[volt-nuts] HP 3458A DC current accuracy

Bob Smither smither at c-c-i.com
Wed Jul 11 22:50:39 UTC 2012

On 07/11/2012 03:49 PM, ed breya wrote:
> That which is more fundamental to the problem is the unavoidable (at room
> temperature) noise from the resistors. Even a "perfect" resistor with zero
> tempco has noise, so if you use resistors to measure current with a
> high-precision voltmeter, eventually you reach a resolution where the noise
> becomes dominant. If you reduce the bandwidth by averaging, the precision should
> reach the basic stability of the resistor - but the (in)stability itself may be
> viewed as noise of very low frequency - always too low to filter out unless you
> have a very long time.
> The resistors chosen for DMM current ranges may just be rational choices and
> compromises for the types of performance to be expected under normal usage and
> conditions, and considering the noise limits to resolution, versus the cost of
> extremely low tempco sample resistors.

I may be off here, but I doubt that thermal (Johnson) noise would limit the
precision of current readings.

As an example - consider using a one ohm resistor to measure 1 mA.  The voltage
corresponding to 1 mA is 1 mV.  Johnson noise is given as:

  en = sqrt(4*k*T*R*B)

or about

  en ~ 0.13 * sqrt(R) nv / sqrt(Hz) at 300 K.

A one ohm resistor in a 1 Hz bandwidth would be 0.13 nV or 0.13 ppm of the 1 mV

Thermals in the circuit could easily reach uv levels as others have suggested.
Another limitation might be resistor excess noise - a 1/f noise source that can
be much larger than the thermal noise - but I would think that engineers at HP
would pick a resistor technology (bulk metal foil) that minimizes that noise source.

Best regards,
Bob Smither, PhD                                   Circuit Concepts, Inc.
   Friendly relations with all nations, entangling alliances with none.
     --Thomas Jefferson
Smither at C-C-I.Com  http://www.C-C-I.Com  281-331-2744(office)  -4616(fax)
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