Equivalent Circuits of the Transition from Coaxial to Microstrip Transmission Line on PCBs

Transcription

1 Equivalent Circuits of the Transition from Coaxial to Microstrip Transmission Line on PCBs Mikolaj Ambrozkiewicz Petr Lorenz Wilhelm Kraemer Rohde & Schwarz GmbH & Co. KG

2 Overview l Motivation l Equivalent model l Optimization of model parameters Results & utilization of valid model l Conclusions l Outlook Connector modeling 2

3 Motivation l Obtain a model for connector transitions (complete junction from K-connector to microstrip line on PCB) l Fit model parameters to reproduce measured data of reference structure l Use valid model for, e.g., deembedding Connector modeling 3

4 Motivation Measured S-Parameters l Measured structure: l S parameters: 10 0 measured structure Sparameters GHz db GHz db DB( S(1,1) ) measurement DB( S(2,1) ) measurement Frequency (GHz) Connector modeling 4

5 Equivalent model Adequate equivalent circuits l First attempt: Connector transition T-Line Connector transition (that s the structure of which we measured the S parameters) l T-Line: trivial l Connector transition: not that trivial l Empirical model: Take a look at the TDR representation Connector modeling 5

6 Equivalent model Find model by analyzing TDR plot l TDR plot shows effective line impedances along the structure: 0.1 TDR plot Re(TDR_LPS(1,1,256,1,1))[*] measurement inductive Z = 0 ' L C (for lossless line) ' line capacitive line with Z 50Ω Time (ns) Connector modeling 6

7 Equivalent model Model for single connector to microstrip transition l Model: TLIN ID=TL1 Z0=Z1 Ohm EL=phi1 Deg F0=10 GHz TLIN ID=TL2 Z0=Z2 Ohm EL=phi2 Deg F0=10 GHz TLIN ID=TL3 Z0=Z3 Ohm EL=phi3 Deg F0=10 GHz K connector PORT P=1 Z=50 Ohm l Second model: PORT P=2 Z=50 Ohm Microstrip line TLIN ID=TL1 Z0=Z1 Ohm EL=phi1 Deg F0=10 GHz TLIN ID=TL2 Z0=Z2 Ohm EL=phi2 Deg F0=10 GHz IND ID=L1 L= nh TLIN ID=TL3 Z0=Z3 Ohm EL=phi3 Deg F0=10 GHz PORT P=1 Z=50 Ohm Total: 7 parameters (one fixed) additionally included PORT P=2 Z=50 Ohm Connector modeling 7

8 Equivalent model Model of the entire measured structure l Assume symmetry l Lossy T-Line, length ~ 5cm (not really the case...) PORT P=1 Z=50 Ohm SUBCKT ID=S1 NET="connector model" Zline=48.38 Lline= PORT P=2 Z=50 Ohm SUBCKT ID=S2 NET="connector model" 1 2 TLINP ID=TL8 Z0=Zline Ohm L=Lline mm Eeff= Loss=12.83 F0=10 GHz symmetry Connector modeling 8

9 Equivalent model Why use lossy T-Line?? l Without lossy T-Line, model will be completely lossless Re(Eqn()) loss_meas loss in structures l Model transmission and return loss simultaneously Eqn() loss_model 0.3 l Loss = 2 1 S S l But: Losses at higher frequencies still not appropriately modeled Frequency (GHz) Connector modeling 9

10 Equivalent model Need for inductance in model l To better model the loss periodicity Re(Eqn()) loss_meas Eqn() loss_model Re(Eqn()) loss_simp_model loss in structures cmp models Frequency (GHz) l Note: inductance does not increase losses by itself lossless Connector modeling 10

11 Equivalent model Losses at high frequencies are not sufficiently modeled l Losses do not scale like expected for frequencies above ~30 GHz Re(Eqn()) loss_meas Eqn() loss_model loss in structures l Restrict frequency range for modeling to about 30 GHz l For frequencies above 30 GHz, the model should be improved to better predict the measured losses Frequency (GHz) Re(Eqn()) loss_meas Eqn() loss_model loss in structures Frequency (GHz) Connector modeling 11

12 Optimization of model parameters l Use combination of random global search and genetic algorithm (GA) l Iterative process l Important: restrict parameter values to reasonable range l Important for GA: Define fitness function l Use Microwave Office: Define variables to be optimized Define reasonable variable range ( constraints ) Define Goal (fitness function) Connector modeling 12

13 Optimization of model parameters Defining fitness function for GA l Match both S11 and S21 at the same time (this can be done by MWO s SModel value available in the Linear->Port Parameters measurement) l But, we focus on S11 (esp. the phase) l Define an own fitness function this can be done by defining the fitness function as output equation l Take complex difference between target and model S Connector modeling 13

14 Optimization of model parameters Fitness function l Allow more deviation at points far from matching, i.e., the origin (this has only minor effect on phase) l Define circles of valid S11 range, Increase circle diameter as abs(s11) increases complex S-plane l Formula used: S( f ) = S 11, meas S ( f ) S 11, meas 11,model ( f ) +α ( f ) l alpha: minimum allowed deviation (for S11 ~ 0, i.e. matching) Connector modeling 14

15 Optimization of model parameters Fitness function as goal in MWO l Realized with Output Equations target values of measured structure s11meas = measurement:s(1,1) s11mod = structure model:s(1,1) alpha=0.1 Sdiff = (s11meas-s11mod)/(abs(s11meas) + alpha) values of current model iteration cost function s21mod = structure model:s(2,1) s21meas = measurement:s(2,1) loss_meas = 1- abs(s21meas)^2 - abs(s11meas)^2 loss_model = 1 - abs(s11mod)^2 - abs(s21mod)^2 losses in structure Connector modeling 15

16 Optimization of model parameters Fitness function II l Calculate difference of S-parameters for every frequency point l Accumulate deviations to total model error l Minimize total model error l Define regions, where model should fit more stringent COST FUNCTION Sdiff Eqn() Sdiff different frequency regions, different weighting for errors Frequency (GHz) Connector modeling 16

17 Optimization of model parameters Defining goals in MWO l Project > Add opt goal l Choose variable l Set goal value and define goal type l Specify frequency range l Enable goal Connector modeling 17

18 Optimization of model parameters Running optimization in MWO l Optimizer Choose optimization algorithm Cost of current solution Run optimization Connector modeling 18

19 Optimization of model parameters Results comparison S11 db 0 l Found parameters: Transition: Z1 = 50 (fixed) phi1 = 152 Z2 = 88.5 phi2 = 2.3 Z3 = 46.9 phi3 = 26.4 TLine: Lline = 53.3 mm Zline = 48.3 l Comparison of measured and modeled S parameters: Note: excellent agreement in phase as well!! Frequency (GHz) comparison S11 PHASE DB( S(1,1) ) structure model DB( S(1,1) ) measurement Ang(S(1,1)) (Deg) structure model Ang(S(1,1)) (Deg) measurement Frequency (GHz) Connector modeling 19

20 Optimization of model parameters Results: Comparison of TDR 0.1 Comparision TDR Re(TDR_LPS(1,1,256,1,1))[*] structure model -0.1 Re(TDR_LPS(1,1,256,1,1))[*] measurement Time (ns) Connector modeling 20

21 Optimization of model parameters Deembedding l 7 db improvement over embedded measurement 0 Sparameter deemdedding GHz db GHz db DB( S(1,1) ) measurement DB( S(1,1) ) deembedding Frequency (GHz) Connector modeling 21

22 Outlook Possible improvements l Assumed symmetry of structure, but structure is not symmetric in reality find simple reference structure with only one transition and a well defined termination l Analyse the variation of the parameters (depending on solder, connector placing, etc) l Improve model for frequency dependent losses and model losses in connectors l Test different optimization algorithms (e.g., differential evolution) Connector modeling 22

23 Conclusions l Empirically developed equivalent model l Determined model parameters by optimization (GA) l Defined own fitness function l Obtained model shows very good agreement with measured data l Deembedding and other applications possible with a valid model l Limitations and further improvements presented Connector modeling 23

24 Thank you for your attention!! l Please feel free to ask questions... l Contact: l And: Mikolaj Ambrozkiewicz mikolaj.ambrozkiewicz@tuhh.de TU Hamburg-Harburg Institut für Hochfrequenztechnik (E-3) Denickestr. 22, Hamburg Germany Petr Lorenz petr.lorenz@rohde-schwarz.com Connector modeling 24