CHAPTER 4 - Impedance Matching
194
Figure 4.5-5 shows the equivalence between shunt capacitors and open circuited stubs. In this figure
(
), and the electrical length of the stub is again lower than 90°.
Figure 4.5-5 Equivalence between shunt capacitor and open-circuited shunt stub with electrical length < 90ι
By equating the admittance of the lumped components to that of the respective stub, we
may obtain the electrical length which our stub needs to be to achieve the required value of
capacitance ( ) or inductance ( ).
For short-circuited stubs used as inductors we get
⇒
For
example if we wanted to use a short-circuited transmission line stub, with a characteristic
impedance of 50Ω, in place of a 4.6 nH inductor at 1 GHz we would need to use the electrical length
show below
Notice
that, since the electrical length of a line is related to frequency, this is a narrow-band
approach. That is to say that the equivalence between and inductor of a specific value and short-
circuited stub of the respective electrical length is only valid at one frequency.
For open-circuited stubs used as capacitors we get
⇒
For example if we wanted to use an open-circuited transmission line stub, with a characteristic
impedance of 50Ω, in place of a 3.2 pF capacitor at 1 GHz we would need to use the electrical length
show below
Again this is a narrow-band equivalence.
Distributed elements such as transmission stubs and series transmission lines segments can
be extremely useful when it comes to impedance matching at high frequency as demonstrated in
video 4.13 and 4.14.
Z
OC
Y
OC
Z
C
Y
C
Conquer Radio Frequency
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