Tag: capacitance

How To Choose A Resistor

How do we choose the right resistor when designing and building an electronic circuit? Here are the major parameters that should be kept into account.

bunch_of_resistors

A resistor is a component made out of a poor conducting material, so that it can offer a resistance to the flow of the current.

You can think to resistance in terms of the obstacles that charges encounter when moving from one end to the other of a conductor. The more obstacles, the higher the resistance. In a metallic wire, for example, the charges are the electrons of the conduction band (see this post and this other one for further details).

In today’s post I would like to address an issue that sometimes is underestimated when designing an electronic circuit: how to choose the right resistor for the job.

Resistors are not all the same. Besides the resistance value that distinguishes one from the other, there are other factors that are important as well.

Here is a list of all the important factors, why they are important, and what are the consequences of not choosing a resistor based on each specific factor.

  • The first thing that comes to mind is the tolerance, which is usually provided on the body of the resistor itself, along with its resistance value.

resistor_color_bands

In color coded resistors, the tolerance is defined by the band that is far away from all the others. In the above picture, for example, it is the gold band, which means that the tolerance is of 5%. In other resistors, where the resistance is explicitly written on the body of the resistor, the tolerance is usually written in clear along with the resistance. More in general, you’ll have to refer to the data sheet provided by the constructor to figure out its tolerance.
Tolerance is an important factor for those circuits that require very precise resistors, like measuring instruments and the like. It is also important when the resistor is used for the polarization of a critical component. If the resistors used in the project have a tolerance that is too high, the whole circuit may not function properly because the actual value of the resistor is too different from the one that was required.

  • Operating Temperature. This depends both from the ambient conditions and by the temperature raise produced by the power dissipation. There are two reasons to keep the temperature range into account. First, resistors slightly change their resistance with the change of the temperature. Using the resistor outside its temperature range would cause a variation greater than the one considered by the tolerance. Second, but not last, when the resistor is traversed by current it heats up. As long as the current stays within a range for which the power dissipation is not exceeded, everything is fine. Otherwise, the resistor can easily overheat and burn.

scorched_resistor

  • Maximum Voltage. Operating a resistor above its maximum voltage rating may cause sparks that would destroy the resistor.

burned_resistor

Resistors used in low power circuits usually have a maximum voltage in the order of at least 100V, and that’s why people usually don’t care or it doesn’t even know that there is such a parameter. In fact, low voltage circuits will normally never exceed the maximum voltage of any resistor. However, there are specific applications where voltages in the circuits can be above the 100V threshold. In such cases, it is important to verify that the resistors used in the circuit can withstand those voltages.

  • Temperature coefficient. This is the parameter that tells us how much the resistance changes per degree Celsius. It depends on the material the resistor is made of, but also on the heat dissipation capability of the component. Some resistors are built with an embedded heat sink to reduce the value of this factor.

power_resistor

This information becomes important in those cases where it is known that the resistor is going to dissipate a considerable amount of power. Based on that, it is possible to figure out if the resistor needs an external heat sink and, eventually, the heat sink thermal resistance.

  • Parasitic Capacitance and Inductance. A real resistor does not have only a resistance but also a very low value of capacity and inductance that may affect its functionality at high frequencies.

equivalent_resistor

These parasitic capacitance and inductance are caused by the physical dimensions and shape of the component and cannot be avoided. When working at high frequencies, these values need to be taken into account, since they will generate both capacitive and inductive reactance that will affect the value of the resistor at the particular frequency it is going to be used.

  • Packaging. This keeps into account where and how the resistor is going to be mounted. It can be a through holes resistor, which is provided with two leads to make the connections. The leads are usually inserted in the holes of a perforated board or of a Printed Circuit Board (PCB). Or, the resistor can be a Surface Mounted one. This has no wires, just two pads that can be directly soldered on a Surface Mounted technology (SMT) PCB. Other factors affecting the packaging include the possibility of attaching it to an external heat sink, and/or the necessity to properly ventilate it, to guarantee enough heat dissipation.

 

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Capacitors – Part 1

A brief introduction to capacitors: what they are, how they are made, and their basic functionality.

capacitorsA capacitor is an electric device capable of storing energy in the form of electric charges (electric field).

In the most simple form, a capacitor is made of two conductive plates facing each other and an insulator in between, which is normally called a dielectric. The two plates are then attached to wires, that are used to connect the capacitor in an electric circuit.

capacitor

The schematic diagram reflects exactly the physical nature of the device:

schematic_symbol

When a capacitor is connected to a power supply, like a battery, electrons leave the plate that is connected to the positive side of the battery, while the same amount of electrons is pushed into the plate connected to the negative side of the battery. Once the difference of charges at the plates of the capacitor is enough to establish a voltage on the capacitor that is identical to the battery, electrons stop moving around the circuit and an equilibrium is reached.

capacitor_and_battery

At this point, if the connection with the battery is severed, the capacitor will retain the amount of charges on its plates: extra charges on the negative plate and defect of charges on the positive plate. If we connect a load to the capacitor, for example a resistor, charges will start moving in the circuit pushed by the voltage at the wires, called electrodes, of the capacitor. So, electrons will leave the negative plate moving toward the load, and an equal amount of electrons will move from the load into the positive plate of the capacitor. The movement of the electrons causes the voltage at the plates of the capacitor to lower until, when an equilibrium of charged is reached, the voltage will be zero and the current will stop flowing through the circuit. At this point all the energy that was stored in the capacitor has been used and the capacitor is said to be discharged.

capacitor_and_load

Both during charge and discharge, the ratio between the amount of charge stored on the capacitor and its voltage remains constant. This can be verified experimentally. We define this constant as the capacitance of the capacitor:

C = Q / V

which is measured in Farad. However, since the Farad is a very big unit, capacitors are normally measured in fractions of Farad, like microFarad (μF, 1 millionth of a Farad)), nanoFarad (nF, one billionth of a Farad), and picoFarad (pF, one trillionth of Farad).

Using the above formula, and calculating the work done to move the charges in and out of the capacitor with the help of some calculus, we can determine the energy stored in a capacitor as:

energy

And, finally, the actual capacitance can also be determined by the physical parameters of the capacitor itself. We can see experimentally that the capacitance is directly proportional to the area of the plates of the capacitor, it is inversely proportional to the distance between the plates, and depends on the type of dielectric in between the plates. The type of dielectric is identified in the formula by the Greek letter ε (epsilon). Each type of dielectric has its own value of ε (permittivity), which is the product of the vacuum permittivity and the relative permittivity of the material.

capacitance

For more information on this subject, please look also to the corresponding video on my YouTube channel.

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