Instrumentation & Measurement Magazine 24-2 - 62

to enhance measurement
accuracy.

Noise System
Calibration
To get rid of the impact
of the noise measurement
system on the noise parameters of the DUT, I need
to calibrate the system to
the probe tip of the output
probe (i.e., the noise referFig. 3. The equivalent circuit model for the high-frequency noise measurement system shown in Fig. 2. during the
ence plane) by obtaining
calibration phase.
the noise parameters of the
noise receiver. I can get the
Step 1: Set A = B = C = D = 0, and use the set of measured Ph
noise parameters via noise temperature [68] or noise power
[17]. In this paper, I use the noise power approach. In the cal- and Pc values to calculate Go by:
ibration phase, I connect a THRU line between the input and
1
output probes and model the noise measurement system as a
Go 
noise source, an impedance tuner, and a receiver connected
kTo f TseffnorhGsh  TseffnorcGsc
in a cascade configuration, as shown in Fig. 3. In this model, 	
2
2 	(2)

1   inr  sh
1   inr  sc 
the impedance tuner includes all of the components from the
  PhGsh 


P
G
c sc
2
2


1   sh
1   sc
source tuner to the input probe. For the noise receiver, on the


other hand, it includes all of the components from the output
probe to the NFA. Here, uRec and iRec = iun,Rec + Ycor·uRec are the where the subscripts h and c represent the parameter in the hot
noise voltage and current, respectively, contributed from the and cold states, respectively.
Step 2: With the receiver gain Go obtained in Step 1, (1)
noise receiver. Also, uRec and iRec are partially correlated through
Ycor·uRec because the uncorrelated portion iun,Rec is usually not becomes:
zero. Based on the system model shown in Fig. 2, I can express
2
Ys  A  B  2Gs  C  2 Bs  D
the measured noise power Pn and the noise parameters of the
2

 	(3)
	
noise receiver by [17]:
1   inr  s
Pn
Gs  


 Tseffnor  .
2


 kToGo f
1  s
PnGs 1   inr  s



kTo f 1   2
	
	(1)





T

seffnor

s

2



Gs  Ys  A  B  2Gs  C  2 Bs  D  Go



Solve A, B, C, and D in (3) using the N different Pc values.
Step 3: To eliminate the impact of A, B, C, and D on Go extraction in Step 1 due to non-zero ΔYs = Ysh - Ysc, with the new
parameter values of A, B, C, and D obtained in Step 2, calculate Go again using the same set of Ph and Pc used in Step 1 by:

where k is Boltzmann's constant, To is the standard temperature (= 290 K), and Δ f is the noise bandwidth. Besides, Ys is the
source admittance seen at the noise reference plane (Ys = Gs + j
· Bs = 1 / Zs), Tseffnor is the normalized effective source tempera2
2


 P G  1   inr  sh  P G  1   inr  sc 
ture (= Tseff / To), Γinr is the input reflection coefficient of the noise
h sh
c sc
2
2


1   sh
1   sc


the source reflection coefficient, and Go is the re- Go
receiver, Γs is
	(4)
2
2

kTo f TseffnorhGsh  TseffnorcGsc   Ysh  Ysc  A  2 Gsh  Gsc   C  2  Bsh  Bsc   D 
ceiver gain. Finally, parameters A, B, C, and D in (1) are the


noise parameters of the noise receiver, which are the noise paRepeat Steps 2 and 3 until the changes in Go (ΔGo) are less
rameters I need to obtain in the calibration phase.
Before conducting the calibration procedure, Ifirst mea- than the specified tolerance.
Step 4: Once obtaining the values of A, B, C, and D, calcusure one set of " hot " noise power P h (P n measured with
the noise source turned on) and " cold " noise power Pc (Pn late the parameters Ru, Giun, and Ycor by:
measured with the noise source turned off) at one source
impedance and N different cold noise powers Pc (N ≥ 4) 	
Ru  A ,	(5)
at other N mutually independent source impedances.
Usually, the source admittances Ys (or source reflection coC 2  D2
Giun B 
,	(6)
efficients Γs) in the hot state (Ysh = Gsh + j · Bsh or Γsh) and cold 	
A
state (Ysc = Gsc + j · Bsc or Γsc) are not the same. I can extract
the receiver gain Go, and the four noise parameters A, B, C,
C
Gcor  ,	(7)
	
and D using the following four steps [17]:
A



62	

IEEE Instrumentation & Measurement Magazine	



April 2021



Instrumentation & Measurement Magazine 24-2

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