Instrumentation & Measurement Magazine 25-6 - 37

Uncertainties in Small-Signal and
Large-Signal Measurements of RF
Amplifiers Using a VNA
Dilbagh Singh, Martin J. Salter, Susan Johny, and Nick M. Ridler
U
ncertainties in typical small-signal and large-signal
amplifier parameters measured using a vector
network analyzer (VNA) are investigated in this
paper. Methods to evaluate the measurement uncertainty in
return losses, input power, output power, power gain, 1 dB
compression point, etc., based on the use of the VNA dynamic
uncertainty option (VNA-DUO) software tool from Keysight
Technologies, are applied to a commercial amplifier between
0.5 GHz and 8 GHz.
Characterizing Amplifier Performance
Amplifiers are used to magnify signals to prevent them
from being obscured by noise. Amplifiers find applications
throughout electronics, and in this paper we focus on radio
frequency (RF) amplifiers i.e., those operating in the frequency
range 100 MHz to 100 GHz [1]. An amplifier responds linearly
to a small input signal but can show non-linear behavior, such
as gain compression and harmonic generation, when the amplitude
of the input signal becomes sufficiently large [2]. The
characterization of an amplifier under different operating conditions
is essential for designers and users of the amplifier. The
small-signal response of RF amplifiers is characterized by their
reflection and transmission coefficients, i.e., by their scattering
parameters (S-parameters) [3]. Other parameters such as saturated
output power, large-signal gain, 1 dB gain compression
point, efficiency, measures of harmonic distortion, and measures
of two-tone intermodulation distortion, etc. are required
to characterize the large-signal, non-linear, response of the
amplifier [2], [3]. The S-parameters of an amplifier vary with
frequency but, due to linearity, are independent of the power
of the input signal. However, the large-signal response of an
amplifier, due to non-linearity, depends on both the frequency
and the power level of the input signal.
One of the main instruments used to characterize the electrical
performance of an amplifier is a vector network analyzer
(VNA) which can measure S-parameters, power, and noise figure
(NF), among other parameters [3]. Imperfections in the
VNA measurement setup can be largely corrected by calibration
[4].
September 2022
To have confidence in the result of a measurement, and
when comparing it with the results of other measurements, it
is important to know the uncertainty in the measurement. Documents
providing guidance on the evaluation of measurement
uncertainty, in general, include [5]-[7] while information specific
to the evaluation of the uncertainty in RF measurements is
given in [8], [9]. In this paper, we have used the VNA dynamic
uncertainty option (VNA-DUO) software tool from Keysight
Technologies [10] to evaluate the measurement uncertainty in
some fundamental parameters of an amplifier. Both small-signal
and large-signal parameters of an amplifier are considered.
To evaluate the measurement uncertainty in S-parameters
at RF frequencies, software tools such as VNA Tools [11], MUF
[12], PIMMS [13], and FAME [14] are used at National Metrology
Institutes (NMIs) around the world. VNA-DUO can
evaluate the measurement uncertainty in S-parameters and
power in real-time once the sources of uncertainty in the VNA
and power meter have been fully characterized. The measurement
uncertainties are evaluated within the VNA and are
displayed as error bars or elliptical uncertainty regions on the
VNA screen. VNA-DUO has recently been commissioned for
use at the UK's National Physical Laboratory (NPL) [15].
An amplifier's small-signal parameters (which characterize
its linear behavior in response to a small-signal stimulus) such
as input return loss, output return loss, small-signal gain, and
reverse isolation are determined from its S-parameters. The uncertainties
in these small-signal parameters can be determined
from the uncertainties in the S-parameters. The S-parameter
uncertainty due to connector repeatability, cable flexing, noise
floor, trace noise, etc. is evaluated in VNA-DUO by the analysis
of series of observations (type A evaluation) and the uncertainty
due to the calibration standards etc. is evaluated by other
means (type B evaluation). The S-parameters are based on ratios
between the incident and scattered waves at the ports of the
amplifier, are independent of the incident power level and do
not require an absolute power calibration of the VNA.
On the other hand, an amplifier's large-signal parameters
(which characterize its non-linear behavior in response to a
large-signal stimulus) such as output power, power gain (GP
),
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