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No. 1001: Using Coaxial Line Elements as Inductors
1
Phone [301] 695-9400 Fax [301] 695-7065 transtech@skyworksinc.com www.trans-techinc.com
Trans-Tech Proprietary Information Products and Product Information are Subject to Change Without Notice. March 9, 2007
No. 1001: Using Coaxial Line Elements as Inductors
APPLICATION NOTE
Coaxial (or coax) line elements can be used below resonance to
simulate high-Q, temperature-stable, compact inductors. More
precisely, shorted coax lines will exhibit an inductive reactance
when used below quarter-wave resonance, and will approximate
the behavior of an ideal inductance or coil over a limited fre-
quency range. As the operating frequency approaches the SRF of
the coax line element, the approximation will be less valid. An
exact equivalent circuit is complex and would include parasitic
elements resulting from a transition from the printed wiring board
to the interior of the coax line. In this note, a first-order model
includes only the ceramic coax line and an estimate of the induc-
tance due to the physical length of the center conductor tab. The
tab inductance will appear in series with the coax line's input
impedance. An ideal, lossless transmission line is assumed to
simplify the calculations. Minor corrections to part length may be
evident from prototype circuit performance.
Let the desired inductive reactance at the design frequency fo be
approximated by
The characteristic impedance, Z
o
, is established by the coax
dimensions and the material dielectric constant
r
, as shown in
Table 1. The cross-section width, W and hole diameter, d, differ
from final catalog part sizes by an allowance of .001" for con-
ductor metallization thickness.
The Z
o
values in Table 1 were computed from the approximation
1
The wavelength in the dielectric,
g
, can be calculated from the
expression in Table 2, with f
o
as the design frequency in MHz.
Z
input
= Z
o
tan() ohms
where:
Zinput = impedance at the coax line terminals (ohms)
Zo
= coax line characteristic impedance (ohms) =
coax electrical length (radians)
= coax line physical length (inches)
g
= wavelength in the dielectric at fo inches
2
g
Profile
1000
(10.5 � 0.5)
2000
(20.6 � 1)
8800
(39 � 1.5)
9000
(90 � 3)
Tab
Inductors
HP
25.3 W
18.1 W
13.1 W
8.6 W
1.8nH
EP
22.5 W
16.1 W
11.7 W
7.7 W
1.0nH
SP
18.3 W
13.1 W
9.5 W
6.3 W
1.0nH
LS
18.4 W
13.1 W
9.5 W
6.3 W
0.9nH
LP
27.4 W
19.6 W
14.2 W
9.4 W
1.0nH
SP
25.7 W
18.4 W
13.3 W
8.8 W
0.6nH
SM
18.4 W
13.1 W
9.5 W
6.3 W
0.6nH
Table 1. Coax Lines Properties vs.
Profile and Material
Z
o
=
n 1.079 r
60
W
d APPLICATION NOTE NO. 1001: USING COAXIAL LINE ELEMENTS AS INDUCTORS
2
Phone [301] 695-9400 Fax [301] 695-7065 transtech@skyworksinc.com www.trans-techinc.com
March 9, 2007 Trans-Tech Proprietary Information Products and Product Information are Subject to Change Without Notice.
Table 2. Wavelength (lg) in Dielectric
Note that the shorted transmission line model requires the con-
stant of the material filling the coax line.
Inductance-Per-Unit-Length formulas are useful only when the
line is very short compared to a wavelength, and are inaccurate
as fo approaches SRF. The equation for input impedance can be
rearranged to determine the part length for a desired inductive
reactance.
The SRF must lie within the recommended frequency range2 for
the same profile and material when used as a coaxial resonator.
This restriction places constraints upon the range of inductive
reactance which can be realized by this technique, although arbi-
trarily high reactance values can be achieved close to SRF. The
designer should prudently analyze the circuit response when fo is
near SRF.
Material
r
Wavelength Formula
for
g
(inches)
1000
10.5 � 0.5
3642 / f
o
2000
20.6 � 1
2601 / f
o
8800
39 � 1.5
1890 / f
o
9000
90 � 3
1244 /
Z
input
Z
o

=
g
2 tan
-1
SRF may be calculated from previously determined values.
The center conductor tab will present a small additional series
inductance which may be included in the total desired inductive
reactance. The tab influence has not been measured, but sug-
gested approximate values are given in Table 1.
Q, or quality factor, may be estimated from:
where:
K
= 240 for 8800 material
= 200 for 9000 material
and W, d and f0 have been defined earlier
References
(1) H. Riblet, An Accurate Approximation of the Impedance of a
Circular Cylinder Concentric with an External Square Tube,
IEEE Trans. Microwave Theory Tech., vol. MTT-31, pp. 841-
844, Oct. 1983
SRF =
g
f
o
4
1 APPLICATION NOTE NO. 1001: USING COAXIAL LINE ELEMENTS AS INDUCTORS
3
Phone [301] 695-9400 Fax [301] 695-7065 transtech@skyworksinc.com www.trans-techinc.com
Trans-Tech Proprietary Information Products and Product Information are Subject to Change Without Notice. March 9, 2007
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