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This filter
rr_filter=(1+bw1*1i*f/fc+bw2*(1i*f/fc).^2+bw3*(1i*f/fc).^3+(1i*f/fc).^4).^-1; has the EXACT power spectrum as was used in moore_01_0311 (and clause 85). rr_filter_POWER= (1+ (1i*f/fc).^8).^-1; To me these are simple single line equations. …Rich From: Charles Moore [mailto:charles.moore@xxxxxxxxxxxxx]
The 4 pole (Tx) and 8 pole 0 phase Butterworth filters in moore_01_0311 were used strictly for mathematical convenience and were not intended to be particularly realistic. There is little enough energy
at the 3dB frequency of the filters in most channels so that we (adam and i) felt that the lack of realism would not be significant. Adding phase pretty much does away with the mathematical simplicity with little gain in realism: a 4 pole Butterworth filter
has higher Q poles than anyone is likely to implement on a chip. |--------------------------------------------------------------------| | Charles Moore | Avago Technologies | APD | charles.moore@xxxxxxxxxxxxx | (970) 288-4561 |--------------------------------------------------------------------|
A 4 pole Butteworth-Thompson minimum phase filter might be: >> f=10e6:10e6:20e9; bw1=2.613126; bw2=3.4142136; bw3=2.613126; fc=13e9*1.5; >> rr_filter=(1+bw1*1i*f/fc+bw2*(1i*f/fc).^2+bw3*(1i*f/fc).^3+(1i*f/fc).^4).^-1; >> subplot(2,1,1); plot(f,20*log10(abs(rr_filter))); subplot(2,1,2); plot(f,unwrap(angle(rr_filter))); Should we use something like this for the Rx filter? A 1 pole is minimum phase. So Tx filter should be OK unless we would like to add more poles for some physical reason. … Rich From: Ran, Adee [mailto:adee.ran@xxxxxxxxx]
RX bandwidth filter and TX edge filter should naturally be lower for PAM4 – about half the bandwidth or NRZ – otherwise crosstalk generation and sensitivity
are unnecessarily high. These filters should include phase, not just magnitude as in moore_01_0311. Phase is significant in the time domain. It is still multiplication, but with complex
values. For the RX filter phase and magnitude we can assume Butterworth filter, which has a rather simple transfer function (see Wikipedia or more professional sources)
and is an approximation for realizable filters. As for the TX filter, can anyone suggest which filter is adequate? Is there a justification for 2nd order and are the poles real or complex conjugate? </Adee> From: Mellitz, Richard
[mailto:richard.mellitz@xxxxxxxxx]
Should filters be different per port type? …Rich From: Mellitz, Richard [mailto:richard.mellitz@xxxxxxxxx]
Perhaps a convenient way to look at TX/RX filtering is convolution of the following. Tx Voltage Amplitude scaling (for NEXT, FEXT, and THRU not coding which will be done in a later algorithm ) Tx edge filter (moore_01_0311) Rx bandwidth filter (moore_01_0311) Tx/Rx block return loss filters (gamma,moore_01_0311) The first three are a straight convolution and with is multiplication in the frequency domain.
The lasts is a chain matrix convolution of RL under worst +1 or -1 reflection coefficient phase conditions and in the frequency domain may look like this sdd21=sdd21.*(1.-gamma_rx)./(1.- sdd11.*gamma_tx + sdd22.*gamma_rx +sdd21.^2.*gamma_tx.*gamma_rx -sdd11.*sdd22.*gamma_tx.*gamma_rx); …Rich |