Practical_Antenna_Handbook_0071639586

C h a p t e r 2 6 : T h e S m i t h C h a r t 579
Now let’s summarize everything we’ve gleaned using the Smith chart. Recall that
1.5 W of 4.5-ÂGHz microwave RF signal was applied to the input of a 50-ÂW transmission
line that was 28 cm long. The load connected to the far end of the transmission line had
an impedance of 36 + j40. From the Smith chart:
Admittance (load) 0.62 – j0.69
VSWR 2.6:1
VSWR (dB):
8.3 dB
Reflection coefficient (V) 0.44
Reflection coefficient (P) 0.2
Reflection coefficient angle 84 degrees
Return loss
–7 dB
Reflection loss
–1.05 dB
Transmission loss coefficient 1.5
Note that in all cases the numerical calculation agrees with the graphical solution of the
problem within the limits of the graphical method.
Stub Matching
A properly designed matching system will provide a conjugate match to a complex
impedance. Some sort of matching system or network is likely to be needed any time
the load impedance Z L differs significantly from the characteristic impedance Z 0 of the
transmission line. In a transmission line system, a shorted stub is often connected in parallel
with the line, at a specific distance back toward the generator from the mismatched
load, in order to effect a match.
As shown schematically in Fig. 26.8, a stub is simply a short section of transmission
line whose two conductors are shorted together at one of its ends and individually attached
to the two conductors of the system transmission line at its other end. A lossless
shorted line exhibits a pure reactance that can vary from –∞ to +∞, depending upon its
length (and repeating every l/2), so a line of critical length L 2 attached across a load
impedance can cancel any possible reactive component. However, because the stub
must also transform the resistive part of the load impedance up or down to match the
system impedance (Z 0 ), another adjustable stub parameter is required. This turns out to
be the stub attachment point L 1 —i.e., the distance from the load back toward the transmitter
(or generator).
Because the stub is connected in parallel with the line, it is generally easier to work
with admittance parameters, rather than impedances. When we do that, at a certain
stage of the process values on the Smith chart represent admittances, consisting of conductances
and susceptances, rather than impedances. The pure resistance line becomes
the pure conductance line, and circles of constant resistance become circles of constant
conductance.
Example 26.3 A parallel-Âwire transmission line is terminated by an antenna with an
impedance Z L = 100 + j60, as shown in Fig. 26.8. Find the closest location (to the load)
and the length of a shorted stub that will reduce the VSWR on the transmission line to
the left of the stub to 1.0:1.