

  • Crosstalk analysis between power domains and sensitive circuits

  • PDN and impedance analysis

  • Stability analysis (NISM, Bode - phase, gain, and stability margins)

  • Input impedance, output impedance, startup, and transient step load response

  • VRM control loop design, stability, and modeling

  • Cascaded VRM and power supply analysis

  • Cascaded VRM modeling

  • DC drop analysis

  • Voltage droop analysis

  • Power Supply Rejection Ratio (PSRR) analysis

  • Rogue wave analysis

  • Target impedance analysis

  • Supports multiphase designs – including current sharing between phases

  • These models support both DCM and CCM modes in addition to the voltage mode and current mode.

  • If applicable, these models also support load-line features.

The Signal Edge Solutions State-Space Average VRM models (SSAM) use the Sandler SSAM, a pre-verified, pre-configured Keysight ADS model. Signal Edge Solutions provides SSAM from the leading power supply and VRM manufacturers, including Texas Instruments, Analog Devices, Monolithic Power Systems, Intersil, Microchip, Renesas, and others. These models are provided as an ADS DesignKit and can be added to your ADS workspace within a few mouse clicks. Our 4-Step Guide details how to add SES models to your ADS workspace.


The Sandler state-space average VRM models with Keysight ADS are revolutionizing the power integrity field by combining accuracy and efficiency while empowering engineers to create true end-to-end power integrity simulations. Customers can benefit from improved design and simulation capabilities by purchasing the models available in our store.

If you’d like more information about our models, to request a customer SSAM, or to receive training on using them, please visit our Contact Us page or e-mail us directly at

For a list of our currently available training options, reference our EMC, SI, and PI Unplugged: Bridging the Education Gap Between Theory and Practice article.

Visit here if you want to learn more about Keysight ADS learning and training resources.

If you want to learn more about the Sandler State-Space Average VRM models, there are multiple chapters cover this topic and other power integrity related topics in Steve Sandler's book "Power Integrity Using ADS.", which you can purchase from our store.

A "Power Integrity Using ADS", by Steve Sandler


  1. PAPER - DesignCon 2023 - VRM Modeling and Stability Analysis for the Power Integrity Engineer

  2. S.M. Sandler, The Inductive Nature of Voltage Control Loops, EDN, Feb 5, 2015,

  3. Power Integrity Using ADS | Signal Edge Solutions

  4. PAPER DesignCon 2024 - Design, Simulation, and Validation of a 2000-Amp Power Rail

  5. SLIDES DesignCon 2024 - Design, Simulation, and Validation of a 2000-Amp Power Rail

  6. State Space Average VRM Models | Signal Edge Solutions

  7. Who Put that Inductor in My Capacitor

  8. SLIDES - DesignCon 2023 - VRM Modeling and Stability Analysis for the Power Integrity Engineer


  10. PAPER DesignCon 2022 - Improved Methodology to Accurately Perform System Level Power Integrity Analysis including an ASIC Die

  11. SLIDES DesignCon 2022 - Improved Methodology to Accurately Perform System Level Power Integrity Analysis including an ASIC Die

  12. S. M. Sandler, “Measurement Based VRM Modeling,” IEEE SPI 2017

  13. S. M. Sandler, “Designing Power for Sensitive Circuits,” Eddison, 2017.

  14. S. Sandler, “How to Design for Power Integrity” Keysight sponsored YouTube Video Series:

  15. PathWave Advanced Design System (ADS) | Keysight

  16. Load-Line Design for a Multi-Phase Buck Converter | Article | MPS (

198 views0 comments


bottom of page