Some background on capacitors and inductors, and some methods to test and measure them.
Having recently purchased an LCR meter for the workshop, reviewed elsewhere this issue, we decided to look at how to do the same operations if you don’t have an LCR meter. This turned out to involve a background look at the components involved, too.
At face value, it may seem odd that a laboratory or workshop would have expensive equipment like signal generators and oscilloscopes, but not a relatively cheap LCR meter. However, these instruments serve many purposes and fill many roles, while the LCR meter is very specific. Additionally, before the advent of small, relatively cheap but properly capable meters like the Peak Atlas LCR40, an accurate and effective LCR meter was still quite expensive. With these points considered, it becomes far more likely that someone would need to find the value of an unknown inductor or capacitor, or verify a known value in fault-finding, without having an LCR meter.
WHAT ARE THEY?
While it would be tempting to assume that if you’re trying to find the value of an inductor or capacitor, that you know how each works. However, there have been many changes in the electronics world over the last few years. It is not uncommon now for hobbyists and makers to have quite a lot of functional knowledge, without always having the underlying theory understood. In many cases, this is a fully functional way to operate, but it does mean a bit of simple theory is in order. Both components store a charge. Both charge up at a certain rate and discharge at a certain rate, depending on their construction and values, and these rates can be modified with external components. The biggest difference is how they work and are constructed.
CAPACITORS
Some makers have been using capacitors since they discovered electronics, fully capable of reading values, understanding, calculating, and applying their use, without ever having thought about what’s inside them. Capacitors consist of two conductors, separated by some form of insulator. That means they happen inadvertently as well as deliberately. Two wires in a twin-core speaker wire will have capacitance between them. To deliberately make a capacitor, the conductors are usually formed into plates and the insulator placed between them. While air is an insulator, it’s not a wonderfully effective one under some conditions. Materials called ‘dielectrics’ are used, and they’re chosen for their insulative properties. The closer the plates can be placed to each other, the greater the capacitance. The bigger the plates, the greater the capacitance.
When a voltage is applied to the plates, the negative plate fills with electrons, which repel the electrons in the opposing plate. They are prevented from flowing between the plates by the dielectric. As the charge builds, the negative plate becomes filled with electrons while the positive plate becomes devoid. Remember, this is electron flow, which is opposite to conventional current flow. Note also that current only flows while the capacitor is charging or discharging. Once there is no more movement of electrons, the current flow stops. This will be important later on.
Theoretically, once a capacitor is charged, it can be removed from the voltage source and the charge will be retained. In the real world the charge slowly dissipates. Humans cannot make anything that is perfect, and even chemicals which are in theory total insulators have tiny amounts of impurities in the real world. There are other leakage paths as well, including a small amount across the air gap between the terminals and in other ways between the plates.
The amount of charge a capacitor can hold determines its value. While sometimes small values are desired, the smallest construction techniques are still valued. There is no sense in making a component big unless it needs to be. There can be penalties including heat problems for overly compact components too but while we need to acknowledge that, it’s not relevant to this case. This means a capacitor as you buy it is not two flat plates separated by a film. Older capacitor technologies like greencaps remain unchanged and are bulkier for a given value than other constructions. Most capacitors that involve a physically separate dielectric are made with layers of plates and dielectric. Wires connect the layers in an alternate fashion to maintain the opposing late arrangement. This includes greencaps, ceramics, MKTs, and other polyester capacitors.
The other main way to make a capacitor is to chemically form the dielectric on one side of the plate. These plates are usually metal foils, with an insulative oxide layer forming the dielectric. A thin fibre layer is often included, soaked in an electrolyte, hence ‘electrolytic’ capacitors. The electrolyte may also be a gel, and it forms the other terminal of the capacitor, which takes the place of a plate. The two most common metals are aluminium, and tantalum. Tantalum performs better, is more accurate, and is more compact, but it costs a lot more, too. Electrolytic capacitors are almost always made from long lengths of foil rolled into cylinders with the leads connected to the relevant surfaces. This gives them their characteristic shape. Some physical dielectric capacitors are also made in cylindrical form.
Generally, electrolytic capacitors, because they’re formed with a chemical layer on one side of the plate rather than separate plates with a film between, are polarised and must be connected the right way. Capacitors formed by separate plates with a dielectric film are not polarised and can function with current flowing either way through the terminals. There are specialised exceptions to this, such as the non-polarised aluminium electrolytic capacitors available for audio use.
INDUCTION
Like capacitance, inductance exists almost anywhere that an electrical current does. Every electric current is surrounded by a magnetic field, which itself is able to cause an electric current in any conductor within the field. This requires some change, however. A DC current will produce a magnetic field as evidenced by a battery-powered electromagnet, but it will not induce a current in a conductor held next to it. This is because electromagnetic induction, as it is known, only occurs when the relationship between a magnetic field and a conductor is changing.
In Alternating Current (AC) situations, this is easy. As the electrical wave rises and falls, the strength of the magnetic field rises and falls with it. The polarity changes are the same, too. If another conductor is in this magnetic field, then the current induced in it is proportional to, but opposite, the current that created the magnetic field. It is this principle that enables transformers to work, and is also why the inputs and outputs of a transformer are 180° out of phase.
AC INDUCTION MAGNETICS
Interestingly, the magnetic field also passes through the conductor which created it, and induces a current in that same wire which opposes the current creating it. This is Lenz’s Law if you want to read more, and is the basis for ‘inductive reactance’, and is quite important to our eventual goal of testing inductors.The amount of reactance is dependent on the frequency at which the current is alternating. Inductive reactance is measured in ohms, and is represented in equations by the letters ‘XL’. Inductance, by the way, is represented in equations by the letter ‘L’, and is measured in Henries, with the symbol ‘H’.
Thankfully, there is a constant at which this relationship occurs. It is 6.28. Therefore:
XL = f6.28L
Where f is the frequency in Hertz and the result is given in ohms. However, while this is useful for calculating how current will behave in a circuit, we can’t use this directly to test an unknown inductor. Measuring XL can’t be done with a resistance meter or multimeter.
There are other ways that a current can be induced via a magnetic field. We stated before that the relationship between a conductor and a magnetic field has to change, and showed how this happens in an alternating current flowing in a wire. However, the movement can be physical, too. If you take a loop of wire and wave a magnet back and forth over it, a voltmeter connected to the coil will move. Moving coil type meters show this the best but few of us have these today. It’s quite an interesting experiment to perform, but at a level that can be constructed on most workshop benches, a digital multimeter will just not work. They don’t respond fast enough to the tiny, brief changes involved.
If you do have an analog voltmeter in the millivolt range and use a strong enough magnet, you’ll see the meter move one way and then the other as you reverse the direction of the magnet’s travel. The directions will switch if you turn the magnet over so the opposite pole is facing the coil, and repeat the same movements.
This is interesting in showing inductance, and it does underpin the operating principle of most electric motors and generators, but it doesn’t help us construct an inductor.
INDUCTORS
As an electrical component, inductors are based on what we’ve learned above but take the idea further. They are physically formed from coils of wire wound around a central axis. Sometimes the coils are touching each other (insulated by enamel coatings and such), and sometimes they are spaced apart.
Sometimes the central axis is empty, called an air-cored inductor. Plastic formers may be used here as they do not affect the magnetic field. Sometimes, iron or ferrite are used. Ferrite is more common because its properties suit higher frequencies better than iron.
These coils may or may not be visible. Many smaller values of inductor are coated in plastic or resin and look a lot like a resistor. The values are even denoted by colour bands. Other inductors are visibly made of wire and can be large or small.
The coils, both secondary and primary, of our recent Slayer Exciter were both inductors. Many wire-wound inductors have no markings on them, so it’s much easier to arrive at an unknown device than with a capacitor.
The upshot of this is that the magnetic field created by the coiled conductor interacts with the current creating it in such a way that the current is opposed. Energy is also stored in the magnetic field.
Once the current is removed, the magnetic field causes a current to flow, the one that was opposing the current that created the magnetic field. This current flows in the opposite direction and is called a back-EMF, for Electromotive Force. This is why inductive loads like relay coils and motors can cause problems for some logic circuits but that’s another story.
Because inductors form a back-EMF that opposes current through the circuit, they can be used as chokes. Remember, the magnetic field has to change relative to the conductor so DC currents pass through, but AC currents are opposed.
How much so depends on a variety of factors, but by far the biggest is the value of the inductor, and in this way, inductors can also be used as filters, passing a current of it is below a certain frequency.
Inductors are used in power supplies, because they can be charged up then switched off. When the current is switched off, the back-EMF occurs, but it is often of a much higher voltage than the current that created the magnetic field in the first place. This is why there are inductors in Switch-Mode Power Supplies. They become voltage multipliers.
Inductors are measured in Henries, abbreviated as H. However, the Henry is a big unit. Typically, inductors in practical use are measured in milliHenries (mH), microHenries (μH), and nanoHenries (nH). This follows the usual decimal multiplier scale where milli is a whole divided by one thousand, or 10-3; micro is a whole divided by one million, or 10-6; and nano is a whole divided by one billion, or 10-9.
RESONANCE
Inductors have a self-resonant frequency. There are situations where this is very helpful: It is the basis for the operation of the Slayer Exciter. This is the rate at which the natural capacitance in the coil and its conductor match the inductance in such a way that the coil oscillates, transferring energy from current in the coil, to the magnetic field around it, to the current into the capacitor and the voltage at its static field.
In other words, it happens when the inductance of the windings equals the capacitance between them and any other stray capacitance. The frequency at which this occurs is dependent on the inductance, core materials, leakage to ground, and all the factors that affect natural or stray capacitance.
It can be hard to determine but doing so is necessary for a properly-tuned Tesla coil if you are to avoid the use of a spark gap. This is one of the reasons we went down the Slayer Exciter road.
LC CIRCUIT
Finally, we get to combine capacitors and inductors. As we just saw, an inductor forms a natural resonant frequency with its stray capacitance. However, connecting an inductor with a bigger, manufactured capacitor means we can design the frequency at which the circuit resonates. These are called LC circuits, because L is the letter we use to represent inductance (not measure it, that’s Henries), and C is the letter we use to represent capacitance (not measure it, that’s the Farad).
Other names include tank circuit, resonant circuit, or tuned circuit. We feel that it is better to stick to ‘LC circuit’ because the other names are not specific and there are other circuits which can be thought of using the same names.
Ideally, the energy stored in the inductor is transferred into the capacitor, which then, as current flow stops, dumps its current back into the inductor for the process to repeat into infinity. Of course, we know nothing does work this way.
There are losses due to impurities and imperfect conductors and materials, and leakage. However, the circuit will oscillate with minimum current input. This is useful in making resonators to oscillate at a known frequency, or to isolate a certain frequency from others. It’s also going to be quite useful when it comes time for us to test an unknown inductor. The frequency can be calculated from:
where fo is the frequency of oscillation (resonant frequency) in Hertz (Hz), L is the inductance in Henries, and C is the capacitance in Farads. As always, calculations must be made in whole units like Farads, not divided units like microfarads.
RLC CIRCUITS
The LC circuit can be modified with a resistor to form an RLC circuit. There are several combinations here, and we can’t go into depth with them here. Where relevant, they will be explained in the testing section. Effectively, the resistor alters the current path in some way. It may slow the current into either the resistor or inductor, or both, altering frequency. It may allow some current to bypass one of the components, also altering characteristics. RLC circuits find most of their use in tuned circuits but there are other uses too.
IN CONCLUSION
There is so, so much more to say about all of what you’ve just read. In particular, we could probably write a whole series of articles on inductors, LC circuits, and RLC circuits. If enough of our audience tells us they want that, then we will do so.
For now, however, we hope you have enough understanding of what’s going on as we explain different ways to test and measure unknown capacitors and inductors.
TESTING UNKNOWN INDUCTORS
It is not unusual to find an unknown inductor in the parts box that has lost its package or bag, or you may have wound your own. There are several methods available to measure these inductors if you do not have an LCR meter on hand.
Method 1: Comparing Impedance
This method involves an oscilloscope and a function generator capable of sweeping through frequencies. While some oscilloscopes offer a function generator built in, these can rarely sweep and you cannot generate and use the oscilloscope function at the same time.
This method works best on a two-channel oscilloscope but a single channel can be made to work. Connect a known resistor in series with the unknown inductor. The more precise the resistor, the better, and don’t just go off its nominal value: Measure it with a multimeter (the most likely case) or an ohm meter (if you have a dedicated one). Connect the function generator across the series-connected resistor and inductor, along with one oscilloscope channel. Connect another oscilloscope channel to the junction between the inductor and resistor.
Set the function generator to output a sine wave, and choose a frequency somewhere around 100kHz. Adjust the oscilloscope until the input voltage (the voltage across the whole circuit) from the function generator peaks near the top and bottom of the screen. If you’re not too familiar with oscilloscopes yet, you do this with the ‘Vertical’ controls, specifically the Volts per Division dial (‘volts/div’ or just ‘V’ being the most common labels).
Adjust it until the top and bottom of the wave reaches the divisions at 75% and 25% respectively. You might also need to fiddle with the Horizontal controls, in particular the sec/div control. This will make the waveform squish or spread.
You should have two waves visible. The one you’ve been adjusting is the one from the output of the function generator. We can’t tell you much about the controls for these because they’re all different, but adjust the frequency until the voltage of the waveform at the junction of the resistor and inductor is half the voltage from the function generator. This will mean the wave will only extend half as far toward the top and bottom of the screen as the first one does. Look for precision, because near enough is not good enough in this case.
We did say that your function generator should have a sweep function. Most function generators will allow you to change the frequency with a dial or up/down buttons. That’s in contrast to many oscilloscopes which have generators built in, where you usually have to set the frequency in a menu and cannot effectively change on the go. However, a sweep function starts at the lowest frequency and increases to the highest, and often then goes backwards. Many function generators allow you to set upper and lower limits for this, and some allow you to set the speed of change. This is really useful, because you can start a sweep and watch the oscilloscope screen until you see the wave from the test point reach half of the output wave from the function generator.
Look at the frequency on the function generator’s display when the wave is at the half-way mark we’re after, and note the frequency. This gives you a starting point instead of guessing. Stop the sweep if your generator allows, or wait until it is finished and manually select your noted frequency. Now, you can manually adjust the frequency from this new starting point until you get the exact half-sized wave we’re after. The frequency at which this occurs is needed in the calculation to find the inductor’s value:
where L is the inductance in Henries (H), f is the frequency in Hertz (Hz), and R is the value of the comparison resistor in ohms (Ω). As always, calculations are in base units and the more decimal places you can tolerate working with, the better. Don’t forget to include the impedance of the function generator output, which is usually 50Ω.
Method 2: Resonant Frequency
This method uses a known capacitor to form an RLC circuit. It’s formed with a parallel LC tank circuit, with a resistor in series on the end. The majority of function generators have a 50Ω impedance output, and some online methods use this as the resistance. However, the majority of references we consulted used an added, larger resistor. Additionally, this method works best with a capacitor of 1% tolerance, but most are 10% which would leave a significant margin of error. There's no rule on value, but start at 100nF.
Use a 1% capacitor (or test with an accurate multimeter), then connect the unknown inductor across the known capacitor. Add the series resistor, set your function generator’s output voltage to 2V peak to peak, and use the PWM mode. Connect with the signal generator, RLC circuit group, and oscilloscope in parallel.
As you vary the frequency of the PWM signal, look for the highest amplitude signal on-screen. As soon as it peaks and starts to fall, you’ve found the resonant frequency of the circuit. A sweep function will help you get close, but use manual adjustments to find the precise point. Take note of the frequency then add it to the calculation:
Where fo is the frequency of oscillation that gives the highest amplitude, C is the capacitance in Farads, and L is the inductance in Henries.
Method 3: LC Series Circuit
This method eliminates concerns over the capacitance of the oscilloscope probe coming into play. Keep the test inductor as close to the signal/function generator as possible, but you can use the full length of your oscilloscope probe. Again for this method, you need a known capacitor value and tolerance becomes an issue here. If you cannot find 1% capacitors, you’ll have to accurately measure one. Values from 1nF to 10nF are popular but again, you’ll have to explore depending on inductor value and other parameters if the starting values don’t work.
Sweep or manually adjust the frequency, but this time you’re looking for a reduction in the amplitude of the waveform. At the frequency that gives maximum reduction, before the amplitude starts increasing again, note the value for this formula:
where f is the frequency of lowest amplitude, C is the capacitor value and L is the resulting inductor value.
Method 4: Voltage/Current Slope
Again using PWM mode on a function generator, set the duty cycle to below 50%. 25% would be a good starting point. Keep the frequency high, to stop the coil becoming saturated. This is when the coil’s magnetic field cannot get any stronger, and so affects the measurements. Connect the coil in series with a current probe to the oscilloscope.
Measure the peak current reached, and the time taken to reach it. The formula is:
where L is the inductance in Henries, V is the voltage of the signal, TON is the time that the voltage is applied for (in other words, the pulse length), and Ipk is the peak current reached.
The biggest drawback with this method is that it requires a current probe for the oscilloscope. These are not common on the domestic market and even not so in the trade market. They are specialised and the cheapest one we could find at a reputable supplier was over $1000. That’s a few dollars more than one of our oscilloscopes.
Method 5: Use An LCR Meter!
STEP 1:
Connect the probes or hooks of the LCR meter to the inductor to be tested.
STEP 2:
Push the ‘Test’ or ‘Analyse’ button.
STEP 3:
Read the result off the screen.
This is far from an exhaustive list. There are other ways to test unknown inductors, and we haven’t even got into testing unknown capacitors yet. All of these methods have their advantages and drawbacks. We have covered some and not others. Some of the problems or considerations with each method are beyond the scope of Classroom.
The simplest and most accurate way of measuring an unknown inductor is a good quality LCR meter. It’s faster, too, and avoids errors from temporary connections and such. By the time you consider the cost of a function generator, it’s false economy to avoid buying an LCR meter unless you already have both an oscilloscope and function generator lying around.
So if you do build switchmode power supplies, work with radio circuits, build Tesla coils or other high-voltage devices, or build filters on a regular basis, you can use any of these methods to find the values of unknown or hand-wound inductors. We went down the LCR meter path, and we don’t regret it at all.