HFSS中高频传输线损耗的精确计算.pdfVIP

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 α = attenuation constant (loss in either metal or dielectric) β = propagation constant (dependent on εo and μo) R, L, C, G = frequency dependent equivalent circuit parameters γ = α + j β = (R + jωL) * (G + jωC) Zo = Zr + j Zi = (R + jωL) / (G + jωC) Transmission Line Refresher log (freq) log (S21)dB [dB/m] log (α)dB [dB/m] Zo [?] Break frequency 1: Zo approaches asymptote value Break frequency 2: skin effect region starts S21 referenced to 50? α referenced to Zo(f) α = (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 δ ? dielectric loss dominates in PCB environments on FR4-like substrates ? loss is directly proportional to frequency and tanδ 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 = ρ/A ? As the current approaches the “skin depth”, the resistance of the line begins to increase with the square root of frequency: δs = ? Conductor loss dominates in high-performance package and chip environment (low dielectric loss substrates or very thin metal) 1 πfσμo 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 α’c = αc [ 1 + 2/π tan-1{1.4(?/δs)2}] * α’c = attenuation for rough surface αc = attenuation for smooth surface δs = skin depth ? = r.m.s. surface roughness hei