Multiport, Multichannel Transmission Line: Modeling and Synthesis Based on the research paper: J. Chen and L. He, “Modeling and Synthesis of Multi-Port Transmission Line for Multi-Channel Communication”, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Sept 2006 Presented by: Pratyush Singh Course: EE201C

Overview Introduction Basics of transmission line Frequency domain models for multi-port transmission lines Voltage response SNR model Signal distortion metrics Synthesis of RF interconnects Conclusion

Introduction Traditional approach On-board or in-package communication: Transmission lines On-chip communication: Traditional interconnects (limited by inherent signal distortion and large RC delays) On-chip communication via transmission lines Transmit baseband digital signals Transmit digital signals via high frequency carriers (modulate base-band signals with high frequency carriers before transmission and let the analog receivers recover the signal) like RF interconnects.

RF Interconnects Transmission via high-frequency carrier signals Composition: CPW/MTL Analog modulators and demodulators Capacitive couplers Advantages: Multiple accesses possible (FDMA, CDMA) Reconfigurable High speed (close to speed of light) Lower distortion and losses Immune to digital switching noise

This work: Develops closed-form SNR models that are effective for a generic network with multiple discontinuities (i.e: ports, junctions, terminations) Presents signal distortion FOMs in terms of amplitude and phase delay Brings up automatic synthesis of RF interconnects; with high quality results showing the advantages and significance of the same (as against the manual designs presented in some earlier works)

Why automatic synthesis? Because the earlier efforts involving manual designs were inherently limited by the level of complexity Limitations in manual design Overdesign lead to large interconnect area Hard to consider multiple ports and branches Long design cycle

Transmission line basics: A transmission line can be described as: R,L,C,G: unit length parameters Characteristic impedance: So the solution: Reflection ratio at terminations:

How circuit is modeled? Between any two discontinuities, a uniform transmission line model has been employed Transceivers have been modeled as linear elements with an impedance and a voltage source Model each frequency channel in frequency domain Multiple frequency channels

Port Voltage Response Each segment between adjacent discontinuities is a transmission line At each port At each branching point

Port Voltage Response (contd.) At each termination: Zt: Impedance of the termination System matrix: sparse band 2n+2b variables with n ports and b branches Complexity of O(n+b) Example: for a two-port line,

Model v/s SPICE simulation Voltage comparison shows high accuracy of the model voltage response

SNR model Isolated communication channel Approx. to first order, neglecting reflections from other discontinuities

SNR model (contd.) Effect of Multiple ports Transmission and reflection rates at port k Zpk: Impedance of port k Z0: Characteristic impedance of transmission line Termination reflection rate

SNR model (contd.) Reflection rate of branch i Z0i: Characteristic impedance of line i. Transmission rate to other branches:

SNR model (contd.) With transmission and reflection from all discontinuities coming into picture, SNR can be expressed as: Vs : signal received by the receiver r Vn : first-order reflection noise from the discontinuities Pn : Intrinsic noise power

FOMs Distortion depends upon attenuation and phase delay. If both are uniform over the frequency band of the channel, the communication is ‘distortionless’ To ensure small distortion following metrics are defined: Phase delay metric: Attenuation metric:

Multiband CPW RF Interconnect Digital signal  Modulation (by transmitter) RF carrier signal Interconnect (coupled via a capacitive coupler)  Receivers (via capacitive couplers) Demodulation  Original digital signal

Automatic Synthesis of RF Interconnect Target: Minimize total area of interconnects and coupler sizes Constraints: SNR (lower bound) Distortion (upper bound) Freedom to decide: w (signal wire width), g (shielding wire width), s (spaces), coupler sizes (defined by the capacitive density) Given: Transceiver sizes, locations, intrinsic noise, interconnect topology

Algorithm Simulated Annealing method Objective function: Where A: area FSi, FPi and FAi: penalty function of violation of SNR, phase delay variation and amplitude variation Ka, Ks, Kpd and Kad: weight factors

Synthesis Results Synthesis of 2-port-2-channel interconnect gave 80% reduction in the area as against the manual design [Chang et al. ’01] In general, total area depends on design and varies up to 3x

Other observations Coupler sizes vary up to 20x even in same design as against the assumption of uniform sizes in manual designs. Receiver couplers are much smaller than transmitter couplers when multiple ports are there. Mismatched interconnects lead to violation of constraints Termination mismatch leads to increase in interconnect area and coupler sizes.

Conclusions RF interconnects are very effective multichannel multiport interconnects used for high speed high bandwidth communications In this work, an efficient multi-port transmission line model was developed for RF interconnects An accurate closed-form SNR model was developed Highly area efficient interconnect designs were synthesized using these models The effectiveness and necessity of these models and automatic synthesis process is observable