# [SI-LIST] Re: Ferrite bead question

• From: Scott McMorrow <scott@xxxxxxxxxxxxx>
• To: ericg@xxxxxxxxxxx
• Date: Mon, 10 Apr 2006 17:31:11 -0400
```Hmmm ...
Lets take an example of a 533 MT/s DDR bus, with a 266 MHz frequency.

One bit time = 1.875 ns
One period = 3.75 ns
Let risetime = 400 ps (10%-90%)
Fknee = .35/400ps = 875 MHz
Assume that driver current is 20 mA/driver
Assume that 64 drivers switch simultaneously
Total current transient = 1.28 Amps in 400 ps.
Assume total voltage swing = 2V pp for SSTL-2.5
Assume a 100 mV power noise allowance (5%)
Power system Ztarget = 100mV/20 mA = 78 mOhms

Computing the Fourier Coefficients for a trapezoid, using a cute little
calculator I found here:
http://www.eecircle.com/applets/001/001.html,    with 400 ps rise time
we get:

Harmonic component
DC - 0.500
1st - 0.312   (266 MHz)
3rd - 0.089  (800 MHz)
5th - 0.037  (1.33 GHz)
7th - 0.013  (1.87 GHz)
9th - 0.001  (2.4 GHz)

For this particular driver, 62% of the AC energy is contained at the
fundamental frequency, 17.8% is contained at the 3rd harmonic, 7.4% is
contained at the 5th harmonic, and 2.6% is contained at the 7th
harmonic.  If we use our one pole filter bandwidth formula of BW =
0.35/risetime, then we are covered up to the 3rd harmonic of the signal
fundamental. But, 20% of the signal energy is still carried in harmonics
above the 3rd.  Our total power system noise in the time domain is
approximately:

Vnoise = 1.28 Amps x ( Z@266 MHz x 0.62 + Z@800MHz x 0.178 + Z@xxxx GHz
x 0.074 + Z@xxxx GHz x 0.026 + Z@xxx GHz x 0.02)

It is not unusual for power system impedance at high frequency
resonances to exhibit a 100:1 increase over the Ztarget at lower
frequencies.  What if our power system had flat impedance of 78 mOhms
out to 1.5 GHz and then climbed to a resonance peak of 7.8 ohms at 1.87 GHz.

Ignoring the 9th harmonic, the noise would be:

Vnoise = 1.28 Amps x ( 0.078 x 0.62 + 0.078 x 0.178 + 0.078 x 0.074 +
7.8 x 0.026)
Vnoise = 1.28 Amps x ( 0.078 Ohms x .872 = 7.8 x 0.026)
Vnoise = 1.28 Amps x ( 0.068 + .2028)
Vnoise = 87 mV below 1.5 GHz + 260 mV @ 1.87 GHz

With a reactive network with a resonance such as this, the resonance
peak would generally be out of phase with the lower frequency noise, so
the result would not be generally additive.  However, that 1.87 GHz peak
would dominate, and show up as ringing in the power system.  I suspect
it would also show up as a healthy signature in the EMI profile,
although I am not expert in these matters.  Which is why those silly EMI
engineers are often concerned about harmonics of the fundamental like
the 7th, 9th and even the 11th.

This particular example is contrived and not quite exact.  But, it is
not unusual at all in designs with planes fragmented like a map of the
Balkans, as Dr Johnson would say. Or in large planes, where planar
resonances are right in the middle of all the switching harmonics.
We've measured power systems where there are some pretty interesting
high frequency resonance peaks, which show up quite well in both the
power system and time domain signal measurements, and are above Fknee.
Remember, according to Dr Johnson, amplitude at the knee frequency is
6.8 dB below the 20 dB/decade rolloff seen in a signal's spectral
energy.  At the 9th harmonic (which can be approximated as one decade
down) we have a total spectral attenuation of 26.8dB, or 21.9 times
lower the the fundamental.  It does not take much resonance "gain" over
the power system target impedance to dwarf noise at the fundamental with
noise at a higher harmonic ... even one beyond the knee.   What's quite
show up as high frequency ringing on a DDR memory bus signal.  But, it
would not have been diagnosed with standard signal integrity tools, and
would only show up when a complete simulation of simultaneous switching
of the bus was performed that included modeling of the device, package,
power planes, bypass capacitors, mounting pads and vias.

This goes back to what I term the "Wack-a-Mole" phenomenon in power
distributions systems.  If you do not fix the fundamental problem of
power system resonances, then all you're doing is moving energy around
from one place to another, just to see it pop up out of another hole.

regards,

scott

Scott McMorrow
Teraspeed Consulting Group LLC
121 North River Drive
Narragansett, RI 02882
(401) 284-1840 Fax

http://www.teraspeed.com

Teraspeed® is the registered service mark of
Teraspeed Consulting Group LLC

Eric Goodill wrote:
> Ken,
> Yeah, that's pretty much exactly what I meant by "pick a probable
> maximum frequency," but I didn't say that in my post. Sorry.
>
> -Eric
>
> kfrobinson@xxxxxxxxxx wrote:
>
>> Eric,
>> The frequency components in a digital system can be estimated from DC to
>> .35/(rise time).  The IC manufactures do give 10-90 rise time.  Pick the
>> fastest rise time IC in your system.
>> Ken
>>
>> -----Original Message-----
>> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
>> On Behalf Of Eric Goodill
>> Sent: Monday, April 10, 2006 12:16 PM
>> To: si-list@xxxxxxxxxxxxx
>> Subject: [SI-LIST] Re: Ferrite bead question
>>
>> Howdy,
>> One thing I've never understood about designing the frequency response
>> of a power delivery system is what are the frequency requirements? That
>> is, where does the vendor give me the spectrum of the current demand for
>> the part? They don't (I'm skipping over they it'd be tough). So the only
>> solution I can see is to pick a probable maximum frequency and say from
>> DC to that frequency we need less than X ohms impedance based on some
>> assumptions about the peak current needs (related to lack of current
>> spectrum). This is probably over designing, but I don't have any other
>> data to use. Do others feel the same way?
>>
>> -Eric
>>
>> Scott McMorrow wrote:
>>
>>
>>> Joel,
>>> I think Lee is being a little bit black and white, but not without
>>> good reason..  Whether or not ferrites "work" in a power filtering
>>> design is a matter of  whether the engineering was performed.  What I
>>> think Lee often sees are systems where no engineering has gone into
>>> the design of ferrite, and they have been thrown into a circuit
>>> without thought. Often because "that's the way we've always done it"
>>> or "that's that way the competitors do it" or because "that's the only
>>>
>>
>>> ferrite we have in our parts system."  The inductance of a ferrite can
>>>
>>
>>> interact with the power system and capacitors to form a pretty nasty
>>> resonance.  This resonance often sits in the low frequency region,
>>> around the VRM output transition region, and has a strong tendency to
>>> cause peaking in the 100 kHz to 1 MHz range.  This peaking can cause
>>> noise modulation of the Serdes, which Lee has often observed.  If the
>>> PCB power delivery network has a lower impedance in the frequencies
>>> that affect the Serdes, than they ferrite filter does, then shorting
>>> the ferrite will help.  But if a ferrite filter network is correctly
>>> designed, it is well matched and does not cause peaking.
>>>
>>> Whether or not noise injected into a Serdes affects it's output is a
>>> function of the internal PLL/DLL design. This is hardly ever
>>> specified, but can be measured.
>>>
>>> Scott
>>>
>>> Scott McMorrow
>>> Teraspeed Consulting Group LLC
>>> 121 North River Drive
>>> Narragansett, RI 02882
>>> (401) 284-1840 Fax
>>>
>>> http://www.teraspeed.com
>>>
>>> Teraspeed(r) is the registered service mark of Teraspeed Consulting
>>> Group LLC
>>>
>> [snipped off the reset of the thread]
>>
>>
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