Mdlx Atc App Note Pi 026

7/27/2019 Mdlx Atc App Note Pi 026

http://slidepdf.com/reader/full/mdlx-atc-app-note-pi-026 1/5

© American Technical Ceramics, 20071 of 5

APPLICATION NOTE 026

C APACITOR PI NETWORK FOR IMPEDANCE M ATCHING

PI Matching Networks

Designing matching networks is one of the key aspects of RF/Microwave design. A lossless network thatmatches an arbitrary load to real impedance has to have at least two reactive elements. However, two elementsdo not give control over the bandwidth and the degree of match simultaneously. Three-element matchingnetworks, 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 theelements 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 isenabled 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 electromagneticsimulation is used to represent the distributed interconnects and discrete models are used for the lumpedcomponents, is also demonstrated.

Capacitors Used as Inductors after SRF

Port

P2

C

Cp

RRs

C

C

LLs

Port

P1

Figure 1 Simple circuit model.

- 0 . 8 - 0 . 6 - 0 .4 - 0 . 2 0. 0 0 .2 0 .4 0 .6 0 .8-1.0 1.0

Inductive

Capacitive

Capacitive

Inductive

SRF

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 resonantfrequency (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 PRFoccurs 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 theresonant frequency the capacitor acts like an inductor. In general, the SRF sets the frequency limit on the usefuloperating range of a capacitor. But in this application, we exploit this phenomenon and use a capacitor as aninductor after SRF to match a complex load to a real load.



© American Technical Ceramics, 2007

PI Network

Term

Term2

Z=25+j*1

Num=2

C

C2C=1.0 pF

Term

Term3

Z=50

Num=2

C

C3C=1.0 pF

C

C1C=27 pF

C

C6C=1.0 pF

C

C5C=1.0 pF

C

C4C=27 pF

Term

Term4

Z=50 Ohm

Num=1

Term

Term1

Z=50 OhmNum=1

Figure 3 Simplified equivalent circuit.

Load

Source

Shunt C

Shunt C

Series L

Figure 4 Typical path traced on the Smith Chart atthe center frequency.

The simplified schematic of the matching network is shown in Figure 3. The design specification is to match animpedance 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 600Lcapacitors (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 thePCB. It is important to note that the inductance of interconnects does play a role in determining the SRF andhence the effective equivalent series inductance.

CAP_ATC_0402_001_MDLXCLR1

ATC_600L_C3

Pad_Gap=G1 mil

Pad_Length=L1 milPad_Width=W1 mil

Tolerance=1.0Sim_mode=0Subst=Sub

C=1 pF


ATC_600L_C2

Pad_Gap=G1 mil


Tolerance=1.0Sim_mode=0Subst=Sub

C=1 pF


ATC_600L_C1

Pad_Gap=G1 mil


Tolerance=1.0Sim_mode=0

Subst=SubC=27 pF

VARSize402

G1=16

Sub="MSub3"L1=15.5W1=28

EqnVar

Term

Term2

Z=25+j*1

Num=2

Term

Term3

Z=50Num=2

TermTerm1

Z=50 OhmNum=1

VAR

VAR1

len=4.5

tand=0.0027er=3.62

EqnVar

S_Param

SP1

Step=50 MHzStop=5 GHzStart=100 MHz

S-PARAMETERS

MTAPER

Taper6

L=24 milW2=W1 milW1=14.1 mil

Subst=Sub

VIAHS

V4

T=1.7 mil

H=60 milD=15 mil

MLIN

TL10

L=len milW=24 milSubst=Sub

MLINTL9

L=len mil

W=24 milSubst=Sub

VIAHS

V3

T=1.7 mil

H=60 milD=15 mil

MTAPER

Taper3

L=24 milW2=W1 milW1=14.1 mil

Subst=Sub

MTEE_ADS

Tee1

W3=14.1 mil

W2=14.1 milW1=14.1 mil

Subst=Sub

MLINTL3

L=25 milW=14.1 mil

Subst=Sub

MLINTL5

L=18.6 milW=14.1 mil

Subst=Sub

MTAPERTaper7

L=72 mil

W2=14.1 milW1=138.23 mil

Subst=SubMLINTL1

L=25 mil

W=14.1 milSubst=Sub

MTAPERTaper1

L=24 mil

W2=W1 milW1=14.1 milSubst=Sub

MSUB

MSub3

Rough=0 mmTanD=0.0021

T=1.7 milHu=1.0e+033 mm

Cond=1.0E+50Mur=1

Er=erH=60 mil

MSub

MTAPERTaper2

L=24 milW2=14.1 mil

W1=W1 milSubst=Sub

MLIN

TL2

L=25 mil

W=14.1 milSubst=Sub

MTEE_ADS

Tee2

W3=14.1 mil

W2=14.1 milW1=14.1 mil

Subst=Sub

MTAPERTaper8

L=72 mil

W2=14.1 milW1=138.23 mil

Subst=Sub

MLINTL8

L=25 milW=14.1 milSubst=Sub

MLINTL11

L=18.6 milW=14.1 mil

Subst=Sub

Figure 5.ADS schematic of the layout used.



VAR

Size0402

G1=16

Sub="MSub3"

L1=15.5

W1=28

EqnVar


ATC_600L_C1

Pad_Gap=G1 mil

Pad_Length=L1 mil

Pad_Width=W1 mil

Tolerance=1.0

Sim_mode=0

Subst=Sub

C=27 pF

Term

Term2

Z=50 Oh

Num=2

Term

Term1

Z=50 Ohm

Num=1

MLIN

TL2

L=25 milW=14.1 mil

Subst=Sub

MTAPER

Taper2

L=24 milW2=14.1 mil

W1=W1 mil

Subst=Sub

MTAPER

Taper1

L=24 milW2=W1 mil

W1=14.1 mil

Subst=Sub

MLIN

TL1

L=25 mil

W=14.1 mil

Subst=Sub

(-Y21)

(Y11+Y12) (Y22+Y21)

1

2

0

3

Figure 6.ADS schematic used to extract Ls (right). Extracted values for nominal Capacitance (C) and seriesInductance (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 areincluded 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) co-simulation results. The layout of the PCB used in the MoM simulation is shown in Figure 9. The taper at theinput and the output side is used to match the 50 line (not shown in the layout) with the mounting pads for thecapacitor. The MoM co-simulation results provide improved comparisons to the measured data, as theinterconnect and ground-via effects are more accurately represented.

1 2 3 40 5

-15

-10

-5

-20

0

MoM

Cosimulation

Measured

Circuit

Simulation

1 2 3 40 5

-30

-20

-10

-40

0

MoM

Cosimulation

Measured

Circuit

Simulation

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 betweenmeasured and simulated data. The substrate-scaling features of the Modelithics Global models enable allsubstrate-related parasitics to be taken into account. To illustrate this feature, a simulation comparing twosubstrates is shown in Figure 11.



1 2 3 40 5

-15

-10

-5

-20

0

MoM

Cosimulation

Measured

Circuit

Simulation

1 2 3 40 5

-30

-20

-10

-40

0

MoM

Cosimulation

Measured

Circuit

Simulation

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. Figure 10 Photograph of the matching circuit.

1 2 3 40 5

-20

-15

-10

-5

-25

0

freq, GHz

RO4350, 60mils

RO4350, 4mils

1 2 3 40 5

-30

-20

-10

-40

0

freq, GHz

RO4350, 60mils

RO4350, 4mils

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 thi s 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 •[email protected] • 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 •[email protected] or visit www.modelithics.com

Mdlx Atc App Note Pi 026

Documents

Transcript of Mdlx Atc App Note Pi 026