Based upon the active line concept, the conversion mechanisms of microscopic low frequency noise (e.g. generation-recombination noise) located in the channel of a Field Effect Transistor (FET) which is driven by a large RF signal is demonstrated. The first consequence is that the based band (low frequency) input gate noise voltage spectral density is dependent on the magnitude of the input RF power applied to the FET. Moreover, the microscopic generation-recombination noise sources located in the channel are responsible of up-converted input gate noise voltage spectral density around the RF frequency

Cappy, A.

Danneville, F.

Graffeuil, J.

Juraver, J-B

Llopis, O.

Tamen, B.

English

AMS Acta - Alm@DL - Università di Bologna

LOW FREQUENCY NOISE CONVERSION
IN FETs UNDER NONLINEAR OPERATION
F. DANNEVILLE, B. TAMEN, A. CAPPY
J-B JURAVER*, O. LLOPIS*, J. GRAFFEUIL*
IEMN, UMR CNRS 8520, Avenue Poincaré, BP 69, 59652 Villeneuve d’Ascq, France
*LAAS-CNRS, 7 Av. du Colonel Roche, 31077 Toulouse, France
francois.danneville@iemn.univ-lille1.fr
ABSTRACT
Based upon the active line concept, the conversion mechanisms of microscopic low frequency noise (e.g.
generation-recombination noise) located in the channel of a Field Effect Transistor (FET) which is driven by
a large RF signal is demonstrated. The first consequence is that the based band (low frequency) input gate
noise voltage spectral density is dependent on the magnitude of the input RF power applied to the FET.
Moreover, the microscopic generation-recombination noise sources located in the channel are responsible of
up-converted input gate noise voltage spectral density around the RF frequency.
INTRODUCTION
One of the most difficult problem encountered in FET noise modeling concerns the study of up-conversion
of base-band low frequency (LF) noise around a RF signal. Basically, part of the LF noise components is
located at the surface between source and gate, or can be located in the substrate ; this leads generally to
noise sources associated with extrinsic resistances such the gate resistance or source resistance. However,
part of the noise can be also located in the channel of the FET ; this noise is related to carriers number
fluctuation, and is called generation-recombination noise (GR). The only way to model such a phenomena is
to develop a physical noise modeling, close to the device physics ; one solution passes through the use of an
active line to describe the FET, which is described in this paper.
THEORETICAL ANALYSIS
(i) Large Signal Analysis
In order to conduct the large signal analysis, let us consider the intrinsic part of the FET described by a
uniform active line, and that the device operates as the active part of a FET amplifier, under large signal
operation (Fig. 1). We assume that the large-signal steady state Vgs(t) and Vds(t) resulting from the application
of the input large RF signal of angular frequency ω0 is known (determined using a harmonic balance
simulator). The elements of the line, e.g. the local transconductance gm(Vgs,Vds), the local channel
conductance ∆g0(Vgs,Vds), and the local gate to channel capacitance ∆c0(Vgs,Vds) of the line, are related to
experimental variations of the FET non-linear elements Gm(Vgs,Vds), Gd(Vgs,Vds), Cgs(Vgs,Vds), and Cgd(Vgs,Vds),
which can be determined quite easily. Since time-varying voltages Vgs(t) and Vds(t) are applied to the line, the
line elements are also time dependent and can be developed in Fourier Series.
In the following, we are going to describe the different steps leading to the noise correlation matrix (NCM)
calculation of the FET.
(ii) Noise Analysis
If we consider small perturbations around the large signal steady state, each element of the line can be
replaced by its conversion matrix. The elements of the conversion matrix are determined in a straightforward
way by the Fourier components of gm(t), ∆g0(t) and ∆c0(t). To perform the noise analysis, we have chosen a
representation with a open circuit between gate and source and a short circuit between drain and source (Fig.
2). A key point is to define the spectral density Sin of the local channel noise sources <in2> (Fig. 2), which is
considered also as uniforms. A GR microscopic noise source owns characteristics time τc ranged typically
between 1µs and 1ms. This means that the period of the microwave signal will be much lower than τc,
consequently, we will consider that <in2> is not modulated by the large signal. A problem also encountered
is to relate Sin to the spectral density Se of the external low-frequency input gate noise voltage <e2> (Fig. 1),
determined experimentally using a low frequency noise measurement system. The following relationship can
be derived from a linear noise analysis of the circuit shown in Fig. 2, when the FET is biased in saturation
(active operation) :
GRDCDCin Segmgdx
LS *2**0*


= (1)
L is the gate length, SeGR is the Generation-Recombination noise component of Se, g0DC and gmDC
correspond respectively to the DC values of the transconductance and channel conductance. Once the
microscopic noise sources are defined, the objective lies in the determination of the noise sources in the
frequency domain at the input and output of the device, taking into account of the particular representation.
The method is similar to those we have used previously in the case of FET mixer noise analysis [1]. By the
end of the calculation, the FET can be described by its noise conversion and noise correlation matrices (Fig.
3). The input ports and output ports are defined for each angular frequency ω + K.ω0, with ω0 corresponding
to the RF angular frequency and ω to the angular frequency deviation from ω0. Note that the 1/f component
of <e2> (Fig. 1) is obviously added to the base band noise source <eg02> of this circuit.
RESULTS
We have performed a complete simulation of a FET amplifier driven by a RF signal at 3.5 GHz. The input
and output RF terminations of the amplifier are simply 50 Ω, the device is a pseudomorphic HEMT
(0.25*200 µm2) biased at Vgs = 0V and Vds = 2V. It was found that the correlation between any input gate
noise voltage and any output drain noise current (Fig. 3) is zero, which is consistent with what has been
observed in FET mixer noise analysis [1]. Moreover, due to the uniform character of the line, there is no
conversion around the RF angular frequency for the drain noise current source; this not at all the case for the
input gate noise voltage, which has strong consequences on the phase noise presented by FET oscillator [2].
For this purpose, we have performed simulations of the amplifier for a large variation of the input RF power
magnitude Pin. The spectral densities of the theoretical and experimental base-band voltage noise source at
the input <eg02(ω)> (including flicker and GR noise components) are represented on Fig.4.
We observe Fig.4b that the spectral density Seg0(ω) of the base-band voltage noise <eg02(ω)> depends
strongly on the magnitude of the input power magnitude Pin. Both the shape and the magnitude are in
agreement with the experimental data shown on Fig 4a [2]. For the lower power level, Seg0(ω) is slightly
dependent on the RF power Pin and close to the spectral density measured in linear operation. However, there
is a strong effect on its magnitude for higher level of Pin, especially for frequency deviations where the GR
noise components are of primary importance. Moreover, we observe on Fig. 5 that the spectral densities of
the up-converted low frequency Generation-Recombination noise sources (around the RF frequency and for
ω = 2.pi.103 rd/s) are reaching values in the same order of magnitude to those of Seg0(ω) for the highest level
of Pin.
CONCLUSION
Using a microscopic approach, low frequency noise conversion mechanisms in FET have been studied and
compared with experimental data for the first time. The results have shown that the  spectral density of the
base-band voltage noise at the input of the device is strongly dependent of the input power level. In addition,
the model is able to describe an important effect : the up-conversion of base-band GR microscopic noise
sources located in the channel around the RF frequency at the device electrodes. Note that such approach can
be used as well to model accurately phase noise performances of FET’s oscillator [3].
REFERENCES
[1] F. DANNEVILLE, G. DAMBRINE, A. CAPPY, “Noise Modeling in MESFET and HEMT Mixers
Using a Uniform  Noisy Line Model”, IEEE Trans. on Electron Devices, vol. 45, n. 10, pp. 2207-2212, 1998.
[2] O. LLOPIS , J. VERDIER, R. PLANA, J. GRAFFEUIL ,“Low Frequency Noise in FET devices operated
under Nonlinear Conditions ; consequences on oscillator phase noise”,  Proceedings of the 1995 EuMC, pp.
285-289.
[3] J. OBREGON, M. PRIGENT, J.C. NALLAMTABY, CAMIADE M., RIGAUD D., QUERE R., “Key
aspects of modeling and design of low phase noise microwave transistor-oscillators”, 2000 (June) IEEE
MTT-S International Microwave Symposium, Workshop on Microwave Oscillators, Boston.
Fig. 1 : FET under large signal operation represented by an active line
Fig. 2 : Circuit used for noise calculation
Fig. 3 : FET representated by a linear noisy multifrequency network.
Vds(t)
D
S
G
Vgs(t)
GATE
S
D
∆c0(Vgs(t),Vds(t))
gm(Vgs(t),Vds(t))
∆g0(Vgs,Vds)
V(x,t)
External low frequency noise
voltage measured in linear
<e2>
GATE
<in2>
local microscopic GR noise sources
distributed along the channel
ω +K. ω 0 ω +K. ω 0
ω ω
ω -K. ω 0 ω -K. ω 0
δ Igs K
δ Igs
-K
δ Igs 0
δ Ids K
δ Ids 0
δ Ids
-K
δ Vgs K
δ Vgs
-K
δ Vgs 0
δ Vds K
δ Vds
-K
δ Vds 0
         Noise sources
   calculated during
noise analysis
eg K
eg
-K
eg 0
id
-K
id K
id 0
1,E+01 1,E+02 1,E+03 1,E+04
Frequency (Hz)
10-16
10-11
In
pu
t n
o
ise
 v
o
lta
ge
 s
pe
ct
ra
l d
en
sit
y 
(V
2 /H
z)
10-12
10-13
10-14
10-15
10 102 103 104 105
Fre e cy ( z)
Pin
(a)
(b)
Fig. 4 : Equivalent input LF noise spectral density measured (a) (-8 dBm < Pin < 4 dBm)
and modeled (b) versus different input RF power at 3.5 GHz
Fig. 5 : Base-band (Seg0(ω)) and Up-converted (Seg1(ω+ω0) or Seg-1(ω+ω0)) spectral densities
of the input gate noise voltage as a function of the input microwave Power Pin.
1 .0 0 E -1 6
1 .0 0 E -1 5
1 .0 0 E -1 4
1 .0 0 E -1 3
1 .0 0 E -1 2
1 .0 0 E -1 1
1 .0 0 E +0 1 1 .0 0 E + 02 1 .0 0 E + 03 1 .0 0 E +04 1 .0 0 E +05
fre q u e n c y  d e v ia tio n   (H z)
S
e
g( ωω
) (
V
.
V
/H
z
)
P in=-8 dB m
P in=-5 dB m
P in=-3 dB m
P in=-2 dB m
P in=-1 dB m
P in=0  d B m
P in=1  d B m
P in=2  d B m
P in=3  d B m
Pin ↑
1,00E-19
1,00E-18
1,00E-17
1,00E-16
1,00E-15
1,00E-14
1,00E-13
1,00E-12
-10 -8 -6 -4 -2 0 2 4
 Pin (dBm)
V.
V/
Hz
Seg0(ω)
Seg1(ω+ω0) or
 Seg
-1(ω-ω0)


Low frequency noise conversion in fets under nonlinear operation

F. DANNEVILLE

B. TAMEN

A. CAPPY

J-B JURAVER

O. LLOPIS

J. GRAFFEUIL

Crossref

LOW FREQUENCY NOISE CONVERSION IN FETS UNDER NONLINEAR OPERATION

AMS Acta

LOW FREQUENCY NOISE CONVERSION
IN FETs UNDER NONLINEAR OPERATION
F. DANNEVILLE, B. TAMEN, A. CAPPY
J-B JURAVER*, O. LLOPIS*, J. GRAFFEUIL*
IEMN, UMR CNRS 8520, Avenue Poincaré, BP 69, 59652 Vill eneuve d’Ascq, France
*LAAS-CNRS, 7 Av. du Colonel Roche, 31077 Toulouse, France
francois.dannevill e@iemn.univ-lill e1.fr
ABSTRACT
Based upon the active line concept, the conversion mechanisms of microscopic low frequency noise (e.g.
generation-recombination noise) located in the channel of a Field Effect Transistor (FET) which is driven by
a large RF signal is demonstrated. The first consequence is that the based band (low frequency) input gate
noise voltage spectral density is dependent on the magnitude of the input RF power applied to the FET.
Moreover, the microscopic generation-recombination noise sources located in the channel are responsible of
up-converted input gate noise voltage spectral density around the RF frequency.
INTRODUCTION
One of the most difficult problem encountered in FET noise modeling concerns the study of up-conversion
of base-band low frequency (LF) noise around a RF signal. Basically, part of the LF noise components is
located at the surface between source and gate, or can be located in the substrate ; this leads generally to
noise sources associated with extrinsic resistances such the gate resistance or source resistance. However,
part of the noise can be also located in the channel of the FET ; this noise is related to carriers number
fluctuation, and is called generation-recombination noise (GR). The only way to model such a phenomena is
to develop a physical noise modeling, close to the device physics ; one solution passes through the use of an
active line to describe the FET, which is described in this paper.
THEORETICAL ANALYSIS
(i) Large Signal Analysis
In order to conduct the large signal analysis, let us consider the intrinsic part of the FET described by a
uniform active line, and that the device operates as the active part of a FET amplifier, under large signal
operation (Fig. 1). We assume that the large-signal steady state Vgs(t) and Vds(t) resulting from the application
of the input large RF signal of angular frequency ω0 is known (determined using a harmonic balance
simulator). The elements of the line, e.g. the local transconductance gm(Vgs,Vds), the local channel
conductance ∆g0(Vgs,Vds), and the local gate to channel capacitance ∆c0(Vgs,Vds) of the line, are related to
experimental variations of the FET non-linear elements Gm(Vgs,Vds), Gd(Vgs,Vds), Cgs(Vgs,Vds), and Cgd(Vgs,Vds),
which can be determined quite easily. Since time-varying voltages Vgs(t) and Vds(t) are applied to the line, the
line elements are also time dependent and can be developed in Fourier Series.
In the following, we are going to describe the different steps leading to the noise correlation matrix (NCM)
calculation of the FET.
(ii) Noise Analysis
If we consider small perturbations around the large signal steady state, each element of the line can be
replaced by its conversion matrix. The elements of the conversion matrix are determined in a straightforward
way by the Fourier components of gm(t), ∆g0(t) and ∆c0(t). To perform the noise analysis, we have chosen a
representation with a open circuit between gate and source and a short circuit between drain and source (Fig.
2). A key point is to define the spectral density Sin of the local channel noise sources <in
2> (Fig. 2), which is
considered also as uniforms. A GR microscopic noise source owns characteristics time τc ranged typically
between 1µs and 1ms. This means that the period of the microwave signal will be much lower than τc,
consequently, we will consider that <in
2> is not modulated by the large signal. A problem also encountered
is to relate Sin to the spectral density Se of the external low-frequency input gate noise voltage <e
2> (Fig. 1),
determined experimentally using a low frequency noise measurement system. The following relationship can
be derived from a linear noise analysis of the circuit shown in Fig. 2, when the FET is biased in saturation
(active operation) :
GRDCDCin Segmgdx
L
S *2**0*



= (1)
L is the gate length, SeGR is the Generation-Recombination noise component of Se, g0DC and gmDC
correspond respectively to the DC values of the transconductance and channel conductance. Once the
microscopic noise sources are defined, the objective lies in the determination of the noise sources in the
frequency domain at the input and output of the device, taking into account of the particular representation.
The method is similar to those we have used previously in the case of FET mixer noise analysis [1]. By the
end of the calculation, the FET can be described by its noise conversion and noise correlation matrices (Fig.
3). The input ports and output ports are defined for each angular frequency ω + K.ω0, with ω0 corresponding
to the RF angular frequency and ω to the angular frequency deviation from ω0. Note that the 1/f component
of <e2> (Fig. 1) is obviously added to the base band noise source <eg0
2> of this circuit.
RESULTS
We have performed a complete simulation of a FET amplifier driven by a RF signal at 3.5 GHz. The input
and output RF terminations of the amplifier are simply 50 Ω, the device is a pseudomorphic HEMT
(0.25*200 µm2) biased at Vgs = 0V and Vds = 2V. It was found that the correlation between any input gate
noise voltage and any output drain noise current (Fig. 3) is zero, which is consistent with what has been
observed in FET mixer noise analysis [1]. Moreover, due to the uniform character of the line, there is no
conversion around the RF angular frequency for the drain noise current source; this not at all the case for the
input gate noise voltage, which has strong consequences on the phase noise presented by FET oscillator [2].
For this purpose, we have performed simulations of the amplifier for a large variation of the input RF power
magnitude Pin. The spectral densities of the theoretical and experimental base-band voltage noise source at
the input <eg0
2(ω)> (including fli cker and GR noise components) are represented on Fig.4.
We observe Fig.4b that the spectral density Seg0(ω) of the base-band voltage noise <eg02(ω)> depends
strongly on the magnitude of the input power magnitude Pin. Both the shape and the magnitude are in
agreement with the experimental data shown on Fig 4a [2]. For the lower power level, Seg0(ω) is slightly
dependent on the RF power Pin and close to the spectral density measured in linear operation. However, there
is a strong effect on its magnitude for higher level of Pin, especially for frequency deviations where the GR
noise components are of primary importance. Moreover, we observe on Fig. 5 that the spectral densities of
the up-converted low frequency Generation-Recombination noise sources (around the RF frequency and for
ω = 2.π.103 rd/s) are reaching values in the same order of magnitude to those of Seg0(ω) for the highest level
of Pin.
CONCLUSION
Using a microscopic approach, low frequency noise conversion mechanisms in FET have been studied and
compared with experimental data for the first time. The results have shown that the  spectral density of the
base-band voltage noise at the input of the device is strongly dependent of the input power level. In addition,
the model is able to describe an important effect : the up-conversion of base-band GR microscopic noise
sources located in the channel around the RF frequency at the device electrodes. Note that such approach can
be used as well to model accurately phase noise performances of FET’s oscillator [3].
REFERENCES
[1] F. DANNEVILLE, G. DAMBRINE, A. CAPPY, “Noise Modeling in MESFET and HEMT Mixers
Using a Uniform  Noisy Line Model” , IEEE Trans. on Electron Devices, vol. 45, n. 10, pp. 2207-2212, 1998.
[2] O. LLOPIS , J. VERDIER, R. PLANA, J. GRAFFEUIL ,“Low Frequency Noise in FET devices operated
under Nonlinear Conditions ; consequences on oscillator phase noise” ,  Proceedings of the 1995 EuMC, pp.
285-289.
[3] J. OBREGON, M. PRIGENT, J.C. NALLAMTABY, CAMIADE M., RIGAUD D., QUERE R., “Key
aspects of modeling and design of low phase noise microwave transistor-oscillators” , 2000 (June) IEEE
MTT-S International Microwave Symposium, Workshop on Microwave Oscillators, Boston.
Fig. 1 : FET under large signal operation represented by an active line
Fig. 2 : Circuit used for noise calculation
Fig. 3 : FET representated by a linear noisy multifrequency network.
Vds(t)
D
S
G
Vgs(t)
GATE
S
D
∆c0(Vgs(t),Vds(t))
gm(Vgs(t),Vds(t))
∆g0(Vgs,Vds)
V(x,t)
External low frequency noise
voltage measured in linear
<e2>
GATE
<in
2>
local microscopic GR noise sources
distributed along the channel
ω +K. ω 0 ω +K. ω 0
ω ω
ω -K. ω 0 ω -K. ω 0
δ Igs K
δ Igs -K
δ Igs 0
δ Ids K
δ Ids 0
δ Ids -K
δ Vgs K
δ Vgs -K
δ Vgs 0
δ Vds K
δ Vds -K
δ Vds 0
         Noise sources
   calculated during
noise analysis
eg K
eg -K
eg 0
id -K
id K
id 0
1,E+01 1,E+02 1,E+03 1,E+04
Frequency (Hz)
10-16
10-11
In
pu
t 
no
is
e 
vo
lt
ag
e 
sp
ec
tr
al
 d
en
si
ty
 (
V
2 /
H
z)
10-12
10-13
10-14
10-15
10 102 103 104 105
Fre e cy ( z)
Pin
(a)
(b)
Fig. 4 : Equivalent input LF noise spectral density measured (a) (-8 dBm < Pin < 4 dBm)
and modeled (b) versus different input RF power at 3.5 GHz
Fig. 5 : Base-band (Seg0(ω)) and Up-converted (Seg1(ω+ω0) or Seg-1(ω+ω0)) spectral densities
of the input gate noise voltage as a function of the input microwave Power Pin.
1 .0 0 E -1 6
1 .0 0 E -1 5
1 .0 0 E -1 4
1 .0 0 E -1 3
1 .0 0 E -1 2
1 .0 0 E -1 1
1 .0 0 E +0 1 1 .0 0 E + 02 1 .0 0 E + 03 1 .0 0 E +04 1 .0 0 E +05
fre q u e n c y  d e v ia tio n   (H z)
S
e
g
( ωω
) 
(V
.V
/H
z
)
P in=-8 dB m
P in=-5 dB m
P in=-3 dB m
P in=-2 dB m
P in=-1 dB m
P in=0  d B m
P in=1  d B m
P in=2  d B m
P in=3  d B m
Pin ↑
1,00E-19
1,00E-18
1,00E-17
1,00E-16
1,00E-15
1,00E-14
1,00E-13
1,00E-12
-10 -8 -6 -4 -2 0 2 4
 Pin (dBm)
V
.V
/H
z
Seg0(ω)
Seg1(ω+ω0) or
 Seg-1(ω-ω0)


LOW FREQUENCY NOISE CONVERSIONIN FETs UNDER NONLINEAR OPERATIONF. DANNEVILLE, B. TAMEN, A. CAPPYJ-B JURAVER*, O. LLOPIS*, J. GRAFFEUIL*IEMN, UMR CNRS 8520, Avenue Poincaré, BP 69, 59652 Villeneuve d’Ascq, France*LAAS-CNRS, 7 Av. du Colonel Roche, 31077 Toulouse, Francefrancois.danneville@iemn.univ-lille1.frABSTRACTBased upon the active line concept, the conversion mechanisms of microscopic low frequency noise (e.g.generation-recombination noise) located in the channel of a Field Effect Transistor (FET) which is driven bya large RF signal is demonstrated. The first consequence is that the based band (low frequency) input gatenoise voltage spectral density is dependent on the magnitude of the input RF power applied to the FET.Moreover, the microscopic generation-recombination noise sources located in the channel are responsible ofup-converted input gate noise voltage spectral density around the RF frequency.INTRODUCTIONOne of the most difficult problem encountered in FET noise modeling concerns the study of up-conversionof base-band low frequency (LF) noise around a RF signal. Basically, part of the LF noise components islocated at the surface between source and gate, or can be located in the substrate ; this leads generally tonoise sources associated with extrinsic resistances such the gate resistance or source resistance. However,part of the noise can be also located in the channel of the FET ; this noise is related to carriers numberfluctuation, and is called generation-recombination noise (GR). The only way to model such a phenomena isto develop a physical noise modeling, close to the device physics ; one solution passes through the use of anactive line to describe the FET, which is described in this paper.THEORETICAL ANALYSIS(i) Large Signal AnalysisIn order to conduct the large signal analysis, let us consider the intrinsic part of the FET described by auniform active line, and that the device operates as the active part of a FET amplifier, under large signaloperation (Fig. 1). We assume that the large-signal steady state Vgs(t) and Vds(t) resulting from the applicationof the input large RF signal of angular frequency ω0 is known (determined using a harmonic balancesimulator). The elements of the line, e.g. the local transconductance gm(Vgs,Vds), the local channelconductance ∆g0(Vgs,Vds), and the local gate to channel capacitance ∆c0(Vgs,Vds) of the line, are related toexperimental variations of the FET non-linear elements Gm(Vgs,Vds), Gd(Vgs,Vds), Cgs(Vgs,Vds), and Cgd(Vgs,Vds),which can be determined quite easily. Since time-varying voltages Vgs(t) and Vds(t) are applied to the line, theline elements are also time dependent and can be developed in Fourier Series.In the following, we are going to describe the different steps leading to the noise correlation matrix (NCM)calculation of the FET.(ii) Noise AnalysisIf we consider small perturbations around the large signal steady state, each element of the line can bereplaced by its conversion matrix. The elements of the conversion matrix are determined in a straightforwardway by the Fourier components of gm(t), ∆g0(t) and ∆c0(t). To perform the noise analysis, we have chosen arepresentation with a open circuit between gate and source and a short circuit between drain and source (Fig.2). A key point is to define the spectral density Sin of the local channel noise sources <in2> (Fig. 2), which isconsidered also as uniforms. A GR microscopic noise source owns characteristics time τc ranged typicallybetween 1µs and 1ms. This means that the period of the microwave signal will be much lower than τc,consequently, we will consider that <in2> is not modulated by the large signal. A problem also encounteredis to relate Sin to the spectral density Se of the external low-frequency input gate noise voltage <e2> (Fig. 1),determined experimentally using a low frequency noise measurement system. The following relationship canbe derived from a linear noise analysis of the circuit shown in Fig. 2, when the FET is biased in saturation(active operation) :GRDCDCin SegmgdxLS *2**0*= (1)L is the gate length, SeGR is the Generation-Recombination noise component of Se, g0DC and gmDCcorrespond respectively to the DC values of the transconductance and channel conductance. Once themicroscopic noise sources are defined, the objective lies in the determination of the noise sources in thefrequency domain at the input and output of the device, taking into account of the particular representation.The method is similar to those we have used previously in the case of FET mixer noise analysis [1]. By theend of the calculation, the FET can be described by its noise conversion and noise correlation matrices (Fig.3). The input ports and output ports are defined for each angular frequency ω + K.ω0, with ω0 correspondingto the RF angular frequency and ω to the angular frequency deviation from ω0. Note that the 1/f componentof <e2> (Fig. 1) is obviously added to the base band noise source <eg02> of this circuit.RESULTSWe have performed a complete simulation of a FET amplifier driven by a RF signal at 3.5 GHz. The inputand output RF terminations of the amplifier are simply 50 Ω, the device is a pseudomorphic HEMT(0.25*200 µm2) biased at Vgs = 0V and Vds = 2V. It was found that the correlation between any input gatenoise voltage and any output drain noise current (Fig. 3) is zero, which is consistent with what has beenobserved in FET mixer noise analysis [1]. Moreover, due to the uniform character of the line, there is noconversion around the RF angular frequency for the drain noise current source; this not at all the case for theinput gate noise voltage, which has strong consequences on the phase noise presented by FET oscillator [2].For this purpose, we have performed simulations of the amplifier for a large variation of the input RF powermagnitude Pin. The spectral densities of the theoretical and experimental base-band voltage noise source atthe input <eg02(ω)> (including flicker and GR noise components) are represented on Fig.4.We observe Fig.4b that the spectral density Seg0(ω) of the base-band voltage noise <eg02(ω)> dependsstrongly on the magnitude of the input power magnitude Pin. Both the shape and the magnitude are inagreement with the experimental data shown on Fig 4a [2]. For the lower power level, Seg0(ω) is slightlydependent on the RF power Pin and close to the spectral density measured in linear operation. However, thereis a strong effect on its magnitude for higher level of Pin, especially for frequency deviations where the GRnoise components are of primary importance. Moreover, we observe on Fig. 5 that the spectral densities ofthe up-converted low frequency Generation-Recombination noise sources (around the RF frequency and forω = 2.pi.103 rd/s) are reaching values in the same order of magnitude to those of Seg0(ω) for the highest levelof Pin.CONCLUSIONUsing a microscopic approach, low frequency noise conversion mechanisms in FET have been studied andcompared with experimental data for the first time. The results have shown that the  spectral density of thebase-band voltage noise at the input of the device is strongly dependent of the input power level. In addition,the model is able to describe an important effect : the up-conversion of base-band GR microscopic noisesources located in the channel around the RF frequency at the device electrodes. Note that such approach canbe used as well to model accurately phase noise performances of FET’s oscillator [3].REFERENCES[1] F. DANNEVILLE, G. DAMBRINE, A. CAPPY, “Noise Modeling in MESFET and HEMT MixersUsing a Uniform  Noisy Line Model”, IEEE Trans. on Electron Devices, vol. 45, n. 10, pp. 2207-2212, 1998.[2] O. LLOPIS , J. VERDIER, R. PLANA, J. GRAFFEUIL ,“Low Frequency Noise in FET devices operatedunder Nonlinear Conditions ; consequences on oscillator phase noise”,  Proceedings of the 1995 EuMC, pp.285-289.[3] J. OBREGON, M. PRIGENT, J.C. NALLAMTABY, CAMIADE M., RIGAUD D., QUERE R., “Keyaspects of modeling and design of low phase noise microwave transistor-oscillators”, 2000 (June) IEEEMTT-S International Microwave Symposium, Workshop on Microwave Oscillators, Boston.Fig. 1 : FET under large signal operation represented by an active lineFig. 2 : Circuit used for noise calculationFig. 3 : FET representated by a linear noisy multifrequency network.Vds(t)DSGVgs(t)GATESD∆c0(Vgs(t),Vds(t))gm(Vgs(t),Vds(t))∆g0(Vgs,Vds)V(x,t)External low frequency noisevoltage measured in linear<e2>GATE<in2>local microscopic GR noise sourcesdistributed along the channelω +K. ω 0 ω +K. ω 0ω ωω -K. ω 0 ω -K. ω 0δ Igs Kδ Igs-Kδ Igs 0δ Ids Kδ Ids 0δ Ids-Kδ Vgs Kδ Vgs-Kδ Vgs 0δ Vds Kδ Vds-Kδ Vds 0         Noise sources   calculated duringnoise analysiseg Keg-Keg 0id-Kid Kid 01,E+01 1,E+02 1,E+03 1,E+04Frequency (Hz)10-1610-11Input noise voltage spectral density (V2 /Hz)10-1210-1310-1410-1510 102 103 104 105Fre e cy ( z)Pin(a)(b)Fig. 4 : Equivalent input LF noise spectral density measured (a) (-8 dBm < Pin < 4 dBm)and modeled (b) versus different input RF power at 3.5 GHzFig. 5 : Base-band (Seg0(ω)) and Up-converted (Seg1(ω+ω0) or Seg-1(ω+ω0)) spectral densitiesof the input gate noise voltage as a function of the input microwave Power Pin.1 .0 0 E -1 61 .0 0 E -1 51 .0 0 E -1 41 .0 0 E -1 31 .0 0 E -1 21 .0 0 E -1 11 .0 0 E +0 1 1 .0 0 E + 02 1 .0 0 E + 03 1 .0 0 E +04 1 .0 0 E +05fre q u e n c y  d e v ia tio n   (H z)Seg( ωω) (V.V/Hz)P in=-8 dB mP in=-5 dB mP in=-3 dB mP in=-2 dB mP in=-1 dB mP in=0  d B mP in=1  d B mP in=2  d B mP in=3  d B mPin ↑1,00E-191,00E-181,00E-171,00E-161,00E-151,00E-141,00E-131,00E-12-10 -8 -6 -4 -2 0 2 4 Pin (dBm)V.V/HzSeg0(ω)Seg1(ω+ω0) or Seg-1(ω-ω0)

Low frequency noise conversion in fets under nonlinear operation

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