Impedance Measurement Uncertainty when Measuring Low Impedance Devices at Low Frequency
For this low frequency and impedance application, the impedance analyzer would provide more accurate measurement results using its I-V technique, compared to the reflection method used by the vector network analyzer (VNA). As a rule-of-thumb, the VNA generally can provide reasonably accurate results over an impedance range that is a factor of 10x (or x/10) of the system's characteristic impedance, Z0. For example, for Z0= 50 ohms, the impedance range would be 5 ohms to 500 ohms. However, for best measurement accuracy, the DUT's impedance should not vary by more than 3 to 5 ohms from Z0.
DUT Characteristics
ZL= 3 ohms ( Note: a 2-port device is assumed)
Reflection coefficient , r = [ZL - Z0]/[ ZL + Z0] = -47/53 = -0.887 (~ -0.9)
Note: The negative sign indicates that the phase characteristic is much like that of a short.
S11/Return Loss (RL) = 1.04 dB
SWR = 16.7 :1
Insertion Loss: unknown/not specified
From its reflection (magnitude) uncertainty curve (page 9, 1-port calibration), a DUT with an S11 (r ) of 0.9 (linear) results in a reflection measurement uncertainty of +/- 0.025 (linear). Even though this graph assumes S21 = S12 = 0, this assumption can be applied here, since the DUT reflects 90% of the incident signal, with the other 10% being transmitted and re-reflected by the receiver's (uncorrected) 18 dB load match. This re-reflected signal is very small compared to the true DUT reflected signal, and therefore may be neglected. However, for best reflection measurement accuracy, it is recommended that:
1) The output of the DUT be terminated with a precision 50-ohm load rather than being connected to the 8712ET's transmission port or,
2) If the DUT output is to be connected to the 8712ET's transmission port, install a precision pad/attenuator to the transmission port to improve its "effective" load match.
Given the above, the impedance and return loss measurement uncertainties are estimated as follows:
1) D S11 (dB) = R.L. meas. uncert (dB)= -20 log (1 + 0.025)= - 0.214dB and,
-20 log (1 - 0.025)= + 0.22 dB
R.L. measure measurment uncertainty = 1.04 dB, +0.22 dB, -0.214 dB
2) ZL = Z0 (1 + r )/(1- r ) , where ZL = measured impedance, Z0 = 50 ohms, r = reflection coefficient
ZL High = 50 [1 + (-0.887 + 0.025)]/[1 - (-0.887 + 0.025)] = 50 (0.138/1.86) = 3.71 ohms
ZL Low = 50 [1 + (-0.887 - 0.025)]/[1- (-0.887 - 0.025)] = 50 (0.088/1.912) = 2.30 ohms
Therefore, the impedance measurement uncertainty is ZL = 3 ohms, +0.71 ohms, -0.70 ohms.