APPLICATION NOTES
50 OHM CHIP RESISTOR TERMINATION NARROW BAND MATCHING
Thin substrate chip resistive terminations have a small capacitance to
ground in parallel with the 50 ohm resistor.
The equivalent circuit is:
RSER
A
XSER
B
50 ohm
RSER =
XSER =
RSH
1+ Q 1 2
SH
XSH
1+ Q 1 2
SH
=
50
1.09
=
167Ω
12
= 46Ω
(
= 14Ω Z SER = –J14Ω
)
For best match over a narrowband, transform the capacitance “C” in
parallel with 50 ohm to the equivalent series circuit as follows:
Shunt to Series Transformation
To match out –j14 ohm at 1-9 GHz requires an inductor such that
RSH
A
B
RSER
A
SER =
XSER
+ 14,
LSER =
14
2πx1.9x109
B
Equivalent Series Connection
CSER = 0,6 pf,
LSER = 1.2 nhy
XSH
Shunt Connection between A and B
RST
QSH =
XST
RSER =
XSER =
RSH
2
SH
+j14 ohm -j14 ohm 46
1+Q
XSH
1+
1
2
Q SH
VSWR = 1.09 at 1.9GHz
VSWR = 1.4:1 without matching
Once the equivalent series connection is known, the XSER element
(which is capacitive) may be matched out with a series inductor at the
center of the band interest.
Note: This result implies that since 50 ohm is the desired final resistance, the specified original RSH should have been 54 ohm.
For example, Chip XXX 50 ohm termination has C = 0.5 pf and is
fabricated on a 25 mil thick alumina substrate.
To match out “C” at 1.9 GHz with a series inductor transform to series
equivalents:
QSH =
50
XSH
,
XSH =
QSH =
50
167
= 0.3,
XSH = 167Ω
Q2SH = 0.09,
1
Q
2
1
2πx1.9x109z0.5x10-12
= 11
SH
KEY: Inches [Millimeters] .XX ±.03 .XXX ±.010 [.X ±0.8 .XX ±0.25]
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