1. 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

2. 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

3. 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.

4. 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

5. 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)

6. 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

7. 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:

8. 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

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

10. 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,

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

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

13. 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

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

15. 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

16. 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:

17. 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

18. 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

19. 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

20. 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

21. 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.

22. 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