Current measurement with DMMs

[desert]

I measured current with three DMMS: 1 pcs 34465A (6.5 with 7.5 current measurement accuracy) and 2 pcs 3458a (8.5).

A current source is used to deliver 4.5uA current, a DMM is in series with a 1M Ohm resistor. DMM “I” port is connected to current source output, DMM “LO” port is connected to 1M Ohm resistor, 1M Ohm resistor is connect to current source GND.

Auto range is used for current measurement. Only one DMM is connected for each time.
The current readings are (10uA range is used for both 34465A and 3458a):
34465A: 4.501uA
1st 3458a: 4.498uA
2nd 3458a: 4.500uA

Then I exchanged the connection of “I” and “LO” of DMMs (DMM “I” is connected to 1M Ohm resistor, DMM “LO” is connected to current source output).
The current readings are (10uA range is used for both 34465A and 3458a):
34465A: -4.500uA
1st 3458a: -4.284uA
2nd 3458a: -4.236uA

Why 3458a DMMs current reading have big changes while 34465A is relative stable?

After that, I connected current source directly with 1M Ohm resistor, no DMM is in series. I connected current source output to a DMM “I” port, “LO” port was left open. The recorded current readings are:
34465A: 11.9nA
1st 3458a: -13.6nA
2nd 3458a: -3nA

Are these readings reasonable? Why 4.5V voltage gives so big current error?

[desert]

And I connected two 3458A in series with 1M ohm resistor, the current readings are not expected (should be 4.5uA for both 3458a, but the result different, I did not recorded the values).

[TimFox]

I used to lecture junior employees (before I retired) that if you don't write it down, it didn't happen.

[Bryn]

I used to lecture junior employees (before I retired) that if you don't write it down, it didn't happen.

Just like the common saying "pics or it didn't happen".

Anyway, for the issue raised, you're better off using a shunt resistor if you want to measure really high currents.

[guenthert]

[..]
Are these readings reasonable? Why 4.5V voltage gives so big current error?

Are you truly using a current source or are you attempting to set the current using a 1MOhm resistor in series with a 4.5V source?

[desert]

It's not high current, around 4.5uA.

[desert]

A current source is used to output 4.5uA.
4.5V is the calculated voltage on the 1M Ohm resistor, the measured value is very close to 4.5V.

[guenthert]

I can only suspect leakage to ground.  A drawing (or better detailed pictures) of the configuration including ground connections would help.

[Kean]

And I connected two 3458A in series with 1M ohm resistor, the current readings are not expected (should be 4.5uA for both 3458a, but the result different, I did not recorded the values).

What is the compliance voltage of the current source?