G/T measurements with a PNA
1 G/T background
A definition of G/T for an active antenna is the gain of an active antenna divided by the
effective noise at the antenna input or:
G /T 
G Ant
TkTB  TE
(1)
Where G Ant is the antenna gain, TkTB is the noise from the antenna impedance (normally T0 or
290K) and TE is the effective noise of the active amplifier after the antenna.
Based on the definition of noise figure [1]
Te  290  ( NF  1)  290  NF  290
(2)
And combining equations (1) and (2) gives
G /T 
G Ant
290  NF
(3)
Or converting to dB
 GAnt 
G / TdB  10  log10 
  10  log10  GAnt   10  log10  NF   10  log10  290 
 290  NF 
G / TdB  GAnt _ dB  NFdB  24.62
Here, and throughout this document, gain will refer to power-gain.
2 Theoretical Example
As an example, consider a standard-gain antenna connected to an amplifier with a 9 dB noise
figure and 20 dB of gain, as illustrated in figure 1
(4)
Gain
Horn
Amplifier
Excess Noise =
DUTRNPI=29 dB
G=20
G=24.7 dB
NF=9 dB
Figure 1: Reference DUT built from a standard gain horn and amplifier
The G/T for this device can be computed as:
NFAmp  10(9/10)  7.943
G Ant  10(24.7/10)  295.12
10  log10 (290)  24.62 dB
G /T 
295.12
 0.128
290   7.942 
(5)
G / TdB  10  log10  G / T   10  log10  0.128  8.92 dB
G / TdB  G Ant _ dB  NFdB  24.62  (24.7  9  24.62)  8.92
Thus, if one knows the gain of the antenna and the noise figure of the constituent amplifier,
then the overall G/T can be simply computed by the dB values. Further, in this calculation, the
gain of the amplifier does not affect the G/T value. However, this is a theoretical example, and
in general the antenna cannot be separated from the amplifier in a real-world Device-UnderTest (DUT), so an alternative method is needed, in which the DUT is measured in an antenna
range, and the range is compensated to account for the range loss, and loss from the
measurement equipment to the range, which can be found in both the cable to the sourcing
and antenna, and the cable from the DUT to the noise receiver.
3 Antenna Range Example and finding G/T
Consider the same sample DUT measured in an antenna range, as shown in Figure 2. Here, the
DUT is stimulated with a signal from the VNA and the overall gain and noise figure of the
system is measured. For the moment, don’t consider the loss of the cables but presume the
system is calibrated at the cable ends.
VNA with built in
NF capabiltiy
TX Horn
AirLoss=-75 dB
NF=9 dB
G=20
G=24.7 dB
GTx=24.7 dB
Excess Noise =
DUTRNPI=29 dB
G/T=-8.92 dB
Figure 2: Antenna Range measurement for G/T
In this example, over-the-air loss of 75 dB is assumed, and the range loss is reduced by the gain
of the TX horn, GTx, causes the overall S21 of the system, and the noise figure of the system, to
degrade by the same amount. In this case the range loss is computed as
RL  GTx  AirLoss
RL  10( GTxdB /10)  10( AirLossdB /10)  10(24.7/10)  10( 75/10)
RL   295.12    31.62  109   9.3325  10 6
(6)
RLdB  10  log10 ( RL)  10  log10 (9.3325  10 6 )  50.3dB
RLdB  GTxdB  AirLossdB  24.7  ( 75)  50.3dB
(Note here that while the term for the AirLoss might imply a positive number, all gains and
losses are expressed linearly as gains and thus a loss of 75 dB is expressed as -75 dB to ensure
consistency in math operations. This is consistent with well-defined use, see [2] )
But in general this range loss is not known, so must be characterized in a separate
measurement using a reference antenna such as a standard gain horn. Figure 3 shows the
measurement of the range loss using the standard gain horn as a receiver. Here the range loss
can be determined from the gain (S21) measurement of the overall range, and knowledge of
the gain of the receiver standard-gain antenna:
 S 21RL   RL  G _ std
2
RL   S 21RL  / G _ std
2
10
RL 

( 25.6/20) 2
2.754  103
 9.331  106
(24.7/10)
10
295.12
RLdB  10  log10  9.331  106   50.3dB

(7)
RLdB  S 21RL _ dB  G _ std dB  25.6  24.7  50.3dB
Here note that up to this point, all gains are expressed as power gains. To be consistent, the
measured power gain in Figure 3 is found from (S21)2.
VNA with built in
NF capabiltiy
TX Horn
Gain
Horn
AirLoss=-75
dB
GTx=24.7 dB
G_std=24.7 dB
Measured S21 = -25.6 dB
Figure 3: Measurement of the Range Loss
Now consider the effect of the range measurement on both the S21 of the overall system and
the NF of the overall system. From first principles, the apparent noise figure of the DUT will
improve by the antenna gain in the DUT (Gant), and degrade by the range loss. Thus the
measured noise figure in this case will be
NFSys 
NFAmp
G Ant  RL

NFAmp  G _ std
G Ant  ( S 21) 2
NFSys _ dB  NFAmp _ dB  RLdB  G Ant _ dB
NFSys _ dB  9dB  ( 50.3dB )  24.7dB  34.6dB
NFSys _ dB  NFAmp _ dB  S 21dB  G Ant _ dB  G _ std dB
NFSys _ dB  9  ( 25.6)  24.7dB  24.7dB  34.6dB
(8)
The first line of equation(8) might seem a little strange, as it is well known that loss (such as
range loss) increases (or multiplies) the noise figure, where here the noise figure is divided by
the range loss (that is subtracted in dB). Again, consistency in applying the linear math requires
loss to be expressed in negative dB, thus to have loss before an amplifier –increase- the noise
figure, the loss (a negative number in dB) must be subtracted from the noise figure. Likewise,
the gain (a positive number dB) is also subtracted from the dB value of noise figure, or placed in
the denominator for linear computations. Note that the system noise figure is the inferred
noise figure of the embedded amplifier in the DUT, plus the overall loss of the combination of
the antenna range and the embedded gain of the DUT antenna.
Finally, combining equations (8) and (3) we can find the G/T as
 GAnt  ( S 21RL )2
 1 
G _ std

G /T  


 NF  290  ( S 21 ) 2  NF  G _ std
Sys
RL


 Amp
G / TdB  G _ std dB  NFSys _ dB  S 21RL _ dB  24.62

G _ std
GAnt


 290  ( S 21RL ) 2 290. NFAmp

(9)
G / TdB  24.7  34.6  ( 25.6)  24.62  8.92
In practice, only the noise figure measurement changes with DUT; the range loss S21 measured
value, the gain of the standard gain antenna for the range loss, and the -24.62 dB term
associated with the log of 290 derived from is 10  log10 (T0 ) are all pre-measured constant
values. If these are saved as traces on a PNA, then the equation editor applied to a noise figure
parameter can be used to compute G/T directly as
G / T  (mag ( S 21G _ std )  mag ( S 21G _ std )) / (290  ( NFSys )mag ( S 21RL )  mag ( S 21RL ))
(10)
Note that in equation (10), it is presumed that the power gain of the antenna will be loaded in
as an S21 file, in which case it must be squared to return to linear power gain. Also note that
this equation will only be correct if the underlying measurement parameter is noise power or
noise figure due to the fact that only for these noise parameters does the formatter in the PNA
presume power gains rather than voltage gains.
4 Calibration (or what about the cables)
From the formulation found in equations (6) and (8), one can see that the effect of port 1 cable
loss will be to increase the range loss and increase the noise figure thus
RLCP1  RL  ( S 21CP1 ) 2  GTx  AirLoss  ( S 21CP1 ) 2
S 21RL _ CP1  S 21RL  S 21CP1
NFCP1 
NFSys
(11)
( S 21CP1 ) 2
1
G _ std
1


2
 NFCP1  290  ( S 21RL _ CP1 )  NFSys

 ( S 21CP1 ) 2

1
G _ std
G / TCP1 

G /T
NFSys 290  ( S 21RL ) 2
G / TCP1 
G _ std
 290  ( S 21RL  S 21CP1 ) 2




Here CP1 denotes Cable-Port1. Thus, equation (11) demonstrates that if the cable from port 1
is not de-embedded for either the range loss measurement or the noise figure measurement,
then there is no effect on the measured value for G/T.
However, inspection shows that the same cannot be said for the cable on port 2. In this case,
adding a cable to port 2 will increase the range loss (more negative), but to the first order, it will
not substantially change the noise figure (provided the excess noise from the DUT is much
greater than the cable loss), thus the G/T value will change by the dB loss of the cable. Due to
this effect, it is recommended that the cable on port 2 of the PNA be measured and deembedded from the noise figure measurement of the PNA.
References:
[1] Dunsmore, Joel, “Handbook of Microwave Component Measurements”, 2012, John-Wiley,
Chichester, UK. Pp. 15-17
[2] Dunsmore, Joel, “Handbook of Microwave Component Measurements”, 2012, John-Wiley,
Chichester, UK. Pg 10