From: Winfield Hill
Subject: Re: Adjustable current source
Date: 18 Dec 2002 14:21:30 -0800
Organization: Rowland Institute
References: <3DFFF5AD.1D45@sneakemail.com> <3E00C854.7CC5@sneakemail.com> <3E0111D8.2D1D@sneakemail.com>
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Mike Monett wrote...
> Winfield Hill wrote:
>> 10pA? No problem.
>> Let's say you make a conventional quiet 10mA current source using
>> a 1.0k sense resistor. The Johnson current-noise density is
>> (4kT/R)^1/2 = 4.0pA/Hz^1/2, so the resistor isn't a problem. We'd
>> like the voltage noise of the 10V reference and controlling opamp
>> to be under say 4pA * 1k = 4nV/Hz^1/2, which isn't a problem either**
>> using the right components. This would yield a 0 to 10mA source with
>> under 5.6pA of current noise. BTW, the shot-noise density of 10mA
>> current is (2 q I)^1/2 = 56pA, but film resistors don't have shot
>> noise (see AoE page 432), so that's no problem. :>)
>> ** At least it's not a problem at frequencies above where the
>> voltage reference's low-pass filter (you did use one didn't you?)
>> becomes effective. :>) But I imagine that at low frequencies
>> voltage reference "noise" will create a messy 1/f noise / drift
>> in your otherwise-quiet current. :>(
> Actually, the current may be closer to 200 mA. According to their spec,
> the main coil sensitivity is 20 MHz/mA. Assuming they use a permanent
> magnet to supply a bias field, the range from 2 to 6 GHz can be covered
> with a 0 to 200 mA source.
I saw that, but I had assumed for low-noise purposes you'd be glad to
use a limited frequency-adjustment range.
> The coil resistance is 20 ohms, so the voltage across the coil is 4V
> at 6 GHz. Another 30 ohms could be added in series to adjust the
> maximum voltage to 10V.
Nope, that's not how I'd attempt to make a 200mA 10pA current source.
Working from a 10pA noise-budget approach, let's assume 8pA from the
resistor and the rest (6pA) from the amplifier/reference. We get 8pA
from a R >= 4kT/i_n^2 = 250-ohm resistor, which means a current-source
sense voltage of up to 0.2A * 250 = 50 volts. That's not so bad, but
it will also dissipate 10 watts at 200mA full-scale, which seems just
a bit strange for a quiet resistor!
The voltage-noise budget for the reference & opamp = 6pA * 250 ohms =
1.5nV, which is tough, but not impossible. Create a "quiet" 50-volt
reference (say 500nV), heavily filter it down to the 1nV level, and
use a quiet 1.0nV or less voltage-noise opamp. We'll have to create
a pair of tracking bootstrapped supplies for the opamp. Maybe a few
other messy details. A veritable piece of cake. :-)