Large-SignalModelingofGaNDevicesforDesigning
HighPowerAmpliersofNextGenerationWirelessCommunicationSystems 201

enhancement of the objective function, another performance quantity, depending on the
final application, will be considered. The main application of GaN-based HEMT is power
amplifier design. For power amplifier design, the output and input impedance, the device
gain, and stability factor are important for the design of matching networks. These factors
can be expressed as a function of S–parameters and fitted during the optimization. The
stability factor defined at the output plane of the device at each frequency can be expressed
as
2112
*
1122
2
22
1
SSSS
S
K
s


(29)
where S
*
is the complex conjugate and Δ
s
is the determinant of S-parameter matrix at each

S
G


.

(31)
The error in the gain may thus, be expressed as



N
m
simmeasG
GG
N
1
1
(32)
where G
meas
and G
sim
are the gains computed from the measured and modeled S-parameters.
The fitting error can be defined in terms of the three error components as



g
and R
s
, for larger devices, C
pgi
cannot be separated completely from
the intrinsic capacitance C
gs
. However, the sum of C
pgi
and C
gs
is in proportion with the gate
width. By direct scaling of the 8x250-μm device, the expected values of C
gda
and C
gdi
for

8x125-μm device are 20 fF and 40 fF, respectively. Due to the smaller values of these
elements and also due to the smaller values of L
g
and L
d
for this device, C
gda
and C
gdi
cannot
be separated form C

= 8x250 μm

W
g
= 8x125 μm

W
g
= 2x50 μm
C
pga
(fF)
C
pgi
(fF)
C
gs
(fF)
233.5
39.6
1508.4
89.8
234.8
538.6
86.9
332.2
255.8
9.97
7.09
15.38

206.4
790.7
0.0
90.9
390.2
0.0
86.3
245
1.0
7.13
29.42
0.0
L
g
(pH)
L
d
(pH)
L
s
(pH)
122.3
110.9
3.6
81.9
75.4
5.7
57.3
54.5
5.6

0.0
0.1
0.0
0.0
0.0
0.0
0.0
0.0
G
m
(mS)
τ (ps)
G
ds
(mS)
0.0
0.0
0.34
0.0
3.3
0.0
0.0
0.0
0.26
0.0
0.0
0.0
G
gsf
(mS)


gsigsfi
gsgsf
iigs
CRjGR
CjG
YYY
1

12,11,





.(34)
By defining a new variable D as
gs
gs
gsf
gs
gs
C
C
G
Y
Y

)1(
]Im[


.(36)
R
i
can be determined from the plot of the real part of ωD versus ω
2
by linear fitting. G
gsf
can
be determined from the real part of Y
gs
at low frequencies (in the megahertz range). The
admittance for the intrinsic gate–drain branch Y
gd
is given by
gdgdgdfgd
gdgdf
igd
CRjGR
CjG
YY
1

12,

1
12,21,
.(38)
By redefining D as
2
22
2



















m

Y
Y
CjGD

 )( .(40)

0
5
10
15
20
25
-6
-4
-2
0
2
0
10
20
32
V
DS
(V)
V
GS
(V)
Fig. 6. Extracted R
gd
and C
ds
as a function of the extrinsic voltages for a GaN HEMT with a
2x50-μm gate width. © 2005 IEEE. Reprinted with permission. 0
5
10
15
20
25
-6
-4
-2
0
2
0
50
100
170
V
DS
(V)
V
GS

5
10
15
20
25
-6
-4
-2
0
2
0
10
20
32
V
DS
(V)
V
GS
(V)
G
m
(mS)
0
5
10
15
20
25
-6


Large-SignalModelingofGaNDevicesforDesigning
HighPowerAmpliersofNextGenerationWirelessCommunicationSystems 203

gsigsfi
gsgsf
iigs
CRjGR
CjG
YYY
1

12,11,




 .(34)
By defining a new variable D as
gs
gs
gsf
gs
gs
C
C
G



)1(
]Im[


.(36)
R
i
can be determined from the plot of the real part of ωD versus ω
2
by linear fitting. G
gsf
can
be determined from the real part of Y
gs
at low frequencies (in the megahertz range). The
admittance for the intrinsic gate–drain branch Y
gd
is given by
gdgdgdfgd
gdgdf
igd
CRjGR
CjG
YY
1



1
12,21,
.(38)
By redefining D as
2
22
2



















gsgsf
eG
Y
Y
CjGD

 )( .(40)

0
5
10
15
20
25
-6
-4
-2
0
2
0
10
20
32
V
DS
(V)
V

ds
(fF)Fig. 6. Extracted R
gd
and C
ds
as a function of the extrinsic voltages for a GaN HEMT with a
2x50-μm gate width. © 2005 IEEE. Reprinted with permission. 0
5
10
15
20
25
-6
-4
-2
0
2
0
50
100
170
V
DS
(V)

(fF)
0
5
10
15
20
25
-6
-4
-2
0
2
0
10
20
32
V
DS
(V)
V
GS
(V)
G
m
(mS)
0
5
10
15
20

as a function of the extrinsic voltages for a GaN HEMT
with a 2x50-μm gate width. © 2005 IEEE. Reprinted with permission.

MobileandWirelessCommunications:Networklayerandcircuitleveldesign204

0
5
10
15
20
25
-6
-4
-2
0
2
0
10
20
V
DS
(V)
V
GS
(V)
R
i
(

)

-2
0
2
0
50
100
V
DS
(V)
V
GS
(V)
G
gsf
(mS)
0
5
10
15
20
25
-6
-4
-2
0
2
0
20
40
V

(41)
C
ds
can be extracted from the plot of the imaginary part of Y
ds
versus ω by linear fitting. Due
to the frequency-dependent effect in the output conductance G
ds
, its value is determined
from the curve of ωRe[Y
ds
] versus ω by linear fitting.

Figs. 6-8 present extracted intrinsic parameters for GaN HEMT using the proposed
procedure under different extrinsic bias voltages. The extraction results show the typical
expected characteristics of GaN HEMT. The reliability of the extraction results was
demonstrated in (Jarndal & Kompa, 2005) in terms of the reverse modeling of the effective
gate length for the same analysed devices. The accuracy of the proposed small signal
modeling approach is verified through S-parameter simulation for different device sizes
under different bias conditions. As it can be seen in Figs. 9 and 10, the model can simulate
the S-parameter accurately. Also it can predict the kink effect in S
22
, which occurs in larger
size FETs (Lu et al., 2001). 0.2
0.4
0.6
0.8

DS
= 25.0 V
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300
150
330
180
0
S
11

S
22

-5xS
12

2xS
21

3
0
2
10
60
240
90
270
120
300
50
33
0
0.1xS
21

10xS
12

S
22

S
11

S
22

0.2
0.4

= 1.0 V, V
DS
= 5.0 VFig. 10. Comparison of measured S-parameters of a 16x250-μm GaN HEMT (circles) with
simulation results (lines) at (V
GS
= -2, V
DS
= 21 V) and (V
GS
= 1 V, V
DS
= 5 V). © 2006 IEEE.
Reprinted with permission.

4. Large-signal modeling

Under RF large-signal operation, the values of the intrinsic-elements of the GaN HEMT
model in Figure 2 vary with time and become dependent on the terminal voltages. Therefore
the intrinsic part of this model can be described by the equivalent-circuit model shown in
Figure 11. In this circuit, two quasi-static gate-current sources I
gs
and I
gd
and two quasi-static
gate-charge sources Q
gs
and Q

25
-6
-4
-2
0
2
0
10
20
V
DS
(V)
V
GS
(V)
R
i
(

)
0
5
10
15
20
25
-6
-4
-2
0

GS
(V)
G
gsf
(mS)
0
5
10
15
20
25
-6
-4
-2
0
2
0
20
40
V
DS
(V)
V
GS
(V)
G
gdf
(mS)
from the curve of ωRe[Y
ds
] versus ω by linear fitting.

Figs. 6-8 present extracted intrinsic parameters for GaN HEMT using the proposed
procedure under different extrinsic bias voltages. The extraction results show the typical
expected characteristics of GaN HEMT. The reliability of the extraction results was
demonstrated in (Jarndal & Kompa, 2005) in terms of the reverse modeling of the effective
gate length for the same analysed devices. The accuracy of the proposed small signal
modeling approach is verified through S-parameter simulation for different device sizes
under different bias conditions. As it can be seen in Figs. 9 and 10, the model can simulate
the S-parameter accurately. Also it can predict the kink effect in S
22
, which occurs in larger
size FETs (Lu et al., 2001). 0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120
300

60
240
90
270
120
300
150
330
180
0
S
11

S
22

-5xS
12

2xS
21

Frequency from 0.5 to 20 GHz
V
GS
= 1.0 V, V
DS
= 3.0 V

Fig. 9. Comparison of measured S-parameters of a 8x125-μm GaN HEMT (circles) with

50
33
0
0.1xS
21

10xS
12

S
22

S
11

S
22

0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
120

= 21 V) and (V
GS
= 1 V, V
DS
= 5 V). © 2006 IEEE.
Reprinted with permission.

4. Large-signal modeling

Under RF large-signal operation, the values of the intrinsic-elements of the GaN HEMT
model in Figure 2 vary with time and become dependent on the terminal voltages. Therefore
the intrinsic part of this model can be described by the equivalent-circuit model shown in
Figure 11. In this circuit, two quasi-static gate-current sources I
gs
and I
gd
and two quasi-static
gate-charge sources Q
gs
and Q
gd
are used to describe the conduction and displacement
currents. The nonquasi-static effect in the channel charge is approximately modeled with
two bias-dependent resistors R
i
and R
gd
in series with Q
gs
and Q

C
DT
, respectively.

V
gs
V
ds
g
d
s
s
+
+
Q V V
gs gs ds
( , )
I V V
gs gs ds
( , )
Q V V
gd gs ds
( , )
I V V
gd gs ds
( , )
R V V
i
( , )
gs ds

th
C
th
R = 1
th

V
ds
ds
I

Fig. 11. Large-signal model for GaN HEMT including self-heating and trapping effects.

This implementation makes the equivalent circuit more physically meaningful; moreover, it
improves the model accuracy for describing the low-frequency dispersion, as shown in
Figure 12. This figure shows simulated frequency dispersion of the channel
transconductance and output conductance, which is related mainly to the surface and buffer
traps. The values of R
GT
, R
DT
, C
GT
, and C
DT
are chosen to result in trapping time constants on
the order of 10
−5
− 10
−4

1.30
Frequency (Hz)
Normalized Gds
Normalized Gm

Fig. 12. Simulated normalized transconductance and output conductance for a 8x125-μm
GaN HEMT at V
DS
= 24 V and V
GS
= -2 V.

4.1. Gate charge and current modeling
The intrinsic elements are extracted as a function of the extrinsic voltages V
GS
and V
DS
as
presented in Figs. 6-8 for 2x50-µm GaN HEMT. To determine the intrinsic charge and
current sources of the large-signal model by integration, a correction has to be carried out
that considers the voltage drop across the extrinsic resistances. Therefore, the intrinsic
voltages can be calculated as


gssdssdDSds
IRIRRVV





and conductances satisfy the integration path-independence rule (Root et al., 1991). Thus,
the gate charges can be determined by integrating the intrinsic capacitances C
gs
, C
gd
, and C
ds

as follows (Schmale & Kompa, 1997):



ds
ds
gs
gs
V
V
gsds
V
V
dsgsdsgsgs
dVVVCdVVVCVVQ
00
),( ),(),(
0
(44)

ds
g
d
s
s
+
+
Q V V
gs gs ds
( , )
I V V
gs gs ds
( , )
Q V V
gd gs ds
( , )
I V V
gd gs ds
( , )
R V V
i
( , )
gs ds
R V V
gs
( , )
gs ds
I V V
ds gs ds
( , )

ds
ds
I

Fig. 11. Large-signal model for GaN HEMT including self-heating and trapping effects.

This implementation makes the equivalent circuit more physically meaningful; moreover, it
improves the model accuracy for describing the low-frequency dispersion, as shown in
Figure 12. This figure shows simulated frequency dispersion of the channel
transconductance and output conductance, which is related mainly to the surface and buffer
traps. The values of R
GT
, R
DT
, C
GT
, and C
DT
are chosen to result in trapping time constants on
the order of 10
−5
− 10
−4
s (Meneghesso et al., 2001). In the current model, the amount of self-
heating-induced current dispersion is controlled by normalized channel temperature rise
ΔT. The normalized temperature rise is the channel temperature divided by the device
thermal resistance R
th
. A low-pass circuit is added to determine the value of ΔT due to the
static and quasi-static dissipated power. The value of the thermal capacitance C

DS
= 24 V and V
GS
= -2 V.

4.1. Gate charge and current modeling
The intrinsic elements are extracted as a function of the extrinsic voltages V
GS
and V
DS
as
presented in Figs. 6-8 for 2x50-µm GaN HEMT. To determine the intrinsic charge and
current sources of the large-signal model by integration, a correction has to be carried out
that considers the voltage drop across the extrinsic resistances. Therefore, the intrinsic
voltages can be calculated as


gssdssdDSds
IRIRRVV 



dssgssgGSgs
IRIRRVV  .

(42)

(43)
This implies that the values of the intrinsic voltages V
gs

V
V
gsds
V
V
dsgsdsgsgs
dVVVCdVVVCVVQ
00
),( ),(),(
0
(44)

MobileandWirelessCommunications:Networklayerandcircuitleveldesign208





ds
ds
gs
gs
V
V

gd
are
determined by the integration of the intrinsic gate conductances G
gfs
and G
gdf
as follows:
dVVVGVVIVVI
gs
gs
V
V
dsgsfdsgsgsdsgsgs
),(),(),(
0
000







ds
ds
gs
gs
V
V
gsgdf

10
15
20
-6
-4
-2
0
2
0
3
6
9
V
ds
(V)
V
gs
(V)
Q
gs
(pC)

0
5
10
15
20
-6
-4
-2

20
-6
-4
-2
0
2
0
7
14
21
V
ds
(V)
V
gs
(V)
I
gs
(mA)
0
5
10
15
20
-6
-4
-2
0
2
-1

independence rule (Wei et al., 1999). Therefore, the RF drain current cannot be derived by
relying on conventional S-parameter measurements. In addition, the self-heating and
trapping cannot be characterized separately by these measurements to get an accurate
current model. The optimal method is to derive the current model from pulsed I–V
measurements under appropriate quiescent bias conditions, as presented in (Jarndal
b
et al.,
2006). The drain current is modeled as (Filicori et al., 1995)
dissdsgsT
dsodsdsgsD
gsogsdsgsG
dsgs
DC
isodsdissgsodsogsdsds
PVV
VVVV
VVVV
VVIPVVVVI
),(
))(,(
))(,(
),(),,,,(
,








− V
gso
)
and (V
ds
− V
dso
) in (48). The self-heating-induced dispersion is caused mainly by the low-
frequency components of the drain signal. Therefore, P
diss
in (48) accounts for the static and
quasistatic intrinsic power dissipation.

A. Trapping and self-heating characterization

Trapping effects can be characterized by pulsed I–V measurements at negligible device self-
heating (Charbonniaud et al., 2003). The surface trapping is characterized by pulsed I–V’s at
two extrinsic quiescent biases equivalent to:
Large-SignalModelingofGaNDevicesforDesigning
HighPowerAmpliersofNextGenerationWirelessCommunicationSystems 209





ds
ds
gs
gs
V

and I
gd
are
determined by the integration of the intrinsic gate conductances G
gfs
and G
gdf
as follows:
dVVVGVVIVVI
gs
gs
V
V
dsgsfdsgsgsdsgsgs
),(),(),(
0
000







ds
ds
gs
gs
V
V

5
10
15
20
-6
-4
-2
0
2
0
3
6
9
V
ds
(V)
V
gs
(V)
Q
gs
(pC)

0
5
10
15
20
-6
-4

15
20
-6
-4
-2
0
2
0
7
14
21
V
ds
(V)
V
gs
(V)
I
gs
(mA)
0
5
10
15
20
-6
-4
-2
0
2

) do not satisfy the integration path-
independence rule (Wei et al., 1999). Therefore, the RF drain current cannot be derived by
relying on conventional S-parameter measurements. In addition, the self-heating and
trapping cannot be characterized separately by these measurements to get an accurate
current model. The optimal method is to derive the current model from pulsed I–V
measurements under appropriate quiescent bias conditions, as presented in (Jarndal
b
et al.,
2006). The drain current is modeled as (Filicori et al., 1995)
dissdsgsT
dsodsdsgsD
gsogsdsgsG
dsgs
DC
isodsdissgsodsogsdsds
PVV
VVVV
VVVV
VVIPVVVVI
),(
))(,(
))(,(
),(),,,,(
,







gs
− V
gso
)
and (V
ds
− V
dso
) in (48). The self-heating-induced dispersion is caused mainly by the low-
frequency components of the drain signal. Therefore, P
diss
in (48) accounts for the static and
quasistatic intrinsic power dissipation.

A. Trapping and self-heating characterization

Trapping effects can be characterized by pulsed I–V measurements at negligible device self-
heating (Charbonniaud et al., 2003). The surface trapping is characterized by pulsed I–V’s at
two extrinsic quiescent biases equivalent to:
MobileandWirelessCommunications:Networklayerandcircuitleveldesign210

V
GSO
< V
P
, V
DSO
= 0 V (P
diss
≈ 0)

characterization (Jarndal
b
et al., 2006).

B. Drain–current-model parameter extraction

0
5
10
15
21
-7
-6
-5
-4
-3
-2
-1
0
-0.015
-0.01
-0.005
0
V
gs
(V) V
ds
(V)




D

Fig. 15. Bias-dependent trapping fitting parameters of the drain–current model in (48)
extracted from the pulsed I–V measurements of a 8x125-μm GaN HEMT. © 2007 IEEE.
Reprinted with permission.

The drain–current-model equation in (48) has four unknowns: I
DC
ds,iso
, α
G
, α
D
, and α
T
. To
determine these unknowns, the equation should be applied to, at least, four pulsed I–V
characteristics at suitable quiescent bias conditions that lead to four highly independent
linear equations. The described I–V characteristics in Section 4.2-A define approximately
four independent states for the drain current. At each state, the drain current can be
assumed to be affected by, at most, one of the dispersion sources (surface trapping, buffer
trapping, or self-heating). By solving the four linear equations, corresponding to the four
characteristics, at each bias point, the values of I
DC
ds,iso
, α
G
, α
D

T

0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
1.2
1.4
V
ds
(V)
I
ds,iso
DC
(A)
V
gs
from -7 V to 1 V in step of 0.5 V

(a) (b)
Fig. 16. (a) Extracted bias-dependent self-heating fitting parameter and (b) isothermal dc
drain current for a 8x125-μm GaN HEMT. © 2007 IEEE. Reprinted with permission.

4.3 Large-signal model implementation and verification
The large-signal model was implemented as a table-based model in ADS. The extrinsic bias-
independent passive elements are represented by lumped elements, whereas the intrinsic
nonlinear part is represented by a symbolically defined device (SDD) component.

DS
= 21.0 V.
Large-SignalModelingofGaNDevicesforDesigning
HighPowerAmpliersofNextGenerationWirelessCommunicationSystems 211

V
GSO
< V
P
, V
DSO
= 0 V (P
diss
≈ 0)
V
GSO
= 0 V, V
DSO
= 0 V (P
diss
≈ 0).
The buffer trapping is characterized by pulsed I–V ’s at two quiescent biases equivalent to:
V
GSO
< V
P
, V
DSO
= 0 V (P
diss

-2
-1
0
-0.015
-0.01
-0.005
0
V
gs
(V) V
ds
(V)


G

0
5
10
15
21
-7
-6
-5
-4
-3
-2
-1
0
1

. To
determine these unknowns, the equation should be applied to, at least, four pulsed I–V
characteristics at suitable quiescent bias conditions that lead to four highly independent
linear equations. The described I–V characteristics in Section 4.2-A define approximately
four independent states for the drain current. At each state, the drain current can be
assumed to be affected by, at most, one of the dispersion sources (surface trapping, buffer
trapping, or self-heating). By solving the four linear equations, corresponding to the four
characteristics, at each bias point, the values of I
DC
ds,iso
, α
G
, α
D
, and α
T
can be determined. Figs.
15 and 16 show the extracted values of these fitting parameters as a function of the intrinsic
voltages.

0
5
10
15
21
-7
-6
-5
-4
-3

DC
(A)
V
gs
from -7 V to 1 V in step of 0.5 V

(a) (b)
Fig. 16. (a) Extracted bias-dependent self-heating fitting parameter and (b) isothermal dc
drain current for a 8x125-μm GaN HEMT. © 2007 IEEE. Reprinted with permission.

4.3 Large-signal model implementation and verification
The large-signal model was implemented as a table-based model in ADS. The extrinsic bias-
independent passive elements are represented by lumped elements, whereas the intrinsic
nonlinear part is represented by a symbolically defined device (SDD) component.

freq (150.0MHz to 20.00GHz)
S22
S11

freq (500.0MHz to 20.00GHz)
S22
S11

-15 -10 -5 0 5 10 15
-
20 20
freq (150.0MHz to 20.00GHz)
40xS12
S21


GSO
= -2.7 V, V
DSO
= 12 V
5 10 15 200 25
0.0
0.2
0.4
0.6
0.8
1.0
-0.2
1.2
I
D
S
(
A
)
V
DS
(V)
V
GS
from –7 V to 1 V, Step 1 V

5 10 15 200 25
0.0
0.2
0.4

0.4
0.0
0.5
-0.06
-0.04
-0.02
-0.00
0.02
0.04
-0.08
0.06
Time (ns)
Ids (A)
Igs (A)
I
gs
I
ds
0.2 0.4 0.6 0.80.0 1.0
0.1
0.2
0.3
0.4
0.0
0.5
-0.06
-0.04
-0.02
-0.00
0.02

0.2 0.4 0.6 0.80.0 1.0
15
20
25
30
35
10
40
-6
-4
-2
-8
0
Time (ns)
Vds (V)
Vgs (V)
V
V
gs
ds

Fig. 19 (Lines) Simulated and (symbols) measured large-signal waveforms for class-AB-
operated 8x125-μm GaN HEMT at 16-dBm input power. © 2006 IEEE. Reprinted with
permission.

The very good agreement between simulation and measurement shows the ability of the
model for describing the bias dependence of the trapping and self-heating effects. In

addition, these simulations verify the convergence behaviour of the model response under
pulsed stimulation, which is very important for digital applications. Large-signal waveform

ou
t
-
f
un
d

(dB
m
)
,
G
a
i
n
(dB)

Gain
P
out

Fig. 20. (Lines) Single-tone power-sweep simulations compared with (symbols)
measurements for class-A-operated 8x125-μm GaN HEMT at 2 GHz in a 50-Ω source and
load environment. © 2007 IEEE. Reprinted with permission.

Figure 20 shows a simulation result of a single-tone input-power sweep for a 8×125-μm GaN
HEMT. The model shows very good results with respect to the fundamental output power
and gain even for input-power levels beyond the 1-dB gain-compression point. The model
also shows good simulation results for the output power of higher harmonic components up
to the third harmonic.


(dB
m
)
,
G
a
i
n
(dB)
P
out
Gain

Fig. 21. (Lines) Simulated and (symbols) measured Pout, Gain and IMD3 versus input
power per tone under two-tone excitation centered at 2 GHz and separated by 100 kHz for
class-AB-operated 8x125-μm GaN HEMT in a 50-Ω source and load environment. © 2007
IEEE. Reprinted with permission.

Large-SignalModelingofGaNDevicesforDesigning
HighPowerAmpliersofNextGenerationWirelessCommunicationSystems 213

The developed large-signal model was verified by independent measurements. The
considered devices are 8×125-μm GaN HEMTs on different wafers. First, the model is
checked whether it is consistent with I–V and S-parameter measurements it has been
derived from. Second, large-signal single- and two-tone simulations are compared with
measurements. S-parameter simulation in comparison with measurement of a 8×125-μm
device is shown in Figure 17. The good agreement between simulation and measurement
verifies the consistency of the large-signal model with the small-signal equivalent-circuit
model. Pulsed I–V simulation has been done at quiescent bias conditions different than the

5 10 15 200 25
0.0
0.2
0.4
0.6
0.8
1.0
-0.2
1.2
I
D
S
(
A
)
V
DS
(V)
V
GSO
= -3.2 V, V
DSO
= 25 V
V
GS
from –7 V to 1 V, Step 1 V

Fig. 18 (Lines) Pulsed I–V simulations and (circles) measurements for a 8x125-μm GaN
HEMT at different quiescent bias conditions. © 2006 IEEE. Reprinted with permission.


-0.04
-0.02
-0.00
0.02
0.04
-0.08
0.06
Time (ns)
Ids (A)
Igs (A)
I
gs
I
ds
0.2 0.4 0.6 0.80.0 1.0
15
20
25
30
35
10
40
-6
-4
-2
-8
0
Time (ns)
Vds (V)
Vgs (V)

model for describing the bias dependence of the trapping and self-heating effects. In

addition, these simulations verify the convergence behaviour of the model response under
pulsed stimulation, which is very important for digital applications. Large-signal waveform
measurements for 8×125-μm GaN HEMTs were done using the measurement setup
described in (Raay & Kompa, 1997) and then simulated by the model. As it can be seen in
Figure 19, very good agreement between measured and simulated current and voltage
waveforms is obtained. This can be related to the improved construction of the model
elements using the spline-approximation technique, as explained in Section 4.1, which
improves the modeling of the higher order harmonics.

11 13 15 17 199 21
-20
0
20
-40
40
Pin (dBm)
Pout (dBm)
2f
o
3f
o
f
o
11 13 15 17 199 21
15
20
25
30

HEMT. The model shows very good results with respect to the fundamental output power
and gain even for input-power levels beyond the 1-dB gain-compression point. The model
also shows good simulation results for the output power of higher harmonic components up
to the third harmonic.

3 5 7 9 11 13 15 17 191 21
-25
-15
-5
5
15
-35
25
Pin (dBm)
IMD3L

(dB
m
)
3 5 7 9 11 13 15 17 191 21
15
20
25
30
10
35
Pin (dBm)
P
ou
t

measurements. The model shows very good results for describing the output power and
gain except at high-power end. The inaccuracy is due to the extrapolation error outside the
region of measurements where the model was derived from. The model accuracy can be
improved by increasing the range of these measurements to cover higher voltage conditions.
The model also shows very good simulation for the third-order IMD. This can also be
related to the use of spline approximation for the construction of the model-element data.

0 2 4 6 8 10 12 14 16 18-2 20
-30
-20
-10
0
10
-40
20
Pin (dBm)
IMD3L (dBm)
Class A (40%I )
Class AB (5%I )
Class C (V < V )
DSS
DSS
GS
P
0 2 4 6 8 10 12 14 16 18-2 20
20
30
40
10
50

Detailed procedures for both small-signal and large-signal model parameter extraction has
been presented. The extracted intrinsic gate capacitances and conductances of distributed
small-signal model were integrated to find the gate charge and current sources of the large-
signal model, assuming that these elements satisfy the integral path-independence

condition. Pulsed I–V measurements under appropriate quiescent bias conditions were used
to accurately characterize and model the drain current and the inherent self-heating and
trapping effects. It is found that using approximation technique for the construction of the
large-signal-model database can improve the model capability for harmonics and IMD
simulations. Large-signal simulations show that the model can accurately describe the
performance of the device under constant external temperature. However, this model can
also be extended to consider the variation of the ambient temperature.

6. References

Ambacher, O.; Smart, J.; Shealy, J.; Weimann, N.; Chu, K.; Murphy, M.; Schaff, W.; Eastman,
L.; Dimitrov, R.; Wittmer, L.; Stutzman, M.; Rieger, W. and Hilsenbeck, J. (1999).
Two-dimensional electron gases induced by spontaneous and piezoelectric
polarization in undoped and doped AlGaN/GaN heterostructures. Journal of
Applied Physics, Vol. 85, (March 1999) page numbers (3222-3232), ISSN 0021-8979.
Ahmed, A.; Srinidhi, E. & Kompa, G. (2005). Efficient PA modeling using neural network
and measurement set-up for memory effect characterization in the power device,
WE1D-5, ISBN 0-7803-8845-3, Proceeding of International Microwave Symposium
Digest, USA, June 2005, Long Beach.
Cabral, P.; Pedro, J. & Carvalho, N. (2004). Nonlinear device model of microwave power
GaN HEMTs for high power amplifier design. IEEE Transaction Microwave Theory
and Techniques, Vol. 52, (November 2004) page numbers (2585-2592), ISSN 0018-
9480.
Cuoco, V.; Van den Heijden, M. & De Vreede, L. (2002). The ‘smoothie’ data base model for
the correct modeling of non-linear distortion in FET devices, Proceeding of

region of measurements where the model was derived from. The model accuracy can be
improved by increasing the range of these measurements to cover higher voltage conditions.
The model also shows very good simulation for the third-order IMD. This can also be
related to the use of spline approximation for the construction of the model-element data.

0 2 4 6 8 10 12 14 16 18-2 20
-30
-20
-10
0
10
-40
20
Pin (dBm)
IMD3L (dBm)
Class A (40%I )
Class AB (5%I )
Class C (V < V )
DSS
DSS
GS
P
0 2 4 6 8 10 12 14 16 18-2 20
20
30
40
10
50
Pin (dBm)
IMR (dB)

small-signal model were integrated to find the gate charge and current sources of the large-
signal model, assuming that these elements satisfy the integral path-independence

condition. Pulsed I–V measurements under appropriate quiescent bias conditions were used
to accurately characterize and model the drain current and the inherent self-heating and
trapping effects. It is found that using approximation technique for the construction of the
large-signal-model database can improve the model capability for harmonics and IMD
simulations. Large-signal simulations show that the model can accurately describe the
performance of the device under constant external temperature. However, this model can
also be extended to consider the variation of the ambient temperature.

6. References

Ambacher, O.; Smart, J.; Shealy, J.; Weimann, N.; Chu, K.; Murphy, M.; Schaff, W.; Eastman,
L.; Dimitrov, R.; Wittmer, L.; Stutzman, M.; Rieger, W. and Hilsenbeck, J. (1999).
Two-dimensional electron gases induced by spontaneous and piezoelectric
polarization in undoped and doped AlGaN/GaN heterostructures. Journal of
Applied Physics, Vol. 85, (March 1999) page numbers (3222-3232), ISSN 0021-8979.
Ahmed, A.; Srinidhi, E. & Kompa, G. (2005). Efficient PA modeling using neural network
and measurement set-up for memory effect characterization in the power device,
WE1D-5, ISBN 0-7803-8845-3, Proceeding of International Microwave Symposium
Digest, USA, June 2005, Long Beach.
Cabral, P.; Pedro, J. & Carvalho, N. (2004). Nonlinear device model of microwave power
GaN HEMTs for high power amplifier design. IEEE Transaction Microwave Theory
and Techniques, Vol. 52, (November 2004) page numbers (2585-2592), ISSN 0018-
9480.
Cuoco, V.; Van den Heijden, M. & De Vreede, L. (2002). The ‘smoothie’ data base model for
the correct modeling of non-linear distortion in FET devices, Proceeding of
International Microwave Symposium Digest, pp. 2149–2152, ISBN 0-7803-7239-5, USA,
February 2002, IEEE, Seattle.

U.; Narayanamurti, V.; DenBaars, S.; and Speck, J. (1998). Scanning capacitance
microscopy imaging of threading dislocations in GaN films grown on (0001)
sapphire by metalorganic chemical vapor deposition. Applied Physics Letters, Vol.
72, (May 1998) page numbers (2247–2249), ISSN 0003-6951.
Jarndal, A. & Kompa, G. (2005). A new small-signal modeling approach applied to GaN
devices. IEEE Transaction Microwave Theory and Techniques, Vol. 53, (November
2005), page numbers (3440–3448), ISSN 0018-9480.
Jarndal
a
, A. & Kompa, G. (2006). An accurate small-signal model for AlGaN-GaN HEMT
suitable for scalable large-signal model construction. IEEE Microwave and Wireless
Components Letters, Vol. 16, (June 2006) page numbers (333–335), ISSN 1531-1309.
Jarndal
b
, A.; Bunz, B. & Kompa, G. (2006). Accurate large-signal modeling of AlGaN-GaN
HEMT including trapping and self-heating induced dispersion, Proceeding IEEE
International Symposium Power Semiconductor Devices and ICs, pp. 1–4, ISBN 0-7803-
9714-2, Italy, June 2006, Napoli.
Jarndal, A. & Kompa, G. (2007). Large-Signal Model for AlGaN/GaN HEMT Accurately
Predicts Trapping and Self-Heating Induced Dispersion and Intermodulation
Distortion. IEEE Transaction Microwave Theory and Techniques, Vol. 54, (November
2007) page numbers (2830-2836), ISSN 0018-9480.
Kohn, E.; Daumiller, I.; Kunze, M.; Neuburger, M.; Seyboth, M.; Jenkins, T.; Sewell, J.;
Norstand, J.; Smorchkova, Y. & Mishra, U. (2003). Transient characteristics of GaN-
based heterostructure field-effect transistors. IEEE Transaction Microwave Theory and
Techniques, Vol. 51, (Februry 2003) page numbers (634–642), ISSN 0018-9480.
Koh, K.; Park, H M. & Hong, S. (2002). A spline large-signal FET model based on bias-
dependent pulsed I–V measurements. IEEE Transaction Microwave Theory and
Techniques, Vol. 50 (November 2002) page numbers (2598–2603), ISSN 0018-9480.
Kotzebue, K. (1976). Maximally Efficient Gain: A Figure of Merit for Linear Active 2-Ports.

transistor scattering parameter S
22
. IEEE Transaction Microwave Theory and
Techniques, Vol. 49, (February 2001) page numbers (333 - 340), ISSN 0018-9480.
Meneghesso, G.; Verzellesi, G. ; Pierobon, R. ; Rampazzo, F.; Chini, A.; Mishra, U.; Canali, C.
& Zanoni, E. (2004). Surface-related drain current dispersion effects in AlGaN-GaN
HEMTs. IEEE Transaction Microwave Theory and Techniques, Vol. 51, (October 2004)
page numbers (1554-1561), ISSN 0018-9480.
Root, D.; Fan, S. & Meyer, J. (1991). Technology Independent Large Signal Non Quasi-Static
FET Models by Direct Construction from Automatically Characterized Device Data,
Proceeding of European Microwave Conference, pp. 927 – 932, EUMA.1991.336465,
Germany, October 1991, IEEE, Stuttgart.
Raay, F.; Quay, R.; Kiefer, R.; Schlechtweg, M. & Weimann, G. (2003). Large signal modeling
of GaN HEMTs with Psat > 4 W/mm at 30 GHz suitable for broadband power
applications, Proceeding of International Microwave Symposium Digest, USA, PA, pp.
451-454, ISBN 0-7803-7695-1, June 2003, IEEE, Philadelphia.
Schmale, I. & Kompa, G. (1997). A physics-based non-linear FET model including dispersion
and high gate-forward currents, Proceeding of International Workshop on
Experimentally Based FET Device Modelling and Related Nonlinear Circuit Design, pp.
27.1-27.7, Report Number: A864133, University of Kassel, Germany, July 1997,
IEEE, Kassel.
Schmale, I. & Kompa, G. (1997). An improved physics-based nonquasistatic FET-model,
Proceeding of European Microwave Conference, pp. 328–330, ISBN 0-7803-4202-X,
Jerusalem, September 1997, IEEE, Israel.
System Manual HP8510B Network Analyzer (1987). HP Company, P/N 08510-90074, USA,
Santa Rosa, July 1987.
Vetury, R; Zhang, N; Keller, S. & Mishra, U. (2001). The impact of surface states on the DC
and RF characteristics of GaN HFETs. IEEE Transaction on Electron Devices, Vol. 48,
(March 2001) page numbers (560-566), ISSN 0018-9383.
Van Raay, F. & Kompa, G. (1997). Combination of waveform and load-pull measurements,

, A.; Bunz, B. & Kompa, G. (2006). Accurate large-signal modeling of AlGaN-GaN
HEMT including trapping and self-heating induced dispersion, Proceeding IEEE
International Symposium Power Semiconductor Devices and ICs, pp. 1–4, ISBN 0-7803-
9714-2, Italy, June 2006, Napoli.
Jarndal, A. & Kompa, G. (2007). Large-Signal Model for AlGaN/GaN HEMT Accurately
Predicts Trapping and Self-Heating Induced Dispersion and Intermodulation
Distortion. IEEE Transaction Microwave Theory and Techniques, Vol. 54, (November
2007) page numbers (2830-2836), ISSN 0018-9480.
Kohn, E.; Daumiller, I.; Kunze, M.; Neuburger, M.; Seyboth, M.; Jenkins, T.; Sewell, J.;
Norstand, J.; Smorchkova, Y. & Mishra, U. (2003). Transient characteristics of GaN-
based heterostructure field-effect transistors. IEEE Transaction Microwave Theory and
Techniques, Vol. 51, (Februry 2003) page numbers (634–642), ISSN 0018-9480.
Koh, K.; Park, H M. & Hong, S. (2002). A spline large-signal FET model based on bias-
dependent pulsed I–V measurements. IEEE Transaction Microwave Theory and
Techniques, Vol. 50 (November 2002) page numbers (2598–2603), ISSN 0018-9480.
Kotzebue, K. (1976). Maximally Efficient Gain: A Figure of Merit for Linear Active 2-Ports.
Electronics Letters, Vol. 12, (September 1976) page numbers (490-491), ISSN 0013-
5194.
Kompa, G. & Novotny, M. (1997). Frequency-dependent measurement error analysis and
refined FET model parameter extraction including bias-dependent series resistors,
Proceeding of International IEEE Workshop on Experimentally Based FET Device
Modelling and Related Nonlinear Circuit Design, pp. 6.1–6.16, Report Number:
A864133, University of Kassel, Germany, July 1997, IEEE, Kassel.
Lossy
a
, R.; Chaturvedi, N.; Heymann, P.; Würfl, J.; Müller, S.; and Köhler, K. (2002). Large
area AlGaN/GaN HEMTs grown on insulating silicon carbide substrates. Physica
Status Solidi (a), Vol. 194, (December 2002) page numbers (460–463), ISSN 0031-8965.

Lossy, R.; Hilsenbeck, J.; Würfl, J. and Obloh, H. (2001). Uniformity and scalability of

applications, Proceeding of International Microwave Symposium Digest, USA, PA, pp.
451-454, ISBN 0-7803-7695-1, June 2003, IEEE, Philadelphia.
Schmale, I. & Kompa, G. (1997). A physics-based non-linear FET model including dispersion
and high gate-forward currents, Proceeding of International Workshop on
Experimentally Based FET Device Modelling and Related Nonlinear Circuit Design, pp.
27.1-27.7, Report Number: A864133, University of Kassel, Germany, July 1997,
IEEE, Kassel.
Schmale, I. & Kompa, G. (1997). An improved physics-based nonquasistatic FET-model,
Proceeding of European Microwave Conference, pp. 328–330, ISBN 0-7803-4202-X,
Jerusalem, September 1997, IEEE, Israel.
System Manual HP8510B Network Analyzer (1987). HP Company, P/N 08510-90074, USA,
Santa Rosa, July 1987.
Vetury, R; Zhang, N; Keller, S. & Mishra, U. (2001). The impact of surface states on the DC
and RF characteristics of GaN HFETs. IEEE Transaction on Electron Devices, Vol. 48,
(March 2001) page numbers (560-566), ISSN 0018-9383.
Van Raay, F. & Kompa, G. (1997). Combination of waveform and load-pull measurements,
Proceeding of International IEEE Workshop on Experimentally Based FET Device
Modelling and Related Nonlinear Circuit Design, pp. 10.1-10.11, Report Number:
A864133, University of Kassel, Germany, July 1997, IEEE, Kassel.
MobileandWirelessCommunications:Networklayerandcircuitleveldesign218

Wei, C.; Tkachenko, Y. & Bartle, D. (1999). Table-based dynamic FET model assembled from
small-signal models. IEEE Transaction Microwave Theory and Techniques, Vol. 47,
(June 1999) page numbers (700–705), ISSN 0018-9480.
PolyphaseFilterDesignMethodologyforWirelesscommunicationApplications 219
Polyphase Filter Design Methodology for Wireless communication
Applications
FayrouzHaddad,LakhdarZaïd,WenceslassRahajandraibeandOussamaFrioui
X


with the local oscillator (LO) signal. The IF is defined as
f
IF
=|f
RF
-f
LO
|

(1)
However, this frequency translation provides a serious problem of frequency image
rejection (Razavi (a), 1997). Hence, classical wireless receiver architectures have been
commonly implemented using the superheterodyne topology, in which the image
suppression is done by off-chip devices such as discrete components, ceramic or surface
acoustic wave (SAW) filters (Razavi, 1996; Samavati et al, 2000; Macedo & Copeland, 1998).
They have high quality factor and good linearity; however, their high cost and their non
11
MobileandWirelessCommunications:Networklayerandcircuitleveldesign220

integration make them less attractive to be used in the emerging integrated receivers (Razavi
(a), 1997; Huang et al, 1999).
To overcome this drawback, zero-IF receiver architectures, in which the RF signal is
transposed directly to baseband, have been proposed (Razavi (b), 1997; Behzad et al, 2003).
Since the LO is at the same frequency as the RF input, this architecture removes the IF and
the image rejection problem, which arises differently in the receiver chain and results from
mismatches between the I (in-phase) and Q (quadrature) paths as well as amplitude
mismatches. Although the direct conversion performs well image rejection, this architecture
suffers from flicker noise, DC offsets and self-mixing at the inputs of the mixers, resulting in
filter saturation and distortion.
To understand how the problem of frequency image arises, consider the process of down-

Fig. 1. Image rejection problem in RF receivers

An important specification to determine the performance of a receiver and to quantify its
degree of image rejection is the image rejection ratio defined as the ratio of the magnitude in
the attenuation band to that in the passband and can be given by
ܫܴܴൌ
ܦ݁ݏ݅ݎ݈݁݀ܵ݅݃݊ܽܮ݁ݒ݈݁
ܫ݉ܽ݃݁݈ܵ݅݃݊ܽܮ݁ݒ݈݁

(2)
The IRR required to ensure signal integrity and suitable bit-error-rate (BER) varies
depending on the application. As an example, for short-range applications where low or
moderate selectivity is required, an image suppression of 45dB is adequate, but is far less
than that required in long-range heterodyne receivers. For example, DECT and DCS-1800
RF
f
LO
f
I
F
f
IF
Image wanted
signal
f
IF
=f
RF
-f
LO

Since the LO is at the same frequency as the RF input, this architecture removes the IF and
the image rejection problem, which arises differently in the receiver chain and results from
mismatches between the I (in-phase) and Q (quadrature) paths as well as amplitude
mismatches. Although the direct conversion performs well image rejection, this architecture
suffers from flicker noise, DC offsets and self-mixing at the inputs of the mixers, resulting in
filter saturation and distortion.
To understand how the problem of frequency image arises, consider the process of down-
conversion as represented in the Fig.1. When mixing the wanted signal band (at f
RF
) with the
LO, the obtained signal band is located at f
IF
. But, since a simple analog multiplication does
not preserve the polarity of the difference between the two mixed signals (i.e cos(ω
1
-
ω
2
)t=cos(ω
2
-ω
1
)t), the signal band at f
RF
-2f
IF
is also translated to the same IF after mixing with
the LO. The signal at f
RF
-2f

signal
f
IF
=f
RF
-f
LO
IF
LO
f
RF
Conversion without
Image-reject filter
RF
f
LO
f
I
F
f
IF
f
IF
IF
LO
Image-reject
Filter
Conversion with
Image-reject filter
f

The half-complex architecture is based on the use of image-reject mixers combined with
passive or active filters. As shown in Fig.2(a), a real RF signal is mixed with a LO complex
signal to feed the IF polyphase filter. The quality of the image rejection inside such an
architecture results mainly from three parameters: i) the balance between I and Q signals
(phase and magnitude error), ii) the adequate matching of mixers iii) the polyphase filter
performances.
There are two well-known architectures using such techniques: the Hartley and Weaver
architectures, depicted in Fig.3 (Razavi (b), 1996; Xu et al, 2001). Generally, the Weaver
topology is preferred to the Hartley architecture. In fact, the 90° phase shifter bloc (Fig.3(a))
comes with hard design constraints in terms of component matching which result to
significant phase error especially at high frequencies. For instance, a change of 20% in
resistors and capacitors (used to generate the quadrature), due to temperature and process
variations, gives an IRR of only 20dB (Maligeorgos & Long, 2000).

Polyphase
Filter
LO
I
Q
RF
IF
ADC
LNA
Band‐pass
Filter
Q
I
Polyphase
Filter
LO

ଶ
൅ʹ
ሺ
ͳ൅οܣ
ሻ
ሺ߮
ଵ
൅߮
ଶ
ሻ
ͳ൅
ሺ
ͳ൅οܣ
ሻ
ଶ
െʹ
ሺ
ͳ൅οܣ
ሻ
ሺ߮
ଵ
൅߮
ଶ
ሻ

(3)
where φ
1
and φ
2

Q
cos(ω
LO
t)
sin(ω
LO
t)
90°
BPF
BPF
+
-
RF IF
I
Q
cos(ω
LO1
t)
sin(ω
LO1
t)
cos(ω
LO2
t)
sin(ω
LO2
t)
0,0 0,2 0,4 0,6 0,8 1,0
20
25

ͳ൅οܣ
ሻ
ଶ
൅ʹ
ሺ
ͳ൅οܣ
ሻ
ሺ߮
ଵ
൅߮
ଶ
ሻ
ͳ൅
ሺ
ͳ൅οܣ
ሻ
ଶ
െʹ
ሺ
ͳ൅οܣ
ሻ
ሺ߮
ଵ
൅߮
ଶ
ሻ

(3)
where φ
1

RF IF
I
Q
cos(ω
LO
t)
sin(ω
LO
t)
90°
BPF
BPF
+
-
RF IF
I
Q
cos(ω
LO1
t)
sin(ω
LO1
t)
cos(ω
LO2
t)
sin(ω
LO2
t)
0,0 0,2 0,4 0,6 0,8 1,0

adaptive zero-forcing sign-sign feedback concept and does not require complicated digital
processing. This algorithm can detect and correct I/Q imbalance continuously, but it
alleviates the need for a high resolution ADC in the digital image rejection device.
Despite the difficulty to realize accurate phase shifters, (Chou & Lee, 2007) demonstrates
that this is not essential in the Weaver architecture. The image rejection is performed by
making the phase mismatch between I and Q signals of the first LO to be equal to that of the
second LO. Thus the design constraints on phase matching are relaxed, and more attention
can be placed on gain matching (Chou & Lee, 2007).
The full-complex architecture (also referred as double quadrature down-conversion)
requires the use of complex polyphase filters. The complex polyphase filters are suitable for
high frequency applications since they can meet the dynamic range and bandwidth
requirement in RF frequencies (Wu & Chou, 2004). In this case, a notch frequency located at
the image frequency is used to reject image signals rather than bandpass filtering. As shown
in Fig.2(b), the RF signal is complex filtered (RF polyphase filter), then the RF and LO
complex signals are multiplied together to feed the IF polyphase filter, to reach about 60dB
of image suppression (Behbahani et al, 2001). The interest of this structure comes from the
fact that the image rejection is supported in the RF domain by the RF polyphase filter and
the quadrature LO, which is advantageous compared to the half-complex architecture. Thus,
the design constraints in terms of image rejection are relaxed in the RF polyphase filter and
the LO compared to the IF polyphase filter.
Summary of performances of numerous image-reject architectures reported above is given
in table 1.

Technology

RF/IF (Hz)

IRR

IIP3


Power
consumption
(Crols &
Steyaert, 1995)
0.7µm
CMOS
900M /3M 46dB 27.9
dBm
24dB 500mW
(Wu & Razavi,
1998)
0.6µm
CMOS
900M / 400M 40dB -8 dBm 4.7dB 72mW
(Banu et al.,
1997)
0.5µm
BiCMOS
900M / 10.7M 50dB -4.5
dBm
4.8dB 60mW
(Lee et al., 1998)
0.8µm
CMOS
1G/ 100M 29dB 0.6 dBm 19dB 108mW
(Behbahani et
al., 1999)
0.6µm
CMOS

5.25G/ 300M 51dB -7dBm 7.2dB 21.6mW
(Chou & Wu,
2005)
0.25µm
CMOS
6M - 30M 48dB -8dBm - 11mW
Table 1. Circuit performances using the Weaver and double quadrature conversion
architectures

2.2 Complex polyphase filters
A Hilbert filter responds to the complex representation of a signal and is based on a shift
transform, ݏ฽ሺݏ൅݆߱
଴
ሻ (Khvedelidze, 2001). It translates the poles and transforms the
lowpass response into a bandpass response centered at ω=ω
0
, while preserving both
amplitude and phase characteristics. Thus, owing to its asymmetric response to positive and
negative frequencies, such a filter may be synthesized to suppress the image and pass the
desired frequency; as the case of polyphase filters (Chou & Wu, 2005).
PolyphaseFilterDesignMethodologyforWirelesscommunicationApplications 225Technology

RF/IF (Hz)

IRR

IIP3

0.6µm
CMOS
270M/ 10M 58.5
dB
-8 dBm 6.1dB 33mW
(Samavati et al.,
2001)
0.24µm
CMOS
5.2G 53dB -7dBm 7.3dB 58.8mW
(Meng et al.,
2005)
GaInP/
GaAs HBT
5.2G / 30M 40dB -10dBm - 150mW
(Wu & Chou,
2003)
0.18µm
CMOS
5G / 20M 50.6dB -13dBm 8.5dB 22.4mW
(Kim & Lee,
2006)
0.18µm
CMOS
5.25G/1G 40dB -8dBm 7.9dB 57.6mW
(Razavi, 2001)
0.25µm
CMOS
5.25G/2.6G 62dB -15dBm 6.4dB 29mW
(Lee et al., 2002)

PPF faces many challenges, so that many researches aim to analyze the sensitivity of the RF
CMOS PPF in RF integrated transceivers (Galal & Tawfik, 1999) and their application in
image rejection. This analysis allows understanding the PPF behavior, but it remains too
theoretical for designers to get quantitative results about influences of process and
mismatch variations on PPF performances.
A polyphase signal is a set of two or more vectors having the same frequency but different
in phase (Galal et al, 2000). If its vectors have the same magnitude and are equally spaced in
phase, it is considered symmetric. Hence, a symmetric two-phase signal consists of two
vectors of equal magnitudes with the same frequency and being separated in phase by 180°.
The phase order of the signal vectors determines the polarity of the polyphase signal
sequence, i.e. a positive sequence has a clockwise phase order, while a negative sequence
has an anticlockwise phase order. This introduces the concept of negative and positive
frequencies (Fig.5). It should be noted that the phase order is different from the direction of
rotation because all sequences, whether positive or negative, consist of vectors rotating
anticlockwise. Since PPF networks have asymmetric responses to inputs of opposite
polarities, they were described as asymmetric (Tetsuo, 1995).
The study of the PPF response can be performed by the way of vector analysis (Galal &
Tawfik, 1999). Since the PPF phases are symmetric, the chain matrix of a single phase
represents the chain matrix of the network. The PPF output is considered as the sum of the
outputs cascaded by each symmetric input alone thanks to linear superposition rules. Fig.6
shows the structure of one phase generalized PPF, where admittance Y1 is connected
between the input and the corresponding output, and Y2 is skewed between the input and
output of adjacent phases. The chain matrix of a single phase can be written as (Galal &
Tawfik, 1999)
൤
ܸ݅݊ǡ݇
ܫ݅݊ǡ݇
൨=
ଵ
௒ଵା௘

Fig. 6. A single phase of a
generalized PPF network
Vin,2Vin,1
Vin,4
Vin,3
Vin,1Vin,2
Vin,3 Vin,4
Y1
e
jθ
V
in
e
-jθ
V
out
V
out
I
out
I
in
V
in