AN258 - Infineon

Realiz ing smal l ind u c tor v alue s on a
PC B b y u sing mic r o s trip li nes
As n eede d fo r e. g. B GA 915 N 7
Applic atio n N ote A N 258
Revision: Rev. 2.0
2011-04-28
RF and P r otecti on D evic es
Edition 2011-04-28
Published by
Infineon Technologies AG
81726 Munich, Germany
© 2011 Infineon Technologies AG
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Inductance of microstrip lines
Application Note AN258
Revision History: 2011-04-28
Previous Revision: prev. Rev. 1.0
Page
Subjects (major changes since last revision)
12 – 13
Chapter on via inductance added
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Application Note AN258, Rev. 2.0
3 / 15
2011-04-28
Inductance of microstrip lines
List of Content, Figures and Tables
Table of Content
1
Introduction ........................................................................................................................................ 5
2
2.1
Microstrip lines used as shunt inductors ........................................................................................ 5
Characteristic impedance of microstrip lines ....................................................................................... 6
3
Inductance of different line widths for fixed thickness of substrate ............................................ 7
4
Inductance of lines on different substrates with fixed line widths ............................................. 10
5
Inductance of vias ............................................................................................................................ 12
Author ................................................................................................................................................ 14
List of Figures
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Cross section of a PCB ........................................................................................................................ 6
Inductance vs. length: Substrate thickness = 40µm ............................................................................ 7
Inductance vs. length: Substrate thickness = 80µm ............................................................................ 7
Inductance vs. length: Substrate thickness = 120µm .......................................................................... 8
Inductance vs. length: Substrate thickness = 150µm .......................................................................... 8
Inductance vs. length: Substrate thickness = 200µm .......................................................................... 9
Inductance vs. length: Substrate thickness = 250µm .......................................................................... 9
Inductance vs. length: Line width = 0.1mm. ....................................................................................... 10
Inductance vs. length: Line width = 0.12mm. ..................................................................................... 10
Inductance vs. length: Line width = 0.15mm. ..................................................................................... 11
Inductance vs. length: Line width = 0.2mm ........................................................................................ 11
Example of a via hole including dimensions ...................................................................................... 12
Via inductance vs. thickness of dielectric: 100 µm ring width ............................................................ 12
Via inductance vs. thickness of dielectric: 150 µm ring width ............................................................ 13
Via inductance vs. thickness of dielectric: 200 µm ring width ............................................................ 13
List of Tables
No table entries found.
Application Note AN258, Rev. 2.0
4 / 15
2011-04-28
Inductance of microstrip lines
Introduction
1
Introduction
The use of distributed microstrip circuit elements is very common at microwave frequencies. At those high
frequencies convertional lumped SMD-elements can not work anymore as their desired performance as an
inductor or capacitor is outweighed by the unavoidable parasitic of such a device.
The principles of microstrip circuit design with distributed elements apply also to lower frequencies where
lumped elements still work as they are supposed. Microstrip elements can become quite big at those
frequencies and therefore use up a lot of PCB space. Despite this they still can be very useful, especially to
realize small inductance values which are not available as SMD elements, as most suppliers offer 1 nH
coils as the smallest value in their line-up.
The inductance values presented in this application note were derived from simulations using frequencies
around 1575 MHz.
2
Microstrip lines used as shunt inductors
A microstrip transmission line involves inductance associated with the flow of current in the conductor and
capacitance associated with the strip separated from ground by the dielectric substrate. This distributed
inductance and capacitance is the basis of the classic L-C model for a transmission line and it accounts for the
term “distributed”. If the line is narrow, the capacitance is small. A narrow, high impedance line behaves like an
inductor if it is less than 90 degrees in electrical length. A wide, low-impedance line looks capacitive.
The impedance, ZS, at the input of a transmission line of characteristic impedance Z0 and length  terminated in
a load, ZL, is given by:
Considering the case where ZL is a short. Then
Since the input impedance of a shorted inductor is jXL,
This means that the reactance of an inductor in a network may be replaced with a transmission line of
characteristic impedance Z0 and length . This equivalence is exact only at the design frequency. The reactance
of an inductor increases linearly with increasing frequency while the reactance of a shorted line increases as
tan . If the line is short, that is  << 90°, then tan    and the input reactance of a shorted line increases
linearly with frequency. Therefore, a shorted line behaves like an inductor over a range of frequencies where the
line is much less than 90° long, preferably less than 30°.
Generally, the equivalence is better with higher impedance and shorter length lines for inductors, and with lower
impedance and shorter length lines for capacitors.
To realize a shorted microstrip transmission line it is necessary to use one or more vias to connect the line to
the GND plane. These vias possess a parasitic inductance that has to be considered to get the total inductance
of the microstrip line under examination.
Application Note AN258, Rev. 2.0
5 / 15
2011-04-28
Inductance of microstrip lines
Microstrip lines used as shunt inductors
2.1
Characteristic impedance of microstrip lines
As seen in the previous section it is necessary to know the length and characteristic impedance of a line to
determine its equivalent inductance.
The closed-form expression for the characteristic impedance, Z0, of a microstrip line as shown in Figure 1,
1
assuming zero strip thickness (t = 0), is given as :
with
and
where err is the effective dielectric constant of the microstrip structure.
The equations show that the characteristic impedance is determined strongly by the ratio h / W of substrate
height to line width.
The effective dielectric constant eff plays some role, as well, but simulations to create the curves in chapter 3
and chapter 4 have shown that this influence can be neglected for the geometries covered in this application
note. These simulations based on a dielectric constant r of 4.2. Changing this value from 2 to 6 had no
effect on the equivalent inductance.
Figure 1
1
Cross section of a PCB
E. O. Hammerstad and O. Jensen, “Accurate Models for Microstrip Computer-Aided Design,” 1980 IEEE MTT-S Digest, pp.
407–409
Application Note AN258, Rev. 2.0
6 / 15
2011-04-28
Inductance of microstrip lines
Inductance of different line widths for fixed thickness of substrate
3
Inductance of different line widths for fixed thickness of substrate
40 µm dielectric
0.1mm
0.12mm
0.15mm
0.2mm
0.6
Increasing line width
Inductance of line [nH]
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
3.5
Length of line [mm]
Figure 2
Inductance vs. length: Substrate thickness = 40µm
80 µm dielectric
0.1mm
0.12mm
0.15mm
0.2mm
0.6
Increasing line width
Inductance of line [nH]
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
Length of line [mm]
Figure 3
Inductance vs. length: Substrate thickness = 80µm
Application Note AN258, Rev. 2.0
7 / 15
2011-04-28
Inductance of microstrip lines
Inductance of different line widths for fixed thickness of substrate
120 µm dielectric
0.1mm
0.12mm
0.15mm
0.2mm
0.55
Increasing line width
0.5
Inductance of line [nH]
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Length of line [mm]
Figure 4
Inductance vs. length: Substrate thickness = 120µm
150 µm dielectric
0.1mm
0.12mm
0.15mm
0.2mm
0.55
Increasing line width
0.5
Inductance of line [nH]
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.4
0.6
0.8
1
1.2
1.4
1.6
Length of line [mm]
Figure 5
Inductance vs. length: Substrate thickness = 150µm
Application Note AN258, Rev. 2.0
8 / 15
2011-04-28
Inductance of microstrip lines
Inductance of different line widths for fixed thickness of substrate
200 µm dielectric
0.1mm
0.12mm
0.15mm
0.2mm
0.6
Increasing line width
0.55
Inductance of line [nH]
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
Length of line [mm]
Figure 6
Inductance vs. length: Substrate thickness = 200µm
250 µm dielectric
0.1mm
0.12mm
0.15mm
0.2mm
0.6
Increasing line width
0.55
Inductance of line [nH]
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Length of line [mm]
Figure 7
Inductance vs. length: Substrate thickness = 250µm
Application Note AN258, Rev. 2.0
9 / 15
2011-04-28
Inductance of microstrip lines
Inductance of lines on different substrates with fixed line widths
4
Inductance of lines on different substrates with fixed line widths
Line width: 0.1mm
40um dielectric
80um dielectric
120um dielectric
150um dielectric
200um dielectric
250um dielectric
0.6
Inductance of line [nH]
0.5
0.4
0.3
0.2
Thickness of diecectric
0.1
0
0
0.5
1
1.5
2
2.5
Length of line [mm]
Figure 8
Inductance vs. length: Line width = 0.1mm.
Line width: 0.12mm
40um dielectric
80um dielectric
120um dielectric
150um dielectric
200um dielectric
250um dielectric
0.6
Inductance of line [nH]
0.5
0.4
0.3
0.2
Thickness of diecectric
0.1
0
0
0.5
1
1.5
2
2.5
Length of line [mm]
Figure 9
Inductance vs. length: Line width = 0.12mm.
Application Note AN258, Rev. 2.0
10 / 15
2011-04-28
Inductance of microstrip lines
Inductance of lines on different substrates with fixed line widths
Line width: 0.15mm
40um dielectric
80um dielectric
120um dielectric
150um dielectric
200um dielectric
250um dielectric
0.6
Inductance of line [nH]
0.5
0.4
0.3
0.2
Thickness of diecectric
0.1
0
0
0.5
1
1.5
2
2.5
3
Length of line [mm]
Figure 10
Inductance vs. length: Line width = 0.15mm.
Line width: 0.2mm
40um dielectric
80um dielectric
120um dielectric
150um dielectric
200um dielectric
250um dielectric
0.6
Inductance of line [nH]
0.5
0.4
0.3
0.2
Thickness of diecectric
0.1
0
0
0.5
1
1.5
2
2.5
3
3.5
Length of line [mm]
Figure 11
Inductance vs. length: Line width = 0.2mm
Application Note AN258, Rev. 2.0
11 / 15
2011-04-28
Inductance of microstrip lines
Inductance of vias
5
Inductance of vias
Figure 12 shows a via hole including the via pad. In this case the diameter of the via hole is 200 µm, this
application note shows inductance values for via diameters of 0.1 mm, 0.15 mm and 0.2 mm. The pad of the via
here is 500 µm, but many PCB manufacturers refer in their design rules rather to the rest ring width, in this
example 150µm. So do we in this document, because the ring width stays constant for different hole diameters
while the pad diameter would change, making the depiction of parameterized curves difficult.
150 um
200 um
500 um
150 um
Figure 12
Example of a via hole including dimensions
100µm Ring
0.1mm
0.15mm
0.2mm
160
140
Inductance of Via (pH)
120
100
80
60
40
20
0
50
100
150
200
250
300
Thickness of Dielectric (µm)
Figure 13
Via inductance vs. thickness of dielectric: 100 µm ring width
Application Note AN258, Rev. 2.0
12 / 15
2011-04-28
Inductance of microstrip lines
Inductance of vias
150µm Ring
0.1mm
0.15mm
0.2mm
160
140
Inductance of Via (pH)
120
100
80
60
40
20
0
50
100
150
200
250
300
250
300
Thickness of Dielectric (µm)
Figure 14
Via inductance vs. thickness of dielectric: 150 µm ring width
200µm Ring
0.1mm
0.15mm
0.2mm
160
140
Inductance of Via (pH)
120
100
80
60
40
20
0
50
100
150
200
Thickness of Dielectric (µm)
Figure 15
Via inductance vs. thickness of dielectric: 200 µm ring width
Application Note AN258, Rev. 2.0
13 / 15
2011-04-28
Inductance of microstrip lines
Author
Author
Dietmar Stolz, Staff Application Engineer of Business Unit “RF and Protection Devices”
Application Note AN258, Rev. 2.0
14 / 15
2011-04-28
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AN258