Sensitivity & Yield Analysis

Transcription

1 Sensitivity & Yield Analysis Introduction Filter & Antenna Examples

2 Outline Background What is sensitivity and yield analysis Application examples Two post filter Aperture coupled patch antenna U-slot patch antenna Conclusions

3 What is Sensitivity Sensitivity of S-parameters with respect to changes of a parameter p: What is it good for? S S S( p p) S( p) p p p The sensitivity helps estimate new S-parameters due to the (small) change of the parameter, at no extra cost Suppose the parameter p changes by a quantity S S S( p p) S( p) sens S( p p) S( p) sens p p p p (Equivalent to 1st order Taylor expansion) p

4 What is Yield Analysis Application: yield analysis What is yield? For every product, there are: Technical specifications Fabrication tolerances The fabrication tolerances will lead to some products not fulfilling the specifications Yield: yield # Passed # Total

5 Typical vs. CST Approach How is yield calculated typically? Parameters vary according to a known probability curve Repeat... Change the value of all parameters Simulate Check if specification (in our case for S-params.) is met... Until the number of simulations is statistically relevant This is a large number of EM simulations - typicaly hundreds or thousands! Knowing the sensitivity, there is no need to perform 3D simulations, at least if the parameters vary in a small range

6 Yield Analysis Setup Only local variations and material properties can be used for Yield Analysis Define parameters as face constraints

7 Yield Analysis Setup (cont) Specify parameters in Solver Yield Analysis dialog and run simulation

8 Post Processing Derivative of the S-Parameter vs. parameter and frequency is directly visible after simulation

9 Perform Yield Analysis Define the manufacturing tolerances of the parameter in terms of the statistical distribution type (Gaussian or Uniform) and the Standard Deviation

10 Yield Analysis As a first step, the Yield Analysis returns a 3 sigma band for the S-Parameter. 3 sigma means that % of the devices are within this band: In the range of 8.9 GHz to 9.1 GHz, the nominal S11-Parameter is completely below (S-Linear) The 3 sigma S11-Paramter are partially above If this is our spec. the yield analysis tells us, what percentage of our devices will be within the allowed range. Yield: %

11 Gaussian or Uniform Distribution? All the mechanical dimensions Post height, Iris Height Material parameters permittivity of substrate All the component values Resistors, Capacitors Other Pre-selected quantities

12 Filter & Antenna Examples Sensitivity & Yield Analysis

13 Two-Post Filter Three independent parameters

14 Mesh Adaption

15 Sensitivity Analysis Results The S-parameters are very sensitive on the post height than on the iris height.

16 Yield Analysis Setup Yield: %

17 Yield Analysis - Results Yield: %

18 Yield Analysis vs. Parameter Sweep +3sigma CST MWS Sweep Yield Analysis -3sigma

19 Aperture Coupled Patch Antenna Reference: P. Bartia, K.V.S. Rao, R.S. Tomar, Millimeter-Wave Microstrip and Printed Circuit Antennas, pp , Artech House, 1991.

20 Variable Order Mesh Elements 2 nd Order Tetrahedrons Solver run total 6.2 GB Total Solver Time 2 h, 41 m Mixed 2 nd Order Tetrahedrons Solver run total 7.8 GB Total Solver Time 47 m

21 Sensitivity Slot Length L slot Yield = %

22 U-Slot Antenna With Radome Reference: A broad-band U-slot rectangular patch antenna on a microwave substrate, IEEE Trans. Antenna & Prop., VOL. 48, NO. 6, June 2000.

23 Radome Material Sensitivity Add rubber radome cover with uncertain permittivity

24 Yield Analysis Calculated Yield: 99.98%

25 Conclusions CST FD solver allows to perform quick Sensitivity & Yield analysis with only ONE pass through 3D EM simulation Sensitivity analysis provides guidance on where to focus on a high level of machining accuracy and vice versa This results in improved yield percentage in mass production Yield calculation accuracy can be limited for wider ranges of parameters or in cases that the sensitivities are strongly nonlinear functions