Negative resistance and oscillation margin of oscillating circuit

     The frequency characteristics of the negative resistance Ri seen at the resonator terminal of the Colpitts-type oscillating circuit are measured under small signal conditions. Although the load capacitance CL does not change much, the load resistance Ri has a frequency-dependent characteristic.

     To oscillate, the negative resistance must be RL ≤ Ri within its frequency range. This characteristic is calculated using circuit constants to obtain the reactance of C1 and C2. Compared with the parallel resistor unit, it can generally be expressed in the following formula in a small frequency range. Ri will not become negative at low frequencies.

     The frequency (compensation frequency fc) at which Ri = 0 in the figure can be selected according to the design value of the circuit constants, which can suppress the fundamental frequency of the crystal oscillator and only generate three times the frequency-determining oscillation.

     In addition, the method of confirming the oscillation margin is to insert the crystal oscillator of the oscillating circuit (part X in Figure 4.4-1) and series pure resistance, turn on and off the power supply, and before starting oscillation, its resistance value will change from large to small. (Do not pay attention to the decrease in the oscillation output frequency caused by inserting the resistance, only judge whether it oscillates). The approximate value of the circuit's negative resistance Ri is the series resistance value at the beginning of the additional oscillation and the crystal oscillator's series resistance R1. As the negative resistance changes with temperature, the upper and lower limits of the temperature range must be confirmed.

     To improve the oscillation margin and starting condition of the oscillating circuit, it is necessary to ensure that the negative resistance Ri of the circuit is at least five times the equivalent resistance RL when the crystal oscillator is loaded. If the ratio is less than this, it can easily cause frequency instability due to the difference between the crystal oscillator and the circuit, and cause adverse phenomena such as no oscillation or longer start-up time.