The input impedance is about 3 ohms, what is the uncertainty in the impedance and return loss measurements

Q: When measuring a device under test (DUT) with a vector network analyzer, what is the uncertainty in the impedance and return loss (S11) measurements if the input impedance is approximately 3 ohms (at 2 MHz)? In this case, is an impedance analyzer better than a vector network analyzer?

A: For low frequency and impedance applications, impedance analyzers using IV technology can obtain more accurate measurement results than vector network analyzers (VNA) using reflection method. The common criterion is that within the impedance range of 10 times (or 1/10) the system characteristic impedance Z0, the vector network analyzer can usually provide results with sufficient accuracy. For example, for Z0 = 50Ω, the impedance range is 5Ω to 500Ω. However, for the best measurement accuracy, the change of DUT impedance relative to Z0 should not exceed 3-5Ω.

Device Under Test (DUT) Characteristics

ZL = 3 Ω (Note: Assuming a two-port device)

Reflection coefficient, r = [ZL - Z0]/[ ZL + Z0] = -47/53 = -0.887 (~ -0.9)

Note: The negative sign indicates that the phase characteristic is very much like a short circuit.

S11/Return Loss (RL) = 1.04 dB

SWR = 16.7 :1

Insertion loss: unknown/unspecified

From its reflection (amplitude) uncertainty curve (one-port calibration), a DUT with S11 (r) of 0.9 (linear) produces a reflection measurement uncertainty of ±0.025 (linear). Although the graph assumes S21 = S12 = 0, since the DUT reflects 90% of the incident signal, the other 10% is transmitted and re-reflected by the receiver (uncorrected) 18 dB load match. Compared to the true DUT reflection signal, the re-reflected signal is small and can be ignored. However, the recommended method for best measurement accuracy is:

1) Terminate the DUT output with a precision 50Ω load instead of connecting it to the transmit port of the vector network analyzer.

2) If the DUT output is connected to the transmission port of a vector network analyzer, install a precision pad/attenuator at the transmission port to improve its "effective" load match.

The impedance and return loss measurement uncertainties can then be estimated as follows:

1) D S11 (dB) = RL Measurement uncertainty (dB) = -20 log (1 + 0.025) = - 0.214dB,

-20 log (1 - 0.025) = + 0.22 dB

RL measurement uncertainty = 1.04 dB, +0.22 dB, -0.214 dB

2) ZL = Z0 (1 + r )/(1- r ) , where ZL = measurement impedance, Z0 = 50 Ω, r = reflection coefficient

ZL High = 50 [1 + (-0.887 + 0.025)]/[1 - (-0.887 + 0.025)] = 50 (0.138/1.86) = 3.71 Ω

ZL Low = 50 [1 + (-0.887 - 0.025)]/[1- (-0.887 - 0.025)] = 50 (0.088/1.912) = 2.30 Ω

The impedance measurement uncertainty is therefore ZL = 3 Ω, +0.71 Ω, -0.70 Ω.