Version 4
SHEET 1 1536 920
WIRE 176 32 160 32
WIRE 224 32 176 32
WIRE 320 32 224 32
WIRE 160 128 160 32
WIRE 224 128 224 32
WIRE 320 176 320 112
WIRE 368 176 320 176
WIRE 464 176 368 176
WIRE 608 176 528 176
WIRE 320 224 320 176
WIRE 608 272 608 176
WIRE 160 304 160 192
WIRE 224 304 224 192
WIRE 224 304 160 304
WIRE 320 304 224 304
WIRE 224 352 224 304
WIRE 608 384 608 352
FLAG 224 352 0
FLAG 176 32 mem
FLAG 368 176 x
FLAG 608 384 0
FLAG 608 176 c
SYMBOL cap 208 128 R0
SYMATTR InstName C1
SYMATTR Value 1nF
SYMBOL cap 144 128 R0
WINDOW 0 -129 12 Left 2
WINDOW 3 -79 52 Left 2
SYMATTR InstName Cmembrane
SYMATTR Value 10nF
SYMBOL ind2 304 16 R0
SYMATTR InstName L1
SYMATTR Value 0.01mH
SYMATTR Type ind
SYMBOL ind2 304 208 R0
SYMATTR InstName L2
SYMATTR Value 0.01mH
SYMATTR Type ind
SYMBOL voltage 608 256 R0
WINDOW 123 0 0 Left 2
WINDOW 39 0 0 Left 2
SYMATTR InstName Vant
SYMATTR Value SINE(0 1 0.3G)
SYMBOL cap 528 160 R90
WINDOW 0 0 32 VBottom 2
WINDOW 3 32 32 VTop 2
SYMATTR InstName Cplunger
SYMATTR Value 10nF
TEXT 24 -56 Left 2 ;Inspired by 'The Thing   Great Seal Bug', Crypto Museum.
TEXT 456 -24 Left 2 !.tran 0 10u 0
TEXT -928 360 Left 2 ;Try Cmembrane 10nF v.s. 40nF.\n10nF --> natural freq. (w_d/2pi) ~ 340KHz\n40nF --> natural freq. (w_d/2pi) ~ 176KHz.
TEXT -944 -16 Left 2 ;Notice that this does not have R.
TEXT -936 24 Left 2 ;It is arranged to achieve under-damped with a1 ~ 0, so that the oscillation does not decay,
TEXT -928 72 Left 2 ;KVL:                    -Vc + Vl1 + Vl2 = 0\nL properties:         -Vc + L1 di/dt + L2 di/dt = 0\nC properties:         -i = (Cmem + C1)  dVc/dt            # parallel C: Ceff = C1 + C2\n(3) plugs into (2):   -Vc - (L1 + L2)(Cmem + C1) d2 Vc/ dt2.\nRe-arrange:          LC d2 Vc/dt2 + 0 d Vc/dt + Vc = 0, where L = L1 + L2, C = Cmem + C1\nThat is,  a2 = LC, a1 = 0, a0 = 1, f(t) = 0.
TEXT -928 624 Left 2 ;(Model A) Only natural response. No antenna modeling.\n(Model B) Classic antenna modeling: RLC + V source, R ~50-75, L and C gets Q factor ~12.\nE.g., L = 40mH, C = 100nF, R = 50.\n(Model C) Simple antenna modeling: V source.\n[.tran 100ms] --> see the difference.\n* To see FFT, right-click > view > FFT.\n(Model D) Inductance coupling modeling.
TEXT 456 8 Left 2 !.ic V(mem) = 0.02m
TEXT -832 264 Left 2 ;Underdamped, natural frequency, w_d = sqrt(4*a0*a2 - a1^2)/(2*a2).\nTherefore, w_d = 1/sqrt(L*C).
TEXT -928 464 Left 2 ;It should be noted that '.ic V(mem) = 0.02m' is crucial in this simulation, \nsince i.c. = 0 results in no natural response (coeff = 0).\n \nIn practice, Cmembrame and C1 have to be at least partially charged. (i.c. is not 0).
TEXT 336 424 Left 2 ;Check out V(x).