Printed Circuit Design & Fab - May 2008 - (Page 16)

What is Inductance? A closed loop creates inductance, so control your signal path by minimizing the loop area. WHILE MANY OF Electromagnetic Induction When the current in a loop changes with respect to time, the magnetic field associated with that current also changes. As this changing magnetic field cuts through a conductor it induces a voltage in the circuit of that conductor. This occurs whether the magnetic field lines cut through a different conductor or the same conductor as the original current. The voltage induced in a single wire loop is equal to the time rate of change of magnetic flux passing through the wire loop.2 This is described in Faraday’s law of electromagnetic induction as: us feel that we understand inductance, in reality inductance1 is a commonly misunderstood concept. Inductance DR. BRUCE is important to ARCHAMBEAULT EMI/EMC and high-speed signal integrity (SI) design considerations since it is one of the primary limiting factors in high-frequency design. Whenever there is metal, and current flows though that metal, inductance is present and will affect the current flow. At high frequencies, this intrinsic inductance dominates all components, traces, and metal planes. Capacitors and resistors too, become inductors at high frequencies. A complete study of inductance would fill many volumes. The purpose of this article is to help the reader better understand the concepts of inductance as it applies to EMI/EMC/SI design, especially on printed circuit boards. One fundamental fact that is taught in first level electronic circuit class is that the current must always return to its source. So, if there is current flow, there must be a closed loop (so that the current can return to its source). This closed loop of current creates inductance. path as the circumference of the area. The left hand side of Equation 1 gives the voltage around this close loop, and the right hand side shows that this voltage will be negative! This negative voltage will inhibit the original current that created the magnetic flux, effectively providing impedance to the original current flow. Simple Rectangular Loop We can simplify the general case provided in Equation 1 to a simple rectangular loop as shown in FIGURE 1. If the loop is small compared to the wavelength of the frequency of interest, then it can be assumed that the magnetic flux is constant over the area A, and Equation 1 can be reduced to: V = −A ∂B ∂t EQ. 2 ∫E • dl = − ∫∫ ∂B ∂t • dS EQ. 1 While equations, such as EQUATION 1, can look intimidating, when we dissect it to interpret the meaning of the equations, it not only makes the concept clearer, but reduces the intimidation factor. Consider the left hand side of Equation (1). This shows an integration that is along a line that closes upon itself. The electric field along that path, multiplied by the length of the path, provides the voltage around this closed loop3. Now, let’s consider the right hand side of Equation 1. We observe the double integral, which is simply the area of a surface, and the amount of timevarying magnetic flux contained within that surface area. Of course, if we have a surface area, there must be a closed loop around the circumference of the surface area. Note that on both sides of the equation, a closed loop is required! The left hand side of Equation 1 shows the closed path as part of the integration and the right hand side shows the closed w The amount of voltage induced from a time-varying magnetic field can be found for any geometry using Equation 1 and for a simple rectangular loop using EQUATION 2. Calculating Self Inductance There are a number of terms to describe inductance. Self-inductance and loop inductance are the most common and mean the same thing. Recall from the previous sections that induction occurs when a time-changing current causes magnetic lines of flux to cut through metal conductors. Until now, only the case where these lines of flux caused by a current in one loop cut through the conductors of another loop was considered. These lines of flux will also cut through the conductors of the original loop as well. This gives rise to the loop’s self-inductance. Area = A V B Isolated Circular Loop h FIGURE 1. Rectangular loop. 16 FIGURE 2. Single turn rectangular loop. The self-inductance of an isolated circular current loop in free space can be found using the fundamental relationship for mutual inductance if the two loops are considered to be overMAY 2008 PRINTED CIRCUIT DESIGN & FAB

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Printed Circuit Design & Fab - May 2008 Contents Our Line Market Watch Around the World Happenings ROI EMC For the Real World PCB East Conference Brochure Positive Plating Don't Let your Signals Stub Their Toes Improve PCB Layout With Skill Utility Programs The Next Generation Design Tool Challenge Thermally Conductive Microwave Materials PCB Dielectric Degradation in Lead-Free Assembly Applications A Tale of Two Trade Shows Eliminating Board Defects Off the Shelf Marketplace Ad Index BGA Bulletin

Printed Circuit Design & Fab - May 2008

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