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Every so often you'll need to measure resistance that is well beyond the range of your digital multimeter's ohms measurement capabilities.  This might be measuring the reverse resistance of a diode in a precision peak-hold circuit, or verifying that there is no leakage across a printed circuit board.  Most multimeters extend to perhaps 20MΩ or so, with a few (typically more expensive bench types) able to measure as much as 200MΩ.  A very ordinary 1N4148 diode has a (datasheet) reverse resistance of around 800MΩ, and that's well outside the ability of all but the most expensive laboratory instruments.

This technique is described very briefly in AN-014, but it's potentially so useful that it was decided that it would make a good app. note itself.

Normally, very expensive laboratory instruments are used to measure very high resistances.  These include the electrometer ^[ 1 ] and 'source-measure units (SMUs).  Both are well outside the scope of the home workshop, and few professional workshops will have anything of the sort either.  It's not often that you need to make these measurements on very high resistance devices, so it should come as no surprise that there's not a great deal of useful information available.

Multimeters (of the digital kind) inject a known current into the external resistor, and measure the voltage across it.  This is why many digital meters will show the forward resistance of a diode as (say) 0.55kΩ - that is not the resistance, simply the forward voltage.  Not all meters do this by default though, so many have a separate 'diode test' function which does show the voltage.

Figure 1 - Traditional Resistance Measurement

The drawing above shows how the resistance is measured.  Most meters have multiple ranges (or are auto-ranging), so I've just shown a single range, suitable for measuring from zero to 1.999kΩ  The 1,999k is what you see with a typical 3½ digit meter - the most significant digit in such meters can only be a zero or a one.

A current of 1mA is applied, so the meter reads the voltage and displays the result as resistance.  The maximum voltage that can be displayed is 1.999V, and a 1k resistor will show 1.000kΩ because it has a voltage of 1V across it.  Of course, 1V at 1mA equals 1k (by Ohm's law).  The maximum resistance you can measure depends on the meter, but most meters will 'top out' at around 20-40MΩ or so.  Some bench meters can measure up to 200MΩ.

Given the above, you may well wonder how it's possible to measure a resistance of 1GΩ or more, as I have done for 1N4148 diodes (amongst other things).  Obviously, no affordable multimeter can measure that much resistance, but with some trickery it can!  The meter is used on its voltage range, and connected in series with the reverse biased diode.  Then a known voltage is applied (say 10V DC), and the meter will show a reading of perhaps 100mV.  Note that measurements must use DC, although AC measurements are theoretically possible.  However, it will be extremely difficult to ensure that no AC noise is licked up by the meter, so the measurement could easily be wrong by an order of magnitude!

Almost all digital multimeters have a 'DC volts' input impedance of around 10MΩ (most of mine measure 11MΩ, so we'll use that for this exercise) on the DC voltage range, so a voltage of 109mV across 11MΩ means the current is 9.91nA.  The remainder of the voltage is across the diode, which must also be passing 9.91nA.  If the applied voltage is 10V, that works out to a total resistance of just over 1GΩ (10V / 9.91nA = 1GΩ).  In the figure below, the 11MΩ meter resistance has been subtracted, giving the external resistance as 998MΩ.

Note that for very high resistance (1GΩ or more) you need a meter that can measure down to 10mV accurately.  Some meters have a millivolt range that might be usable, but you may find that the meter expects a low source impedance when measuring on the millivolts range.  For example, my bench meter has a small DC offset when used on the millivolts range, which is likely due to the use of an internal amplifier which has a small (about 4mV) DC offset that makes it unusable for this application.

Some meters have different input impedances depending on the range.  This is easily measured with switched range meters, but it's not so easy if the meter is auto-ranging.  Because the end result of a measurement using this technique is such a high resistance anyway, a variation of ±1MΩ is probably neither here nor there.  Although I recommend a test voltage of 10V, you can use higher voltages if necessary.  Be very careful to ensure that the voltage is less than the expected breakdown voltage of the component you are testing, and be especially careful (for your own safety) if particularly high voltages are used.  The power supply used for the test should have current limiting (so it's not damaged by an accidental short-circuit), or use a series resistor to limit the maximum current if you accidentally short out the supply.  As explained below, regulation has to be excellent to enable accurate measurements.

Figure 2 - Voltmeter Resistance Measurement

Extreme precision is not necessary (one could subtract the 109mV or 11MΩ for example as I've done here), but the end result is 'good enough' for most measurements.  This is particularly true since such high resistance values may be dependent on temperature and/ or humidity, and even the smallest amount of moisture can affect the reading dramatically.  I measured between tracks of a 50mm length of Veroboard, and when dry I obtained 6.2mV (almost 18GΩ), but just breathing on it dropped the resistance to well below 1GΩ (albeit briefly).

C1 (10nF, 100V) is optional.  Surprisingly, it doesn't have to be an extra-low-leakage capacitor, because it's in parallel with the 10MΩ or so of the meter.  Provided it has better than 100MΩ of dielectric resistance (and most ordinary caps will be far better than that) it won't affect the reading.  The charge time isn't as great as you may expect (typically a couple of seconds), but it will help to remove any noise which will make the reading unstable.  The low frequency limit is determined by the cap value and the meter's input impedance (R_int).  With 10nF, it's around 1.6Hz, so most mains noise should be attenuated quite well.

This is a very useful technique if you ever need to measure particularly high resistances, and it doesn't appear to be widely known.  There are (of course) specialised meters for measuring extraordinarily high resistances, but the humble digital multimeter does a perfectly acceptable job with some care.  Quite obviously, the DUT (device under test) must be suspended away from anything that may be ever-so-slightly conductive, and the meter leads also have to be very well insulated.  The smallest amount of leakage can create a very large error.

You also need to check your meter's specifications to determine the error.  Most are better than 1%, but the least significant digit may make a big difference for very low leakage test devices.  The specifications will typically state accuracy as (for example) ±1%, ±2 'counts' (the least significant digit).  That means that 100mV could be shown as anything between 97mV and 103mV, and the error is worse as the voltage is reduced.

It's only after you've done this type of measurement a few times that you really come to grips with the extraordinarily high impedances that exist in some circuits.  Even printed circuit tracks may be suspect unless the appropriate points are protected by a guard track or similar (which is not possible with Veroboard).  If you've never heard of a 'guard track', see Designing With Opamps, High Impedance Amplifiers.  The guard track (or ring) effectively 'bootstraps' the enclosed circuit, protecting it from external (surface) leakage.

It's educational to monitor the reverse resistance of a 1N4148 (or any other) diode, while holding a soldering iron nearby - not touching, but a couple of millimetres away.  Even a small amount of heat will reduce the reverse resistance (aka leakage) dramatically.  At a barely noticeable elevated temperature, you may see the monitored voltage rise from 100mV to 400mV or more, indicating that the leakage has quadrupled.  That's roughly the equivalent of the resistance falling from 1GΩ to around 250MΩ.  That's a big difference, and it may be critical in some circuits.

Noise may be a problem when taking measurements like this, because impedances are all very high.  Some meters are better than others at rejecting mains hum and other extraneous noise, which can make the final reading unsteady.  If the impedance is particularly high, you can't even use a capacitor to filter it out, because the cap's dielectric may not be much better than the device being tested.  You can use a larger (preferably polypropylene) cap in parallel with the meter (rather than the 10nF cap shown above), as they have a very high resistance dielectric.  This will make the measurement process a little slower though, because the cap has to charge via the external resistance of perhaps several GΩ, and the final circuit may still not be able to eliminate 50/60Hz hum effectively.  The arrangement shown in Figure 2 has been used many times now, and is very successful.

It's important that the external supply is free of noise and very well regulated.  Small voltage changes that have no effect whatsoever on normal circuits will cause the meter reading to change.  This is especially troublesome when measuring capacitor dielectrics, because the capacitor will pass low frequency variations and cause an unsteady reading that may not be able to be interpreted with any accuracy.  I know this from personal experience, and have had to resort to using an external regulator after my (regulated) power supply to ensure that the output voltage is as stable as possible.  Only very low current is necessary, as we are looking at devices that draw only a few nA or even pA of current once settled.

If this is something you discover you need to use often, it would be worthwhile to make up a very short lead for your meter (essentially a banana plug with a stub of wire), with an alligator clip at the end to hold one end of the DUT.  Make another short lead for the common terminal on the meter.  The negative of the external supply clips onto the the common lead, and the positive goes to the other end of the DUT.  This helps to minimise external hum pickup, and also ensures that there is the greatest possible impedance at all points of interest.

The insulation resistance of the leads from you power supply is of no consequence, and even the internal insulation resistance of the meter is relatively unimportant (it's in parallel with 10-11MΩ).  The only point of specific interest is the connection from the DUT to the external supply, and if that's in mid air it's effectively infinite.  No PCB material (or anything else) should bridge the DUT itself, as the leakage is an unknown quantity.

This apparently simple technique doesn't seem to be as widely known as it should be.  It's not something you need very often, and some may never need it at all.  I've used it several times while developing projects or special designs for clients, and it's certainly a far better proposition than spending $thousands on specialised equipment that may only be used every couple of years.

If you want to get accurate readings, you'll need to use a second multimeter to measure the input impedance of the one you intend to use.  Not all specifications include the input impedance, and around 10MΩ is often assumed, but as I found with several of my meters, they are actually 11MΩ.  The error isn't great, so you may not feel that it's necessary to verify the actual impedance.

This technique doesn't place your meter or the DUT at risk (provided the external voltage is less than the breakdown voltage of the DUT).  The meter is in voltage mode so is a high impedance, and even a shorted DUT won't harm the meter.  The test voltage depends on what you're testing, but 10V is a good starting point for most measurements.  If you must use higher voltages, do so with extreme care.  Anything over 50V is potentially dangerous, and you do so at your own risk.

1. Electrometer - Wikipedia

No other references to this technique have been located on-line.  Some might exist, but even an extensive search failed to locate anything even remotely close.  One was found, but it was published after I suggested this technique in AN-014, so it's not unreasonable to assume that my technique was used as inspiration.

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