Other Capacitor Configurations
From the more technical point of view, capacitors store energy in the form of an electric field. A simple capacitor consists of two conductive plates separated by an insulating "dielectric". Even more technical, capacitance is directly proportional to the surface area of these plates and inversely proportional to the separation between them.
From a more practical perspective, I tend to think of capacitors in one of two ways depending on the application. In situations where the ability to store energy is being directly exploited, such as power supply decoupling and RC timing circuits, it is useful to think of a capacitor as it is described above. As a low capacity and inefficient rechargeable cell.
In applications where a capacitor is interacting with an AC signal it can be more useful to think of a capacitor as a device which passes AC signals of frequencies proportional to the capacitance value while impeding DC signals.
The capacity of a capacitor is measured in Farads, abbreviated with a capital F. The Farad is actually a very large unit so most common capacitor values are stated in picofarads (pF), nano Farads (nF) or micro Farads (µF).
The image below contains the five basic types of capacitor; Ceramic, Polyester, MKT, Tantalum and Electrolytic. Value ranges given below are approximate.
1. Disc Ceramic: While they are limited to quite small values, disc ceramics boast small and solid construction with comparatively high voltage ratings. They range from 1pF to 0.47µF and are not polarised. This type can often be used to replace a polyester capacitor of the same value.
2. Polyester "Green Caps": Ranging from 0.01µF to 5µF polyester capacitors have similar properties to disc ceramics with some larger values and a slightly larger construction. They are not polarised.
3. MKT Polyester: A variation of polyester capacitors used where price matters less than performance. High temperature stability and accuracy land MKT capacitors in higher end audio circuits and power supplies. They range from 1nF to about 10µF. (values over 1µF are quite expensive) MKTs are not polarised.
4. Tantalum: Tantalum capacitors pack a large capacity into a relatively small and tough package compared to electrolytics, but pay for this in voltage ratings. The device pictured above is 100µF (like the electrolytic next to it) but is rated at 3.6V, compared to 16V. They are often polarised and range from 0.1µF to 100µF.
5. Radial Electrolytic: Used for all values above 0.1µF. Electrolytics have lower accuracy and temperature stability than most other types and are almost always polarised. It's usually best to only use an electrolytic when no other type can be used, or for all values over 100µF. Cheap electrolytics are usually made from plastic and rubber and therefore melt easily during soldering.
6. Axial Electrolytic: The same as other electrolytics but the leads emerge from each end, rather than the same end as in the radial types.
Most capacitors use a 4 character code similar to the four band color code on resistors. The first two characters are numeric and represent the two most significant figures of the value (in pF), the third is the multiplier or the number of zeros, and the fourth (if it exists) is a letter representing a tolerance. For example, "473K" works out to 47000pF, 47nF or 0.047µF at 10% tolerance. This is called the IEC code. IEC tolerance characters are shown in the table below.
Electrolytics almost always have their value explicitly stated in µF along with their voltage rating. Disc ceramics with values under 100pF often simply have their value stated in pF, but if the marking has three numeric characters it should be read as IEC instead. Some MKT capacitors will have a value followed by or including a metric abbreviation. (eg. 47n = 47nF) If the metric abbreviation is included it acts as a decimal point. (eg. 4n7 = 4.7nF)
When no voltage rating is specified for a disc ceramic, polyester or MKT capacitor it is usually safe to assume an arbitrary figure like 50V.
A capacitor is "charged" by applying electrical energy (DC) to the dielectric in the form of a potential difference between the components leads. The capacitor will draw current as it charges, inducing a measurable voltage drop across the component. By using a series resistor to limit the charging current the time it takes for a capacitor to charge can be controlled with some accuracy. Below is the basic RC (resistor/capacitor) circuit.
As the capacitor charges the voltage measured between V and GND in the above diagram increases exponentially. If the top of the resistor was connected to GND instead of V+ (ie. the capacitor was shorted with the resistor) then the capacitor will discharge through the resistor and the voltage measured across it will decrease exponentially. This is illustrated below.
The time taken for a charging capacitor to reach 63% of the applied voltage or for a discharging capacitor to fall to 37% is called the "time constant", represented by the Greek letter τ (tau) and marked as "1T" on the above graph. A capacitor is taken to be fully charged or discharged after about five time constants because real world losses (such as leakage) will prevent the capacitor from ever being completely charged. The percentages shown above are not selected at random, but rather derived from the equation for the exponential curve on which the RC circuit is modelled; y = e-τ while discharging and y = 1-e -τ when charging. The constant e-1 is approximately 0.37 or 37%.
Interesting as it may be, the mathematics of it is not terribly important for basic practical application of RC timing circuits. The important thing to know is the simple formula below which is used to calculate the time constant.
If the capacitor value C in Farads and the resistor value R in ohms are both accurately known quantities then the duration of a single time constant can be calculated by simply multiplying these two quantities as in the formula. For example a 47µF capacitor with a 100KΩ series resistor will take 4.7 seconds to reach a 63% state of charge. (0.000047 x 100000 = 4.7)
It's important to understand that R and C are not necessary exactly as they are marked and that the actual timing is usually just "close enough". Oscillators and timing circuits based on resistors and capacitors will always be relatively inaccurate and to make matters worse they'll vary with temperature. Where high accuracy and stability is important other approaches are required, such as crystals or resonators.
Placing a relatively large (greater than 100µF) capacitor across a power supply helps to smooth out noise, this is well known. The practice is called "decoupling", and is most easily understood if the capacitor is thought of as a storage cell. (my first definition) When a decoupled power supply is switched on, the capacitor across it will charge to Vcc and proceed to do nothing except draw a small amount of current to compensate for it's own leakage. However, if Vcc falls briefly under load the capacitor will present a potential higher than Vcc and the stored energy will flow into the load, helping to maintain the supply voltage. Should Vcc "spike", the capacitor will begin to charge as there is a now a potential difference across the dielectric, effectively absorbing some of the spike's energy.
It's not uncommon to find a power supply decoupled by a large electrolytic or tantalum capacitor (say 47µF) and a small ceramic or polyester (like 100nF) in parallel. The larger capacitor is most effective and absorbing droops and spikes in the supply voltage as described above, while the smaller capacitor is for ripple rejection. The much shorter time constant of this part is better suited to deal with higher frequency variations in voltage, such as 50/60Hz ripple from a mains power supply.
Power supply decoupling has a few drawbacks:
A word of warning; If Vcc is shorted to ground (ie. 0Ω) large amounts of current are demanded from the power supply. Ohms Law will come up with current as mathematically undefined, ie. infinite current. Power supplies are usually designed to cope with overload in a variety of ways, the simplest of all being a fuse, but capacitors are not. Irregardless of how the power supply reacts the capacitor will deliver all it's energy to the load very briefly, in the order of tens of amps. (similar to shorted car battery, but very brief) Regulator circuitry is more prone to damage due to the low impedance of regulator IC's presenting an alternate path to ground, the circuit itself is ironically protected by the short circuit.
Worrying about this is really just paranoia, but I like to call it food for thought.
The ability of the capacitor to pass AC signals while blocking DC signals is most often used in audio circuits, in order to allow opamps to work of a single supply potential. (or just to protect against DC inputs, which can be noisy)
Obviously, an operational amplifier cannot produce an output voltage outside Vcc or Vss, which is why audio equipment often requires "dual power supplies" to give the opamps a power supply with which they can amplify the negative half of a signal. Unfortunately, many situations make dual power supplies impractical or even impossible, (eg. battery powered equipment) so a work around is required.
The red part of the signal will not be present on the output.
The image above shows an input signal which is unbiased, or centred around 0V. With the single positive supply potential between Vcc and Vss connected to the opamp in the circuit above the negative side of the input signal will not appear on the output. (red) However, the AC coupling capacitor(s) and voltage divider present a solution.
The capacitor on the input will remove any DC offset from the input signal, (a precaution which is not necessary if the input is known to be free of DC bias) and the voltage divider will provide its own DC offset of half Vcc, resulting in the second waveform in the above image. This waveform is inside the supply voltages and will not be clipped. The output from the opamp is then passed through another AC coupling capacitor, (this one is always necessary) to remove the DC offset from the voltage divider.
Other Capacitor Configurations:
Like other passives, capacitors can be combined in parallel or series to create more interesting values. The maths is also somewhat similar:
Note that the result for series capacitance is also a reciprocal and must be reciprocated to obtain the correct result. The need for unusual capacitor values is rare for the average hobbyist, but knowledge of the above rules can be of use. If you are prototyping something and need a large capacitor you don't have, it's useful to know a bunch of smaller ones in parallel will deliver similar results.
Neither series or parallel layouts have any effect on the voltage rating of the capacitors used.
If you have any comments or questions please don't hesitate to contact me.
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