Agilent Technologies 8510-58 manual Linear delay Actual delay = Fco/f2, Offset Z0

The convention for definition of offset delay in waveguide requires entry of the delay assuming no dispersion. For waveguide transmission line, the Agilent 8510 calculates the effects of dispersion as a function of frequency as follows:

Linear delay

Actual delay =

1 - (fco/f)2

For the WR-62 calibration kit, offset delay is zero for the “thru” (std #4) and the “load” (std #3). To find the offset delay of the 1/8 λ and 3/8 λ offset shorts, precise offset length measurements are nec- essary. For the 1/8 λ offset short, l = 3.24605 mm, εr = 1.000649, c = 2.997925 x 108m/s.

Delay = (3.24605 x 10 -3m) (√1.000649) = 10.8309 pS 2.997925 x 108 m/s

fco = lower cutoff frequency f = measurement frequency

Note

To assure accurate definition of offset delay, a physical measurement of offset length is recom- mended.

The actual length of offset shorts will vary by man- ufacturer. For example, the physical length of a

1/8 λ offset depends on the center frequency chosen. In waveguide this may correspond to the arith- metic or geometric mean frequency. The arithmetic mean frequency is simply (F1 + F2)/2, where F1 and F2 are minimum and maximum operating frequen- cies of the waveguide type. The geometric mean frequency is calculated as the square root of F1 x F2. The corresponding (λg) is then calculated from the mean frequency and the cutoff frequency of the waveguide type. Fractional wavelength offsets are then specified with respect to this wavelength.

For the 3/8 λ offset short, I = 9.7377 mm, εr = 1.000649, c = 2.997925 x 108 m/s.

Delay = (9.7377 x 10-3m) (√1.000649) = 32.4925 pS 2.997925 x 108 m/s

Offset Z0

Offset Z0 is the characteristic impedance within the offset length. For coaxial type offset standards, specify the real (resistive) part of the characteris- tic impedance in the transmission media. The char- acteristic impedance in lossless coaxial transmission media can be calculated from its physical geometry as follows.

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