[SI-LIST] Re: HSPICE - adding jitter to ethernet serial link
- From: "Alfred P. Neves" <al.neves@xxxxxxxxxxx>
- To: <Chris.Cheng@xxxxxxxxxxxx>, <hassan@xxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Wed, 15 Feb 2006 17:40:16 -0800
Chris,
Your comment reminds me of Eric Polya's book "How to Solve It" stating
that given a difficult problem, make it a simpler problem and solve that
first. This insight can be used to tackle the larger problem. I
remember the late Bob Widlar completely understanding a circuit problem
very completely before progressing to a more complicated version and
designing really good circuits with very little or no computer
simulation at all.
Also, in the case of RJ, simply "adding" does not work. Both the DJ and
RJ each have their own unique probability density function and they need
to be convolved using a model like dual-dirac. So although you can get
HSPICE to run an eye diagram with RJ it does nothing for compliance or
reliability of the system.
BTW, I do however disagree with your statement about the CDR jitter
function. You can get a very good picture of CDR jitter function by
simply examining the recovered clock output (RCLK) with a spectrum
analyzer (if the recovered clock is available). Examining the power
spectral density will tell you if there is peaking, what the loop
bandwidth is, how much gain etc., and allow you to treat the CDR as a
simple control loop with phase-frequency as the state variable. Mike
Li's (Wavecrest Corp) 2 and 3 pole PLL extraction using their TIA also
does some really cool PLL analysis (see 2006 DesignCon paper by him)
using autocorrelation analysis and gives you similar results.
Alfred P. Neves <*)))))><{
Teraspeed Consulting Group LLC
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735 SE 16th Ave.
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-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
On Behalf Of Chris Cheng
Sent: Wednesday, February 15, 2006 5:14 PM
To: hassan@xxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: HSPICE - adding jitter to ethernet serial link
I am a firm believer of divide and conquer. The same reason you don't =
simulate your Tx/Rx PLL jitter while you are doing your prop delay =
analysis. They are separate components of a BERT budget. You are asking
= for trouble and unnecessary complexity if you try to do it all in the
= same time in SPICE or IBIS. Besides, who really knows what his Tx Rj
is anyways ? Further more, without knowing your CDR jitter transfer, how
do you know = the BERT is really that bad AFTER your CDR recover the
clock that is = used to capture your data ?
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx
[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Hassan O. Ali
Sent: Wednesday, February 15, 2006 3:05 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: HSPICE - adding jitter to ethernet serial link
I don't know how the two methods would compare. What do you think?
Best regards.
Hassan.
On Feb 15, "Chris Cheng" <Chris.Cheng@xxxxxxxxxxxx> wrote:
>=20
> If the channel is indeed linear, what's the difference between not =
doing =3D
> Rj at all and simulate your PRBS, get the minium eye opening (Dj) then
> =
=3D
> add a seperate Rj convoluted with impulse response ?=3D20
>=20
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx
>[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Hassan O. Ali
> Sent: Wednesday, February 15, 2006 2:18 PM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: HSPICE - adding jitter to ethernet serial link
>=20 =20
> Chris,
>=20
> The HSPICE approach allows you to see the effect of source RJ as well
=
as =3D
> both source and=3D20
> channel-induced DJ. I think the convolution you're referring to =
doesn't =3D
> consider source=3D20
> DJ.
>=20
> I'm thinking out loud here, but I think in simulation, if the input =
=3D
> pattern is known, it=3D20
> doesn't need many bits to simulate a case of worst-case jitter (or =3D
> eye-opening) for a=3D20
> particular BER requirement.=3D20
>=20
> For example, for a BER of 10E-14, the max pk-to-pk RJ is approx. 15.3
>=
=3D
> times RJ(rms). To=3D20
> simulate the worst-case total jitter, In the PWL source you could use
> =
=3D
> that amount of max=3D20
> pk-to-pk RJ right at the bit where you expect the worst-case ISI e.g.
> =
at =3D
> a lone "1" that=3D20
> follows a long run of 0's. In other words, I think you can =
strategically =3D
> define source=3D20
> RJ and DJ amounts along your bit stream and cover the entire =
eye-pattern =3D
> voltage/time=3D20
> bounds in just a few bits. Anyone out there has done this? =20
> Best regards.
>=20
> Hassan.
>=20
>=20
>=20
> On Feb 15, "Chris Cheng" <Chris.Cheng@xxxxxxxxxxxx> wrote:
> >=3D20
> > If your channel response is linear. How does a separate analysis =
with =3D
> Rj only=3D20
> convoluted with the impulse response of the channel different from =
what =3D
> you are doing ?=3D20
> How many bit do you think is need to simulate in SPICE a BERT of =
10e-14 =3D
> or -18 ?
> > =3D20
> > ________________________________
> >=3D20
> > From: si-list-bounce@xxxxxxxxxxxxx on behalf of Hassan O. Ali
> > Sent: Wed 2/15/2006 9:02 AM
> > To: si-list@xxxxxxxxxxxxx
> > Subject: [SI-LIST] Re: HSPICE - adding jitter to ethernet serial =
link
> >=3D20
> >=3D20
> >=3D20
> > A piece-wise linear (PWL) source implemented as below in an HSPICE =
=3D
> subcircuit may be
> > used to simulate RJ and DJ effects on the output.
> >=3D20
> > The total jitter (J) factors (e.g. 0.512, 0.221, etc.) in this case
> >=
=3D
> were generated with
> > a random number generator. The bit pattern is random but is supposed
> > =
=3D
> to mimic an 8B/10B
> > encoding where the maximum run-length (maximum number of consecutive
> > =
=3D
> 1's or 0's) is 5.
> > The pattern length was arbitrarily chosen as 160 bits. =3D20
> > Mind you, this is just one arbitrary way of including DJ and RJ =3D
> effects. I'm sure more
> > elaborate ways exist.
> >=3D20
> > Best regards.
> >=3D20
> > Hassan.
> >=3D20
> >=3D20
> > ************************************************
> > * HSPICE PWL voltage source
> > * Parameter description:
> > * TR - Rise/Fall time of the PWL source
> > * UI - Unit Interval time (Bit width =3D3D 1/BitRate)
> > * HI - Voltage value representing bit "1"
> > * LO - Voltage value representing bit "0"
> > * JD - Peak-to-peak deterministic jitter
> > * JR - Peak-to-peak random jitter
> > ************************************************
> > .SUBCKT pwl_source node1 node2
> > +TR=3D3DTRval UI=3D3DUIval HI=3D3DHIval LO=3D3DLOval JD=3D3DJDval
> > +JR=3D3DJRval
> > .param J=3D3D'(JD+JR/2)'
> > vsrc node1 node2 PWL
> > + 0.0 'HI', '0.512*J+UI*1' 'HI',
> > + '0.512*J+UI*1+TR' 'LO', '0.221*J+UI*2' 'LO',
> > + '0.221*J+UI*2+TR' 'LO', '0.868*J+UI*3' 'LO',
> > + '0.868*J+UI*3+TR' 'LO', '0.358*J+UI*4' 'LO',
> > + '0.358*J+UI*4+TR' 'LO', '0.379*J+UI*5' 'LO',
> > + '0.379*J+UI*5+TR' 'HI', '-0.003*J+UI*6' 'HI',
> > + '-0.003*J+UI*6+TR' 'LO', '0.2*J+UI*7' 'LO',
> > + '0.2*J+UI*7+TR' 'LO', '0.238*J+UI*8' 'LO',
> > + '0.238*J+UI*8+TR' 'LO', '0.197*J+UI*9' 'LO',
> > + '0.197*J+UI*9+TR' 'LO', '-0.424*J+UI*10' 'LO',
> > + '-0.424*J+UI*10+TR' 'HI', '-0.608*J+UI*11' 'HI',
> > + '-0.608*J+UI*11+TR' 'HI', '-0.47*J+UI*12' 'HI',
> > + '-0.47*J+UI*12+TR' 'LO', '-0.124*J+UI*13' 'LO',
> > + '-0.124*J+UI*13+TR' 'LO', '-0.094*J+UI*14' 'LO',
> > + '-0.094*J+UI*14+TR' 'LO', '-0.657*J+UI*15' 'LO',
> > + '-0.657*J+UI*15+TR' 'HI', '0.48*J+UI*16' 'HI',
> > + '0.48*J+UI*16+TR' 'LO', '-0.052*J+UI*17' 'LO',
> > + '-0.052*J+UI*17+TR' 'LO', '0.208*J+UI*18' 'LO',
> > + '0.208*J+UI*18+TR' 'HI', '-0.15*J+UI*19' 'HI',
> > + '-0.15*J+UI*19+TR' 'HI', '-0.097*J+UI*20' 'HI',
> > + '-0.097*J+UI*20+TR' 'LO', '0.089*J+UI*21' 'LO',
> > + '0.089*J+UI*21+TR' 'LO', '-0.535*J+UI*22' 'LO',
> > + '-0.535*J+UI*22+TR' 'LO', '0.096*J+UI*23' 'LO',
> > + '0.096*J+UI*23+TR' 'LO', '-0.433*J+UI*24' 'LO',
> > + '-0.433*J+UI*24+TR' 'LO', '0.603*J+UI*25' 'LO',
> > + '0.603*J+UI*25+TR' 'LO', '-0.119*J+UI*26' 'LO',
> > + '-0.119*J+UI*26+TR' 'HI', '-0.847*J+UI*27' 'HI',
> > + '-0.847*J+UI*27+TR' 'HI', '-0.234*J+UI*28' 'HI',
> > + '-0.234*J+UI*28+TR' 'HI', '-0.056*J+UI*29' 'HI',
> > + '-0.056*J+UI*29+TR' 'LO', '-0.535*J+UI*30' 'LO',
> > + '-0.535*J+UI*30+TR' 'LO', '-0.564*J+UI*31' 'LO',
> > + '-0.564*J+UI*31+TR' 'HI', '-0.191*J+UI*32' 'HI',
> > + '-0.191*J+UI*32+TR' 'LO', '0.16*J+UI*33' 'LO',
> > + '0.16*J+UI*33+TR' 'LO', '-0.552*J+UI*34' 'LO',
> > + '-0.552*J+UI*34+TR' 'LO', '0.277*J+UI*35' 'LO',
> > + '0.277*J+UI*35+TR' 'HI', '-0.491*J+UI*36' 'HI',
> > + '-0.491*J+UI*36+TR' 'LO', '0.463*J+UI*37' 'LO',
> > + '0.463*J+UI*37+TR' 'LO', '-0.166*J+UI*38' 'LO',
> > + '-0.166*J+UI*38+TR' 'HI', '-0.592*J+UI*39' 'HI',
> > + '-0.592*J+UI*39+TR' 'HI', '0.667*J+UI*40' 'HI',
> > + '0.667*J+UI*40+TR' 'LO', '-0.296*J+UI*41' 'LO',
> > + '-0.296*J+UI*41+TR' 'LO', '-0.11*J+UI*42' 'LO',
> > + '-0.11*J+UI*42+TR' 'HI', '-0.608*J+UI*43' 'HI',
> > + '-0.608*J+UI*43+TR' 'HI', '-0.351*J+UI*44' 'HI',
> > + '-0.351*J+UI*44+TR' 'LO', '0.818*J+UI*45' 'LO',
> > + '0.818*J+UI*45+TR' 'HI', '-0.365*J+UI*46' 'HI',
> > + '-0.365*J+UI*46+TR' 'LO', '0.201*J+UI*47' 'LO',
> > + '0.201*J+UI*47+TR' 'LO', '-0.247*J+UI*48' 'LO',
> > + '-0.247*J+UI*48+TR' 'LO', '0.446*J+UI*49' 'LO',
> > + '0.446*J+UI*49+TR' 'HI', '0.329*J+UI*50' 'HI',
> > + '0.329*J+UI*50+TR' 'LO', '0.706*J+UI*51' 'LO',
> > + '0.706*J+UI*51+TR' 'HI', '-0.165*J+UI*52' 'HI',
> > + '-0.165*J+UI*52+TR' 'LO', '0.302*J+UI*53' 'LO',
> > + '0.302*J+UI*53+TR' 'LO', '0.03*J+UI*54' 'LO',
> > + '0.03*J+UI*54+TR' 'HI', '0.152*J+UI*55' 'HI',
> > + '0.152*J+UI*55+TR' 'LO', '-0.255*J+UI*56' 'LO',
> > + '-0.255*J+UI*56+TR' 'HI', '-0.237*J+UI*57' 'HI',
> > + '-0.237*J+UI*57+TR' 'LO', '0.014*J+UI*58' 'LO',
> > + '0.014*J+UI*58+TR' 'LO', '0.64*J+UI*59' 'LO',
> > + '0.64*J+UI*59+TR' 'LO', '-0.162*J+UI*60' 'LO',
> > + '-0.162*J+UI*60+TR' 'LO', '0.311*J+UI*61' 'LO',
> > + '0.311*J+UI*61+TR' 'LO', '0.33*J+UI*62' 'LO',
> > + '0.33*J+UI*62+TR' 'LO', '-0.301*J+UI*63' 'LO',
> > + '-0.301*J+UI*63+TR' 'HI', '-0.513*J+UI*64' 'HI',
> > + '-0.513*J+UI*64+TR' 'LO', '0.102*J+UI*65' 'LO',
> > + '0.102*J+UI*65+TR' 'LO', '-0.695*J+UI*66' 'LO',
> > + '-0.695*J+UI*66+TR' 'LO', '-0.308*J+UI*67' 'LO',
> > + '-0.308*J+UI*67+TR' 'LO', '-0.444*J+UI*68' 'LO',
> > + '-0.444*J+UI*68+TR' 'LO', '0.387*J+UI*69' 'LO',
> > + '0.387*J+UI*69+TR' 'LO', '-0.031*J+UI*70' 'LO',
> > + '-0.031*J+UI*70+TR' 'HI', '-0.599*J+UI*71' 'HI',
> > + '-0.599*J+UI*71+TR' 'LO', '-0.071*J+UI*72' 'LO',
> > + '-0.071*J+UI*72+TR' 'LO', '0.077*J+UI*73' 'LO',
> > + '0.077*J+UI*73+TR' 'HI', '0.663*J+UI*74' 'HI',
> > + '0.663*J+UI*74+TR' 'HI', '-0.526*J+UI*75' 'HI',
> > + '-0.526*J+UI*75+TR' 'LO', '0*J+UI*76' 'LO',
> > + '0*J+UI*76+TR' 'LO', '0.193*J+UI*77' 'LO',
> > + '0.193*J+UI*77+TR' 'LO', '0.479*J+UI*78' 'LO',
> > + '0.479*J+UI*78+TR' 'LO', '-0.055*J+UI*79' 'LO',
> > + '-0.055*J+UI*79+TR' 'HI', '0.161*J+UI*80' 'HI',
> > + '0.161*J+UI*80+TR' 'LO', '0.404*J+UI*81' 'LO',
> > + '0.404*J+UI*81+TR' 'LO', '-0.249*J+UI*82' 'LO',
> > + '-0.249*J+UI*82+TR' 'HI', '-0.255*J+UI*83' 'HI',
> > + '-0.255*J+UI*83+TR' 'LO', '-0.668*J+UI*84' 'LO',
> > + '-0.668*J+UI*84+TR' 'HI', '-0.481*J+UI*85' 'HI',
> > + '-0.481*J+UI*85+TR' 'LO', '0.553*J+UI*86' 'LO',
> > + '0.553*J+UI*86+TR' 'LO', '0.16*J+UI*87' 'LO',
> > + '0.16*J+UI*87+TR' 'HI', '0.392*J+UI*88' 'HI',
> > + '0.392*J+UI*88+TR' 'LO', '-0.056*J+UI*89' 'LO',
> > + '-0.056*J+UI*89+TR' 'LO', '0.267*J+UI*90' 'LO',
> > + '0.267*J+UI*90+TR' 'LO', '0.384*J+UI*91' 'LO',
> > + '0.384*J+UI*91+TR' 'LO', '0.79*J+UI*92' 'LO',
> > + '0.79*J+UI*92+TR' 'LO', '-0.734*J+UI*93' 'LO',
> > + '-0.734*J+UI*93+TR' 'LO', '-0.006*J+UI*94' 'LO',
> > + '-0.006*J+UI*94+TR' 'HI', '-0.01*J+UI*95' 'HI',
> > + '-0.01*J+UI*95+TR' 'HI', '-0.039*J+UI*96' 'HI',
> > + '-0.039*J+UI*96+TR' 'LO', '0.648*J+UI*97' 'LO',
> > + '0.648*J+UI*97+TR' 'HI', '0.099*J+UI*98' 'HI',
> > + '0.099*J+UI*98+TR' 'LO', '0.409*J+UI*99' 'LO',
> > + '0.409*J+UI*99+TR' 'HI', '0.808*J+UI*100' 'HI',
> > + '0.808*J+UI*100+TR' 'HI', '0.458*J+UI*101' 'HI',
> > + '0.458*J+UI*101+TR' 'LO', '0.709*J+UI*102' 'LO',
> > + '0.709*J+UI*102+TR' 'LO', '0.489*J+UI*103' 'LO',
> > + '0.489*J+UI*103+TR' 'HI', '0.309*J+UI*104' 'HI',
> > + '0.309*J+UI*104+TR' 'LO', '0.637*J+UI*105' 'LO',
> > + '0.637*J+UI*105+TR' 'LO', '0.225*J+UI*106' 'LO',
> > + '0.225*J+UI*106+TR' 'LO', '-0.052*J+UI*107' 'LO',
> > + '-0.052*J+UI*107+TR' 'HI', '-0.1*J+UI*108' 'HI',
> > + '-0.1*J+UI*108+TR' 'HI', '0.288*J+UI*109' 'HI',
> > + '0.288*J+UI*109+TR' 'LO', '-0.219*J+UI*110' 'LO',
> > + '-0.219*J+UI*110+TR' 'LO', '-0.129*J+UI*111' 'LO',
> > + '-0.129*J+UI*111+TR' 'LO', '0.035*J+UI*112' 'LO',
> > + '0.035*J+UI*112+TR' 'LO', '0.131*J+UI*113' 'LO',
> > + '0.131*J+UI*113+TR' 'HI', '-0.23*J+UI*114' 'HI',
> > + '-0.23*J+UI*114+TR' 'LO', '0.24*J+UI*115' 'LO',
> > + '0.24*J+UI*115+TR' 'LO', '0.684*J+UI*116' 'LO',
> > + '0.684*J+UI*116+TR' 'LO', '0.027*J+UI*117' 'LO',
> > + '0.027*J+UI*117+TR' 'HI', '0.351*J+UI*118' 'HI',
> > + '0.351*J+UI*118+TR' 'LO', '-0.562*J+UI*119' 'LO',
> > + '-0.562*J+UI*119+TR' 'LO', '0.831*J+UI*120' 'LO',
> > + '0.831*J+UI*120+TR' 'LO', '-0.524*J+UI*121' 'LO',
> > + '-0.524*J+UI*121+TR' 'HI', '-0.041*J+UI*122' 'HI',
> > + '-0.041*J+UI*122+TR' 'HI', '0.675*J+UI*123' 'HI',
> > + '0.675*J+UI*123+TR' 'HI', '-0.035*J+UI*124' 'HI',
> > + '-0.035*J+UI*124+TR' 'HI', '0.083*J+UI*125' 'HI',
> > + '0.083*J+UI*125+TR' 'LO', '-0.247*J+UI*126' 'LO',
> > + '-0.247*J+UI*126+TR' 'HI', '-0.372*J+UI*127' 'HI',
> > + '-0.372*J+UI*127+TR' 'LO', '-0.44*J+UI*128' 'LO',
> > + '-0.44*J+UI*128+TR' 'HI', '-0.861*J+UI*129' 'HI',
> > + '-0.861*J+UI*129+TR' 'LO', '0.162*J+UI*130' 'LO',
> > + '0.162*J+UI*130+TR' 'HI', '-0.228*J+UI*131' 'HI',
> > + '-0.228*J+UI*131+TR' 'HI', '0.606*J+UI*132' 'HI',
> > + '0.606*J+UI*132+TR' 'HI', '-0.002*J+UI*133' 'HI',
> > + '-0.002*J+UI*133+TR' 'LO', '0.385*J+UI*134' 'LO',
> > + '0.385*J+UI*134+TR' 'HI', '0.012*J+UI*135' 'HI',
> > + '0.012*J+UI*135+TR' 'LO', '0.14*J+UI*136' 'LO',
> > + '0.14*J+UI*136+TR' 'LO', '-0.286*J+UI*137' 'LO',
> > + '-0.286*J+UI*137+TR' 'HI', '-0.124*J+UI*138' 'HI',
> > + '-0.124*J+UI*138+TR' 'HI', '0.132*J+UI*139' 'HI',
> > + '0.132*J+UI*139+TR' 'HI', '0.65*J+UI*140' 'HI',
> > + '0.65*J+UI*140+TR' 'LO', '0.422*J+UI*141' 'LO',
> > + '0.422*J+UI*141+TR' 'HI', '-0.173*J+UI*142' 'HI',
> > + '-0.173*J+UI*142+TR' 'HI', '-0.701*J+UI*143' 'HI',
> > + '-0.701*J+UI*143+TR' 'HI', '0.674*J+UI*144' 'HI',
> > + '0.674*J+UI*144+TR' 'LO', '-0.063*J+UI*145' 'LO',
> > + '-0.063*J+UI*145+TR' 'LO', '0.697*J+UI*146' 'LO',
> > + '0.697*J+UI*146+TR' 'HI', '-0.464*J+UI*147' 'HI',
> > + '-0.464*J+UI*147+TR' 'HI', '0.241*J+UI*148' 'HI',
> > + '0.241*J+UI*148+TR' 'LO', '0.158*J+UI*149' 'LO',
> > + '0.158*J+UI*149+TR' 'HI', '0.725*J+UI*150' 'HI',
> > + '0.725*J+UI*150+TR' 'LO', '-0.715*J+UI*151' 'LO',
> > + '-0.715*J+UI*151+TR' 'HI', '0.379*J+UI*152' 'HI',
> > + '0.379*J+UI*152+TR' 'HI', '-0.341*J+UI*153' 'HI',
> > + '-0.341*J+UI*153+TR' 'LO', '0.387*J+UI*154' 'LO',
> > + '0.387*J+UI*154+TR' 'HI', '-0.158*J+UI*155' 'HI',
> > + '-0.158*J+UI*155+TR' 'LO', '0.637*J+UI*156' 'LO',
> > + '0.637*J+UI*156+TR' 'LO', '-0.883*J+UI*157' 'LO',
> > + '-0.883*J+UI*157+TR' 'LO', '-0.083*J+UI*158' 'LO',
> > + '-0.083*J+UI*158+TR' 'HI', '-0.087*J+UI*159' 'HI',
> > + '-0.087*J+UI*159+TR' 'HI', '0.573*J+UI*160' 'HI',
> > .ends
> >=3D20
> >=3D20
> >=3D20
> >=3D20
> >=3D20
> > On Feb 15, "Chris Cheng" <Chris.Cheng@xxxxxxxxxxxx> wrote:
> > >
> > > May be its just me but Rj only makes sense when you are trying to
> > > =
=3D
> extract a BERT=3D20
> curve
> > which seems to be a MATLAB job.
> > > If you have your Tx Rj, channel model and jitter transfer of your
> > > =
=3D
> CDR, the rest of=3D20
> the
> > work is straight forward.
> > > >
> > > >
> > > > At 10:40 AM 2/7/2006 -0800, Ali Burney wrote:
> > > >=3D20
> > > >> Hi,
> > > >>
> > > >>
> > > >> I am running gigabit Ethernet link simulation using HSPICE and
> > > >> =
=3D
> have a=3D3D20
> > > >> question on adding jitter to the transmitted data. Is there any
> > > >> =
=3D
> way to=3D3D20
> > > >> add Gaussian jitter to the transmitted data? I know that tools
> > > >> =
=3D
> such as
> > > >> =3D20
> > > >
> > > >=3D20
> > > >> Hyperlynx allow you to add transmit jitter.
> > > >>
> > > >>
> > > >>
> > > >> Thanks and best regards,
> > > >>
> > > >>
> > > >>
> > > >> A Burney
> > > >>
> > > >>
> > > >>
> > > >>
> >=3D20
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