Behavioral Models

Behavioral modeling or black-box modeling does not require you to provide the specifications of all the physical systems in your model. The type of modeling depends on the input and output measurements of the component or systems.

In RF PCB Toolbox™ you can:

Perform the behavioral analysis on a PCB component by using the sparameters function with the Behavioral property set to true.
Convert a PCB component into a behavioral PCB element using the pcbElement object.

The components and shapes that support behavioral modeling are:

Bends	`bendRightAngle` `bendCurved` `bendMitered` Note The `sparameters` function does not support the behavioral model for objects with unequal widths such as `bendRightAngle`, `bendCurved`, and `bendMitered` objects.
Traces	`traceTee` `traceCross` Note The `sparameters` function does not support the behavioral model for Asymmetric tee- and cross-junction traces.
Transmission line objects	`microstripLine` `coplanarWaveguide`
Inductor	`spiralInductor`
Capacitor	`interdigitalCapacitor`
Splitter and Couplers	`couplerRatrace` `couplerBranchline` `wilkinsonSplitter` `wilkinsonSplitterWideband` `wilkinsonSplitterUnequal` `splitterTee`
Filters	`filterCoupledLine` `filterHairpin` `filterStepImpedanceLowPass` `filterStub`
Stubs	`stubRadialShunt`
Phase Shifter	`phaseShifter`
Vias	`viaSingleEnded`

Perform Behavioral Analysis of PCB Component

The main advantage of behavioral modeling as compared to full-wave electromagnetic (EM) modeling is that you can analyze the PCB component faster using behavioral modeling.

Consider an interdigital capacitor with default properties. Calculate the S-parameters of this component.

capacitor = interdigitalCapacitor;
tic
sparameters(capacitor,4e9)
toc

ans = 

  sparameters: S-parameters object

       NumPorts: 2
    Frequencies: 4.0000e+09
     Parameters: [2×2 double]
      Impedance: 50

  rfparam(obj,i,j) returns S-parameter Sij

Elapsed time is 176.844515 seconds.

The S-parameters function takes 176.9 seconds to run.

Now calculate the S-parameters of this capacitor with the Behavioral property in sparameters function set to true.

capacitor = interdigitalCapacitor;
tic
sparameters(capacitor,4e9,Behavioral=true)
toc

ans = 

  sparameters: S-parameters object

       NumPorts: 2
    Frequencies: 4.0000e+09
     Parameters: [2×2 double]
      Impedance: 50

  rfparam(obj,i,j) returns S-parameter Sij

Elapsed time is 0.295000 seconds.

The S-parameters function takes 0.30 seconds.

Convert PCB Component to Behavioral Circuit Element

You can convert a PCB component into a behavioral PCB element by using the pcbElement object, and then add this PCB element to an RF Toolbox™ circuit object. You can convert only PCB components that support behavioral analysis to behavioral PCB elements. For a complete list of objects and shapes that support behavioral analysis, see the introduction.

Create a RF Toolbox circuit object of two interdigital capacitors. Use the behavioral model in the first capacitor and the full-wave model in the second capacitor.

ckt = circuit;
c1 = interdigitalCapacitor;
c2 = interdigitalCapacitor('NumFingers',3);
p = pcbElement(c2,'Behavioral',false);
add(ckt,[1 2 0 0],c1) % default pcbElement created automatically
add(ckt,[2 3 0 0],p)
setports(ckt,[1 0],[3 0])
tic
S = sparameters(ckt,8e9)
toc

S = 

  sparameters: S-parameters object

       NumPorts: 2
    Frequencies: 8.0000e+09
     Parameters: [2×2 double]
      Impedance: 50

  rfparam(obj,i,j) returns S-parameter Sij

Elapsed time is 1.997850 seconds.

The S-parameters function takes 1.9 seconds.

Now calculate the S-parameters of the circuit with both capacitors as full-wave model circuit elements.

ckt = circuit;
c1 = interdigitalCapacitor;
c2 = interdigitalCapacitor('NumFingers',3);
p1 = pcbElement(c1,'Behavioral',false);
p2 = pcbElement(c2,'Behavioral',false);
add(ckt,[1 2 0 0],p1) % default pcbElement created automatically
add(ckt,[2 3 0 0],p2)
setports(ckt,[1 0],[3 0])
tic
S = sparameters(ckt,8e9)
toc

S = 

  sparameters: S-parameters object

       NumPorts: 2
    Frequencies: 8.0000e+09
     Parameters: [2×2 double]
      Impedance: 50

  rfparam(obj,i,j) returns S-parameter Sij

Elapsed time is 3.482307 seconds.

The S-parameters function takes 3.5 seconds.

Comparing the two circuits shows a small difference in the time taken to calculate the S-parameters. Now consider an entire PCB board with many PCB components. You can perform behavioral modeling on almost all noncritical components and full-wave modeling on the critical components of a PCB board.