TRL Calibration Explained: Thru, Reflect and Line

The idea behind TRL

Most VNA calibrations rely on standards whose electrical behavior you know well: a short, an open and a matched load. That works in coax, where good standards exist. It works poorly in a test fixture, in waveguide or on a printed board, where you cannot buy a trustworthy lumped load.

TRL avoids the problem. It uses three standards: Thru, Reflect and Line. Of these, only the line has to be known, and only two things about it: its characteristic impedance and its length. The thru can be a zero-length connection or a short line. The reflect needs no known value at all.

The VNA measures all three standards. The measurements give enough equations to solve for the error terms of both test ports, and for the unknown reflection coefficient of the reflect. Nothing needs to be modeled as a lumped element.

The three standards

Thru. The two ports are connected directly, or through a short line. The thru sets the reference plane at its center. If it has non-zero length, that length and its loss must be accounted for.

Reflect. This is any high-reflection device, such as an open or a short. Its exact value need not be known. The only requirement is that it presents the same reflection at both ports. In a fixture this means two identical copies, or one device that is fully symmetric.

Because the reflect is solved for rather than assumed, it does not have to be an ideal Γ = −1 or Γ = +1. A real short with some inductance works, as long as |Γ| is high and both ports see the same thing. The calibration needs only a rough idea of the reflect, enough to tell an open from a short (the phase must be known to within ±90°).

Line. A transmission line of the same type as the thru, but longer. It adds a known delay and gives the calibration a second transmission measurement with a different phase. That difference is what lets the math separate the error terms from the true line response.

Why the line sets the reference impedance

In SOLT, the reference impedance is defined by the load. If the load is not exactly 50 Ω, the calibration is not exactly 50 Ω.

TRL defines the reference impedance by the characteristic impedance of the line standard, not by a lumped load. After calibration, S-parameters are referenced to Z0 of that line. This is why the line must be built accurately and its impedance understood. If you fabricate the line yourself, errors in its width, dielectric thickness or permittivity change Z0, and the calibration inherits the change. A field-solver check such as the Microstrip Impedance and Width Calculator (FR-4, Rogers) helps before you build the board.

A uniform line is also what the math assumes. The line and the thru must have the same cross-section and the same Z0. A change in width, a via or a connector transition between them breaks the assumption.

Choosing the line length

The line must be longer than the thru by a length that gives a phase difference between about 20° and 160° at the frequency of use. The phase difference grows with frequency:

Here Δl is the length difference between line and thru, and λ is the wavelength in the line. Near 0° the line looks like the thru, so the two measurements carry almost the same information and the solution becomes ill-conditioned. Near 180° the same happens, because the line again looks like the thru with a sign change.

One line therefore gives a limited bandwidth. Since the phase is proportional to frequency, the ratio of the highest to the lowest usable frequency is 160 / 20 = 8. Covering a wide band requires several lines of different lengths, each used over its own sub-band. The software then switches or blends between them.

A line that is a quarter wavelength longer than the thru adds 90° of phase shift, which lies in the useful range. It is the natural choice for the center of a band.

Worked example

Suppose you want the line to be centered on a frequency f0 where it is a quarter wavelength longer than the thru.

1. At f0 the phase difference is 90°, so Δl = λ / 4.
2. Phase is proportional to frequency (for a non-dispersive line), so at frequency f the difference is 90° × f / f0.
3. The lower limit is where it equals 20°: f = f0 × 20 / 90 ≈ 0.22 f0.
4. The upper limit is where it equals 160°: f = f0 × 160 / 90 ≈ 1.78 f0.
5. The ratio is 1.78 / 0.22 = 8, as expected.

If f0 is 2 GHz, the usable range for this one line is about 0.44 GHz to 3.56 GHz. A calibration up to, say, 10 GHz would need additional, shorter lines. The longer line takes the lowest band and a shorter one takes the next.

At the low end, a physically long line is needed for a given phase, which is one reason broadband TRL kits contain several lines.

Where TRL fits: fixtures, waveguide and on-board microstrip

Fixtures. When a device sits in a fixture, the connector-to-device transition is part of the error. TRL standards can be built in the same fixture, with the same launch, so the reference plane moves to the device itself.

Waveguide. There are no practical lumped loads in waveguide. A thru, a flush short as the reflect and a quarter-wave-longer section as the line are easy to make precisely, because only the length matters.

On-board microstrip. On a board, you can print the standards beside the device: a thru, a short or open as the reflect, and a longer line. All share the same substrate and the same processing, so the line's impedance is as good as the board's control of width and dielectric. This is also where you must check that the reflect really is the same at both ports.

In plain words · for students and beginners

TRL in plain words

An everyday picture

Imagine you want to measure how long a road is, but your odometer reads wrong and you do not know by how much. You drive a short known stretch, then a longer known stretch. Comparing the two readings tells you how the odometer is wrong, even though you never trusted it.

TRL works the same way. The thru and the line are two "known" trips. The VNA compares what it reads on each to learn its own errors. The reflect is a helper that must look the same on both sides.

The picture breaks down in one place: the line has to be built carefully. It is the one thing you cannot guess.

The same example in simple steps

The VNA measures a two-port device and reports four numbers, as in the drawing above. TRL makes those numbers trustworthy. Here is the line-length example again.

1. Pick the middle frequency, f0. Make the line a quarter wavelength longer than the thru. That adds 90° of phase.
2. The line works only when the extra phase is between 20° and 160°.
3. At 20° the frequency is about 0.22 times f0. At 160° it is about 1.78 times f0.
4. With f0 = 2 GHz, that is about 0.44 GHz to 3.56 GHz.
5. For frequencies outside that range, add another line of a different length.

Mistakes beginners make

• Using a line that is too short or too long. If the extra phase is near 0° or near 180°, the line looks like the thru, and the calibration fails.
• Different reflects at the two ports. The reflect value does not matter, but it must be the same on both sides.
• Careless line impedance. The line's impedance becomes the reference. If it is off, every later result is off.
• Using one line for a very wide band. One line covers only about an 8:1 frequency range.

Remember

• TRL needs only the line impedance and the line length to be known.
• The reflect can be any high-reflection device, as long as it is the same at both ports.
• The line must add 20° to 160° of phase, so wide bands need several lines.

Related pages on RF View

• Microstrip Impedance and Width Calculator (FR-4, Rogers)