Welcome to Tim’s Blackboard! This is the place to find discussions on interesting topics related to signal integrity and power integrity.

This week on Tim’s Blackboard, I will resolve the arrival time inconsistency shown in the previous post.

# Introduction

Last week, we sent an impulse through a section of 50-Ohm, 6-inch microstrip transmission line and expected the impulse to arrive at 1 nsec. However, the impulse arrived 0.88 nsec at the output, see Fig. 1.

*Fig. 1: ADS simulation result from last week's post. We expected the impulse to reach the output at 1 nsec, but the impulse arrived at 0.88 nsec.*

# Assumption, Assumption, Assumption

The answer to our question is in the assumption we made when we were calculating the time delay. The rule of thumb for the speed of propagation, 6 inch/nsec, assumes the Dk (dielectric constant) to be 4.

The speed of light in vacuum is 3*10^{8 }m/sec, or 30 cm/nsec, and alternatively, about 12 inch/nsec. To calculate the speed of propagation in a different medium, we divide the speed of light in vacuum by the square root of Dk:

Given an FR4 substrate with Dk = 4, the speed of propagation is:

# Microstrip and Effective Dk

The Dk of FR4 is indeed 4, but that's not the whole story. When a signal propagates in a microstrip environment, it sees both FR4 and air. The result of the signal interacting with both medium is a **lower effective DK.**

A lower effective Dk would **increase** the propagation speed and **lower **the delay: consistent with last week’s result.

Having a guess of what was happening, we proceed to verify whether our guess is correct.

# Consistency Test

Since the possible root cause of the early arrive time is the lower Dk due to air, we need to ensure the signal only sees the Dk of FR4. To do so, we place the same transmission line in a stripline environment, where the trace is only surrounded by FR4 material.

*Fig. 2: The same 6-inch transmission line with 20 mil trace width. Note the height of the substrate is changed so the impedance of the line is still 50 Ohms.*

To make sure we are doing an apples-to-apples comparison, the substrate height is increased so the impedance of the transmission is still 50 Ohms, see Fig. 2.

We then perform the identical simulation with the new substrate. Shown in Fig.3, the result of the impulse indeed arrives at 1 nsec, and our guess is now a valid root cause for the shorter delay.

*Fig. 3: Signal arrives at the predicted 1 nsec after switching the same 6-inch line into a stripline environment while maintaining impedance of 50 Ohms.*

# Inconsistency Resolved

Much like the melting trace paradox, our initial assumption was once again inaccurate. However, since we used a rule of thumb to quickly get the numbers for the propagation speed of light in FR4, some degree of inaccuracy could be expected.

As Dr. Eric Bogatin put it, “An okay answer now is better than a good answer later.” As long as we know the underlining assumption in the approximation, it is perfectly fine to use a rule of thumb to quickly estimate the result one is expecting.

That's this week's Tim's Blackboard. See you next week!

**Use ADS simulations to perform consistency tests:**

Thanks Tim!