# Instrumentation & Measurement Magazine 24-2 - 63

```Table 1 - Measured Four Noise Parameters of the Noise Receiver [69]
Frequency
(GHz)

4

6

8

10

12

14

16

18

20

22

24

26

NFmin (dB)

3.70

4.08

3.81

3.63

3.62

3.62

3.58

3.60

3.79

3.69

3.74

4.25

Rn (Ω)

22.6

35.7

20.9

31.7

27.6

23.3

23.5

22.1

22.3

37.9

20.6

43.8

Gopt (mS)

19.6

14.3

22.4

13.8

16.1

18.8

18.4

19.9

21.0

12.2

23.2

12.6

Bopt (mS)

-4.4

3.1

-11.9

11.6

-10.4

7.9

-3.1

-1.5

7.5

-8.4

19.7

-7.2

and
Bcor 

D
.	(8)
A

Finally, obtaining the four noise parameters of the noise receiver by:
NFmin 
1  2 RuGcor  2 RuGiun   RuGcor  ,	(9)
2

measurement because of the reduced noise power from the
device compared to those from the instrument. To ensure an
accurate thermal noise measurement, the DUT needs to provide sufficiently large noise power compared to the total noise
power resulted from the instrument. With the four noise parameters of the noise receiver obtained in the calibration phase
shown in Table 1, I can calculate Gcor, Bcor, and Gu by [69]:
Gcor


Rn  Ru ,	(10)

Gopt


Giun
2
,	(11)
 Gcor
Ru

and

Bcor   Bopt ,	(14)

and



Bopt   Bcor .	(12)

After obtaining the noise parameters of the noise receiver,
I can de-embed the noise effect from the noise system from
the noise factor of the DUT using Friis' equation [22]. Table 1 shows the measured four noise parameters of the noise



2
2
Gu Rn  Gopt
 Gcor
.	(15)

NFmin  1
 Gopt ,	(13)
2 Rn

where Gu is the equivalent noise conductance that results in
the uncorrelated noise current iun,Rec. Based on the noise theory,
I can calculate the uncorrelated noise current of the receiver
iun,Rec, the input-referred noise voltage current sources of the
noise receiver uRec and iRec, respectively, by:

2

iun
4 kToGu f ,	(16)
,Rec

2

uRec
4 kTo Rn f ,	(17)

System Aware Device Design
One of the challenges in thermal noise characterization is the
design of DUTs, especially for choosing the size of the transistor. When the channel length of MOSFETs is scaled down,
for a fixed device width, the increasing current might be too
high and causes a considerable dc voltage drop between the
external power supply and the intrinsic device. It creates inaccuracies when modeling the bias dependence for the noise
sources of interest. On the other hand, if I reduce the width of
the transistor, it increases the inaccuracy for the thermal noise

and

2
2
2
2
iRec
 i Rec  iun ,Rec  iun
 4 kTo  Ycor  Rn  Gu  f .	(18)
,Rec



2
2
Table 2 shows the noise sources iRec
and uRec
of the noise receiver using the measured noise parameters from Table 1.

Table 2 - Measured noise sources of the noise receiver [69]
Frequency
(GHz)

4

6

8

10

12

14

16

18

20

22

24

26

2
​iRec ​
(10−22 A2/Hz)

1.46

1.22

2.15

1.66

1.62

1.54

1.31

1.41

1.77

1.33

3.05

1.48

2
u
​ Rec ​
(10−19 V2/Hz)

3.63

5.71

3.35

5.08

4.42

3.73

3.76

3.54

3.57

6.07

3.30

7.02

April 2021

IEEE Instrumentation & Measurement Magazine	63

```

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