# Electrical Components of Printed Circuit Board Design

• Print
This chapter is from the book

## Inductance

Inductors seem to be very difficult components for many people to understand. Appendix B is devoted to explaining why inductors do what they do (induct). Here, I try to give an intuitive understanding of what happens when there is an inductor in a circuit.

The hydraulic analog for an inductor (Figure 3-7) is a paddle wheel with significant mass. When the pump applies pressure through the pipe, the paddle wheel's inertia resists the initial pressure, and pressure builds up behind it in the pipe. The pressure begins to overcome the inertia, and the paddle begins to turn. As long as there is pressure behind it, the paddle wheel will continue to speed up until it reaches an equilibrium with the flow.

Figure 3-7. Hydraulic analog for an inductor.

Most of us probably don't see many paddle wheels, so let's consider a perhaps more familiar illustration of inertia first. When your car is sitting in the driveway and won't start, think of what happens when you try to push it. It is very hard to get started, and you have to push it very hard to get it started. But once it starts to roll, it can be equally hard to stop. Some of us have had the unfortunate experience of having our car roll into another car or into the side of our garage before we could stop it again.

I had an opportunity once to open and close a huge (5,000 lb.) bank vault door. It was beautifully balanced on its hinges, and swung easily after I got it started. It took considerable effort to stop it again before it swung so far that it closed. It was a beautiful example of almost pure inertia.

So now think what happens when we turn on the pump (voltage). Pressure builds instantly against the vanes of the paddle wheel (inductor) but no water (current) flows. The pressure must "work" against the inertia for a moment before the wheel begins to turn. After a period of time, the wheel begins to turn and allow water (current) to flow. How long this takes is a function of how much force is applied and how much inertia there is in the paddle wheel. The force will continue to speed up the wheel until the wheel reaches an equilibrium speed such that all the water will flow unimpeded around the loop and there will be no pressure at all across the wheel.

Now, suppose we turn off the pump. The paddle wheel's inertia will cause it to continue to turn, forcing water to continue to flow around the loop. It is as though the paddle wheel takes over the pump's function. Reverse pressure will build up across the pump as water is forced to its "back" side and drawn away from its front. This will continue until the force that is built up is finally able to counteract the inertia of the paddle wheel, and the paddle wheel slows to a stop.

So it is with electrons. When we place a battery across an inductor, there is force (voltage) across the inductor, but in the first instant there is no current flow. Current does begin to flow, however, and after a moment the current will reach an equilibrium and flow unimpeded around the loop. At that point the voltage across the inductor has dropped to zero. How quickly the current begins to flow and how quickly it reaches equilibrium depend on how large the inductor is. It takes longer for this to happen with a larger inductor than it does with a smaller inductor.

The impedance to the initial flow of current has its source in the buildup of the magnetic field around the conductor. For a more extended discussion of this characteristic see Appendix B, "Why Inductors Induct." After the current stabilizes there is a stable magnetic field around the wire. Now when we remove the source of current, the magnetic field around the conductor begins to collapse, generating the continuing force to keep current flowing in the same direction. Electrons will continue to flow and build up on the far side of the inductor. As they build up, the charge (voltage) increases. When the voltage increases enough, it will repel the further flow of electrons. The force will finally balance against the "inertia" of the inductor. At that point, the flow will stop.

So, as with a capacitor, what happens to the relationship between voltage and current with an inductor is time dependent. At the instant when voltage is first applied, voltage appears across the inductor but no current flows. Thus, voltage leads current, or current lags voltage through an inductor. In this sense, an inductor behaves exactly the opposite as a capacitor.

Also, in contrast to a capacitor, consider what happens when we pump water in one direction, then reverse the pump and pump it in the other direction. If we reverse the direction of the pump quickly, before the "inertia" can be overcome, very little water flows at all. On the other hand, if we pump for a longer time in one direction, then reverse the pump and pump in the other direction for a while, a reasonable flow will exist. A large inertia (inductor) will resist the flow more and for a longer time, and a smaller inertia will let the flow start more quickly.

Thus, the effect of the inductor is a function of both the size of the inductor and the frequency. Flow is small if the inductor is large or if the frequency is high; flow is larger if the inductor is smaller or the frequency is lower (see Table 3-2).

Table 3-2. Inductor size and frequency both affect the flow of current.

Suppose two inductors are connected in series (Figure 3-8). If L1 is much larger than L2 (i.e., the first paddle wheel is much larger than the other), the current (flow) cannot be larger than that allowed by the larger one. The second, smaller inductor will not have much effect, unless it is about the same size as the larger one. By the time the force can overcome the inertia of the larger one, the smaller one's inertia has already been overcome.

Figure 3-8. Hydraulic analog of two inductors connected in series.

As is the case with resistors, inductors in series add together. So the equivalent inductance, Leq, if two inductors are connected in series is given by Equation 3-11:

Equation 3-11

Note that if L2 is very much larger than L1, then the equation for Leq reduces to Equation 3-12:

Equation 3-12

If there are two inductors in parallel, however (Figure 3-9), the current will not be less than what the smaller one will allow. The smaller inductor's inertia is quickly overcome by the force, so current flows through it whether or not the inertia of the larger one has been overcome. If the other inductor is small enough, additional current can flow through it. Thus, parallel inductors combine into a single equivalent, Leq, in the same manner that parallel resistors do (see Equation 3-13):

Figure 3-9. Hydraulic analog of two inductors connected in parallel.

Equation 3-13

Note also that if one inductor, say L2, is very large, the equivalent parallel inductance simply reduces to Equation 3-14:

Equation 3-14

Note that inductors combine exactly as resistors do. Inductors and capacitors are opposites in this characteristic also.

The measure of inductance is the henry (Joseph Henry). Remember the measure of capacitance is the farad, and the voltage across a capacitor will rise one volt when one amp flows onto the plates. A current flowing through an inductor may generate a voltage across it, also. But from the preceding it is clear that, in the case of an inductor, we are not talking about a DC current. A DC current does not generate voltage across an inductor just as a steady flow past the paddle wheel does not need a force to keep it going (once the paddle wheel is up to speed). Force builds up across an inductance when the current flow through it is changing, working against the inertia of the inductance. One henry of inductance will cause one volt to appear across it when the current through it is changing at the rate of one amp per second, or, more generally:

• 🔖 Save To Your Account

### InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

## Overview

Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

## Collection and Use of Information

To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

### Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

### Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

### Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

### Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

### Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

### Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

## Other Collection and Use of Information

### Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

### Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

### Do Not Track

This site currently does not respond to Do Not Track signals.

## Security

Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

## Children

This site is not directed to children under the age of 13.

## Marketing

Pearson may send or direct marketing communications to users, provided that

• Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
• Such marketing is consistent with applicable law and Pearson's legal obligations.
• Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
• Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

## Correcting/Updating Personal Information

If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

## Choice/Opt-out

Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

## Sale of Personal Information

Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

## Supplemental Privacy Statement for California Residents

California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

## Sharing and Disclosure

Pearson may disclose personal information, as follows:

• As required by law.
• With the consent of the individual (or their parent, if the individual is a minor)
• In response to a subpoena, court order or legal process, to the extent permitted or required by law
• To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
• In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
• To investigate or address actual or suspected fraud or other illegal activities
• To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
• To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
• To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.