Monday, October 8, 2012

How to Calculate Power Supply Accuracy

If we go back a couple decades’ the output level of an instrumentation power supply typically had to be set by turning the supply's analog knob and watching the display of your voltmeter connected to the supply's output to achieve an accurate voltage level. Today that is still true with low end power supplies, but mid range and high performance supplies can deliver an accurate user set voltage level that you can trust. In this post we will take a look at power supply accuracy specs including how to determine a power supply’s voltage level accuracy as well as some other power supply accuracy calculations.

There are typically 5 specifications found on a power supply's data sheet that relate to its voltage level accuracy, they are:
  • Load Effect (Load Regulation): Voltage variations on the supply’s output level caused by changes to the load that the supply is connected to. The error here is caused by the supplies regulation circuitry not able to maintain the exact voltage level after a load change or change in current draw from the supply.
  • Source Effect (Line Regulation): Error on the supply’s set voltage level caused by non-ideal input AC line power. 
  • Programming resolution: When setting a supply’s level, that level is turned into a digital value that is used by a digital to analog converter (DAC). The output of the DAC is used by the supply internally as a reference to set the correct output voltage level. In the digital to analog conversion process there is always quantization error and that is what the programming resolution represents. The higher resolution the DAC (more bits) the less error.
  • Programming Accuracy: This is the key specification that encompasses includes the three just mentioned (load effect, source effect, and prog resolution) as well as parts tolerances such as amplifier drift.
  • Programming Temperature Coefficient: If the power supply is not being operated in its ideal temperature range a temperature coefficient error value is added for every degree out of that range.
As mentioned above, the only specs we need to calculate the supply's output accuracy are the programming accuracy spec, which includes load effect, source effect, and programming resolution, and the programming temperature coefficient spec, but only if we are not in the spec'd ideal temperature range. Of course just like every instrument, the supply's output accuracy cannot be computed until after the spec'd warm-up time which is typically no more than 30 min. Here is what our output accuracy calculation looks like:

Error Tolerance +/- = Prog Accuracy + Temp Coeff (if not in ideal temp range)

The specs will typically be in the form of a static value (such as 4 mV), a percentage of the voltage range, a percentage of the programmed voltage level, or a combination of two of them.

Let's walk through an example calculation using Agilent's N6761A Precision DC Power Module which is part of the N6700 family of modular power supplies. The N6761A is a high performance supply so it will have a high accuracy output level (low error tolerance). Below is a snapshot from the N6761A's data sheet showing the programming accuracy spec as well as other specs. 

For our example we will be operating the N6761A after a 30 min warm-up time at 5 V (low range) with a load pulling 4 A at an environmental temperature of 29 degrees C. Notice in the programming accuracy row that the ideal temperature range is 23 C +/- 5, since we are operating at 29 C we are 1 degree out of the temperature range so we will have to add temp coefficient error to our calculation. The voltage programming accuracy spec for the N6761A in the low range is 0.016% + 1.5 mV. The temperature coefficient spec is 40 ppm + 70 uV. Let's go through the terms of our accuracy calculation:
  • Programming accuracy is 0.016% of programmed value plus 1.5 mV, which is 5*.00016 + .0015 =  2.3 mV
  • Temperature coefficient is 1 degree so 1*(5*30e-6 + 40 uV) = 190 uV 
@ 5 V Err Tolerance is +/- = 2.3 mV + 0.19 mV = 2.49 mV

That is pretty good accuracy for a power supply that is just slightly out of its ideal temperature range! One thing to note from this calculation is that we are assuming that we are looking at the power supply level over some averaged time period lets say 10 power line cycles or 166.7 ms. If we are looking at some instantaneous point on the voltage level of the power supply we can see higher error due to noise. The noise on a supply level is covered in the Output Ripple and Noise or PARD spec on the supply's data sheet. In the above data sheet figure we can see the N6761A has a PARD spec of 4.5 mVpp and 0.35 mVRMS. If we had a high resolution scope we could see the noise on the supply level. If we take an average measurement of the supply level the noise cancels out. 

When working with a supply that has built in measurement capability (like most supplies on the market today) remember that the measurement accuracy is separate from the programming accuracy. Also the measurement accuracy error spec may be worse or larger than the programming accuracy spec. As an example, below is a figure from Agilent's N6741B power supply data sheet. The voltage programming accuracy spec is circled in green and the voltage measurement accuracy is circled in red.

As you can see the voltage measurement accuracy is worse than the voltage programming accuracy. In cases like this it is more accurate to use the programmed voltage level and not the measured voltage value.

In the accuracy calculation we did it was assumed that the supply was being used in constant voltage mode (CV), where the supply regulates the output voltage at a set level and allows the current to fluctuate as the load changes (most common way to use a power supply). What if you are operating the supply in constant current mode (CC), where the supply regulates at a certain current level and the voltage is allowed to fluctuate with the load? The calculation is the same except you use the current specs versus the voltage specs.

In this post we discussed what specs are used to make a power supply output level accuracy calculation. We then walked through an example calculation using Agilent's N6761A precision power module. We also compared measurement accuracy to programming accuracy. If you have any questions from this post feel free to email me and if you have anything to add use the comments section below.

Blog post on Power Supply Resolution versus Accuracy


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