Real-world circuit elements

The circuit elements discussed in the previous article are ideal circuit elements. Real-world circuit elements come close to the ideal mathematical models, but inevitably will be imperfect. Being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions.

One simple variation from ideal is that physical devices like resistors, inductors, and capacitors $(\text{R, L, C})$‍ have some level of tolerance around the ideal value (the tighter the tolerance, the more money you pay). Real components never have exactly their specified values.

Real circuit elements deviate from the ideal equations when voltage or current are taken to extremes. The straight line mathematical abstraction of a resistor does not go out to $\mathrm{\infty }$‍ voltage or $\mathrm{\infty }$‍ current for real resistors. The model breaks down at some point and the component could be destroyed. Abstract models of all the ideal components and sources have a limited range in the real world.

A real component is not just that component. Using a resistor as an example: because the wires connected to the ends of a resistor generate a surrounding magnetic field, it will inevitably display some inductive properties. In addition, resistors are made of conducting materials, and are usually located near other conductors. Together these conductors act like the plates of a capacitor, so resistors also display some capacitive properties.

These parasitic effects can be relevant at high frequencies, or when voltage or current changes sharply. If parasitics matter, you can model a component as a combination of ideal elements, as shown here for a resistor:

The properties of real-world components are sensitive to their environment. Most components show some degree of temperature sensitivity; parameters drift high or low depending on how hot or cold the component is. If your circuit has to work over a wide temperature range, you will want to know the temperature behavior of the components you use.

Note: In the electrical engineering subjects covered at Khan Academy, you won't have to worry about parasitic effects. They are mentioned here so you know they exist. When you simulate electronic circuits, you don't need to complicate matters by modeling all potential parasitic effects, unless you have (or learn of) a reason to think they are important.

When making real resistors, the goal is to create a component that comes as close as possible to performing like the ideal resistor equation, Ohm's Law, $v=i\text{R}$‍.

The resistance value of a resistor depends on two things:

The bulk material (what it is made of) affects how difficult it is for electrons to flow through. You could think of it as how often electrons bump into the atoms in the material as they try to flow through. This property of a bulk material is called resistivity. You might also hear the term conductivity, which is just the inverse of resistivity.

After selecting a bulk material with a certain resistivity, the resistance of the resistor is determined by its shape. A longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material. A resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section, because electrons have a greater number of available paths to follow.

A real resistor breaks down (as in burns out and is destroyed) if the power dissipated by the resistor is greater than what its construction materials can withstand. Resistors come with a power rating that should not be exceeded. If you try to dissipate $1$‍ watt in a $1/8$‍ watt resistor, you may end up with a burned chunk of something that is no longer a resistor.

Example of a conventional axial resistor:

The color bands indicate the resistor value and tolerance. The bands on this resistor are Orange Orange Brown Gold. From the resistor color code chart, the first two bands corresponds to the digits of the value, $33$‍. The third band is the multiplier, brown stands for $\times {10}^1$‍. The fourth (last) band indicates the tolerance, gold is $\pm 5\mathrm{\%}$‍. The resistor value is $330\mathrm{\Omega }\pm 5\mathrm{\%}$‍.

This is a precision resistor with 5 color bands:

Read the bands from left to right: Red Red Blue Brown Brown $=22611$‍. The first three bands $(226)$‍ are the value. The fourth band is the multiplier $(\times {10}^1)$‍, The fifth (last) band indicates the tolerance, brown is $1\mathrm{\%}$‍. The resistor value is $2260\mathrm{\Omega }\pm 1\mathrm{\%}$‍.

This is a surface mount resistor:

The resistance value is encoded in the $3$‍-digit code: $102$‍, meaning $10\times {10}^2=1000\mathrm{\Omega }$‍. The size specification of this resistor happens to be "0603 Metric", indicating its footprint is $0.6\text{mm}\times 0.3\text{mm}$‍.

Example of a resistor in an integrated circuit:

The designer selects one of the integrated circuit layers with high resistivity and creates (draws) a serpentine pattern to achieve the desired resistance.

When making real capacitors, the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation, $i=\text{C}\text{d}v/\text{d}t.$‍

A capacitor is constructed from two conducting surfaces placed close to each other. Between the plates there can be air, or any other kind of insulating material. The capacitance value depends on a number of factors, the area of the plates, the distance between the plates (the thickness of the insulator), and on the physical properties of the insulating material.

You can learn more about capacitors and how/why they work in the capacitors and capacitance section in Khan Academy Physics.

Real capacitors:

Cylindrical capacitors (black, dark blue, or silver, upper left) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package.

The circle-shaped capacitors (aqua blue and orange, bottom) are simply two metal disks facing each other, separated by an insulator.

Adjustable capacitors (white, right) have air as the insulator. One set of plates rotates to overlap more or less area to the stationary set of plates. Variable air capacitors are used to tune radios, for example.

The most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down. When this happens, a spark can burn through the insulation and jump between the plates. No more capacitor. Real capacitors have a voltage rating that should not be exceeded.

Since a capacitor has connection wires, it inevitably has a small parasitic resistance and inductance. The parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current, such as when it is connected to the power pin of a digital chip. Providing a sudden surge of current to the digital chip means the inductance of the capacitor connections should be very low.

The material separating the capacitor plates is supposed to be insulating (allow zero current). But not all insulators are perfect, so tiny currents can seep through. These so-called leakage currents appear to flow straight through the capacitor, even if the voltage is not changing (when $\text{d}v/\text{d}t=0)$‍. Paths for leakage current also happen if the circuit is not clean, and currents flow around the capacitor, along the surface of the component.

A surface mount capacitor is shown here:

Leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned.

A surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers.

When creating an inductor, the goal is to come as close as possible to the ideal inductor equation, $v=\text{L}\text{d}i/\text{d}t.$‍

A full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article. To learn more about inductors and magnetic fields, see the magnetic fields section of Khan Academy Physics.

Any conductor carrying a current generates a magnetic field in the surrounding region, as represented by the red lines in these images. The magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil.

A good way to think about inductance is to make the comparison to mass in a mechanical system. Magnetic energy is stored in an inductor in the same way kinetic energy is stored in a moving mass. Think of a rotating flywheel (a wheel with a heavy rim). You can't stop a spinning flywheel in an instant. An inductor is similar. The current in an inductor does not stop instantaneously, just like the flywheel. The magnetic field energy keeps pushing it along.

Making inductors: To achieve higher levels of inductance (higher $\text{L}$‍), inductors are made by winding wire in a coil. The magnetic field can be intensified even more by placing a suitable magnetic material inside the coil. This is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite. (You can't see the ferrite core shaped like a donut, it is covered by the copper wire.)

The ferrite core concentrates and intensifies the magnetic field, which increases the value of the inductance, $\text{L}$‍.

Real inductors differ from the ideal equation in a few important ways. Since inductors are made of long wires, they often have a significant parasitic resistance.

The other unavoidable feature of inductors is that they take up a lot of space. The magnetic field exists in the volume of space around and inside the inductor, and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance. This is why it is rare to see an inductor designed into an integrated circuit.

We finish up with this astonishing image of an air-core inductor. This large copper coil (an inductor) was part of a wireless telegraph station built in New Jersey, USA in 1912. It could send a message 4000 miles (6400 km), all the way across the Atlantic Ocean to Germany. Wow. Needless to say, most inductors are much smaller.