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### Course: Electrical engineering>Unit 2

Lesson 1: Circuit elements

# Real-world circuit elements

Real-world (non-ideal) circuit elements come close to their mathematical ideal models. It is important to understand the limits.

## Non-ideal 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 $\left(\text{R, L, C}\right)$ 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.

## Real-world resistors

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, $v=i\phantom{\rule{0.167em}{0ex}}\text{R}$.
The resistance value of a resistor depends on two things:
• what it is made of
• how it is shaped
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 resistor is a circuit element, a physical object.
• Resistivity is a property of a bulk material.
• Resistance is property of a resistor, determined by both the resistivity of the material and the shape of the resistor.
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, $3\phantom{\rule{0.167em}{0ex}}3$. The third band is the multiplier, brown stands for $×{10}^{1}$. The fourth (last) band indicates the tolerance, gold is $±5\mathrm{%}$. The resistor value is $330\phantom{\rule{0.167em}{0ex}}\mathrm{\Omega }\phantom{\rule{0.167em}{0ex}}±5\mathrm{%}$.
This is a precision resistor with 5 color bands:
Read the bands from left to right: Red Red Blue Brown Brown $=2\phantom{\rule{0.167em}{0ex}}2\phantom{\rule{0.167em}{0ex}}6\phantom{\rule{0.167em}{0ex}}1\phantom{\rule{0.167em}{0ex}}1$. The first three bands $\left(2\phantom{\rule{0.167em}{0ex}}2\phantom{\rule{0.167em}{0ex}}6\right)$ are the value. The fourth band is the multiplier $\left(×{10}^{1}\right)$, The fifth (last) band indicates the tolerance, brown is $1\mathrm{%}$. The resistor value is $2260\phantom{\rule{0.167em}{0ex}}\mathrm{\Omega }\phantom{\rule{0.167em}{0ex}}±1\mathrm{%}$.
This is a surface mount resistor:
The resistance value is encoded in the $3$-digit code: $102$, meaning $10×{10}^{2}=1000\phantom{\rule{0.167em}{0ex}}\mathrm{\Omega }$. The size specification of this resistor happens to be "0603 Metric", indicating its footprint is $0.6\phantom{\rule{0.167em}{0ex}}\text{mm}×0.3\phantom{\rule{0.167em}{0ex}}\text{mm}$.
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.

## Real-world capacitors

When making real capacitors, the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation, $i=\text{C}\phantom{\rule{0.167em}{0ex}}\text{d}v/\text{d}t.$
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.
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 $\text{d}v/\text{d}t=0\right)$. 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.

## Real-world inductors

When creating an inductor, the goal is to come as close as possible to the ideal inductor equation, $v=\text{L}\phantom{\rule{0.167em}{0ex}}\text{d}i/\text{d}t.$
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.

## Want to join the conversation?

• What are some real-life examples where "parasitic effects" become relevant?
• DC line loss is an example of a parasitic effect, When DC voltage is carried over a long distance it can lose voltage. If you had a DC power supply with +20V at the voltage source, and measured the voltage at the end of a 75 foot wire, It may show +19.5V. While marginal, it is a very real world example.
• What is used in an integrated circuit to replace an inductor that takes too much space?
• Hello Thierry,

Good catch. Inductors are indeed hard to miniaturize.

For many applications a capacitors can serve the same function. Especially when combined with one or more op-amps. You can make filters of any type including low pass, high pass, notch, and bandpass.

This is an interesting application https://en.wikipedia.org/wiki/Gyrator

Finally, there are some application where it is more efficient to keep the inductor. In this situation a discrete inductor will be placed along side the integrated circuit. This is very common in switched mode power supplies.

Regards,

APD
• Can the parasitic effects of an inductor, a resistor, or a capacitator be useful in any situations?
• How do you calculate "parasitic effects" in a given situation?
• Usually, you can't; being deviations from the ideal, calculable values, they have to be measured, not calculated. In some cases, such as when designing real components for manufacture, it is possible to calculate estimates for likely parasitic effects of the component resulting from a particular design, by a fairly lengthy analysis of the known (pre-measured) properties of the materials involved and the shapes and configurations of the pieces of those materials in the proposed design.
• 1. What is IC layer mean (under the example of a resistor in an integrated circuit)?
2. what is a bulk material and how is it different from just...material?
3. what is R,L,C (from the second paragraph)?
• "IC" stands for "integrated circuit". These are the silicon chips inside all your electronic gadgets. We use the word "integrated" because a single little piece of silicon has many different components "integrated" into a single assembly.

"Bulk" material is just .. material. The "bulk" word implies that we have a large amount of resistive material (like buckets full) that we are about to form into many separate small resistors.

R, L, and C stand for Resistor, Inductor, and Capacitor. These are the three basic "passive" components we use in electrical engineering.
• what would be a situation in which you would want to avoid your circuit having a sudden loss of current and an inductor could help ?
• When the electrical power lines are blown down, the resulting loss of power causes the current to drop and a switch is thrown to stop power surge. If there is a generator on stand-by, the generator would start up and the power source would be switched to the generator. When the power comes back on, a switch would senses the power change and switch back to normal.
There are numerous ways that current loss modifies how we use electronics.
• How do you read a resistor from left to right if you can flip it over?
• That's a really good question. Sometimes it's very hard to tell which is the starting band of the color code. Your first step should be to figure out which band is the tolerance band so you can orient the resistor properly.

4-band resistors have tolerances down to 5%. The colors for the tolerance (silver, gold) are supposed to look different than any of the regular "number-colors". But sometimes you can't tell brown=1 apart from gold=5%. When I can't tell the color for sure, I decode the resistor value both ways and pick the one I know is a standard manufactured value (there aren't that many different values, and you get to recognize them after a while).

The 5-band resistor has a red band at one end and a brown at the other end. The tolerance could be 2% or 1%. Look at the gap between the last brown band and the previous brown band. That gap is ever so slightly larger than the other gaps. That's a tip-off that brown is the tolerance band, 1%. It's not much to go on, but that's all the info there is.

Instead of going blind reading colored bands, the real way to do it is is to measure the resistor with an ohmmeter. If I'm building something and there are resistors all over my bench, that's what I always do.
• Can anyone explain how capacitors and inductors are used in real circuits and its purposes?
• Blackbird,

They are everywhere!

Motors, electrical power grid, power supplies, radio, computers. In fact, pick any electrical device and you will likely find an inductor or capacitor inside.

Unfortunately, Khan Academy is just starting this electrical community. You will have to look elsewhere to find your answers. May I suggest you start by researching and then building a crystal radio.

Happy soldering,

APD