The Classroom

# Measuring Capacitors

Daniel Koch

Issue 45, April 2021

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Measure unknown capacitors or check for faulty ones using different techniques and instruments.

Last month, we touched on capacitors while looking at inductors and how to measure them. We needed that explanation to help understand what was going on with the inductor circuits, but we ran out of space to discuss how to measure capacitors themselves. That turned out to be a good thing, because there’s far more to say than we were originally planning to.

While many capacitors have their values marked on them, there are still situations where the value needs to be measured. Sometimes, a fault will be suspected, and comparing a measured value to a labelled value will provide answers. At other times, tolerance may be an issue when commonly available ranges of capacitors are often 10% tolerance at best. That’s fine for a power supply rail filter, but not for a tuned circuit. Additionally, more and more labelling systems are becoming used as Chinese manufacturers go their own way. Sometimes, the value is just not clear. Additionally, you may need to find the capacitance of a circuit or component group.

For a theory recap in capacitors themselves, you might like to visit last month’s Classroom (Issue 44), which covered the construction and operation of capacitors. However, a very brief summary is in order.

A capacitor is formed from two conducting plates separated by an insulator called a dielectric. If a potential difference is applied across the plates, a charge builds up. The charge in Coulombs (Q) is equal to the capacitance in Farads (C) multiplied by the potential difference in Volts (V): Q=CV

# TIME CONSTANT

The main property that interests us for testing purposes is the Time Constant. This is represented by the Greek letter Tau, appearing as ‘T’. The time constant is the time taken when a capacitor is charged via a series resistance, to reach 63.2% of the applied DC voltage. It can also be taken as the time to discharge from the applied voltage to 36.8%. It just so happens that T=RC, where T is the time taken in seconds, R is the resistance in Ohms, and C is the capacitance in Farads.

The very useful thing about time constants in RC networks is that the charging curve is generally known. And it just so happens that the capacitor is 63.2% charged in one time constant, then the graph shallows off as charging slows. This becomes very useful later on, as this 63.2% occurs at the five eights point. Many maker-accessible oscilloscopes have either eight or ten vertical graduations.

Technically, the time constant concept applies to any capacitor without a resistor in series, because all capacitors have some Equivalent Series Resistance (ESR). However, often the ESR is difficult to determine, or just too small to be useful. Generally, capacitance measuring tools, be they stand-alone or in a multimeter, use a known internal resistance, and a square wave. The time taken and voltage across the capacitor is measured and used to calculate the capacitance.

# ESR

No component manufactured by humans is pure or perfect. Theory lessons often assume ideal components while exploring concepts, and this is a valid approach. It’s no use explaining the complicating or extraneous factors involved to someone who is still trying to make sense of the basic concept. It’s the same with capacitors. Typically, there is an element of resistance and inductance to every capacitor. We don’t focus on inductance alone very often in this setting, because it’s largely academic and rarely if ever results in any effect. Equivalent Series Resistance is different, and the effects of inductance are considered in it.

ESR is a property of all resistors, but varies wildly with material and construction types. In some smaller capacitors or certain constructions, it can be ignored. In others, it’s a significant problem. This applies particularly to Aluminium Electrolytic capacitors. Because the ESR affects charge and discharge rates, it affects the maximum current a capacitor can handle. Because large electrolytics are often used to supply bulk current in power supply filtering or similar situations, care must be taken to choose the right capacitor. Most quality electrolytics have a low enough ESR to do the jobs asked of them, but some very cheap ones are an issue.

A look at many catalogue listings from electronics suppliers reveals that there are low-ESR electrolytics produced, too. These are especially constructed to have less ESR than their counterparts, and are particularly useful for high-frequency circuits. Remember, if the ESR impacts the time a capacitor can charge and discharge in, then it affects the maximum frequency that capacitor can be used at. This is because the higher the frequency, the shorter the time available for a charge/discharge cycle to take place in.

There are different standards by which to measure ESR. In fact, one of the sources referred to for this article noted that ESR is “easier to define than specify”. One of the reasons for this is that ESR is not constant. Because it is made up of accidental inductance within the materials and leads of the capacitor, as well as the resistance created by the same, ESR is affected by temperature, frequency, and age. Many materials change or degrade over time, and electrolytes are a serious offender here. At very high frequencies or temperatures, they can dry out and become irrelevant.

We tend to only worry about ESR in electrolytic capacitors. Other types are generally better sealed, made of more stable materials, and less temperature- and frequency- sensitive. However, most other types are only commonly useful for values below around 1μF. After this, either aluminium or tantalum electrolytics are the main option. In linear power supply situations, ESR standards are generally given as 120Hz, while switchmode power supply components need to be certified at 100kHz or more. Other applications will usually consider ESR at the self-resonant frequency of the component or the intended frequency of operation.

WARNING: Make sure any capacitor is discharged safely before and after any testing. To avoid discharge currents that are too high, use a resistance of at least 1kΩ , which is fine for voltages in the maker-safe range below 50V.

# BASIC FAULT TESTING

A healthy capacitor will read ‘open circuit’ on a regular multimeter set for DC resistance, because even the current path that does exist in the imperfect component has a higher resistance than most multimeters will work at. Many multimeters stop at 10MΩ resistance. Our DMM has a range of 40MΩ, and a 1000μF 16V electro we tested read 39MΩ.

If measuring an electrolytic capacitor reveals a resistance reading that is high but still lower than around 1MΩ (in other words, if you see a reading at all on most meters), the capacitor is likely to have developed very high leakage and is failing. Just for comparison, we tested a 10μF 16V and 1μF 63V and got readings of O/L (out of range) on both.

In some cases, the reading will be quite low indeed. Any capacitor which results in a reading on a multimeter of any less than six figures can realistically be considered short circuit, although there are some uncommon exceptions and caveats to this. Non-electrolytics are even less likely to give a reading in the range of the meter.

# TESTING ESR

Because of the above factors, ESR is difficult to test. While there are a variety of ways to do it, they’re even more involved than the ones we’re going to detail shortly for finding unknown capacitors. For most makers who need to know the ESR of capacitors, purchasing a dedicated ESR meter is really the best option. If you work with power supplies, high-frequency, or audio circuits on a regular basis, then the ESR meter will make your life a lot easier.

Not only does an ESR meter allow you to gain the data for some of the complex calculations involved in those circuits (way beyond the scope of Classroom), it also allows much easier fault finding. Data is available for the expected ESR of most capacitor types, so comparing it to the measured value can help determine a faulty item.

We recently purchased an ESR meter for ourselves from our friends at Element 14. We bought the Peak Electronic Design Atlas ESR70 model. This has the benefit of being a test meter for establishing the value of low resistances, as well as giving the value of the capacitor measured. It tests at the industry-standard 100kHz. It includes an automatic discharge function, but any capacitor charged to dangerous voltages or with significant current should still be discharged first. We tested ours on a 1000μF 16V standard aluminium electrolytic capacitor with a 10% tolerance.

One of the reasons we like this instrument so much is that it is simple to use:

STEP 1: Connect the component to the leads.

STEP 2: Press the ‘Test’ button.

STEP 3: Wait.

STEP 4: Read the value off the screen.

Just for thoroughness, we hooked up the same capacitor, after discharging it, to our Peak Atlas LCR40 reviewed recently. This instrument is more accurate in determining actual capacitance, as the ESR meter only does this as a secondary function at 100kHz. The LCR40 performs the test with a DC current, and measures charge time, and discharge time after removal of the current. While the ESR meter showed a capacitance of 1116μF, the LCR40 showed 1088μF. That’s fairly close for a capacitor of this size under such different test conditions.

# DETERMINING UNKNOWN CAPACITORS

Of course, what we really set out to do with this installment of Classroom was demonstrate several methods of determining the value of unknown capacitors. These could be unlabelled capacitors or ones whose labelling has become damaged, but far more commonly these methods will be used to determine if a capacitor has the value it is supposed to have. We’ll work through several options which use test equipment or special circuits, before sharing a design we’ve modified and compiled from several different projects online using an Arduino to make a basic capacitance meter.

# MULTIMETER

Multimeters are becoming more and more affordable, and examples with the ability to measure capacitance can now be found for under \$50. In fact, we found examples for less than \$20 but they were not from reputable sellers and did not appear to possess any build or design quality.

The challenge with these meters is accuracy. While many state 5% or even less, our experience has not filled us with confidence regarding the truth of these claims, even among units from the big retailers. If they really are accurate to 5% or less, then that’s good enough to determine if a capacitor you have is faulty or not. It is not, however, good enough for constructing, say, a tuned circuit unless it will be designed with a fair range of adjustment.

Additionally, the upper and lower range limits can be an issue. Often, capacitors in the low picoFarads will not be measured properly. Our multimeter’s capacitance function has a lowest range of 4nF, but we found values of 500pF or less were starting to show results implying a lack of accuracy. Additionally, an upper range of 100μF is stated, and sure enough, a 1000μF capacitor attached to the probes read O/L.

Despite this, if your most common capacitor demands fall within the ranges the option is still attractive.

To use a multimeter that measures capacitance, you may have to select a dedicated position on the mode dial, or a group position on the mode dial and use the function or mode button to select capacitance. Be careful, because on the latter option, it’s really easy to forget the mode button step, and get very confused about the reading. If the reading is in, say, ohms, you’ll realise. If the reading is just O/L (out of range) you may not realise, and write off the capacitor as faulty.

The best advice is to read the manual for your meter carefully and familiarise yourself with its functions, methods, and limitations before you try to test a capacitor. This way, you’re more likely to get the results you need.

# CAPACITANCE BRIDGE

One of the oldest methods of determining unknown capacitance is a bridge circuit. Bridge circuits can be made for determining the unknown value of many different components, and work by balancing a known value against an unknown value, and measuring the difference. All are variations or derivatives of the Wien Bridge.

In its simple form, the bridge is built with two resistors and two capacitors, a null detector and an AC voltage. One capacitor is known, while the other is not. The resistor in series with the unknown capacitor needs to be variable. In the middle is installed a ‘null detector’, which is a sensitive voltmeter capable of reading AC voltage and having a centre zero point. The variable resistor is adjusted until the voltmeter reads 0V, which represents a balanced circuit. When that occurs, the resistance of the variable resistor needs to be measured and the following equation performed:

Where CX is the unknown capacitance in Farads, RV is the value of the adjusted resistance in Ohms, RF is the value of the fixed resistance in Ohms, and CS is the value of the known capacitor in Farads. The known capacitor is referred to as the ‘standard’ capacitor and is often a high-accuracy type meant for testing, hence the ‘s’ designator.

However, the simple capacitance bridge circuits commonly found online and in educational texts suffer from a major problem: They really only work with near-perfect capacitors, which means air-gap, quality mica capacitors, or some film and ceramic capacitors. On anything else, stray voltage paths cause problems. However, when it comes to determining faulty caps, it will probably get you pretty close. It may even be good enough for some filter circuit design if absolute accuracy is not required, and it will certainly be a good exercise for those so inclined to compare the results against other methods.

An alternative is a Series Resistance Capacitance Bridge. The circuit is constructed with a series resistor and a known mica capacitor (chosen for their superior stability and consistency), and the other resistance is the ESR of the target capacitor. There are too many challenges with this circuit to warrant explaining it: The maths is well beyond Classroom thanks to a bunch of other factors involved, and the mica capacitors necessary are hard to get.

# MULTIMETER TIME CONSTANT

This particular method is rough, rather inaccurate, but highly accessible. By using a large value resistor to construct the RC network, we can slow the charging time enough to use a multimeter and stopwatch. While few of us have a stopwatch lying around, nearly all of us have one in the clock app of our smartphones. The only other thing needed is a multimeter to measure the voltage, and perhaps a calculator to figure out what 63.2% of the applied voltage is if you don’t want to use paper and pen, or your head. Again, that’s in your phone.

Start by measuring the voltage of the supply. This will give an accurate number to calculate 63.2% of rather than the nominal value of the power supply. Then, turn off the supply and use clip leads to attach it and the multimeter probes to the RC network. Make sure the resistor is on the positive side of the capacitor (this method really only works with values big enough to be unavailable in anything other than electrolytics) and touch it to the ground to ensure you’re starting with a discharged capacitor.

Now, have your stopwatch ready. Turn on the power and start the stopwatch at the same instant. Watch the multimeter display, and as the voltage approaches the calculated value for 63.2% of your supply voltage, get ready to hit the stop button on the stopwatch. This time in seconds, decimals included, is the value for your calculations. Because of the inaccuracies inherent in this method, you may wish to repeat it several times and find the average of the times.

If T = RC, then C = T ÷ R, with capacitance C in Farads, time T in seconds, and resistance R on Ohms.

# DSO TIME CONSTANT

A far more accurate way of conducting the previous test is to use an oscilloscope. Because almost all oscilloscopes today are Digital Storage Oscilloscopes (DSO), it is possible to make them graph a waveform and retain the image. Using the graduations on the screen, it is possible to gain reasonably accurate time measurement, more so than using the stopwatch method.

The value of the resistor used here can and should be much smaller, though the exact value varies with the value of the capacitor. For capacitors in the picoFarad range, a resistor in the tens of ohms might do. For a capacitor in the milliFarad range, a resistor of a few thousand ohms might be better. The actual values may depend on your chosen signal generator, and in some cases, the 50Ω output will be fine. If it is not, don’t forget to add it to the value of the resistor in your calculations.

Items needed are a DSO, function generator with the capability to generate a square wave output, test capacitor, and known resistor. You may also want a multimeter to measure the exact value of the resistor. Generally, a DSO with two channels and a function generator with two outputs works best here. You’ll see why as we run the set-up.

Plug channel one of the function generator into channel one of the DSO. This is best done with a BNC to BNC cable, but can be done with a BNC to crocodile clip lead and DSO probe if necessary. This channel is the reference to adjust the frequency of the test signal. Set the generator to display a square wave of a nominal frequency which will vary greatly. See below. Now, connect a BNC to crocodile clip lead from the second channel of the function generator to the RC network. Clip the DSO probe onto the other side and plug it into the DSO’s second channel. Be careful to preserve polarity; that is, the grounds of both leads together, and with the negative lead of the capacitor if it is polarised.

Because the first time constant is reached when the capacitor is half-charged, measuring with the DSO screen becomes much easier. Adjust the vertical resolution until the reference signal takes up eight graduations. Turn off the second channel if it makes things easier. Now, turn on the second channel and adjust the frequency of the signal generator until the capacitor finishes charging very close to the end of the high period of the square wave signal. If the frequency is too low, the capacitor finishes charging too early, and if it is too high, the capacitor will not charge all the way.

When you have the waveforms as they should be, adjust the DSO’s horizontal controls to spread out the signal and allow more of the x-axis to be used for time calculation. This makes the measurement more accurate. The time may be in milliseconds or microseconds, so be sure to convert back to seconds for the calculation.

Now, you can perform the same calculation as in the multimeter version, but we’ll repeat it here so you don’t have to turn or scroll pages.

If T = RC, then C = T ÷ R, with capacitance C in Farads, time T in seconds, and resistance R on Ohms.

That’s it, you’ve measured the value of an unknown or suspect capacitor. We recommend trying it first on several good capacitors to get the technique right before you try a suspect one.

# LCR METER

The final testing method for finding an unknown capacitor is to connect it to an LCR meter. Much like we did with the inductors last month, the method is a bit simpler than any above. The device will display what parameters it has used to perform the test, but generally capacitance will be tested with a DC signal.

STEP 1: Connect the component to the leads.

STEP 2: Press the ‘Test’ button.

STEP 3: Wait.

STEP 4: Read the value off the screen, including the parameters.

# Arduino Capacitance Meter

While this build may not turn into a serious piece of test equipment, it could still be a handy one for near-enough measurements. It’s also a bit of fun.

The build utilises the time constant principle again. The basic premise is to have an Arduino apply a voltage to a test capacitor, and start a timer at the same instant. It uses the Analog to Digital Converter to monitor the rising voltage, and time the duration between the start, and the voltage reaching 63.2% of the total. For extra accuracy, we’ve included a section of code to reference the supply voltage before the test is performed, in order to eliminate errors from differences between the nominal and actual supply voltage.

The build is so simple that we don’t feel step-by-step instructions are necessary. The Fritzing and schematic should be enough. However, there are some features that are worth pointing out. The Arduino can sink 6mA or 9mA depending on the version, so we went with a maximum of 6mA. At 5V, that requires an 830Ω resistor. We went with 1kΩ jst to be safe and easy. When the Arduino is discharging the capacitor, it will use the same pin as it used to charge it.

We have included some maths in the code to return the value in microFarads, nanoFarads, or picoFarads. You have to choose which, however. You can do this by removing the // comment delineators in front of the relevant section of code. We have also set the system up to measure both the charge time from 0% to 63.2%, and the discharge time from 100% to 36.8%, then average the two for a more accurate result.

The final points to note are that 63.2% and 36.8% of a 1024 ADC signal are not whole bits, so we went to the closest bit. And it was very close in both cases. 63.2% equates to 646.168 (remember we start at 0 and count to 1023 for a 1024-bit number, so 1024 x 63.2% is actually 647.168), so we went with 646. 36.8% equals 375.832, so we went with 376. The output is to the serial monitor, so this needs to remain connected to the computer hosting it. Pushing the button begins the test.

Everything else will be explained with comments within the code, so that we can update and modify it without making this article outdated, as we find issues or better ways of doing things.

Parts Required:IDJaycarAltronicsCore Electronics
1 x Solderless Breadboard-PB8820P1002CE05102
1 x Pack of Breadboard Wire Links-PB8850P1014ACE05631
5 x Plug-to-plug Jumper Leads-WC6027P1017PRT-12795
1 x Arduino Uno or Compatible Board-XC4410Z6240A000066
1 x 1kΩ Resistors*R1RR0573R7558COM-10969
1 x 10kΩ Resistors*R2RR0596R7582COM-10969
1 x 100nF CapacitorC1RM7125R3025BCE05188
1 x Tactile Pushbutton*SW1SP0608S1135COM-10302

## Parts Required:

* Quantity shown, may be sold in packs.

# WHERE TO FROM HERE?

You could alter the code to perform the test multiple times and take the average to gain a more accurate result, or compare it and see if there's any difference. The other main change we can think of is to build an LCD or some other display into the code and make the whole circuit self-contained. If you’re really feeling adventurous, you could figure out the expected times for charging different capacitors and factor that into the timing result to automatically give a value in pico, nano, or microFarads depending on which range the time falls into. The maths on that would involve making sure the base calculation stays in Farads, so the result can be compared against the expected values range before the conversion is performed.