What are the calibration kit coefficients?

The open, short and load standards in the calibration kit must all have a mathematical model of them. For the load this is very simple - a 50 Ω resistor is assumed. The load must be a high quality, having a high return loss throughout the frequency range of the kit.

The opens and shorts are quite different. Each will be considered to have a transmission line will have some length L, typically of the order of a few mm, which causes a delay dT typically of the order of a few 10s of ps. A short will be terminated in an inductor, although the inductance of that is usually negligible. The open will be terminated in a capacitance due to the fringe capacitance, of the order of 100 fF. This fringe capacitance can not be ignored, and neither can it be considered independent of frequency. The capacitance is normally represented by a 3rd order polynomial as a function of frequency. HP, Agilent, Anritsu, Keysight and Copper Mountain all use the following definition

C_fringing=C0x10^-15 + C1x10^-27f + C2x10^-36f²+C3x10^-45f³

Rohde and Schwarz, Anritsu don't specify a delay of the standard, but a length. Care needs to be taken to be sure the units are correct. One of Kirkby Microwave's customers assumed the VNA wanted an offset length in mm, whereas actually the VNA was expecting the value in metres. Needless to say, having a coefficient 1000x wrong caused problems. The following are a set of typical coefficients for one of our SMA calibration kits. Since the end of 2017, kits have individually measured parameters, but for earlier SMA kits, the following will apply.

SMA Female short - use these for kits dispatched prior to the end of 2017

Offset delay: 41.398 ps
Z0: 50 Ω
Offset loss: 3.0 GΩ/s
L0: 0 (if your VNA supports entry of inductance coefficients. Many do not.)
L1: 0 (if your VNA supports entry of inductance coefficients. Many do not.)
L2: 0 (if your VNA supports entry of inductance coefficients. Many do not.)
L3: 0 (if your VNA supports entry of inductance coefficients. Many do not.)
Minimum frequency: 0 MHz
Maximum frequency: 7 GHz

Note, the female short is usually indicated as SHORT -F- in all recent VNAs. However, in the old HP series, including models like the 8714, 8753, 8510, 8719, 8720, 8722 and others, it is rather confusingly SHORT (M)), with the (M) indicating that it connects to a male test port! Agilent have dropped this convention in newer instruments, but some of the ENA series uses this too.

SMA Female open - used these parameters for kits dispatched before the end of 2017

Offset delay: 39.8 ps
C0: 53.004
C1: 135.167
C2: 95.6305
C3: 30.937
Z0: 50 Ω
Offset loss: 3.0 GΩ/s
Minimum frequency: 0 MHz
Maximum frequency: 7 GHz

Note, the female open is usually indicated as OPEN -F- in all recent VNAs. However, in the old HP series, including models like the 8714, 8753, 8510, 8719, 8720, 8722 and others, it is rather confusingly OPEN (M)), with the (M) indicating that it connects to a male test port! Agilent have dropped this convention in newer instruments, but some of the ENA series uses this too.

SMA Male short - use these for kits for purchased dispatched prior to the end of 2017

Offset delay: 57.834 ps
Z0: 50 Ω
Offset loss: 3.0 GΩ/s
L0: 0 (if your VNA supports entry of inductance coefficients. Many do not.)
L1: 0 (if your VNA supports entry of inductance coefficients. Many do not.)
L2: 0 (if your VNA supports entry of inductance coefficients. Many do not.)
L3: 0 (if your VNA supports entry of inductance coefficients. Many do not.)
Minimum frequency: 0 MHz
Maximum frequency: 7 GHz

Note, the male short is usually indicated as SHORT -M- in all recent VNAs. However, in the old HP series, including models like the 8714, 8753, 8510, 8719, 8720, 8722 and others, it is rather confusingly SHORT (G)), with the (F) indicating that it connects to a female test port! Agilent have dropped this convention in newer instruments, but some of the ENA series uses this too.

SMA Male open - used these parameters for kits dispatched before the end of 2017

Offset delay: 55.1 ps
C0: 50.389
C1: 761.36
C2: -968.22
C3: 68.376
Z0: 50 Ω
Offset loss: 3.0 GΩ/s
Minimum frequency: 0 MHz
Maximum frequency: 7 GHz

Note, the male open is usually indicated as OPEN -M- in all recent VNAs. However, in the old HP series, including models like the 8714, 8753, 8510, 8719, 8720, 8722 and others, it is rather confusingly OPEN (F)), with the (F) indicating that it connects to a female test port! Agilent have dropped this convention in newer instruments, but some of the ENA series uses this too.

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