Power Tip 56: Estimate PWB interconnect inductance

March 01, 2013 //By Robert Kollman
Power Tip 56: Estimate PWB interconnect inductance
Robert Kollman of Texas Instruments examinessome 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.

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.

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

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