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Microstrip Propagation Times Slower Than We Think

Microstrip Propagation Times Slower than We Think 1 Most of us have been using incorrect values for the Propagation speed of our Microstrip traces! The correction factor for r we have been using all this time is based on an incorrect premise. This article explains why and develops a superior model for estimating Propagation speeds and Propagation delays for Microstrip configurations. Signal Propagation Speeds Electrical signals on wires and traces travel at the speed of light: 186,280 miles/second! That works out to ft/nanosecond, or in/nanosecond, if you do the arithmetic.

Microstrip Propagation Times Slower Than We Think 2 Case (b) illustrates the same trace, but with a thinner spacing between the trace and plane.

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Transcription of Microstrip Propagation Times Slower Than We Think

1 Microstrip Propagation Times Slower than We Think 1 Most of us have been using incorrect values for the Propagation speed of our Microstrip traces! The correction factor for r we have been using all this time is based on an incorrect premise. This article explains why and develops a superior model for estimating Propagation speeds and Propagation delays for Microstrip configurations. Signal Propagation Speeds Electrical signals on wires and traces travel at the speed of light: 186,280 miles/second! That works out to ft/nanosecond, or in/nanosecond, if you do the arithmetic.

2 The speed of light slows down in any other medium by the square root of the relative dielectric coefficient of the medium. Signal Propagation time is the inverse of this figure, or ns/in. In an earlier article on this site1 I posed the question of what happens if we string a wire across a lake and measure the Propagation speed, and then lower the wire into the lake and measure the Propagation speed when the wire is under water. I pointed out that the Propagation speed through the wire under water would be about 1/9th that of the wire in the air! Same signal, same copper, same electrons.

3 But only one-ninth the Propagation speed (9 Times the Propagation time ). You see, moving electrons (current) create an electromagnetic field around the wire (or trace). The issue is not how fast the electrons can travel through the wire, the issue is how fast the electromagnetic field can travel through the medium it travels through. In the example above the medium the electromagnetic wave travels through is water. On our circuit boards the medium is the board material, usually (but not always) FR4. So, for example, a stripline trace in FR4 with an r of would travel at the speed of light divided by the square root of 4 (which is 2) or about 6 /ns.

4 Most of us are pretty comfortable with this figure. Microstrip Environment The Propagation speed for a Microstrip trace poses the problem that the trace is in a mixed environment. The medium underneath the trace is the board dielectric. The medium above the trace is air. So the electromagnetic wave travels through this mixed medium at a speed somewhere between that of the speed of light and the Propagation speed in stripline (approximately one-half that of the speed of light.) There is a correction factor for r that has been traditionally used for Microstrip environments. It apparently derives from work done in 19672 and is as follows: But there is a problem with this.

5 This correction factor is a constant, yet we sometimes observe that different width Microstrip traces may have different Propagation speeds even though they are in otherwise identical Figure 1 suggests why. Electromagnetic Fields Figure 1 case (a) illustrates how the electric field lines might be concentrated under a Microstrip trace. The trace is referenced to a plane. The return signal will be on the plane directly under the trace. So, the electric field lines will extend from the trace to the plane. Most of the field lines are under the trace, in the dielectric environment, but many extend upwards into the air before they curve back down to the plane.

6 Copyright 2002 by UltraCAD Design, Inc. and Mentor Graphics Corporation ' =+Equation 1 Microstrip Propagation Times Slower than We Think 2 Case (b) illustrates the same trace, but with a thinner spacing between the trace and plane. Since the spacing between the trace and the plane is closer in case (b), the field intensity will be stronger than in case (a), and the field lines will drop more quickly to the plane. We can Think of this situation as case (b) having a higher percentage of its field lines internal to the dielectric, and a lower percentage of its field lines in the air.

7 Since the Propagation speed is Slower in the dielectric, we can speculate that the signal Propagation speed for case (b) will be Slower than case (a). Now consider case (c). Here we have a very wide trace. Most of the field lines will be in the dielectric between the trace and the plane, with only a small percentage of them above the trace in the air. Therefore, we might speculate that the speed of this trace will be Slower yet. Let s imagine the trace width taken to its limit infinitely wide. If the trace is infinitely wide, then ALL the field lines will be within the dielectric.

8 In fact, there is little conceptual difference in Propagation speed between an infinitely wide Microstrip trace and a stripline trace. BOTH have the electromagnetic field lines fully contained within the dielectric. The issue becomes looking at the concentration of field lines under the trace. If the (percentage) concentration of field lines increases under the trace, the Propagation speed will slow down. Two things contribute to an increase in the concentration of field lines underneath the trace: 1. Bringing the trace closer to the plane. 2. Increasing the t race width. (Note: Increasing the trace thickness has a minor effect on Propagation speed, but the effect is much smaller than with the other variables and will be ignored in this paper.)

9 Each of these will cause the Propagation speed to slow down. Therefore the typical Propagation speed adjustment we have been using for Microstrip (Equation 1) cannot be sufficient since it is simply a constant (it only depends on r). Alternative Approach I propose this as an alternative approach. Note that, in the limit, the Propagation speed for a Microstrip trace is the same as for a stripline trace. The limit is reached with an infinitely wide trace or a zero separation between trace and plane. Under any other conditions, the Propagation speed increases. Therefore, we should Think of the Microstrip Propagation speed as some factor of the Propagation speed for the same trace in a stripline environment surrounded by a material with the same dielectric coefficient.

10 This latter figure is easy to calculate, it is simply the speed of light, in/ns, divided by the square root of the relative dielectric coefficient: Figure 1 Field concentration strength depends on several factors (c) (b) (a) Microstrip Propagation Times Slower than We Think 3 (Note: Up to this point we have talked about Propagation speed. From now on we are going to talk about Propagation time , which is the inverse of Propagation speed. Propagation time is expressed in units of time per unit length, or, when multiplied by length, simply in units of time .)


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