HFSS中高频传输线损耗的精确计算

Accounting for High Frequency Transmission Line Loss Effects in HFSS Andrew Byers Tektronix Transmission Line Refresher Transmission line characteristics describe a particular mode Number of modes = number of conductors -1 a = attenuation constant (loss in either metal or dielectric) b = propagation constant (dependent on eo and mo) R, L, C, G = frequency dependent equivalent circuit parameters g = a + j b = (R + jwL) * (G + jwC) Zo = Zr + j Zi = (R + jwL) / (G + jwC) Transmission Line Refresher log (freq) log (S21)dB [dB/m] log (a)dB [dB/m] Zo [W] Break frequency 1: Zo approaches asymptote value Break frequency 2: skin effect region starts S21 referenced to 50W a referenced to Zo(f) a = (R/2Zo) “log-log” scale reference: National Bureau of Standards Tech Note 1042 Frequency-dependent Loss Mechanisms in Transmission Lines Dielectric Loss • function of dielectric loss tangent, tan d • dielectric loss dominates in PCB environments on FR4-like substrates • loss is directly proportional to frequency and tand Frequency-dependent Loss Mechanisms in Transmission Lines Conductor Losses • Current crowds to surface of transmission line as frequency increases • Resistance of line inversely proportional to current-carrying cross-section: R = r/A • As the current approaches the “skin depth”, the resistance of the line begins to increase with the square root of frequency: ds = • Conductor loss dominates in high-performance package and chip environment (low dielectric loss substrates or very thin metal) 1 pfsmo Frequency-dependent Loss Mechanisms in Transmission Lines Surface Roughness • Surface of conductors can be “rough” - sometimes intentionally to aid in metal adhesion to substrate surface • increase in total current travel distance will result in an increase in loss with frequency surface roughness a’c = ac [ 1 + 2/p tan-1{1.4(D/ds)2}] * a’c = attenuation for rough surface ac = attenuation for smooth surface ds = skin depth D = r.m.s. surface roughness height * Edwards, Terry. Foundations for Microstrip Circuit Design. John Wiley and Sons, 1992. PCB Microstrip HFSS Simulations Typical PCB dimensions: w=8mils, t=1.6mils, h=4mils, er = 4 loss properties: tand = 0.04 s = 5.8E7 HFSS Simulations: - lossy dielectric only - lossy metal (solve inside) only - lossy metal (surface) only - both lossy dielectric and metal (inside) - both lossy dielectric and metal (surface) inspect the attenuation constant, a, to view loss characteristics ... [8.686dB/m = 1Np/m] HFSS v9 view PCB Microstrip SOME OBSERVATIONS: Dielectric loss dominates at freq > 200MHz Conductor loss DOES contribute at freq < 5GHz Solving on surface only makes the skin depth approximation across all frequencies, ignoring the “transition region”. Solving inside the metal has an upper frequency limitation dependent on mesh density. * on a “log-log” scale, a slope of 1 is dielectric loss, a slope of 0.5 is skin effect loss m=1 m=0.5 Package Stripline Simulations and Measured Data Cross-section measured dimensions: w=79um, h1=60um, h2=138um, t=5um loss properties: tand = 0.008 s = 5.8E7 w h1 t h2 Measured data taken on a test package using the ‘TRL’ calibration procedure to deembed the RF probe pads and extract the line characteristics. er=3.4 HFSS v9 view Package Stripline Results meshing limitation Uncorrected HFSS has two modes with nearly identical Beta values - at approximately 4 GHz, the modal results cross over and the recorded alpha effectively “flip-flops”. Corrected version uses mode 1 data before 4GHz, mode 2 data after 4GHz. Measured data still shows more loss than the HFSS simulations... dielectric loss only conductor loss only dielectric + conductor modal “flip-flop” Package Stripline - Surface Roughness • In the stripline configuration, current spreads on BOTH sides of stripline • Adjust surface roughness calculation by half to account for current distribution surface roughness r.m.s = 1um SEM cross sectional pictures • Surface roughness on bottom side of stripline Package Stripline - Surface Roughness HFSS simulation with no S.R. is not lossy enough. HFSS simulation with 1um S.R. calculation is too lossy. HFSS simulation with 1um S.R. calculation, assuming half current distribution on rough side, fits measured data very well. m=1 m=0.5 a’c = ac [ 1 + 0.5*(2/p tan-1{1.4(D/ds)2})] a’c = ac [ 1 + (2/p tan-1{1.4(D/ds)2})] Package Stripline - Surface Roughness Package Stripline - Surface Roughness (from HFSS v9 help) On-chip Microstrip Simulations and Measured Data Design dimensions: w=2.4um, h=3.25um, t=2.07um tand = 0.001 s = 3.22E7 w t h Measured data taken directly on a test wafer using the ‘TRL’ calibration procedure to deembed the RF probe pads and extract the line characteristics. passivation removed SiO2 er=4.1 HFSS v9 view On-chip Microstrip SOME OBSERVATIONS: Skin effect mechanism dominates up to measurement frequency limit of 40GHz. Slope of measured data starts to increase after 30 GHz, could be start of dielectric loss component. Solving inside metal is necessary whenever line dimensions are close to skin depth. Solving inside captures the “transition region”, which is dependent on the trace geometry. m=1 m=0.5 BGA Transition Design and Modeling Frequency Domain Time Domain differential symmetry plane BGA Transition: Measured vs. Modeled Correlation 25 ps rise time at the package tline. Lossy nature of the transmission line is modeled in HFSS. BGA transition signature is predicted. Allows for confidence in simulation setup: ability to improve design! board tline package tline BGA BGA Transition Design and Modeling Procedure: Use HFSS to simulate R and L curves for transmission lines Develop time-domain transmission line models which incorporate the correct loss mechanisms. Model BGA transition in HFSS and match to equivalent model with Designer. HFSS v9 view BGA Transition Design Flow: Using Designer and HFSS feedlines Comparing measured to modeled TDR in SPICE package transmission line 52 Ohms PCB transmission line 53 Ohms TRL-calibrated measurement to 40GHz -> transform to time domain. SPICE simulated transition using BGA model generated in Designer and transmission line loss characteristics found with HFSS. Closing Remarks • Different transmission environments = different dominant loss mechanisms -> the beauty of log-log plots • Solving for surface currents only -> know your skin depth • The surface roughness adjustment - got teeth? • Be aware of “transition region” to skin effect -> might be smack dab in the middle of your bandwidth! • Other possible loss mechanisms include: • radiation from discontinuities • proximity effect - current crowding in diff pairs • dispersion and higher-order mode propagation