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Design Article

Power Tip 56: Estimate PWB interconnect inductance

2/20/2013 4:13 PM EST

Printed wiring board (PWB) interconnect inductance can make or break the performance of a power supply. A large interconnect inductance can raise the high-frequency impedance of a gate drive circuit, impacting efficiency, or it can degrade the effectiveness of filter capacitors. In this Power Tip, we examine some simple formulas for interconnect inductance in free space and over a ground plane. We will find that the ground plane significantly reduces trace inductance and is critical for optimal performance in power supplies.

The simplest trace to consider is a rectangular conductor in free space. A formula for its inductance is shown in Figure 1. Note that the inductance is a strong function of length but has a logarithmic relationship to the width of the conductor. While the recommendation of making a conductor as wide as possible to reduce its inductance is substantiated by the expression, the benefit of wide conductors is diminished by the logarithm. This is clearly shown in the table, which contains some sample conductor widths and calculates the resulting inductance of a one-inch-long conductor. For instance, a 10 mil (0.25 mm), 2 oz (1.8 mil or 0.07 mm) conductor has an inductance of about 24 nH, if it is one-inch (25 mm) long. If its width is increased by 50 times, the inductance only drops by a factor of four due to the logarithm in the expression.

Click on image to enlarge.

Figure 1: Inductance of a free space conductor has a logarithmic relationship to width.

Ground planes in circuit boards are used to ease routing, minimize the ground voltage variation, provide electrical and magnetic shielding, control impedances, and to help cool the components. Additionally, they provide the opportunity to reduce the inductance of circuit conductors in the PWB. Figure 2 presents a simple formula for the calculation of a conductor over a ground plane. The expression shows linear relationships between inductance, conductor height over the plane and its length. So to a first order, minimizing the separation of the conductor and ground or increasing the conductor width lets you drive the inductance toward zero. The table presents some sample calculations that can be compared with Figure 1. For instance, we found that a 0.10-inch-wide conductor in free space had an inductance of 14 nH per inch. That same conductor placed over a ground plane of a two-sided board (0.06 inches thick) would have 3 nH per inch. That is a 5:1 reduction in interconnect inductance, which translates into faster gate drives, more effective filtering capacitors and reduced circuit losses from proximity effects. The table also shows that with a six-layer board where the dielectric thickness is reduced to 0.01 inch, the inductance is reduced by another factor of six. Clearly, when routing boards, you will want to put your ground layers as close to the board surface as possible to minimize inductance connecting the components on the surface.

Click on image to enlarge.

Figure 2: Inductance of conductor over plane can be driven arbitrarily small.

To summarize, inductances of conductors on single-layer boards are high due to the lack of a ground-plane layer. This can be mitigated somewhat by routing conductor pairs together. However, ground planes offer the ability to make order of magnitude reductions in this stray inductance, which will result in lower impedance signal paths. This can provide improved efficiency with improved gate drives, better electromagnetic interference (EMI) performance due to improved filter performance, and lower crosstalk due to lower impedance nodes.

Robert Kollman is a senior applications manager and distinguished member of technical staff at Texas Instruments. He has more than 30 years of experience in the power electronics business and has designed magnetics for power electronics ranging from sub-watt to sub-megawatt with operating frequencies into the megahertz range. Robert earned a BSEE from Texas A&M University and an MSEE from Southern Methodist University.

Stuart.Currie

2/21/2013 3:09 PM EST

Good Article. I think I caught a typo.
height and width metric dimensions in Table 2 are likely in (mm) not (cm).

gootee

3/1/2013 10:03 AM EST

Yes, the units for the left half of table 2 (and in the accompanying equation) should be mm, not cm, and the inductances/mm in the third column should be divided by 10. OR, the numbers in the first two columns could be divided by 10.

Plasman

4/4/2013 3:59 PM EDT

The first part this article is impracticle and misleading. The dominate factor of trace inductance is loop area and not length. Two 5 inch traces (drive and return) routed 1 inch apart would have much more inductance than the same traces routed 0.01 inches apart on a single layer board. The reason that adding the ground plane helps is that the effective area is reduces since the distance between the traces is reduced. For real life engineering, theoretical calculations of per unit length inductance of traces in free space with no consideration of return path are worthless.