[SI-LIST] Re: A Question about Target Impedance Threshold computation

  • From: "Smith, Larry" <larrys@xxxxxxxxxxxxxxxx>
  • To: "weirsi@xxxxxxxxxx" <weirsi@xxxxxxxxxx>, "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
  • Date: Mon, 1 Jul 2013 04:58:29 +0000

Hi all, just catching up on some back email here..  The target impedance 
concept can be applied at many levels of assembly.

If there are several identical power consuming chips on the PCB, a target 
impedance can be calculated according to the sum of the current consumed by 
each of them.  It is highly likely that all of them will draw DC current at the 
same time so the DC target impedance needs to take into account the maximum DC 
current of each device.  

At low frequency, it is possible for the several devices to draw current 
transients at the same time so a conservative approach is to linearly add the 
several transient currents when making the target impedance calculation.  This 
may be appropriate when sizing the DC VRM and bulk/ceramic capacitors that are 
effective around the 1 MHz frequency band.  

As frequency goes up, it is more difficult to meet a conservatively calculated 
target impedance.  But it is also more difficult for the several current 
consumers to draw transient current in phase at exactly the same time.  It is 
more appropriate to add the transient currents in a statistical fashion with an 
RMS summation rather than linear summation.  This essentially assumes that the 
transient currents are statistically independent.  My rule of thumb is that 
transient currents from circuits on different clock domains are statistically 
independent.  The target impedance calculated by this method is easier to meet 
and is used with minimum risk if the transient currents from the several 
consumers are truly statistically independent.

Then within a single chip, there may be several circuit blocks that draw 
current from the same power rail.  The same concept applies here: if the 
circuit blocks are statistically independent (which is most likely the case if 
they are on different clock domains) then their transient currents can be 
RMS'ed together.  This is usually a good thing to do at die/package resonant 
frequencies which are often around the 100 MHz band.  It is really difficult to 
line up the current transients in time from several independent blocks so that 
they stimulate a 100 MHz resonance in a coherent manor.  

Using these concepts, a target impedance for a single chip can be calculated 
statistically from knowledge of circuit blocks drawing current from the voltage 
rail in question.  And at the PCB level, transient current drawn by several 
chips can be calculated statistically.  This makes the target impedance a 
function of frequency.  Steven Ohlsen's comment is correct, "It seems that the 
current portion of the target impedance equation varies from point to point on 
the board depending on a host of very complicated relationships."  It is really 
up to the component supplier to provide the target impedance for a chip and 
then for the board designer to combine the target impedances for the several 
chips on the same PCB power rail by adding linearly at DC and low frequencies 
and statistically at higher frequencies.  

In summary, it is highly probable that all circuits on the PCB will draw DC 
current at the same time and the VRM must be sized accordingly.  But as we get 
up into the 1 MHz, 10 MHz, 100 MHz and 1 GHz bands, the probability of drawing 
transient currents in phase at the same frequency greatly diminishes.  The 
target impedance at the different chip locations on the PCB should reflect this 
in different frequency bands.  

Regards,
Larry Smith

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On 
Behalf Of steve weir
Sent: Thursday, June 13, 2013 3:07 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: A Question about Target Impedance Threshold computation

Steven, target impedance applies at the point of use.  In some cases, 
interconnect impedance can become significant even at supra-audio frequencies 
in the 100's of kHz, but almost always is an issue by the low Mhz.  The target 
Z relation is also just a guideline.  It assumes resistive Z which is rarely 
the case over the frequency range any given PDN needs to support.

Steve.
On 6/13/2013 1:32 PM, Steven J Ohlsen wrote:
> Hello,
> I am somewhat new to the world of Power Integrity.  I hope this isn't 
> a dumb question, but I can not find any answer in the books I have or 
> online either.  I understand that the equation for Target Impedance is 
> (allowed Voltage Variation)/(max change of current).  However this 
> seems like a
> "50,000 ft" rule-of-thumb.  If your design meets this criteria then 
> all is well.  But if your design has difficulty reaching this 
> impedance target then what.  My observation is that when you get down 
> to the board level for example, there can be 30-40 balls on the 
> voltage regulator (and maybe multiple voltage regulators), and 50-100 
> balls on the device under test, and numerous decoupling capacitors 
> scattered around, between what points does the target impedance apply?  
> If you look at the board geometries then the current from Voltage 
> Regulator to Device may travel through a 1-inch (or more) wide path on 
> the power plane.  Current is also provided by the decoupling 
> capacitors whose current (probably) has a different path to the device 
> under test .  It seems that the current portion of the target 
> impedance equation varies from point to point on the board depending 
> on a host of very complicated relationships.  Simply dividing the 
> current portion of the target impedance equation by the number of 
> balls on the voltage regulator or by the number of balls on the device 
> under test also seems incorrect.  Is there a more design specific method to 
> compute the target impedance?
>
> Thank You all for your responses.
> Steven Ohlsen
>
>
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