A few days ago, I purchased some crystals from BD6CR. However, when I tried to use them, I found myself struggling: how do I measure the parameters of the crystal? I vaguely remember seeing a SERIES XTAL in NanoVNA. (S21)The options were there, so I looked through them and wrote a short note.
Measurement process:
1. Connect the two ends of the crystal to the inner cores of the two SMA ports on the NanoVNA.
2. We need to examine the S21 phase angle of the NanoVNA, and by adjusting the frequency upper and lower limits of the NanoVNA according to the crystal calibration frequency, we can observe the process of the phase angle changing from 90° to -90° and from -90° to 90°. Alternatively, we can examine the series impedance (S21), which allows us to see the impedance change from -∞ to +∞, and then back to -∞. As shown in the figure, yellow represents the phase angle, and green represents the series impedance.
3. Open Measurement - SERIES XTAL to view crystal parameters.
4. Due to the limited number of measurement points in the NanoVNA, the error will inevitably be significant. Reducing the frequency range can help minimize this error.
Knowledge: Equivalent circuits for crystals
A single crystal oscillator can be represented by the circuit shown below.
C0 (which is Cg in NanoVNA) and two capacitors connected in parallel: the capacitance between the two electrodes;
Dynamic L equivalent inductance: Represents the inertia of mechanical vibration.
CM dynamic equivalent capacitance: Represents the compliance of the crystal oscillator.
Rм dynamic equivalent resistance: Represents the circuit's losses.
Common circuit simulation software simulates crystal oscillators and typically uses these four parameters.
Knowledge: The amplitude-frequency characteristic curve and phase-frequency characteristic curve of a crystal oscillator.
In the region between Fs and Fa (which corresponds to Fp in NanoVNA), the crystal exhibits capacitive behavior, operating in a parallel resonance state.
In this case, Fs represents the resonant frequency of a series RLC circuit when the inductive reactance X = 0.
$F_s = \frac{1}{2\pi\sqrt{L_m C_m}}$
Fa is the parallel resonant frequency when the inductive reactance X approaches infinity:
$F_a = F_s \sqrt{1 + \frac{C_m}{C_0}}$
The crystal oscillator has different operating frequencies depending on the load capacitance CL.
The specific working frequency F formula is:
F = Fs (1 + Cм/2)(C_0+C_L)} )
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