1. RG58 coaxial cable model in CST CABLE STUDIO S. Caniggia

2. Outline Introduction S parameter computation Voltage computations in time domain with a step source Voltage computations in time domain with an Ultra Wide Band (UWB) source Conclusion

3. Introduction Typical source and load voltage waveforms for an interconnect matched at both ends: lossless TL (dashed line), frequency-dependent lossy TL (solid line) [1, Fig.7.3] When TL has characteristic impedance different from the loads, distortions occur

4. S parameter computation Cable: RG58 Length: 5cm Frequency range: 0-10GHz Characteristic Impedance Z0: 49.94Ω SPICE simulation performed by MC9 [2] Comparison between CST & SPICE

5. Equivalent circuit used by CST for S11 & S21 computation 50 Ω RG58: length=5 cm, Z0=49.94Ω Equivalent circuit to compute S parameters by CST DESIGN STUDIO File: Ex_coax_S_5cm.cst

6. Equivalent circuit used by MC9 (SPICE) for theoretic S11 & S21 computation rs ts εrεr 2rw Coaxial cable geometry 50Ω SPICE circuit [1, clause 11.2.3] Z0=49.94Ω File:S_LOSSYTL_ANALYTICAL_110GHZ.CIR (MC9)

7. S11 & S21 CST: Ohmic losses CST: Ohmic & dielectric losses MC9: Skin effect only MC9: Skin effect of internal wire only See also Fig.7.22 of [1] for result validation

8. Comments on computation of S parameters S11 parameters have the same resonant frequencies but differ of about 20 dB in magnitude; this means that CST uses a Z0 slight lower than the declared nominal value of 49.94 Ω. S21 parameters are in good agreement when CST uses ohmic setting and MC9 considers the skin effect of the internal wire only.

9. Voltage computations in time domain Cable: RG58 Length: 1.83m Line terminations: 50Ω Source: step waveform with rise time tr=0.1ns Frequency range: 0-10GHz Characteristic Impedance Z0: 49.94Ω SPICE simulation performed by MC9 [2] Comparison between CST & SPICE results

10. Coaxial cable structure 50 Ω Z0=49.94 Ω Length:1.83m V1 V2 Vsource=2 V trise=0.1 ns Source

11. MC9 model (Step source) Coaxial cable matched at both ends and modeled as a cascade of 610 cells including the skin effect [1, chapter7] V 1 =V S V 2 =V L Step signal

12. CST model (Step source) RG58 model with length 1.83 m Skin effect only 10GHz Vinit:0.0 Vpulse:2.0 Tdelay:1e-9 Trise:0.1e-9 Thold:100e-9 Tfall:0.1e-9 Ttotal:200e-9 File: Ex_coax_S_1_83_10GHz.cst

13. Voltages V1 & V2 SPICE CST V1 V2 V1 V2 V1 V2 V1 V2 ns Samples 1001 in transient1 task Samples 5001 in transient1 task ? ?

14. Comments on computation of V voltages V1: the voltages at source end computed by SPICE and CST are in good agreement V2: the voltages at load end computed by SPICE and CST are in good agreement except for the oscillations in CST computation dependent on samples setting in transient task of CST

15. Coaxial cable with source an UWB signal The same coaxial cable of previous example has as source an ultra wide band (UWB) signal instead of a step waveform.

16. MC9 model (UWB source) Coaxial cable matched at both ends and modeled as a cascade of 610 cells including the skin effect: comparison between measured (dashed line) and computed (solid line) waveforms [1, chapter7] Validation Model

17. CST model (UWB source) File: Ex_coax_UWB.cst New_uwb_input_by2.txt Ohmic losses RG58

18. Comments on coaxial cable with UWB source SPICE runs in some minutes and gives waveform on 50-Ω load in good agreement with measurement CST does not run due to instability reason

19. Conclusion The 2D (TL) modeling in CST CABLE STUDIO should be revised because it provides unexpected oscillations on arrival signal when the source is a step signal and the line is matched at both ends. There are instability problems in CST when the source is an ultra wide band signal. It is suggested to use the model presented in [1, chapter 7] that consists of a cascade of ideal transmission lines electrically short followed by a network computed by vector fitting technique to take into account losses.

20. Reference [1] S. Caniggia, Francesca Maradei, “Signal Integrity and Radiated Emission”, John Wiley & Sons, 2008 [2] www.spectrum-soft.comwww.spectrum-soft.com