APPLICATION NOTE 026
CAPACITOR PI NETWORK FOR IMPEDANCE MATCHING
PI Matching Networks
Designing matching networks is one of the key aspects of RF/Microwave design. A lossless network that
matches an arbitrary load to real impedance has to have at least two reactive elements. However, two elements
do not give control over the bandwidth and the degree of match simultaneously. Three-element matching
networks, i.e. Pi- and Tee-networks, provide additional control of the frequency response.
In this application note we explore the idea of designing an all-capacitor Pi matching network by using one of the
elements beyond its self-resonant frequency, when it has become inductive rather than capacitive. Essentially,
the effective series inductance (ESL) of the series element in the Pi network is utilized. The design process is
enabled via the broad-band accuracy of the Modelithics Global capacitor models, in particular those for ATC
600L 0402 capacitors. The use of method of moments co-simulation, wherein numerical electromagnetic
simulation is used to represent the distributed interconnects and discrete models are used for the lumped
components, is also demonstrated.
Capacitors Used as Inductors after SRF
Port
P1
Capacitive
L
Ls
SRF
C
C
C
Cp
R
Rs
-1.0 -0.8 -0.6 -0.4 -0.2 0.0
0.2
0.4
0.6
0.8
1.0
Inductive
Inductive
Capacitive
Port
P2
Figure 1 Simple circuit model.
Figure 2 Frequency response of simple model (S21 on left, S11 on right).
Figure 1 shows a simplified two port equivalent circuit of a capacitor; C – Capacitance, Ls – Series Inductance,
Cp – Parallel capacitance, Rs – Series resistance. As there are three reactive components in the circuit model,
there are at least two resonant frequencies – the series resonant frequency (SRF) and the parallel resonant
frequency (PRF). At the SRF the capacitor’s impedance is a minimum, while at the PRF it is a maximum.
Usually, the parallel capacitance (Cp) is much smaller than the nominal component value (C) and the PRF
occurs at a higher frequency than the SRF.
Figure 2 shows a 2-port S-Parameter simulation of the circuit shown in Figure 1. It can be seen that at above the
resonant frequency the capacitor acts like an inductor. In general, the SRF sets the frequency limit on the useful
operating range of a capacitor. But in this application, we exploit this phenomenon and use a capacitor as an
inductor after SRF to match a complex load to a real load.
© American Technical Ceramics, 2007
1 of 5
PI Network
C
C1
C=27 pF
Term
Term1
Num=1
Z=50 Ohm
C
C2
C=1.0 pF
Load
C
C3
C=1.0 pF
Term
Term3
Num=2
Z=50
Series L
Shunt C
Shunt C
C
C4
C=27 pF
Term
Term4
Num=1
Z=50 Ohm
C
C6
C=1.0 pF
Source
C
C5
C=1.0 pF
Term
Term2
Num=2
Z=25+j*12
Figure 3 Simplified equivalent circuit.
Figure 4 Typical path traced on the Smith Chart at
the center frequency.
The simplified schematic of the matching network is shown in Figure 3. The design specification is to match an
impedance of 25+j12 to a 50 load at 1.6GHz. As mentioned earlier, the basic idea is to use the capacitor C1
(27pF) in the series arm of the PI network, as an inductor after SRF. The new pad-scalable model for ATC 600L
capacitors (CAP-ATC-0402-101) and Rogers 60 mil-thick R04003 (r = 3.6) substrate were used in the design.
The impedance transformation at the center frequency is illustrated in Figure 4. Figure 5 shows the layout of the
PCB. It is important to note that the inductance of interconnects does play a role in determining the SRF and
hence the effective equivalent series inductance.
MTEE_ADS
MTAPER
Taper7
Tee1
MLIN
Subst=Sub
Subst=Sub TL1
W1=138.23 milW1=14.1 mil Subst=Sub
W2=14.1 mil W2=14.1 mil W=14.1 mil
W3=14.1 mil L=25 mil
L=72 mil
Term
Term1
Num=1
Z=50 Ohm
CAP_ATC_0402_001_MDLXCLR1
ATC_600L_C1
C=27 pF
Subst=Sub
MTEE_ADS
Sim_mode=0
MLIN
Tee2
Tolerance=1.0
TL2
Subst=Sub
Pad_Width=W1 mil
Subst=Sub
W1=14.1 mil
Pad_Length=L1 mil
W=14.1 mil
W2=14.1 mil
Pad_Gap=G1 mil
L=25 mil W3=14.1 mil
MLIN
TL5
Subst=Sub
W=14.1 mil
L=18.6 mil
MTAPER
MTAPER
MLIN
Taper2
MLIN
Taper1
Subst=Sub TL8
TL3
Subst=Sub
W1=W1 mil Subst=Sub
Subst=Sub
W1=14.1 mil
W2=14.1 mil W=14.1 mil
W=14.1 mil W2=W1 mil
L=25 mil
L=24 mil
L=25 mil
L=24 mil
MTAPER
CAP_ATC_0402_001_MDLXCLR1
MTAPER
MSub
Taper3
ATC_600L_C2
Taper6
Subst=Sub
C=1 pF
Subst=Sub
MSUB
W1=14.1 mil Subst=Sub
W1=14.1 mil
MSub3
W2=W1
mil
Sim_mode=0
W2=W1 mil
H=60 mil
L=24
mil
L=24 mil
Tolerance=1.0
Er=er
Pad_Width=W1 mil
Mur=1
S-PARAMETERS
Pad_Length=L1 mil
Cond=1.0E+50
Pad_Gap=G1 mil
Hu=1.0e+033 mm
S_Param
MLIN
T=1.7 mil
SP1
TL10
MLIN
TanD=0.0021
Start=100 MHz
Subst=Sub
TL9
Rough=0 mm
Stop=5 GHz
W=24 mil
Subst=Sub
Step=50 MHz
L=len mil
Var
W=24 mil
VAR
Var
Eqn
VIAHS
Eqn VAR
L=len mil
Size402
V3
VAR1
W1=28
D=15 mil
er=3.62
L1=15.5
H=60 mil
tand=0.0027
Sub="MSub3"
T=1.7 mil
len=4.5
G1=16
MLIN
TL11
Subst=Sub
W=14.1 mil
L=18.6 mil
Term
Term2
Num=2
Z=25+j*1
Term
Term3
Num=2
Z=50
CAP_ATC_0402_001_MDLXCLR1
ATC_600L_C3
C=1 pF
Subst=Sub
Sim_mode=0
Tolerance=1.0
Pad_Width=W1 mil
Pad_Length=L1 mil
Pad_Gap=G1 mil
VIAHS
V4
D=15 mil
H=60 mil
T=1.7 mil
Figure 5.ADS schematic of the layout used.
© American Technical Ceramics, 2007
MTAPER
Taper8
Subst=Sub
W1=138.23 mil
W2=14.1 mil
L=72 mil
3
(-Y21)
(Y11+Y12)
(Y22+Y21)
Term
Term1
Num=1
Z=50 Ohm
MTAPER
Taper1
Subst=Sub
W1=14.1 mil
W2=W1 mil
L=24 mil
MLIN
TL1
Subst=Sub
W=14.1 mil
L=25 mil
MTAPER
Taper2
MLIN
Subst=Sub TL2
W1=W1 mil Subst=Sub
W2=14.1 milW=14.1 mil
L=24 mil
L=25 mil
CAP_ATC_0402_001_MDLXCLR1
ATC_600L_C1
C=27 pF
Var
Eqn VAR
Subst=Sub
Size0402
Sim_mode=0
W1=28
Tolerance=1.0
L1=15.5
Pad_Width=W1 mil
Sub="MSub3"
Pad_Length=L1 mil
G1=16
Pad_Gap=G1 mil
2
1
0
Term
Term2
Num=2
Z=50 Ohm
Figure 6.ADS schematic used to extract Ls (right). Extracted values for nominal Capacitance (C) and series
Inductance (Ls) (left)
Figure 6 shows the schematic of the circuit used to extract the equivalent capacitance (C) and inductance (Ls)
of the series element in the matching network; these values are found by using Y21. When -Imag(Y21) > 0, C=Imag(Y21)/(2f), and when -Imag(Y21) < 0, Ls=1/(Imag(Y21)2f). The microstrip and taper sections are
included with the capacitor effects in this calculation. It is interesting to note that the Ls value is fairly constant at
~2.2 nH after the SRF.
Results
Figures 7 and 8 compare the measured result with circuit simulation and method-of-moments (MoM) cosimulation results. The layout of the PCB used in the MoM simulation is shown in Figure 9. The taper at the
input and the output side is used to match the 50 line (not shown in the layout) with the mounting pads for the
capacitor. The MoM co-simulation results provide improved comparisons to the measured data, as the
interconnect and ground-via effects are more accurately represented.
0
0
-5
MoM
Cosimulation
-10
Circuit
Simulation
-10
Circuit
Simulation
MoM
Cosimulation
-20
-15
-30
Measured
-20
0
1
2
3
4
5
Measured
-40
0
1
2
3
4
Figure 7 Comparison between simulated and measured response when port 2 is terminated with 50.
The properties of the substrate (thickness and r) used are critical in obtaining a good correlation between
measured and simulated data. The substrate-scaling features of the Modelithics Global models enable all
substrate-related parasitics to be taken into account. To illustrate this feature, a simulation comparing two
substrates is shown in Figure 11.
5
0
0
Circuit
Simulation
-5
MoM
Cosimulation
-10
-15
Circuit
Simulation
-10
MoM
Cosimulation
-20
Measured
-30
Measured
-40
-20
0
1
2
3
4
0
5
1
2
3
4
5
Figure 8 Comparison between simulated and measured response when port 2 is terminated with 25+j12.
Figure 9 Layout of the PCB used in the MoM Simulation.
0
Figure 10 Photograph of the matching circuit.
0
RO4350, 4mils
-5
-10
RO4350, 4mils
-10
-20
-15
RO4350, 60mils
RO4350, 60mils
-30
-20
-25
0
1
2
freq, GHz
3
4
5
-40
0
1
2
3
4
5
freq, GHz
Figure 11.Comparison of simulated results Case1: RO4350 60 mils substrate, Case2: RO4350 4 mils substrate
and Case3: RO4350 60 mils substrate using ideal components. Port 2 is terminated with 25+j12
About this work
This work was performed as a collaboration between American Technical Ceramics and Modelithics,
Inc, funded by ATC. University of South Florida MS student Aswin Jayaraman assisted with the
development of this material under grant funding provided by Modelithics, Inc..
Contact information
For information about ATC products and support, please contact American Technical Ceramics, One
Norden Lane, Huntington Station, NY, 11746 • voice 631-622-4700 • fax 631-622-4748 •
sales@atceramics.com • www.atceramics.com
For more information about Modelithics products and services, please contact Modelithics, Inc. , 3650
Spectrum Blvd. , Suite 170, Tampa, FL 33612 • voice 888- 359-6539 • fax 813-558-1102 •
sales@modelithics.com or visit www.modelithics.com