# Fast Frequency Acquisition and Phase Locking of Nonplanar Ring Oscillators
## 3 Principle of Frequency Acquisition  
In the FDCM, the beat signal frequency is measured digitally, and a control signal is generated for frequency acquisition. A block diagram of the FDCM is shown in Figure 2. The frequency of the beat signal is firstly divided by 200 and converted into square pulses. The dividable frequency ranges from 10 kHz to 300 MHz. The pulse repetition frequency is measured via a microprogrammed control unit (MCU). The measuring period is set to be 5 ms. From the measured frequency in the current measuring period and the previous period, the frequency control direction and the frequency shift amount were obtained. An MCU generates corresponding binary data to the digital/analog (D/A) converter, in which the frequency control signal is generated. After passing through the amplifier, the control signal is sent to a low pass filter. It is then sent to the \(V_{c2}\) port of the PZT driver. The low pass filter is essential for stable phase locking. In the locking status of the OPLL, the phase step and minor frequency step can cause a transient response in the phase error signal. Some frequency steps might be caused by the high frequency components of the D/A-converted signal. If the amplitude of the transient response signal reaches the threshold of the FDCM, it will function and generate a small frequency shifting signal. This is a false shifting signal and might result in losing lock. With a low pass filter of a 400 Hz bandwidth, the shifting signal is smoothed. The phase locking loop can precisely track the smoothed minor frequency shift, and keep a stable residual phase error. One frequency control cycle includes a frequency measuring period, 5 ms, and a frequency shifting period, 1 ms. The step response time of the low pass filter is close to 1 ms. Thus, the frequency shifting period is set to 1 ms.  
Figure 1: Block diagram of the optical frequency acquisition and the phase-locking loop. Figure 2: Block diagram of the frequency discrimination and control module (FDCM). Figure 3 shows the flow chart of the frequency discrimination and control program. The program is mainly achieved via an MCU. After program initialization, pulses that are sent to the module during the measuring period are counted. The frequency difference \(\Delta f_{p}\) in the current measuring period is computed from the counted pulse number. If \(\Delta f_{p}\) is less than critical frequency difference \(\Delta f_{c}\), then the frequency locking is achieved. Thus, the FDCM will maintain the frequency control voltage, and the loop will be locked under the function of the loop filter. The lock-in range and pull-in range of the loop are 15 kHz and 700 kHz, respectively. The critical frequency difference \(\Delta f_{c}\) can be set to 40 kHz, with a locking time less than 1 ms under the function of the loop filter. If \(\Delta f_{p}\) is larger than the frequency difference in the last measuring period, \(\Delta f_{b}\), then the frequency control direction is incorrect. If the current frequency control cycle is the second cycle, the wrong control direction is caused by a random chosen direction in the first frequency control cycle. Otherwise, the wrong control direction is caused by fast laser frequency drift during the last frequency control cycle. The frequency control direction will thus be changed, and the frequency shift amount is determined by \(\Delta f_{p}\) and the PZT tuning coefficient. If \(\Delta f_{p}\) is less than \(\Delta f_{b}\), then the frequency control direction is correct. The local laser frequency will be controlled in the correct direction until \(\Delta f_{p}\) is less than \(\Delta f_{c}\). Phase locking will thus be achieved via the loop filter. The choice of division ratio is a tradeoff between the maximum measurable frequency (MMF) and measurement accuracy (MA). The crystal oscillating frequency of the MCU is 24 MHz, corresponding to a machine cycle of 0.5 us. For a division ratio of 200, MMF is 200 MHz, and MA is 40 kHz.