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I need to use a positive and negative potential on a circuit including an instrumentation amplifier. My lab only has single supply power supplies (only offers positive voltage). I know that I can reverse the polarity and achieve a negative potential, but this means using multiple power supplies. (I am pretty sure that I cannot reverse the polarity on a single rail to fulfill both my negative and positive potential needs as this will cause a short). I do indeed need to tie the grounds for both supplies to one another, correct?

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Yes, as long as the two supply outputs are floating (i.e. no common connection between them prior to connecting) then simply connecting two terminals together to serve as the common ground is fine.

You would connect the negative terminal of supply 1 to the positive terminal of supply 2, then use the free terminal of supply 1 as positive rail, the connected terminals as circuit ground, and the negative terminal of supply 2 as your negative rail.

enter image description here

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Your belief that the power supplies "offer only positive voltage" is fundamentally flawed. Most lab power supplies have two terminals, with the electric potential difference (colloquially, voltage) between them regulated to some value set by the controls.

Because voltage is a difference, it means they do not have one terminal with no voltage and another one with positive voltage. You can call one 0V and another 5V, if you want. You can also call one -1382787V and the other one -1382782V, if you want. Or \$\pi V\$ and \$(\pi+5)V\$. Or -5V and 0V. Any two numbers \$A\$ and \$B\$ where \$B-A = 5V\$ will do.

This is because every lab supply I've seen has galvanically isolated outputs. See:

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We can take the two different terminal of the different supplies to connect that as a common and then take the positive and negative supply from the remaining terminals
Just Like: https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcQsBjhkP0UbpyK_7Cj5grFbVxWxrKqxAKvsucb_5kO-qMFbdAI8

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