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2.5.5 Temperature
Effects of Calibration
There are temperature dependent losses in microwave feedthroughs, semirigid
cables, and probe bodies and tips. As the sample stage cools to 4.2 K, for example,
there is approximately a 294 K temperature gradient set up over the length of the
semirigid coaxial cable. In addition, the structures of a calibration or test substrate
have a temperature dependent response. Measurements have shown that there is
approximately 1 to 2 dB less insertion loss at 67 GHz as measured in S21/S12 at 4.3 K
compared to the same measurement at 300 K.
To illustrate this phenomenon, FIGURE 2-35 shows the calibrated S-parameter
response of a pair of 67 GHz GSG microwave probes measured on a 50
)
through
structure at 4.3 K temperature using a SOLT calibration that was performed at 300 K
temperature. Note the error in the calibration as compared to FIGURE 2-34. The error
is due in part to the temperature changes in the arms and probes, as well as the
coplanar waveguide physically changing geometry, which causes errors in the VNA
calibration correction coefficients. The calibration error is on the order of 1 to 2 dB for
this particular calibration that spans 40 MHz to 67 GHz and represents a 294 K
temperature change from the calibration temperature to the measurement
temperature. This example represents a wide band measurement over a large change
in temperature. It is described here as an extreme case; the error will be less for
narrower band measurements or for measurements over smaller temperature
variations. For the most accurate measurements, it is recommended to perform a
calibration at the actual measurement temperature.
FIGURE 2-35
Calibrated S-parameter response of 67 GHz GSG
microwave probes measured on a 50
)
through structure at 4.3 K
after calibration with a CS-5 substrate at 300 K
