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Module 5: Advanced Transmission Lines Topic 4: Frequency Domain Analysis

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Module 5: Advanced Transmission Lines Topic 4: Frequency Domain Analysis

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    1. © H. Heck 2008 Section 5.4 1 Module 5: Advanced Transmission Lines Topic 4: Frequency Domain Analysis OGI ECE564 Howard Heck

    2. © H. Heck 2008 Section 5.4 2 Where Are We? Introduction Transmission Line Basics Analysis Tools Metrics & Methodology Advanced Transmission Lines Losses Intersymbol Interference Crosstalk Frequency Domain Analysis 2 Port Networks & S-Parameters Multi-Gb/s Signaling Special Topics

    3. © H. Heck 2008 Section 5.4 3 Contents Motivation Wave Equation Revisited Frequency Dependence Reflection Coefficient and Impedance Input Impedance Examples Summary References

    4. © H. Heck 2008 Section 5.4 4 Motivation At high frequencies, losses become significant. This makes time domain analysis difficult, as the properties are frequency dependent. Skin effect, dielectric loss & dispersion We need to develop the means to understand those effects. Example: How would we measure R, L, G, C for a PCB trace? Frequency domain analysis allows discrete characterization of a linear network at each frequency. Characterization at a single frequency is much easier Frequency Analysis has advantages: Ease and accuracy of measurement at high frequencies Simplified mathematics Allows separation of electrical phenomena (loss, resonance … etc).

    5. © H. Heck 2008 Section 5.4 5 Key Concepts The input impedance & the input reflection coefficient of a transmission line is dependent on: Termination and characteristic impedance Delay Frequency S-Parameters are used to extract electrical parameters. Transmission line parameters (R,L,C,G, TD and Zo) Vias, connectors, socket … equivalent circuits Periodic behavior of S-parameters can be used to gain intuition of signal integrity problems. We’ll study S-parameters in section 5.5.

    6. © H. Heck 2008 Section 5.4 6 Derive the lossy wave equation Add a sinusoidal stimulus

    7. © H. Heck 2008 Section 5.4 7 Wave Equation Revisited Goal: derive the frequency dependent impedance and reflection coefficients. Method: Starting with the RLGC equivalent circuit, we derive the differential equations.

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