# Multiple power supplies in series: Negative voltage on one of them possible?

It is common practice to connect multiple power supplies in series to obtain a higher voltage; examples: 1, 2, 3, 4. Many power supplies are designed to handle this application well. However, users are cautioned to check the manual of a power supply if it is really recommended to use it in series with another one.

One issue that might arise is called polarity reversal, i.e. a negative voltage being forced on the output of the "weakest" supply in the chain of series-connected devices. How is this possible?

Note: Same story for batteries. One should make sure that the same type of battery is used together with another, and that multiple series-connected batteries are in equally good (or mediocre) shape.

The condition to consider for this to happen is a load beyond the rating of the supplies in question. Most severely, a short circuit. A short circuit need not be permanent and can even be a part of normal use: A motor, when starting, or a capacitor, when being charged from 0 V, looks like a short circuit, too.

To explain how a negative voltage can appear on one supply's output, let's use a diagram with some arrows. Supply A's output voltage shall be called VA, supply B's output VB, and the voltage across the load shall be called VL.

With KVL:

$V_A + V_B = V_L$

This is true for normal operation, when we want to use, for example, two supplies with VA = VB = 12 V for a load that needs VL = 24 V:

$12V + 12V = 24V$

For a short circuit, VL = 0 V, and KVL still applies. Thus, $V_A + V_B = 0$ or

$V_A = -V_B$

If we want to avoid negative voltages on any of the two supplies, the only possible solution is

$V_A = V_B = 0$

However, because of $V = R \cdot I$, and because any real power supply has a non-zero internal resistance, this also means that no current must flow. Now, a power supply will try to deliver current. Since the current or power limit of the two supplies will not be exactly equal, the "stronger" supply will be able to maintain a small, positive output voltage, and the only way to solve the KVL equation is by back-feeding the other supply, with a negative voltage across its output.