Agilent Technologies 8719D User Manual page 372

The line standard must meet specific frequency related criteria, in conjunction with the length
used by the thru standard. In particular, the insertion phase of the line must not be the same
as the thru. The optimal line length is 114 wavelength (90 degrees) relative to a zero length
thru at the center frequency of interest, and between 20 and 160 degrees of phase difference
over the frequency range of interest. (Note: these phase values can be fN x 180 degrees
where N is an integer.) If two lines are used (LRL), the difference in electrical length of
the two lines should meet these optimal conditions. Measurement uncertainty will increase
this condition is not recommended.
For a transmission media that exhibits linear phase over the frequency range of interest, the
following expression can be used to determine a suitable line length of one-quarter wavelength
at the center frequency
divided by 2):
let:
VF = Velocity Factor = 1 (for this example)
Thus, the length to initially check is 5 cm.
Next, use the following to verify the insertion phase at fl and f2:
where:
f = frequency
1 = length of line
v = velocity = speed of light x velocity factor
which can be reduced to the following using frequencies in MHz and length in centimeters:
So for an air line (velocity factor approximately 1) at 1000 MHz, the insertion phase is
60 degrees for a 5 cm line; it is 120 degrees at 2000 MHz. This line would be a suitable line
standard.
For microstrip and other fabricated standards, the velocity factor is signiflcant. In those cases,
the phase calculation must be divided by that factor. For example, if the dielectric constant for
a substrate is 10, and the corresponding "effective" dielectric constant for microstrip is 6.5,
then the "effective" velocity factor equals 0.39 (1 i square root of 6.5).
Using the first equation with a velocity factor of 0.39, the initial length to test would be
1.95 cm. This length provides an insertion phase at 1000 MHz of 60 degrees; at 2000 MHz,
120 degrees (the insertion phase should be the same as the air line because the velocity factor
was accounted for when using the first equation).
Application and Operation Concepte
equals the sum of the start frequency and stop frequency
(which
Electrical length (cm) = (LINE - 0 length THRU)
Electrical length (cm) =
Phase (degrees) =
Phase (degrees) approx =
(15000 x V'F)
fx 1)
0.012 x f(MHz) x
V F