Theory of Operation
Coaxial RF Power Standards Instruction and Service Manual
4-6
Sources of Calibration Error
Due to the high repeatability of the RF Power Standards and the accuracy of the Type IV Bridge,
the major sources of error stem from impedance mismatch and the uncertainty of the calibration
factor of the standard (K1 if calibrating a Feedthrough Power Standard or K2 if calibrating a DUT).
When an RF Power Standard is calibrated, an uncertainty is reported for each calibration point.
Even Standards calibrated by NIST have a reported uncertainty associated with each calibration
factor. This uncertainty figure (for K
1
or K
2
) is one of the largest contributors to the uncertainty
budget for the calibration at the next stage (K
2
or K
1S
).
Impedance mismatch is the term used to describe the differences in impedance between RF
devices. This difference in impedance causes some of the RF power to be reflected back from one
device to another; thus, not all applied RF power is transferred from one device to another. The
amount of power that is not transferred can be characterized as the reflection coefficient, or
Γ
.
The reflection coefficient for TEGAM RF Power Standards is included as part of the factory
calibration data. Mismatch error (M
ER
) is determined from the reflection coefficients of both the
Feedthrough Standard and the DUT as follows:
M
ER
= 1- 1
(1
±
|
Γ
1
| x |
Γ
2
|)
2
Where:
M
ER
= residual mismatch error,
Γ
1
= reflection coefficient for the Feedthrough Standard,
Γ
2
= reflection coefficient for the DUT.
When calibrating the Feedthrough Power Standard, the power splitter is removed and its
reflection coefficient is measured with a network analyzer. The power splitter is replaced in the
Feedthrough Power Standard assembly and the reflection coefficient of the “sensor” port of the
power splitter is the reflection coefficient for the entire assembly. Since the Feedthrough Power
Standard is actually calibrated as an assembly, any impedance mismatch between the actual
thermistor mount and the splitter are automatically factored in the calibration factor. Using the
equation above,
Γ
1
becomes the reflection coefficient for the Terminating Standard and
Γ
2
becomes the reflection coefficient for the Feedthrough Standard.
Reflection Coefficient is a complex number expressed as a vector quantity. A vector quantity has
two components a magnitude and phase angle. The magnitude of the reflection coefficient is
symbolized by the Greek letter rho (
ρ)
and the phase angle by the Greek letter phi (
φ).
Often, the
magnitude is the only part of the reflection coefficient used, which will yield a “worse case”
mismatch uncertainty. Sometimes the Standing Wave Ratio (SWR) of a device is given rather
than the reflection coefficient (
Γ)
. SWR is a scalar quantity and related to
ρ
follows:
ρ
= S - 1
S + 1
Where:
ρ
= magnitude of the reflection coefficient,
S = Standing Wave Ratio (SWR).
Gamma Correction
If both the
ρ
and
φ
of the reflection coefficient are known for both the K1 and K2 or K2 and K1S
(TEGAM provides this data for the RF Standards as part of the factory calibration), then Gamma
corrections can be applied to the calibration factor. Applying Gamma corrections to the calibration
factor reduces the total uncertainty of the calibration by eliminating M
ER
.
