Q Calculations of L-C Circuits and Transmission Lines ... - Ve2azx.net

Figure 5 — Q factor versus line length for RG-58C, at 16.229 MHz.
Figure 2 — Resonant modes for shorted and open lines along
with the relevant equations for Q calculations.
Figure 6 — Q factor versus line length for RG-58C, at 162.29 MHz.
Figure 3 — Q factor of a shorted line. Q factor versus frequency for a
10 foot length of RG-58C, giving first resonance at ~16.229 MHz (f q
).
Solid line is resonator Q, dotted line is the apparent Q.
Figure 7 — Q factor versus line length at 500 MHz for a 50 Ω
microstrip, 114 mil wide, above a 62 mil thick FR4 substrate.
Figure 4 — Q factor of an open line. Q factor versus frequency for
a 10 foot length of RG-58C, giving first resonance at ~16.229 MHz
(f q
). Solid line is resonator Q, dotted line is the apparent Q.
process is repeated twice until we get a final value for Z o .
We are now ready to calculate the stub impedances, using the complex
value of Z o , for both open and short lines. Equation 32 or 33 will
be used to calculate the stub impedances.
Zo
Zsopen
(Eq 32)
tanh( len)
where len is the line length in feet and Z o the stub line complex
impedance.
The shorted stub impedance may be calculated as:
46 Sep/Oct 2006