Instrumentation & Measurement Magazine 24-2 - 64

The noise current from the noise source uRec flowing into the
noise receiver depends on the output impedance Zout seen at
the output of the DUT. I can compute the equivalent input-referred noise current iueq,Rec from uRec by:
iueq ,Rec 

	

uRec
.	(19)
Zout,DUT

I can then calculate the total input-referred noise current
from the noise receiver iin2 ,Rec for the DUT to overcome by:



2



2
2
*
*
	(20)
iin2 ,Rec iueq,Rec  i Rec  iueq
 iRec
 Re iueq,Rec iRec
 i Rec iueq
,Rec
,Rec

where Re( ) represents the real part of the complex power. According to the definition of iRec, the input-referred noise current
iRec iun ,Rec  Ycor uRec, and I can then further simplify iin2 ,Rec by:
iRec is
iin2 ,Rec


	

2
uRec

Zout,DUT
2
Rec

 u

2

*
 Ycor
2
2
 i Rec
 uRec
 2  Re 
Z
 out ,DUT


1


 Zout,DUT

2

*
 Ycor
 2  Re 
Z
 out ,DUT






Device Characterization
Noisy Two-port Network Theory
Like the impedance (Z), admittance (Y), and transmission (or
chain) matrices used to characterize the small-signal performance of a linear two-port network, I can characterize the
noise performance of a noisy two-port network using noise
correlation matrices. For a noisy two-port network with only
passive components, I can calculate its correlation impedance
matrix CZ or correlation admittance matrix CY by [67]:

	(21)

 2
   i Rec .

 

Zout,DUT, in general, is a function of device sizes, bias conditions, operation frequencies, and source impedance Zs. In this
2
for
paper, I assume Zout,DUT = 50 Ω to compute the largest iin,Rec
the worst-case scenario in practice. Then, I can compute the
2
largest iinmax ,Rec at each operation frequency by:
	

from the output-referred noise current i2. For i1, in addition to
the induced gate noise, I characterize the gate resistance [70]
and control its noise using the number of fingers. For i2, since
it mainly comes from the channel thermal noise, I change the
channel width to control i2. As observed in [69], the aspect ratio
W/L of the device should be in the range of 3 - 5 to ensure the
accuracy of thermal noise measurement.

 1
G  2
2
.	(22)
iin2 max ,Rec uRec
  2  cor   iRec
25 
50


Fig. 4 shows the measured maximum input-referred noise
current iin2 max ,Rec (▲) for a 50 Ω DUT output impedance. I can see
that to characterize the noise up to 26 GHz, the noise power
from the DUT has to be higher than 6.2×10−22 A2/Hz at 26 GHz
for this measurement setup.
To estimate the DUT size, I assign half of the required noise
current from the input-referred noise current i1 and half of it


C z 2 kT  Re  Z 	(23)

	
and


CY 2 kT  Re Y 	(24)

	

where T is the ambient temperature in Kelvin, and Z (or Y) is
the 2 × 2 impedance (or admittance) matrix of the two-port
network. As can be seen, if I connect two networks in series,
the overall correlation impedance matrix will be equal to the
sum of the individual correlation impedance matrix. On the
other hand, if I connect two networks in parallel, the overall
correlation admittance matrix will be equal to the sum of the
individual correlation admittance matrix.
For a network with active components like transistors, I can
characterize this noisy two-port using its correlation chain matrix CA by [67]:

	

C
C12 A 
C A   11 A

C21 A C 22 A 

Rn

 2 kTo 
 NFmin  1
 RnYopt

2


NFmin  1
* 	(25)
 RnYopt

2

2

Rn Yopt



where the asterisk denotes the complex conjugate. If I connect
two networks in a cascade configuration, the overall correlation chain matrix will be:
	

Fig. 4. Measured maximum input-referred noise current iin2 max ,Rec (A2/Hz) of
the noise receiver with a 50 Ω DUT output impedance.
64	


C A A1C A 2 A1†  C A 2	(26)

where A1 is the 2 × 2 chain matrix of the first network, CA1 and
CA2 are the correlation chain matrices of the first and the second
†
matrix, respectively, and the † sign in A1 denotes Hermitian
conjugation (transpose and complex conjugate).
On the contrary, if I obtain the correlation chain matrix CA, I
can calculate the noise parameters NFmin, Rn, and Yopt by:

IEEE Instrumentation & Measurement Magazine	

April 2021



Instrumentation & Measurement Magazine 24-2

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