Version 4
SHEET 1 1536 768
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 320 224 320 176
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
FLAG 224 352 0
FLAG 176 32 mem
FLAG 368 176 x
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 40nF
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
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 -928 472 Left 2 ;(Model 1) Try with 'ic V(mem) = 1' to see natural response (non-decaying oscillation).\n[.tran 0.3ms] --> see the difference.\n(Model 2a) Try classic antenna simulation: RLC + V source, R ~50-75, L and C gets Q factor ~12.\nE.g., L = 40mH, C = 100nF, R = 50.\n(Model 2b) Try classic basic antenna simulation: V source.\n[.tran 100ms] --> see the difference.\n* To see FFT, right-click > view > FFT.\n(Model 3) Try inductance coupling: C + L (with coupling to another circuit)\n- Cmembrane = 20pF --> V(e) second peak at 221.44kHz\n- Cmembrane = 200pF --> V(e) second peak at 221.44kHz. \n---> cannot see the difference.
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).