FOCUS MICROWAVES GROUP

Behavioral Modeling

Cardiff Model the intuitive advanced behavioral model

V05/18powered byCardiff Models
Non-linear measurement data has been exploited in various ways to create behavioral models for high frequency
components. Formulations of these models have been
defined in terms of traveling waves, with a desire to represent nonlinear behavior of high frequency transistors
through a direct extension from linear s-parameters.
The Mesuro model portfolio is comprised of two models- each targeted at a particular end use - Cardiff Model
Lite (CML), where the desired output is a local model, andCardiff Model+ (CM+), which incorporates higher ordermixing terms allowing a single model to fit over a rangeof impedance space.
The Cardiff Model+ formulation has a number of uniquebenefits over alternative approaches where formulations
are truncated. Once the formulation is extended, themodel moves away from a local model, where multiple
models are required to define an impedance space (i.eload lookup), to a model that has a set of coefficients that
describes the behavior of a device over an entire impedance space. This dramatically reduces file size and also
allows any interpolation to be defined by the model itself rather than relying upon the interpolation algorithm
in the simulator. Also, as harmonic superposition is notassumed in the CM+ formulation, a full harmonic mixing model is uncovered describing harmonic interactions
and improving model accuracy particularly for complex
modes of operation.
An example setup is shown below, the Mesuro phase reference and modeling framework is compatible with all
major VNA’s.

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measured b2

modelled b2Behavioral Models
Cardiff Model+ is a behavioral modeling strategy, based ona polynomial fit of the measurement data.

b2,1 = P1 ⋅ g  v1, 0 , a1,1 , v2, 0 , a2,1 , Q1 P1 • Generalized to an nth odd order in terms of the relative phasecomponent of the incident wave a (p,h) at harmonic h andport p.

P1 = ∠a1,1 =• The formulation is flexible in the number of coefficients andmixing terms allowing the best possible model fit for different
devices.

K p ,h ,m = g v1, 0 , a1,1 , v2, 0 , a2,1

• The formulation is scalable to include input and output harmonics and does not assume superposition ensuring modelaccuracy.

 m = + ( w+1) 2m
b p ,h = P ⋅  ∑ K p ,h ,m  Q1   P1  
 −( w−1)2 m=
(a1,1a1,1Q1 = ∠a2,1 =a2,1a2,1)

h1

Measurement strategy
For fundamental (F0) and harmonic (2F0 and 3F0) model generation, the load-F0 impedance is swept through a
pre-defined sweep plan; centred around the optimum for
power and efficiency performance.
• The model is generated directly from Load Pull data and no
special configuration is required.
• The model can capture fundamental and harmonic behavior at the source and/or load of the DUT. For an F0 modelgeneration the harmonic frequencies remain static, and need
to be swept in a nested fashion for harmonic model generation.
• Measurements of calibrated a and b waves and dc values
v1dc, v2dc, i1dc, i2dc are captured and stored in a file indexedby fundamental load impedance and input drive.
• Fundamental source-pull is not necessary, as the effectof source pull is captured by the model (in FDCS), however it
can aid in minimising the input return loss and thus provide
a facility for driving the DUT into compression.

Verification• Once the model is generated, the model coefficients can beused to model the data that filled the model.
• Error bars, time-domain waveforms and other plots are
displayed to check the accuracy of the model.
• This allows the user to save time by verifying the modeled
data before importing it into the CAD environment.

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3Result Comparison
As the aim of a behavioral model is to predict performanceover a defined set of operating conditions, the model fits
to measured data and the prediction of circuit is excellent.

Efficiency (%)

Simulated

Efficiency (%)

MeasuredPower (dBm)

Power (dBm)

EDA example using CM+
The Cardiff Model portfolio is fully supported in all major
EDS tools including AWR Microwave office and Keysight
Advanced Design System.

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info@focus-microwaves.com

These models are ideal for release to customers. They areaccurate and as they are black box no reverse engineeringof the underlying technology is possible.

+1 514 684 4554

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