Theory, Design and Tests on a Prototype Module of a Compact ...

96 5. RADIOFREQUENCY MEASUREMENT
range is set around the resonance, the locus of impedance
points describes a complete circle which should be seen on
the display.
• Next, we use the phase offset option to make the circle symmetric
respect to the real axis of Smith Chart. By this way,
we put our point of view in a detuned short position.
• Last, we store the data on a diskette, in order to continue the
procedure on a personal computer.
By using definitions (5.21), we can write
Zbb
Z0
=
=
β
1 + j2Q0(δ − δ0) =
β
1 + j2Qextβ(δ − δ0) .
β
1 + j2QL(1 + β)(δ − δ0)
(5.25)
By then, we use a matlab program that numerically finds the frequency
points where the following relation occurs
Zbb
Z0
= β
1 ± j ,
<strong>and</strong>, in this case, it is true that 2Q0(δ − δ0) = ±1. Let us call δ1 <strong>and</strong>
δ2 the two points where they occur, then
Q0 =
1
δ1 − δ2
= f0
, (5.26)
f1 − f2
f1 <strong>and</strong> f2 are called half power points. In analogous way, we can find
points where
Zbb
Z0
=
β
1 ± j(1 + β)
→ Ybb
Y0
= G ± jB = 1
β
± j( 1
β
+ 1)
<strong>and</strong>, in this case, it is true that 2QL(δ − δ0) = ±1. Then, it is sufficient
to find the points where B = G + 1, let us call δ3 <strong>and</strong> δ4 the two points
where it occurs, next
QL =
1
δ3 − δ4
Finally, we can find points where
Zbb
Z0
= β
1 ± jβ
→ Ybb
Y0
= f0
, (5.27)
f3 − f4
= G ± jB = 1
β
± j1
<strong>and</strong>, in this case, it is true that 2Qext(δ−δ0) = ±1. Then, it is sufficient
to find the points where B = 1, let us call δ5 <strong>and</strong> δ6 the two points
where it occurs, next
1
Qext = =
δ5 − δ6
f0
, (5.28)
f5 − f6
Of course, this procedure could be manually carried out, by using
Smith Chart. The relevant points are shown in figure 5.27. Finally,