Howland current source

[awallin]

I made a 500uA Howland current source using an OP2177 and a 4x10k resistor array with resistance-matching to +/- 0.05 %.
I did some measurements and calculations and wrote about them in my blog:
http://www.anderswallin.net/2013/10/howland-constant-current-source/

Anyone care to verify the calculation? The TI app-note says "up to 1 MOhm output resistance with 1% resistors", so at least my result of 3.6 MOhms with 0.05% is roughly in the same ball-park.

How does one measure these high output impedances? When changing the load between 0 Ohms and 600 Ohms my current changed from 500 uA by <100 nA. I borrowed a 3458A for this, but if the output impedance would have been 10x higher even the 3458A would not have measured a change in current! Some amplification or smarter way of measuring required!?

Anyway this shows that getting really high output-impedances seems to require a design where one or more resistors can be trimmed on-board for best results.
This may be mostly of academic interest as I am using this in a precision Pt100 temperature measurement application where I also collect the voltage over a Pt100 'reference-resistor', so any changes in the current will be seen and can be corrected for.

AW

[Dr. Frank]

Hi,
your calculation of 3.6MOhm is correct, as the differential output resistance is defined as R = dU / dI.
Also your method is ok.

This type of GND referenced current source has the disadvantage that it needs matched resistors, but you might trim one of them (R1) to increase the output resistance to near infinity.
A further disadvantage is the common mode voltage on the OpAmp, which might be included in the calculation.

I did not examine your calculation, but you better should calculate the total differential (for your own exercise  ) which should give a more clear mathematical expression for the output impedance over mismatch.

You do not necessarily need a 3458A, (ok it has very versatile DCI ranges, but 7.5 digits only in that mode)
I assume, you did not set up the 3458A correctly, much higher values of output resistance should be possible to measure with that box...

Therefore any 6.5 digit, high impedance DMM as a 34401A will also do the job:
Use it in DCV mode, high impedance, put an appropriate stable shunt resistor in parallel, 2k in this case, yielding max. resolution at 1.000000 V for 500µA, i.e you can determine changes as low as 500pA on the last digit, while switching between 0 Ohm and 10k for a 5V voltage swing (instead of only 0.3V for 600Ohm), in series with the instrument .

Using +/-15V for the OPAMP should give enough volt compliance.

If the current change happens on the last digit only,  you would measure 1,000,000 * 10k = 10GOhm of diff. output resistance.
That's geeky enough, isn't it?

Frank

[Dr. Frank]

Hi,

I just have done that measurement on my own current source, just to demonstrate the capability of this measurement.

I used a 1 kOhm shunt for measuring a constant current of 1mA, giving a resolution of 1nA on the last digit of the 34401A, in 1V, 6 digit slow mode.
The display is absolutely stable.

Between 0 Ohm and 10kOhm in series with the shunt , there's a change of 1-2 nA in current only!

That calculates to dU/dI = 10V/2nA = 5 GOhm at least for the differential output impedance.

This setup therefore should be capable to detect easily your much lower impedance.

Frank