[SI-LIST] Re: inductance, Q-factor of antenna for RFID tag

  • From: olaney@xxxxxxxx
  • To: stein_axel@xxxxxxxxx
  • Date: Mon, 8 Jun 2009 12:38:10 -0700

Axel:
Presumably you are operating at the usual RFID frequency of 125 KHz, most
likely crystal controlled.  At this frequency everything is in the near
field and your "antenna" can be modeled as a loosely coupled inductor
with respect to the RFID tag.  Since you want to maximize that coupling,
the most important parameter is the area of your antenna loop.  You want
to keep your winding as close to the periphery of the board as is
reasonable.  This is also true for the individual turns.  Spiraling down
toward zero radius is wasted effort, so keep the turns bunched together.

Copper skin depth at 125 KHz is 0.19mm or .0074 inches.  Your trace
thickness is a fraction of this, so current will occupy the entire cross
section.  A straightforward way to boost Q under these circumstances is
to increase trace thickness.  Make the width sufficient to keep average
current density within bounds.  However, the trace width will be much
larger than skin depth, so current will flow preferentially along the
edges of the trace. This is where most of the I^2R loss will occur and it
will be higher than that of a uniform distribution. When designing the
turns, keep the ratio of width to pitch between 0.7 and 0.8.  Too close
increases proximity effect losses, too far wastes area.  Increasing the
width means fewer turns and lower inductance, but the parameter of
interest is not inductance per se.  The generated field is proportional
to NI, the product of turns and current.  Design for maximum NI and
(within bounds) let L be what it needs to be.

This makes the question sort of circular.  For a parallel resonant tank
circuit, the circulating current is Q times the drive voltage divided by
inductor impedance at the driving frequency.  Alternatively, the drive
current will be that which the inductor alone would draw, divided by Q. 
The point of maximizing Q is, of course, to let the circulating current
do the work while keeping the drive current low.  You need to know Q to
find I but you need to know I to design the inductor that determines Q.

There is a limit to the game.  There is a tolerance associated with the
resonating capacitor.  The inductance and therefore center frequency of
your fixed tuned circuit will pull somewhat depending on what metal is
nearby.  When the resonant peak shifts against the fixed frequency drive
you will have correspondingly large changes in opposite directions for
drive current and receive amplitude.  How much is proportional to Q and
there is such a thing as too much.

The optimal Q for this application will keep the amplitude within, say, 3
dB of center response after detuning.  Since you generally will not
control the details of mounting in the field, proximity effects can only
be estimated.  Play around with the various expected mounting
configurations to estimate delta L, factor in the capacitor tolerance to
compute delta F, then divide Fcenter by delta F to get your target Q. 
Anything higher than that is wasted and potentially detrimental to your
driver.  Of course, too much Q is a good problem to have.  The real
question is whether the target Q is even possible.  If not, then driver
capability is the main constraint.

Orin Laney

On Mon, 8 Jun 2009 03:40:47 -0700 (PDT) axel stein <stein_axel@xxxxxxxxx>
writes:
> Hi all,
> I am looking into increasing inductance and the Q factor of the 
> antenna for an RFID tag. The antenna is etched on a printed circuit 
> board. The antenna is a planar coil, the conductor is basically 
> rectangular shape (some slight taper at the edges) and the traces 
> are wounded in a rectangular shape with rounded edges.
> For sure, increasing the number of windings will increase L. But how 
> will L and Q react, if I widen the lines (line-to-line pitch 
> constant = reducing spacing, keeping all other parameters constant, 
> ) or if I increase the copper thickness (perpendicular to the PCB 
> surface).
> 
> Unfortunately, I do not have a 3D solver that can help me answering 
> these questions. Anyone out there, that can give me some feedback?
> 
> Thanks for your help,
> axel
> 
> 
>       
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