Instrumentation & Measurement Magazine 24-2 - 66

Step 5: Subtract the parallel parasitics YOPEN from YDUT and
YSHORT to get YI,DUT and YI,SHORT, respectively.
Step 6: De-embed the parallel parasitics CY,OPEN from CY,DUT
to get CYI,DUT.
Step 7: Convert the YI,DUT and YI,SHORT to their impedance
matrices ZI,DUT and ZI,SHORT, respectively.
Step 8: Convert the correlation admittance matrix CYI,DUT
to its correlation impedance matrix CZI,DUT using the ZI,DUT and
transformation matrix TZY in Table 3.
Step 9: Convert the correlation admittance matrix CYI,SHORT
to its correlation impedance matrix CZI,SHORT using ZI,SHORT and
the transformation matrix TZY in Table 3.
Step 10: De-embed the series parasitics ZI,SHORT from ZI,DUT
to get the impedance matrix Zintr of the intrinsic transistor.
Step 11: De-embed the series parasitics CZI,SHORT from CZI,DUT
to get the correlation impedance matrix CZ,intr of the intrinsic
transistor.
Step 12: Convert the Zintr of the intrinsic transistor to its
chain matrix Aintr.
Step 13: Convert the correlation impedance matrix CZ,intr to
its correlation chain matrix CA,intr using Aintr and the transformation matrix TAZ in Table III.
Step 14: Calculate the noise parameters NFmin,intr, Rn,intr, and
Yopt,intr of the intrinsic transistor from the correlation chain matrix CA,intr using (27)-(29).
On the other hand, if the characterization frequency is in the
tens or hundreds of GHz or the distributed effects of the metal
interconnections are very pronounced, I use OPEN and THRU
dummy structures assuming that the probe pads, metal interconnections, and the transistor are in a cascade configuration.
Here I assume that the metal interconnection I1 at the input port
of the transistor and the metal interconnection I2 at the output
port of the transistor are not the same, and I lay out two THRU
structures, namely THRU1 and THRU2. The de-embedding
procedure assuming a cascade configuration is as follows [71]:
Step 1: Measure the scattering parameters S DUT, S OPEN,
STHRU1, and STHRU2 of the DUT, OPEN, THRU1, and THRU2
dummy structures. Convert SOPEN to its admittance matrix
YOPEN.
Step 2: Measure the noise parameters NFmin,DUT, Rn,DUT, and
Yopt,DUT of the DUT, and calculate the correlation chain matrix
CA,DUT using (25).
Step 3: Calculate the chain matrix APAD of the probe pads by:
	


1
APAD  
y

 11,OPEN y12,OPEN

0
	(32)
1 

where y11,OPEN and y12,OPEN are the elements in YOPEN.
Step 4: Convert STHRU1 and STHRU2 to their chain matrices
ATHRU1 and ATHRU2, respectively.
Step 5: Calculate the chain matrices AIN and AOUT by:
	

1
AIN  ATHRU 1 APAD
	(33)

and
	
66	

1
AOUT  APAD
ATHRU 2 .	(34)

Step 6: Convert SDUT to its chain matrix ADUT, and calculate
the chain matrix Aintr of the intrinsic transistor by:
1
.	(35)
Aintr  AIN1 ADUT AOUT

	

Step 7: Convert the chain matrices AIN and AOUT to their impedance matrices ZIN and ZOUT, respectively.
Step 8: Calculate the correlation impedance matrices CZ,IN
and CZ,OUT from ZIN and ZOUT, respectively, using (23).
Step 9: Convert the correlation impedance matrices CZ,IN
and CZ,OUT to their correlation chain matrices CA,IN and CA,OUT
using AIN, AOUT, and the transformation matrix TAZ in Table 3.
Step 10: Calculate the correlation chain matrix CA,intr of the
intrinsic transistor by:
	



C A,intr 
AIN1 C A,DUT  C A ,IN

 A 
†
IN

1

†
 Aintr C A,OUT Aintr
.	(36)

Step 11: Calculate the noise parameters NFmin,intr, Rn,intr, and
Yopt,intr of the intrinsic transistor from the correlation chain matrix CA,intr using (27)-(29).

Noise Source Extraction
After obtaining the four intrinsic noise parameters of a transistor in the previous section, I need to extract the noise sources
of interest, namely the channel thermal noise, induced gate
noise, and their correlation from these intrinsic noise parameters in order to provide insight to model these noise sources for
circuit simulation. Channel thermal noise modeling of nanometer MOSFETs is essential for devices used in the front-end
transceivers. When transistors operate in the ranges of tens or
hundreds of gigahertz, the random potential fluctuations in
the channel results in the channel thermal noise at the drain
terminal. On the other hand, the gate terminal also experiences
the potential fluctuations in the channel through the coupling
of gate oxide capacitance, which results in the so-called induced gate noise. Since the channel thermal noise at the drain
terminal and the induced gate noise at the gate terminal come
from the same potential fluctuations in the channel, these two
noise sources correlate with each other.
I start with the noise source extraction by first choosing a
proper high-frequency equivalent circuit, as shown in Fig. 6,
which is accurate enough to capture the high-frequency behavior of a MOSFET. It consists of two parts-an internal part and
an external part. The internal part includes the gate-to-source
capacitance CGS, gate-to-drain capacitance CGD, transconductance gm, body transconductance gmb, and output resistance RDS.
The external part, on the other hand, includes all the components outside of the dashed box, namely the gate resistance RG,
source resistance RS, drain resistance RD, source-to-substrate
junction capacitance CSB, drain-to-substrate junction capacitance CDB, and the substrate resistances RDB, RSB, and RDSB,
respectively. In addition to these lumped elements, the equivalent circuit also includes noise current sources (those with
double arrows), which include the channel thermal noise id,
the induced gate noise ig, and the thermal noise iG, iS, iD, iDB, iSB,
and iDSB caused by the parasitic resistances RG, RS, RD, RDB, RSB,

IEEE Instrumentation & Measurement Magazine	

April 2021



Instrumentation & Measurement Magazine 24-2

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 24-2

No label
Instrumentation & Measurement Magazine 24-2 - No label
Instrumentation & Measurement Magazine 24-2 - Cover2
Instrumentation & Measurement Magazine 24-2 - 1
Instrumentation & Measurement Magazine 24-2 - 2
Instrumentation & Measurement Magazine 24-2 - 3
Instrumentation & Measurement Magazine 24-2 - 4
Instrumentation & Measurement Magazine 24-2 - 5
Instrumentation & Measurement Magazine 24-2 - 6
Instrumentation & Measurement Magazine 24-2 - 7
Instrumentation & Measurement Magazine 24-2 - 8
Instrumentation & Measurement Magazine 24-2 - 9
Instrumentation & Measurement Magazine 24-2 - 10
Instrumentation & Measurement Magazine 24-2 - 11
Instrumentation & Measurement Magazine 24-2 - 12
Instrumentation & Measurement Magazine 24-2 - 13
Instrumentation & Measurement Magazine 24-2 - 14
Instrumentation & Measurement Magazine 24-2 - 15
Instrumentation & Measurement Magazine 24-2 - 16
Instrumentation & Measurement Magazine 24-2 - 17
Instrumentation & Measurement Magazine 24-2 - 18
Instrumentation & Measurement Magazine 24-2 - 19
Instrumentation & Measurement Magazine 24-2 - 20
Instrumentation & Measurement Magazine 24-2 - 21
Instrumentation & Measurement Magazine 24-2 - 22
Instrumentation & Measurement Magazine 24-2 - 23
Instrumentation & Measurement Magazine 24-2 - 24
Instrumentation & Measurement Magazine 24-2 - 25
Instrumentation & Measurement Magazine 24-2 - 26
Instrumentation & Measurement Magazine 24-2 - 27
Instrumentation & Measurement Magazine 24-2 - 28
Instrumentation & Measurement Magazine 24-2 - 29
Instrumentation & Measurement Magazine 24-2 - 30
Instrumentation & Measurement Magazine 24-2 - 31
Instrumentation & Measurement Magazine 24-2 - 32
Instrumentation & Measurement Magazine 24-2 - 33
Instrumentation & Measurement Magazine 24-2 - 34
Instrumentation & Measurement Magazine 24-2 - 35
Instrumentation & Measurement Magazine 24-2 - 36
Instrumentation & Measurement Magazine 24-2 - 37
Instrumentation & Measurement Magazine 24-2 - 38
Instrumentation & Measurement Magazine 24-2 - 39
Instrumentation & Measurement Magazine 24-2 - 40
Instrumentation & Measurement Magazine 24-2 - 41
Instrumentation & Measurement Magazine 24-2 - 42
Instrumentation & Measurement Magazine 24-2 - 43
Instrumentation & Measurement Magazine 24-2 - 44
Instrumentation & Measurement Magazine 24-2 - 45
Instrumentation & Measurement Magazine 24-2 - 46
Instrumentation & Measurement Magazine 24-2 - 47
Instrumentation & Measurement Magazine 24-2 - 48
Instrumentation & Measurement Magazine 24-2 - 49
Instrumentation & Measurement Magazine 24-2 - 50
Instrumentation & Measurement Magazine 24-2 - 51
Instrumentation & Measurement Magazine 24-2 - 52
Instrumentation & Measurement Magazine 24-2 - 53
Instrumentation & Measurement Magazine 24-2 - 54
Instrumentation & Measurement Magazine 24-2 - 55
Instrumentation & Measurement Magazine 24-2 - 56
Instrumentation & Measurement Magazine 24-2 - 57
Instrumentation & Measurement Magazine 24-2 - 58
Instrumentation & Measurement Magazine 24-2 - 59
Instrumentation & Measurement Magazine 24-2 - 60
Instrumentation & Measurement Magazine 24-2 - 61
Instrumentation & Measurement Magazine 24-2 - 62
Instrumentation & Measurement Magazine 24-2 - 63
Instrumentation & Measurement Magazine 24-2 - 64
Instrumentation & Measurement Magazine 24-2 - 65
Instrumentation & Measurement Magazine 24-2 - 66
Instrumentation & Measurement Magazine 24-2 - 67
Instrumentation & Measurement Magazine 24-2 - 68
Instrumentation & Measurement Magazine 24-2 - 69
Instrumentation & Measurement Magazine 24-2 - 70
Instrumentation & Measurement Magazine 24-2 - 71
Instrumentation & Measurement Magazine 24-2 - 72
Instrumentation & Measurement Magazine 24-2 - 73
Instrumentation & Measurement Magazine 24-2 - 74
Instrumentation & Measurement Magazine 24-2 - 75
Instrumentation & Measurement Magazine 24-2 - 76
Instrumentation & Measurement Magazine 24-2 - 77
Instrumentation & Measurement Magazine 24-2 - 78
Instrumentation & Measurement Magazine 24-2 - 79
Instrumentation & Measurement Magazine 24-2 - 80
Instrumentation & Measurement Magazine 24-2 - 81
Instrumentation & Measurement Magazine 24-2 - 82
Instrumentation & Measurement Magazine 24-2 - 83
Instrumentation & Measurement Magazine 24-2 - 84
Instrumentation & Measurement Magazine 24-2 - 85
Instrumentation & Measurement Magazine 24-2 - 86
Instrumentation & Measurement Magazine 24-2 - 87
Instrumentation & Measurement Magazine 24-2 - 88
Instrumentation & Measurement Magazine 24-2 - 89
Instrumentation & Measurement Magazine 24-2 - 90
Instrumentation & Measurement Magazine 24-2 - 91
Instrumentation & Measurement Magazine 24-2 - 92
Instrumentation & Measurement Magazine 24-2 - 93
Instrumentation & Measurement Magazine 24-2 - 94
Instrumentation & Measurement Magazine 24-2 - 95
Instrumentation & Measurement Magazine 24-2 - 96
Instrumentation & Measurement Magazine 24-2 - 97
Instrumentation & Measurement Magazine 24-2 - 98
Instrumentation & Measurement Magazine 24-2 - 99
Instrumentation & Measurement Magazine 24-2 - 100
Instrumentation & Measurement Magazine 24-2 - 101
Instrumentation & Measurement Magazine 24-2 - 102
Instrumentation & Measurement Magazine 24-2 - 103
Instrumentation & Measurement Magazine 24-2 - 104
Instrumentation & Measurement Magazine 24-2 - 105
Instrumentation & Measurement Magazine 24-2 - 106
Instrumentation & Measurement Magazine 24-2 - 107
Instrumentation & Measurement Magazine 24-2 - 108
Instrumentation & Measurement Magazine 24-2 - 109
Instrumentation & Measurement Magazine 24-2 - 110
Instrumentation & Measurement Magazine 24-2 - 111
Instrumentation & Measurement Magazine 24-2 - 112
Instrumentation & Measurement Magazine 24-2 - 113
Instrumentation & Measurement Magazine 24-2 - 114
Instrumentation & Measurement Magazine 24-2 - 115
Instrumentation & Measurement Magazine 24-2 - 116
Instrumentation & Measurement Magazine 24-2 - 117
Instrumentation & Measurement Magazine 24-2 - 118
Instrumentation & Measurement Magazine 24-2 - 119
Instrumentation & Measurement Magazine 24-2 - 120
Instrumentation & Measurement Magazine 24-2 - 121
Instrumentation & Measurement Magazine 24-2 - 122
Instrumentation & Measurement Magazine 24-2 - 123
Instrumentation & Measurement Magazine 24-2 - 124
Instrumentation & Measurement Magazine 24-2 - 125
Instrumentation & Measurement Magazine 24-2 - 126
Instrumentation & Measurement Magazine 24-2 - 127
Instrumentation & Measurement Magazine 24-2 - 128
Instrumentation & Measurement Magazine 24-2 - 129
Instrumentation & Measurement Magazine 24-2 - 130
Instrumentation & Measurement Magazine 24-2 - 131
Instrumentation & Measurement Magazine 24-2 - 132
Instrumentation & Measurement Magazine 24-2 - Cover3
Instrumentation & Measurement Magazine 24-2 - Cover4
https://www.nxtbook.com/allen/iamm/25-9
https://www.nxtbook.com/allen/iamm/25-8
https://www.nxtbook.com/allen/iamm/25-7
https://www.nxtbook.com/allen/iamm/25-6
https://www.nxtbook.com/allen/iamm/25-5
https://www.nxtbook.com/allen/iamm/25-4
https://www.nxtbook.com/allen/iamm/25-3
https://www.nxtbook.com/allen/iamm/instrumentation-measurement-magazine-25-2
https://www.nxtbook.com/allen/iamm/25-1
https://www.nxtbook.com/allen/iamm/24-9
https://www.nxtbook.com/allen/iamm/24-7
https://www.nxtbook.com/allen/iamm/24-8
https://www.nxtbook.com/allen/iamm/24-6
https://www.nxtbook.com/allen/iamm/24-5
https://www.nxtbook.com/allen/iamm/24-4
https://www.nxtbook.com/allen/iamm/24-3
https://www.nxtbook.com/allen/iamm/24-2
https://www.nxtbook.com/allen/iamm/24-1
https://www.nxtbook.com/allen/iamm/23-9
https://www.nxtbook.com/allen/iamm/23-8
https://www.nxtbook.com/allen/iamm/23-6
https://www.nxtbook.com/allen/iamm/23-5
https://www.nxtbook.com/allen/iamm/23-2
https://www.nxtbook.com/allen/iamm/23-3
https://www.nxtbook.com/allen/iamm/23-4
https://www.nxtbookmedia.com