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From: Winfield Hill
Subject: Re: Current Source Multiplexer
Date: 23 Nov 2002 09:08:34 -0800
Organization: Rowland Institute
X-Newsreader: Direct Read News 4.11
>John Larkin wrote >
>> Ken ddreamer_kNOSPAM@hotmail.com wrote:
>>> I have a project about to start that requires the use of a current
>>> multiplexer. Specifically there are N current sources ranging between
>>> 1 nA and 10 mA, only one of which should appear at the output.
>>> Has anyone ever had to deal with a circuit like this? I am hoping for
>>> a circuit that will not degrade bandwidth or introduce error, even at
>>> 1 nA (impossible I know, but I can always hope:)
>> An HC4051 will probably work OK; they leak in the picoamps. Can't be
>> specific about AC crosstalk.
>> Caution: if the unused current sources are allowed to pull up to the
>> 4051 Vcc rail, current will be squirted into the chip substrate diodes
>> and all hell will break loose; don't let this happen.
>> Uh, "1 nA" and "bandwidth" really don't belong together.
> BW will degrade at low currents due to parasitic and other capacitances,
> so "1 nA" and "bandwidth" can be used in the same sentence :)
A few back-of-the envelope calculations show that you don't seem to be
in any danger of going beyond achievable limits with straightforward
technology. A CD4051-style multiplexers would be a good choice if you
are unwilling to have a separate preamp for each channel. While it does
create typically 30pF per eight channels on the selected sensor channel,
this doesn't preclude measuring to the sub-nA level with 90kHz bandwidth.
In fact the rather high 90pF value for HC4051 chips might be acceptable.
To measure down to 1nA currents, we'll say your noise spec is 0.2nA rms
noise, which gives us 0.6 pA/Hz^1/2 noise density for a 90kHz bandwidth.
Here's how to do the relevant calculations:
First we'll consider the value of trans-resistance amplifier's resistor.
We'll ignore the issue of range changes, etc. for now. Our first concern
is Johnson noise, which is i_n = (4kT/R)^1/2 so we get R > 4kT / i_n^2
which is satisfied for Rf values above 38k. Another criteria might be
signal size, if we want say 1mV output from 1nA input, then Rf = 1.0Meg.
What about the required opamp bandwidth, it must have a high enough gain
to force the signal current through the Rf rather than the shunting input
capacitance. The relevant equation is f_T > fc^2 / fRC, where fc = 90kHz
and fRC would be 3.5kHz for 1M and 45pF of total input-node capacitance.
This tells us f_T must be at least 2.3MHz, which is rather relaxed, and
why I suggested even the 90pF HC series multiplexers might be acceptable.
What about the i_n = w e_n Cin noise? en-C noise is often a killer at
high frequencies. Will the e_n < i_n/wC voltage-noise requirement for
our opamp be achievable? For 45pF and 90kHz we get e_n under 23nV per
root Hz, which is also an easy spec to meet. For example, a FET opamp
I like to use for difficult wideband low-current measurement problems
is Burr-Brown's OPA655, whish has a 230MHz bandwidth and 6nV noise, so
your requirements are far from the usual limits.
> I agree that unused current source will need to be shunted away from the
> switch. It is surprising that a standard analog multiplexor does not exist
> to act as a "current switch" when unused inputs are automatically shunted.
It's possible a small Schottky diode to ground on each input will solve
the problem. But the issue is the voltage drop of a small diode at 10mA
and whether the resulting 4051 parasitic currents would exceed say 200pA.
Certainly a 4066 switch section can be turned on for each un-addressed
sensor as a bullet-proof solution.
You're still left with the problem of a huge 1nA to 10mA dynamic range.
Our 1M resistor creating 1mV at 1nA reaches 10V full scale at only 10uA,
so clearly you need a range-changing circuit or another approach. One
possibility is a log amplifier. You could set it up for 1.0V/decade and
thereby handle 8 decades of 0.1nA to 10mA signal. This method can be
used with an offset to an exponential converter to create easily-changed
Another possibility is a current-to-frequency converter. While these can
easily handle your dynamic range, the time needed to measure the lowest
frequencies may be unacceptable.
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