Instrumentation & Measurement Magazine 25-6 - 39

Table 1 - Uncertainty contributions considered in the measurement of various amplifier parameters
using a VNA. The numbers indicate the relative size of each contribution for each parameter
with (1) denoting the largest contribution
Uncertainty
contributions
Power Meter
Calibration Standards
Connector Repeatability
Electrical Noise
Amplifier parameters
S-parameters
✗
✓ (1)
✓ (2)
✓ (3)
Input
Power
✓ (1)
✓ (2)
✓ (3)
✓ (4)
calibration standards, mechanical tolerances or on polynomial-based
models. Some manufacturers provide an
uncertainty characterization of some of their calibration
kits.
◗ Uncertainty due to electrical noise in the VNA. This
source of uncertainty is characterized by repeat measurements
(typically 20 repeats) of both a well-matched
standard and a high reflect standard made on each port
of the VNA. The standards are not disconnected from the
VNA between measurements.
◗ Uncertainty due to cable flexing and connector repeatability.
This source of uncertainty is characterized by
repeat measurements (typically 20 repeats) of both a
well-matched standard and a high reflect standard made
on each port of the VNA. The flexible RF cable (if present)
is moved, and the standards are disconnected from
the VNA and reconnected with a different orientation
between measurements.
◗ Uncertainty in the power meter used in the power calibration
of the VNA.
Once these sources of uncertainty have been characterized,
VNA-DUO propagates the uncertainties to S-parameters and
power measured by the VNA. The sources of uncertainty in
various amplifier parameters measured on a VNA and their
relative importance are listed in Table 1.
Evaluation of Uncertainties
The power gain (GP
) of an amplifier excited at port 1 is defined
as the ratio of the output power, i.e., power delivered to the
load (PL
GP   22
IN
P BA

P AB

where A1 and B1
and B2
11
are, respectively, the complex-valued incident
and scattered wave amplitudes at port 1 of the amplifier
and A2
an amplifier terminated with a matched load, |A2
(1) becomes:
2
G 
September 2022
B2
P 22
11
AB

(2)
are the corresponding quantities at port 2. For
|= 0, and so
22
L 22
), to the input power, i.e., power accepted at the input
to the amplifier (PIN). It can be calculated from the measured incident
and scattered waves using (1):
(1)
Output
Power
✓ (1)
✓ (2)
✓ (3)
✓ (4)
Power
Gain
✓ (1)
✓ (2)
✓ (3)
✓ (4)
Gain
Compression
✓ (1)
✓ (2)
✓ (3)
✓ (4)
Henceforth, in this paper, only the power gain into a matched
load will be considered.
The uncertainty in the input power (u(PIN
|), (u(|B1
|), and u(|B2
)) and in the
power gain (u(GP)) are calculated from the uncertainties in
the linear magnitudes of the incident and scattered waves
(u(|A1
of uncertainty (LPU) as:

uPIN
uG
P2 1 u B
IN1
   4GP u B
P1
PP P

2 22G AP 1
GB
22



IN
u A

IN
The 1 dB compression point of an amplifier (P1dB
) and is expressed as:
ss IN 1dB
P 
1dB
1.2589
GP
.
 (4)
) is defined
to be the linear output power from the amplifier when its gain
is reduced by 1 dB (i.e., by a factor of 1.2589) from its linear
small-signal gain (Gss
(5)
where PIN1dB is the linear input power corresponding to the output
power P1dB
The relative uncertainty in linear P1dB (u(P1dB
(u(Gss
)/GP0
(u(PIN1dB)/PIN1dB
) as follows:

1dB
  
   
GP
uP P  
uG u PIN 1dB
22
ss
1dB
  
  
ss
IN 1dB
(6)
To calculate the uncertainty in a logrithmic quantity (i.e.,
a quantity expressed in dB) given the uncertainty in the corresponding
linear quantity, the nominal linear value and the
maximum linear value (i.e., nominal value + uncertainty) were
converted to dB and the difference in those dB values was used
as the uncertainty expressed in dB.
Experimental Details
Measurements were made using VNA-DUO installed on a
Keysight N5247B PNA-X VNA and a high-power test-set
IEEE Instrumentation & Measurement Magazine
39
)/P1dB
)
is calculated by adding in quadrature the relative uncertainty
in Gss
) and the relative uncertainty in PIN1dB
 A u A B1 u B1
22
1
22
1

4 (3)

|)) using the law of propagation
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