From: Winfield Hill
Subject: Re: Adjustable current source
Date: 19 Dec 2002 04:06:21 -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.
>> Actually, the current may be closer to 200 mA. ...
> 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!
Hmm, 10 watts, that resistor's going to get hot! We can't use room
temp for 4kT, which means the resistor must be a higher value, which
means it'll dissipate even more power at 200mA, which means... OK,
let's use a 500 ohm resistor, requiring 100V and dissipating 20W at
200mA. We'll use a large 100W wire-wound unit bolted to the chassis,
say its temperature gets up to 77C = 350K, so it's Johnson noise is
6.4pA. That means our opamp/reference noise component can be 7.7pA,
and the opamp/reference voltage noise requirement is a more relaxed
3.8nV. So going to a higher resistor value is helpful, even if it
does require a 100V 20W low-noise reference rather than 50V and 10W.
> 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. :-)
Mike, I'm glad your requirement was only 10pA/root-Hz, had it been
5pA, or 2pA instead...