Test Cable Flexure and Phase Stability After Calibration

A calibration is a snapshot. It records the loss and phase of everything between the instrument and the reference plane at the moment you press the button. If the test cable changes afterwards, the snapshot is wrong, and the instrument cannot know. This article shows how big the error is, how to estimate it from phase, and which handling rules prevent it.

What the calibration assumes

Vector error correction treats the test cable as a fixed part of the error model. Its loss, its phase delay and its small reflections are all folded into the stored error terms. The correction is only valid while those terms stay the same.

A cable is not a rigid part. Bending it changes its geometry slightly. Twisting it, pulling on it or moving a connector changes the conditions at the ends. Each of these changes the loss and the phase of the cable. The calibration cannot track either one.

The result depends on where the cable sits in the setup:

• A cable that carries the transmitted signal adds error to the transmission measurement.
• A cable that feeds the reflection measurement changes the reflected signal as well, because the signal passes through it twice.
• Any change that adds a small reflection at a connector acts like the echo shown below, and it adds to or subtracts from the true reflection depending on phase.

Because the error terms no longer match the real cable, the corrected data contains an uncancelled error. It appears as ripple across frequency, as a phase drift between sweeps, or as both.

Electrical length and wavelength in the cable

Phase is just length measured in wavelengths. The electrical length of a line is:

Here θ is the electrical length in degrees, ℓ is the physical length and λ is the wavelength in the cable.

The wavelength inside a cable is shorter than in free space. With a velocity factor of 0.7, the wavelength in the cable is 0.7 times the free-space wavelength:

At 1 GHz the free-space wavelength is about 0.3 m. A cable with velocity factor 0.7 therefore has a wavelength of about 0.21 m at 1 GHz.

Worked example: 1 cm of movement

Suppose you calibrate a setup, then bend the cable so that its electrical length changes by 1 cm. The cable has velocity factor 0.7 and you measure at 1 GHz.

1. Free-space wavelength: about 0.3 m.
2. Wavelength in the cable: 0.7 × 0.3 m = 0.21 m.
3. Phase change: 360 × 0.01 / 0.21 ≈ 17 degrees.

A 17-degree phase error is large. It is not a small correction on a transmission phase measurement, and it can move a reflection result noticeably. And the cable moved by only one centimetre.

Phase error from a length change increases in proportion to frequency. The same 1 cm at 2 GHz gives about 34 degrees, and at 3 GHz about 51 degrees. Doubling the frequency doubles the error, because the same length is twice as many wavelengths. This is why a setup that behaves at low frequency can fall apart near the top of the sweep.

Estimating electrical length from phase

You can run the same relation backwards. If you can see a phase change, you can estimate how much electrical length changed:

Take the 1 GHz, velocity factor 0.7 case again, where λ is about 0.21 m. Suppose a reference trace shows a phase change of 36 degrees after you move the cable. Then:

Δℓ = 36 / 360 × 0.21 m = 0.021 m, or about 2.1 cm.

This is a useful check. A thru connection with the cable in place should show a stable phase. If the phase trace shifts when you touch the cable, the shift tells you the equivalent change in length. A change of a few degrees means the cable is stable enough for your purpose. A change of tens of degrees means the calibration is no longer valid, and you should recalibrate with the cable in its final position.

To read the phase correctly across a sweep, unwrap it first. A raw phase trace jumps by 360 degrees at the edge of the display, and those jumps are display wraps, not real changes.

Handling rules for test cables

These rules follow from the physics above. None of them needs special equipment.

• Calibrate in the final position. Route the cable the way it will stay, then calibrate. Do not calibrate with the cable in a convenient shape and rearrange it afterwards.
• Do not move the cable after calibration. If the setup must change, treat the calibration as lost.
• Fix the cable. Support it so that its weight does not pull on the connector, and so that it cannot swing when someone touches the bench.
• Use gentle, wide bends. Avoid tight curves, kinks and twists. A bent cable is a changed cable.
• Tighten connectors the same way every time. A connector that is slightly loose or tightened unevenly changes the phase and the reflection. A consistent method gives repeatable results.
• Keep a short cable when you can. A shorter cable has fewer wavelengths in it, so the same movement matters less.
• Test after any disturbance. Check the thru phase or a known reference before you trust a measurement taken after anyone touched the setup.
• Recalibrate when in doubt. A new calibration costs a few minutes. A wrong measurement can cost far more.

When you save the data afterwards, the stored file has no record of how the cable moved. See How to Open an S2P (Touchstone) File: 6 Ways and a Free Viewer for reading the saved result and spotting ripple that should not be there.

In plain words · for students and beginners

Cable flexure in plain words

The idea in everyday terms

Think of a long garden hose with water flowing through it. You measure how long the water takes to arrive. Then someone picks up the hose and lays it in a longer loop. The water now takes longer, but your notes still say the old time.

A test cable is the same. Your calibration wrote down how long the signal takes and how much it weakens. If you move the cable, both values change, but the notes do not.

The comparison breaks down in one place. Water in a hose just arrives later. A radio signal is a wave, so a change in length shows up as a shift in the wave's phase. A shift in phase can add to the signal or cancel it, which is why the result can ripple up and down.

The same example in simple steps

Phase tells you how far along its cycle a wave is. One full cycle is 360 degrees.

1. At 1 GHz, a wave in free space is about 0.3 m long.
2. Inside a cable with velocity factor 0.7, the wave is shorter: 0.7 × 0.3 m = 0.21 m. (Velocity factor is how fast the signal travels in the cable compared with free space.)
3. A 1 cm change is 0.01 m. Divide it by 0.21 m to see what fraction of a wave it is, then multiply by 360 degrees.
4. The answer is about 17 degrees.

Now raise the frequency. The wave gets shorter, so the same 1 cm is a bigger part of a wave. The error grows in proportion to frequency. At 2 GHz it is about 34 degrees.

A two-port is a device with one connection on each side, like a cable or a filter. Its four S-parameters describe how the signal goes through and how it reflects back. Your cable is part of that picture, so a changed cable changes what the instrument reports.

Mistakes beginners make

• Calibrating, then tidying up. Straightening or moving the cable "to make room" after calibration quietly breaks the calibration.
• Thinking a small movement is harmless. One centimetre looks tiny, but it is about 17 degrees at 1 GHz.
• Judging only at low frequency. The error grows with frequency, so a setup can look fine at the bottom of the sweep and fail at the top.
• Blaming the device under test. Ripple or drifting phase often comes from the cable, not from the part you are measuring.
• Reading wrapped phase as a real change. Phase displays jump by 360 degrees at the edge. Those jumps are not movements of the cable.

Remember

• A calibration only holds while the cable stays as it was when you calibrated.
• Length change in degrees is 360 × length change / wavelength in the cable, and it grows in proportion to frequency.
• Calibrate in the final position, fix the cable in place, and recalibrate if anything moves.

Related pages on RF View

• How to Open an S2P (Touchstone) File: 6 Ways and a Free Viewer