A  Filter  Bank  of  High-­‐Q  Bandpass  Filters  to  Find  Fourier  Series  Coefficients  for  TRDMA  system  

Jinyanzi  Luo,  Dr.Benjamin  Belzer  School  of  Electrical  Engineering  and  Computer  Science  Washington  State  University,  Pullman,  WA  99164  

Motivation ●  Previously proposed TRDMA systems utilized digital sampling,

which is not practical for WiNoCs due to extremely short-duration on-chip impulse response, so analog TRDMA system is need to be designed.

●  TRDMA offers a power and area efficient method by creating

spatial channels between each Tx/Rx pair in WiNoC.

Time Reversal Division Multiple Access (TRDMA)

●  A wirelessly transmitted signal will take multiple paths to a receiving antenna, a phenomenon known as the multipath effect. TRDMA takes advantage of this multipath effect via channel reciprocity to spatially and temporally focus all of a signal’s energy on a desired receiver. Utilizing TRDMA for wireless network-on-chip (WiNoC) application can:

1. Reduce the power needed to transmit information

between processors that are far apart.

2. Enable multiple omni-directional antennas to transmit information to multiple receivers simultaneously using spatial multiplexing, while avoiding temporal inter-symbol interference(ISI).

●  An impulse at a receiving node using TRDMA can be achieved

by sending a time-reversed impulse response from a transmitting antenna. In order to accomplish this:

1. The impulse response from Rx to Tx must first be

obtained by Tx during a recording phase.

2. The impulse response must then be time-reversed and sent by the Tx during the transmitting phase.

●  At WiNoC data rates (ten of Gb/s) it is currently not possible to

digitally record the impulse response, so the impulse response must be learned via an analog circuit

●  On-chip antennas that employ Wireless Network-on-chip (WiNoc) systems allow wireless communication between cores across long distances.

Introduction I  would  like  to  specially  thank  :  

●  Dr.Benjamin  Belzer,  Joe  Balyon,  and    Jorge  Pires  for  their  help  on  this  project.    

●  Noel  Wang  and  Kevin  Johnson  for  providing  a  foundaWon  for  this  research.  

●  WSU  EECS  faculty  and  staff  for  making  this  research  possible.  This  work  was  supported  by  the  NaWonal  Science  FoundaWon’s  REU  program  under  grant  number  CNS  1359461  

Acknowledgement

Results

Method ●  A commercial circuit simulation software package called Cadence is

used to construct the filter bank. ●  The input signal of the bank is the impulse response from a Finite

Difference Time Domain simulation of on-chip wireless transmission.

Conclusion

Future Work

Fourier Series ●  Fourier discovered that a periodic function can be represented

by an infinite sum of sine or cosine functions that are harmonically related.

●  Signals can be approximated by Fourier Series via the following the expression:

●  A time-reversed version of the waveform is computed by inverting the signs in front of the bn coefficients.

●  Self-calibration circuit for the coefficient sampling times is needed.

●  Summing all the coefficients to generate the time-reversed waveform of the incoming impulse.

●  These antennas suffer from high power dissipation and timing delays due to their token-passing wireless access control protocols.

●  The Fourier Series (FS) coefficients are needed to recreate or to store

the impulse waveform that is sent from Rx to Tx during the recording phase.

●  To demonstrate the feasibility of analog TRDMA with FS

approximations, a filter bank of high-Q bandpass filters are designed in order to calculate the FS coefficients

Introduction Cont.

Fig 3. Filter Bank Circuitry: contains integrator, voltage followers/buffer, voltage gains, switches, capacitors, resistors and bandpass filters.

Fig 2. Two GHz High-Q bandpass filter circuitry, which is derived from inductor-less Antoniou circuit

Fig 1. Block diagram for computing the first 10 FS coefficients with bandpass filters

Fig 3. a0 waveforms: switch opens at T = 2𝝅/⍵0, where ⍵0 is fundamental frequency we set it to 1GHz, so T=1ns

Fig 5. A square wave going through the second filter for finding the second pair of FS coefficients

Fig 4. Found delays through the filters, which did not happen in LTSpice simulation

●  Switches in the bank are calibrated to open at correct peak and zero-crossing time for cosine and sine input waveforms.

●  The coefficients became less accurate after the 7th filter, no solution has found yet to what caused this phenomenon.

●  At the high frequencies simulated by Cadence, the delays through the circuits must be taken into account when sampling the an and bn coefficients.

Fig 6. Four methods of computing Fourier Series Coefficients are compared with the ideal coefficients given in mathematical formulas.