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LM234: How load resistance impacts set current?

Part Number: LM234
Other Parts Discussed in Thread: LM334, TL431LI, LM4041-N

Hello guys,

I am using LM234Z-3 in my current design with the intention to give me either 1mA (Rset = 68Ohm) or 2mA (Rset = 34Ohm) constant current for my load that can be in the range of up to 5Kohm.

Bellow is the schematic around LM234. As you can see, my V+ node of LM234 is supplied with +12V. What I noted while testing on the board is that LM234 delivers 1mA constant current for loads of up to 3.2KOhms and 2mA constant current for loads of up to 1.7Kohm. When the load resistance is above the threshold, constant current starts dropping down.

Do you, guys, have any idea what might cause constant current to drop? By reading LM234 datasheet I could not find any info on how load resistance influences constant current.

Also, do you have any better idea on how to design constant current source for the loads whose resistance can vary in a range from 100Ohm to 5Kohm?