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What are TRL, LRL, TRM, and LRM calibrations?

These are variations of the so-called "self-calibration" method, and are alternatives to the traditional two-port error correction that uses short, open, load, and through standards (SOLT cal).  They offer equivalent accuracy (sometimes better), and have the advantage that fewer and simpler standards are needed.  They are particularly useful for measurements of non-coaxial devices, such as fixtures and microstrip circuits.  The different names represent the three standards that are used in each type of calibration:

  • TRL = Through, Reflect, Line
  • LRL = Line, Reflect, Line
  • TRM = Through, Reflect, Match
  • LRM = Line, Reflect, Match

Compared to the SOLT cal, the requirements on these standards are much easier to meet, so they are more easily constructed.  During the calibration process, there are more measurements made of the standards than there are unknown error terms.  The calibration math ends up with ten equations and eight unknowns, so there is redundant information, which can be used to calculate the propagation constant of the Line standard, and the reflection coefficient of the Reflect standard.  Here are the requirements for each standard:

The Through standard should have zero length (so its loss and Z0 are unimportant).

The shorter Line standard, which is often referred to as a non-zero length Through standard, should have the same Z0 as the longer Line standard.  Its propagation constant (delay and loss) need be accurately specified only if it is used to set the reference planes (see Tip 1).  If you want the reference planes to be set to the middle of the non-zero length Through, then you should specify its delay to be zero (see Tip 19).

The Reflect standard should have a high reflection coefficient, but its magnitude need not be known.  The phase of its reflection coefficient must be approximately specified, to within +/- 1/4 wavelength or +/- 90 degrees.  It is important that the exact same Reflect standard be used to calibrate both measurement ports.  Ideally, only one Reflect standard is constructed, and it is connected first to port 1, and then to port 2.

The Line standard must have a known Z0, since this will determine the characteristic impedance of the calibrated measurements.  However, the Line's Z0 need not be exactly equal to the desired characteristic impedance (see Tip 11).  The optimal length of the Line is 1/4 wavelength longer than the Through or shorter Line at the band center.  The difference between the phase shifts of the Line and Through standards should be between 20 and 160 degrees at all frequencies to minimize measurement uncertainty.  A cal kit may need to include two or more Line standards of different lengths to cover a wide frequency range.

The Match standard is simply a load; its impedance sets the characteristic impedance of the calibrated measurements.  The same load should be used on both ports.  It is used in place of the Line standard at low frequencies, where 1/4 wavelength would be much too long.  A broadband cal kit may include one Match standard and several Line standards to cover the complete frequency range.

For more information about TRL calibration, see:

  • G. Engen and C. Hoer, "Thru-Reflect-Line: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer", IEEE Transactions on Microwave Theory and Techniques, December 1979.
  • J. Curran, "Applying TRL Calibration for Noncoaxial Measurements," Microwave System News, March 1988.
  • M. Maury Jr., S. March, and G. Simpson, "LRL Calibration of Vector Automatic Network Analyzers," Microwave Journal, May 1987.
  • Application Note 1287-9, "In-Fixture Measurements Using Vector Network Analyzers", Agilent Technologies.
  • Product Note 8510-8, "Applying the HP 8510B TRL Calibration for Non-Coaxial Measurements", Agilent Technologies.

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