# How to Obtain Positive and Negative Voltage Rails from a Single Output Power Supply

## What are complementary positive and negative power supplies?

A complementary power supply provides equal and opposite polarity voltages relative to a common node. This is useful for op amp circuits that often require a positive 12 and a negative 12 voltage rail. Many benchtop power supplies feature this option with a mode known as tracking, allowing a single control for both positive and negative outputs.

Not all power supplies feature this option. Also, not all supplies have dual outputs.

## How can a complementary output be synthesized from a single output power supply?

Suppose we have an op-amp circuit that requires +/- 12 VDC voltage rails. How do we provide the complementary outputs when all we have is a variable 24 VDC power supply as shown in Figure 1?

Before you say it can’t be done, consider how the power supply is constructed. Benchtop supplies such as the B&K Precision 1550 are designed for floating outputs. In an ideal world there is no electrical connection between the ground and the black and red DC outputs. Such a power supply acts like a battery where we are free to wire the terminals in any way we choose.

Tech Tip: The analogy between a DC power supply and a battery is incomplete. Unlike a battery, the general-purpose DC power supply will not accept a reverse charging current. Many supplies have reverse voltage (diode) protection. Some power supplies clamp the output voltage to the internal DC rail. In extreme situations, a reverse current will cause irreversible power supply damage.

Figure 1: Picture of a single output regulated power supply with a resistive center tap to provide positive and negative voltages.

## Resistors are used to provide a virtual ground

Since our power supply is perfectly capable of providing a floating 24 VDC, the desired split +/- 12 VDC is a question of reference. We can use resistors to provide a virtual ground; again, with the understanding that the power supply outputs float. The center tap solution is shown in Figure 2 along with a slightly unbalanced load. The output is reasonably well balanced with voltage rails at 12.5 and -11.5 VDC relative to ground.

Figure 2: Schematic showing how the output of a 24 VDC supply is center tapped to provide +/- 12 VDC.

## Limitations of the single to dual rail technique

There are some serious limitations to this technique. The most important constraint is the balance between the load’s positive and negative current demands. This has a significant impact on the resistor choice. For example, if the load is perfectly balanced with the positive and negative loads drawing the same current, the center tap resistors may have a high value such as 10 kΩ. On the other hand, if there is a great mismatch, the tap resistors must have a low value. In fact, it may be necessary to “burn” significant amounts of energy to retain the voltage balance.

### Example 1 showing an unbalanced system with small currents

Our first example is taken from Figure 2. Here the load represented by constant current sources is slightly unbalanced with the load demanding 2 mA from the positive rail and 3 mA from the negative rail.

We could enter the values in the simulator to see the results as I have done with this MultisimLive example. Another solution is to dust off the circuit theory textbook and solve the system using a supernode method. The solution for the Figure 2 circuit is shown in Figure 3. In this example the circuit has been redrawn into the traditional textbook configuration with the floating power supply top-and-center. The common ground node is moved to the base of the schematic.

Figure 3: Hand-drawn schematic and supernode equation solving for the rail voltages in an unbalanced system.

### Example 2 showing an unbalanced system with relatively large currents

Suppose the loads were changed to 100 and 200 mA respectively. Let’s assume that the tap resistors must consume at least ten times the load current. With that stipulation, let’s set the tap resistors to 50 Ω. I’ll leave it to you to solve the equation, however your results should show the rails at 14.5 and -9.5 VDC.

### High power dissipation penalty for unbalanced systems

If this unbalance is unacceptable, we can shift to a 25 Ω pair. The rails are now at 13.25 and 10.75 VDC. We could continue to lower the resistance to improve the balance.

However, there is a catch:

P_{TapResistors} = \dfrac{E^2}{R} = \dfrac{24^2}{25 + 25} = 11.5 \ W

Those little ½ W resistors shown in Figure 1 must be increased to 10 W devices - allowing for a 2x safety margin. Together, they consume a significant portion of the power supply’s output. As some point, we pass into the zone of silliness when we consider the energy budget for a reasonable design.

## Conclusion

While this center tap method works in a pinch, we spend more energy attempting to balance the rails than to power the load. Consequently, the technique has limited applicability relegated to low-power circuits.

With that said, this has been a good review of circuit theory. It expands our understanding of the floating power supply. It also answers the age-old question:

When will I ever need to use nodal analysis?

Best Wishes,

APDahlen