Verifying trace S-parameters is more than just good practice — it's essential for confident measurement, simulation, and design space exploration in modern EDA tools. Especially in high-speed digital systems where traces are long, applying a few key principles can provide valuable insights into data and provide a head start in design explorations. 

Trust but Verify Trace S-Parameters

As Dr. Eric Bogatin, the signal integrity evangelist, teaches in Rule 9: “Never perform a measurement or simulation without anticipating what you expect to see.”¹ In this article, what to expect from the S-parameters of a single-ended trace will be discussed. An S-parameter analysis is shown in Figure 1. A sine wave at a given frequency, f₀, is launched at Port 1.

Figure 1. In an S-parameter analysis, the S11 represents the reflection coefficient and the S21 represents the transmission coefficient. By examining the S11 and S21, we create confidence in our S-parameter data.

The S11 represents the reflection coefficient and the return loss at Port 1. S21 represents the transmission coefficient and the insertion loss to Port 2. Given a single-ended 6-in. trace, four essential things to expect and check with S-parameter data will be discussed.

Check the Low-Frequency Behavior (S11 and S21)

At the low end of the frequency, a few megahertz (MHz), a typical trace (a few inches) is very short compared to the wavelength of the stimulus signal. For example, a 1 MHz sine wave in FR4 material has a wavelength of approximately 6000 in. A typical 6-in. trace is only 0.1% of the wavelength.

Because the physical length of the trace is only 0.1% of the wavelength at 1 MHz, the signal experiences minimal phase change after traversing the trace (see Figure 2).

Figure 2. A typical 6-in. trace is electrically short in comparison to the 6000-in. wavelength of a 1 MHz signal. Because the trace is electrically short, there is minimal phase shift, and the trace looks transparent to the signal. 

As a result, the trace will look transparent to the signal. At the lowest frequency, this means no signal is being reflected. The return loss, expressed in S11 in the dB scale, has a large negative dB value at the lowest frequency. Since no low frequency signal is reflected, all of it must be transmitted. As a result, the insertion loss, expressed in S21 in the dB scale, approaches 0 dB at the lowest frequency, as shown in Figure 3.

Figure 3. At the lowest frequency, the typical trace looks transparent to the signal. One should expect the return loss to have a large negative dB value, and the insertion loss to have a value of 0 dB.

Spot the First S11 Resonance Peak

Let’s assume this 6-in. trace has a characteristic trace impedance of 50 Ω. Since all printed circuit board traces have loss, the assumed 50 Ω trace impedance will have an imaginary part. The trace impedance is a complex number.

In a typical S-parameter analysis, the reference impedance of the ports is 50 Ω (a purely real number). This mismatch between the purely real port impedance and complex trace impedance creates reflections. Constructive interference of reflections at Port 1 results in a peak in S11.

When the reflections add destructively, a dip in S11 can be observed, as shown in Figure 4. The first peak of S11 is the frequency where the physical length of the transmission line corresponds to a quarter of a wavelength. At this frequency, the reflection at Port 1 adds constructively with the reflection from Port 2, creating a peak in return loss.

Figure 4. Because of the reflections adding constructively and destructively at different frequencies, peaks and dips in the return loss plot can be observed. This is a signature of trace return loss.   

The equation below helps to estimate the frequency at which one should expect the peak of S11.

                                                                                                     (1) 

where Dk is the dielectric constant and len is the trace length in inches.

Assuming the substrate is FR4 and has the dielectric constant (Dk) of 4, and that the strip line trace is about 6 in., one should expect the first return loss (S11 in dB) peak around 250 MHz (see Figure 5).

Figure 5. One should expect the 6-in. stripline trace in an FR4 environment to have a first return loss peak at around 250 MHz.

Typically, a microstrip line in an FR4 substrate has an effective Dk that will be lower than 4, which will increase the resonance frequency. Figure 6 shows a measured 6-in. microstrip line. As expected, the first peak (310 MHz) is at a higher frequency than the simulated (250 MHz).

Figure 6. A microstrip line has a dielectric constant, Dk, smaller than 4, which pushes the first peak to a higher frequency.

Use S21 Phase as a Consistency Check

Because the S11 peak is the result of the quarter-wave-length constructive interference, the phase of S21 should tell us a consistent story. That is, at the frequency where the S11 has a peak, the phase of S21 should be 90°, indicating the quarter-wave nature of the interference. As demonstrated in Figure 7, by plotting the S11 on the right y-axis and overlaying the phase of S21 on the left y-axis, one can notice the peaks of the S11 align with the 90° phase shift in the phase of S21.

Figure 7. An overlay of the phase of the insertion loss and return loss demonstrates the consistency check for the first peak. At the frequency where the return loss peak occurs, one expects a 90° phase shift in the insertion loss.

This is a great example of Eric Bogatin’s Rule 10: “While you can never prove you are correct, you can demonstrate the result is consistent with other analyses or measurements.”¹ By using the available S21 phase information in the S-parameter, one is able to provide the consistency test for the S11 peak.

Expect Ramp-Up in Real Measurements

So far, the S11 plot example appears clean and flat over all frequencies because the trace was created and solved using Controlled Impedance Line Designer in Keysight Advanced Design System. The solver handles arbitrary dielectric layers and arbitrary metal thickness.²

In a typical 2D cross-section transmission line solver, one first defines the substrate stackup, dielectric properties, and the controlled impedance line configuration. The controlled impedance line can be in a microstrip or stripline environment. One can also define a single-ended line or a differential pair.

Once the dimensions of the substrate, trace width, spacing, and thickness are in place, the electromagnetic solver begins the cross-sectional impedance per-unit-length calculation. Internally, the per-unit-length impedance is the result of the computation. The user can then scale the per-unit-length result to different trace lengths. In this ideal modeling of a controlled impedance trace with arbitrary length, the S11 peak should drop off as frequency increases due to the conductor and dielectric loss in the trace. If the S-parameter of the trace is measured, one should expect the ripples to increase (ramp-up) as the frequency increases, as shown in Figure 8.

Figure 8. Because of the unavoidable small impedance discontinuities in measurement connectors and fixtures, the return loss of the measured 6-in. trace shows a distinct ramp-up as the frequency increases. The return loss of the simulated 6-in. trace remains flat across the frequencies.

The small impedance discontinuities in the connectors or fixtures cause this behavior to happen. One should always expect a level of S11 ramp-up in S-parameter measurements. In practice, ripple ramp-up with frequency is a telltale sign of real-world discontinuities, such as fixtures or connectors.

Summary: Think like an SI Detective

S-parameter data can reveal more than what it initially shows. Like a good detective, one can question the evidence. The checks provided in this article help to:

• Validate measurement consistency and setup at low frequencies
• Estimate trace length and match it to expected behavior
• Confirm quarter-wave effects using S21 phase as a sanity check
• Spot a real measurement by watching for S11 ramp-up.

With these checks, one can extract not just confidence — but insight — from S-parameters, laying the groundwork for smarter simulation, cleaner correlation, and better signal integrity overall.

REFERENCES

1. E. Bogatin, “Bogatin’s 20 Rules for Engineers,” Signal Integrity Journal, February 3, 2020. 
2. Keysight Technologies, "Multilayer Interconnects - Advanced Design System 2025 Update 2 Documentation". Accessed: June 24, 2025.