I designed the crystal using spice capacitor parameters. This models the fundamental, but does not model overtones. The code needed to compute crystal equivalent spice capacitor parameters is as follows;
' Crystal specifications wanted.
Fp = 7.040e6 ' crystal parallel resonant frequency, Hz
CL = 20e-12 ' at load capacitance, farads
Q = 20e3 ' crystal Q factor
R1 = 60 ' crystal series resistance, ohms
C0 = 5e-12 ' crystal shunt capacitance, farads
' variables needed for initial temp approximation and final value.
Fs_tmp, Fs ' series resonant frequency, Hz
Wo_tmp, Wo ' angular frequency, rad/sec
C1_tmp, C1 ' crystal motional capacitance
L1 ' crystal motional inductance
' initial computation.
Fs_tmp = Fp
Wo_tmp = Fp * TwoPi
C1_tmp = 1 / ( Q * Wo_tmp * R1 )
Fs = Fp / ( 1 + C1_tmp / ( 2 * ( C0 + CL ) ) )
Wo = TwoPi * Fs
' Refine to final values.
C1 = 1 / ( Q * Wo_tmp * R1 )
L1 = 1 / ( Wo^2 * C1 )
' It generated these capacitor parameters;
Basic capacitance = 18.8393 f F = 0.0188393 pF.
Series inductance = 27.149 mH.
Series resistance = 60.0 ohm.
Parallel capacitance = 5.0 pF.
For a parallel frequency of 7.040 MHz @ Load capacitance = 20 pF
The series frequency is 7.037348 MHz
Here is the crystal model and simple output response.
View attachment 227696
View attachment 227697
Once simulating the circuit, change the tuning capacitor of the tank, to sweep across the synthetic crystal. Watch the initial transient ringing to see it decay, which implies it has loss not gain.I have searched many of the texts on oscillator design and have not found any similar design, ECO with a tank, or other similar topology.
I find it hard to believe this is an electron coupled oscillator with 390pF between the base emitter terminals.
There is a problem with crystal series traps in that, even when not resonant at the oscillator frequency, it will pass all the distortion and noise to the output.