Parallel LC Resonator

The experimenter can assemble the circuit shown at the upper left of Fig. 11.5. The 1,000 mfd capacitor is used, and the 12 volt secondary of the transformer is the inductor, using just one yellow wire and the center-tapped black wire. 

Then attach the vertical input of the oscilloscope to the resonator output. The scope can be set as on page 122, except that the TRIGGER SOURCE should be VERT, and the TIME/DIV should be 0.1 s (a tenth of a second per square division on the screen). The channel 2 (Y) sensitivity can be about 2 V/DIV. Place the bright spot (or line) in the middle of the screen, using POSITION [Y]. 

The capacitor has a small amount of inductance, and the inductor a small amount of capacitance, so either one alone will also show some resonance, but not as much as both together. If the 120 volt primary coil is used instead, there is not as much action, because not enough current flows to build up a strong magnetic field. (Note RC resonators, as on page 178, are similar to LC types.) 

---

The waveguide discontinuities shown in Fig. 4.23(a) to Fig. 4.23(f) illustrate most clearly the use of E and H field disturbances to realize capacitive and inductive components. An E-plane discontinuity (Fig. 4.23(a)) can be modeled approximately by a frequency-dependent capacitor. H-plane discontinuities (Fig. 4.23(b) and Fig. 4.23(c)) resemble inductors as does the circular his of Fig. 4.23(d). The resonant waveguide iris of Fig. 4.23(e) disturbs both the E and H fields and can be modeled by a parallel LC resonant circuit near the frequency of resonance. Posts in waveguide are used both as reactive elements (Fig. 4.23(f)) and to mount active devices (Fig. 4.23(g)). The equivalent chcuits of microstrip discontinuities (Fig. 4.23(k) to Fig. 4.23(o)) are again modeled by capacitive elements if the E field is interrupted and by inductive elements if the H field (or current) is interrupted. The stub shown in Fig. 4.23(j) presents a short chcuit to the through transmission line when the length of the stub is A. /4. When the stubs are electrically short (shunt capacitances in the through transmission Hne. 

---