measuring very low resistance (nano- to microOhms)

[Ronnie]

Please help to find the method of measuring very-very low resistance. The range is from 0.0001 up to 5 mOhms.

Actually, I need the difference between two resistors, each of them is 2-5 mOhms. And the decimation should be such that I would be able to measure with a precision about 100 nOhms.

The Keithley models 622X (AC and DC current source) and 2182A nanovoltmeter combination can measure down to 10 n? with low power and low noise http://www.keithley.com/products/dcac/sensitive/acdc/?mn=62212182A   

[ElektroQuark]

Keithley's low level measurement handbook (available for free from keithley.com after registration)

Any link for download without registration?
Thanks.

[ejeffrey]

You can look at cryogenic resistance bridges.  There are several schematics published for them, and many are capable of measuring resistances with 7 digit accuracy and femtowatts of power dissipation.

The secret is in two parts: the first was mentioned: AC excitation.  The second important point is to do synchronous detection (as a lock-in amplifier).   You can do this with a couple of analog switches/multiplexors.  You just create a constance current source of 10 milliamp, and use some analog switches to turn it into a square wave that reverses the current polarity at ~18 Hz.  Then you amplify the voltage just a bit with a differential output amplifier (one that has normal and inverted outputs).  Use a second analog switch to alternately connect the two amplifier outputs to charge a capacitor.

10 milliamp through 1 microohm generates a voltage of 10 nanovolt.  A low noise amplifier can have 1 nV/sqrt(Hz), and if you average for 100 seconds, you can get your noise floor down to 10 nanoohms (in principle).  By passing the current through both resistors and using a difference amplifier, you could directly measure the resistance difference with some improvement in the needed dynamic range.

Of course, every part of the signal path is quite important.  The analog switches must have very low (or very balanced) charge injection, the first stage amplifier must be very low noise, and have enough gain that noise introduced later doesn't affect the result, but not so much that it clips due to interfering signals.  The switching frequency should be chosen so you get good rejection at 50/60 Hz -- either a sub-harmonic of the local line frequency, or faster than the line frequency and far from any harmonic.

The ultimate limit is given by the johnson noise of the resistor, but this circuit will not approach that even closely.  The voltage noise of transistors is just too high compared to such a low source impedance.  You could get 100 times or more improvement in the resolution by using a high ratio signal transformer to boost the voltage before the input amplifier.

[Ronnie]

Any link for download without registration?
Thanks.

This is the 6th Edition.

[aluck]

ejeffrey, thanks a lot!

Now all I have to do is just to make this thing work and go enjoy my well-deserved vacation somewhere in the Mediterranean

[ElektroQuark]

Any link for download without registration?
Thanks.

This is the 6th Edition.

Thank you Ronnie.
It seems some others have downloaded from your link too.

[Ronnie]

I have a hardcopy of the handbook given to me for free by Keithley representative in the Philippines sometime May 2005. The handbook is really nice to have as it helps me solve low level analog circuits problem especially leakage current in the sub pA at work. It is highly recommended