Voltage Dividers

The safe measurement of high voltage can be accomplished by using a suitable voltage divider to reduce the high voltage by a known and constant ratio to a potential that is within the range of a voltage meter (VOM, DMM, etc.). In theory, this only requires 2 resistors in series with one end of the chain (R-2 or tail) connected to ground and the other to the high voltage (R-1 or head). Meter reading is taken across the tail resistor. The values of the resistors are chosen so that the ratio of R-1 to R-2 performs the required reduction (e.g. 100:1 or 1000:1, etc.). For a series comprised of a 100MegOhm (100M) resistor and a 1M resistor, the divide ratio is 100:1 and 7500 Volts would be read as 75 Volts on the meter. The value of R-2 is inversely proportional to divide ratio. That is, with R-1 constant, as the value of R-2 in Ohms decreases the divide ratio increases. 1000M and 1M would allow a reading of 7.5 which can be seen as a direct reading of ‘Kilovolts’. Also, this could obviously be accomplished with 100M and 100K resistors. This all seems simple and pretty straightforward, right?

Well, there are a couple of other factors involved. The meter used also has an internal resistance between the probes so that placing them across R-2 results in a pair of resistors in parallel. This means that the effective value of R-2 is the reciprocal of the sum of the reciprocals of the values of the 2 resistors: 1/R-2 = 1/R(tail) + 1/R(meter). Many modern DMM’s have a precision internal resistance of 10M. With such a meter, for a 100:1 divide using 100M for R-1, the tail resistor should be approximately 1.11M. The math is: 1/1.00M= 1/1.11M + 1/10M. The effective R-2 is then 1 MegOhm. In practice, I would recommend using a suitable potentiometer for the tail resistor, adjust it until the meter reading is correct for a known voltage, measure the actual resistance of that leg of the pot, and finally create a series of resistors that add to that resistance and treat them as a single resistor. For the mathematically challenged, a useful JAVASCRIPT divider calculator can be found on Bill Bowden’s Website (along with many other useful features.

The picture above shows my simple divider that may be used in open air up to several thousand volts. The flat blue resistor is about 1.5” long and is an OHMITE SLIMOX thick film resistor – 100M, 15 kV, 2 Watts that sells for about $4.00 at Mouser (a 1000M analogue is the same price). The tail is made up of ¼ Watt resistors totaling 1.11M.

In high current applications, R-1 must also have power rating sufficient to allow dissipation of the heat lost in the reduction.

In high voltage applications, the divider must me able to stand off the high voltage without complications created by corona or even arcing through or completely around R-1. Submerging the divider in transformer oil will boost its voltage handling ability somewhat but a proper high voltage resistor should be used in applications over 15,000 Volts. ******Attempting to directly measure 100’s of Kilovolts or even Megavolts should not be undertaken by anyone without careful planning and the right equipment.******

Our Very High Voltage work has necessitated the creation of a VERY STOUT 1000:1 divider array. R-1 was chosen to be 100.5. MegOhm To create this value, a very high voltage rated resistor measuring 93 MegOhm was placed in series with a smaller 7.5 MegOhm resistor to total 100.5 MOhm.

R-2 is a single 200 Watt wirewound 101.6 KOhm power resistor.

The chain is secured inside of a length of 4" PVC pipe that was filled with transformer oil and sealed.

Binding posts were installed in the shell and connected to the test points on the resistor chain inside. Attached to the lower 2 posts that are the measuring points on either side of R-2 is a full wave bridge rectifier that is glued to the shell externally.

The DC output of this bridge is carried to a tunable DC kilovolt meter.

Note that this is slightly different from measuring with a DMM as outlined above. The internal resistance of panel meters can vary widely and some may require DC input. The one I chose to use is a DC meter. It is certainly possible to place a fixed value resistor across the meter as determined by the equation at the top of the page. I chose instead to use a potentiometer with a range covering the calculated value. In this way, I have the ability to calibrate the meter periodically against a known voltage input.

Double Divider

The above design is an effective voltage divider but its limitation becomes apparent when attempting to measure split-phase voltage sources. When the secondary of a transformer is mid-point grounded or when two transformers are used in tandem with their outputs out of phase, the resulting output current is said to be single split-phase. The potential difference from one half of the phase (one side of the output) to the other is twice the potential difference from that same point to ground. A common low voltage example of this is the 240 VAC US residential service in most of our homes. The distribution transformer has its secondary mid-point grounded, resulting in split-phase current delivered to the home. Each side of the phase is 120 Volts to ground but because in one side of the phase the voltage wave is rising and in the other it is falling 180 degrees out of phase, there is an average RMS voltage difference between them of 240 VAC.

In high voltage work, the transformers (NST, x-ray, etc.) often supply split phase output to allow the use of lighter and less expensive components. Using the divider constructed above, it is only possible to measure one half of the output voltage from such a source because the other end of the divider is connected to ground. NEVER CONNECT R2 TO THE OTHER SIDE OF THE OUTPUT. The low value of R2 will allow dangerous high voltage to pass through the meter, destroying it instantly and utterly, and also possibly through the body of the one holding it with fatal results.

Our quest then was to develop a ‘double’ divider system capable measuring both sides of the phase and displaying the total output voltage on a meter. Several designs were investigated but the successful one consisted of two separate and identical dividers side-by-side with the measurement being taken across the series R2a – Ground – R2b as shown below. The value of R2’s to be used was not readily apparent, but it seemed at first that perhaps ½ of the calculated value should be used for R2 in each divider. Surprisingly, empirically generated data revealed that the value of R2 should in fact be approximately the calculated value itself.

In order to reduce the bulk and increase portability, one group member suggested the use of smaller separate enclosures for each of the R1’s and R2’s. To this end, two 150,000 Volt 125 MegOhm resistors

were secured inside of 18” lengths of 3” PVC pipe by means of binding post terminals set into the walls.

The R2’s were calculated to be 125 kOhm and 2 series of resistors totaling that value were constructed. The system was tested with a known 3900 VAC input and the reading on the DMM was slightly off. Three (3) kOhm additional resistance was added to each series and the system retested. This time, the reading on the DMM was 3.9 as expected. It appears that in a double divider such as this the two R1’s and the two R2’s must each be treated as a single series resistance mathematically. Then, R1 would equal 250 MegOhm and thus requiring R2 to be 250 kOhm. With a 10 MegOhm internal resistance in the meter, the calculation would be: 1/250,000 = 1/256,000 + 1/10,000,000. R2 would then have to be 256 kOhm. Treating the two R2’s as a single series resistance, they would therefore need to be 128 kOhm each, which exactly matches the empirical data. This, of course begs the question of why R2 cannot be just a single 256 kOhm resistor. The only problem with this is the issue of where to put the ground reference. This is interesting and perhaps someone will investigate this. At any rate, each resistor series was secured inside of 8” lengths of 2” PVC pipe by the same means as the R1’s.

Silicone rubber sealant was applied around joints and penetrations on all tubes. The caps were installed and the tubes will be filled with dry transformer oil. They will then be mounted to a rolling platform.