Design of Wide-Range High-Precision Cesium Oven Temperature Control System for Time-Keeping Cesium Beam Frequency Standards

Abstract

The temperature fluctuation of a cesium oven has a significant impact on the performance of time-keeping cesium beam frequency standards. We have designed a circuit system for the precise temperature control of the cesium oven used in it. The use of a 24-bit analog-to-digital converter ensures a temperature measurement resolution more than 0.5 mK within the working range. The digital PID algorithm guarantees the accuracy of error signal computation, and a 16-bit digital-to-analog converter improves the resolution of the control current adjustment. Ultimately, we achieved the goal of keeping the temperature fluctuation of the cesium oven to less than 4 mK within a working range of 120 °C. The results indicate that the circuit system effectively ensures the performance of the cesium beam frequency standard.

1. Introduction

In much scientific research, temperature is an important influencing factor [1,2,3,4,5], especially in situations where atomic beams need to be generated [6]. Also, many types of atomic clocks or precision instruments need to consider the impact of temperature on the final output signal [7,8,9,10,11].

Time-keeping cesium beam frequency standards are widely used in defense, communication, power, transportation, and other fields [12]. As a device for generating cesium atomic beams, the cesium oven is the foundation for the normal operation of time-keeping cesium beam frequency standards. A cesium oven is placed inside a sealed cesium beam tube, which is equipped with a cesium bulb [13]. When the vacuum degree of the cesium beam tube reaches the required level, the cesium bulb is punctured by a high voltage, allowing the cesium atomic beam to pass through the puncture hole and be collimated by a collimator before being ejected. It then interacts with laser, microwave, and static magnetic fields to form clock transition signals [14,15].

The melting point of metallic cesium is 28 °C, and the boiling point is about 671 °C [16]. As the temperature rises, gaseous cesium atoms will continue to be ejected and form a cesium atomic beam. Generally speaking, when the cesium oven temperature is around 100 °C, the number of atoms in the cesium atomic beam can meet the requirements of atomic transition excited by the 9.2 GHz microwave field [17]. However, as the cesium atoms in the bulb are consumed, the number of cesium atoms will gradually decrease. If it drops to a certain extent, the number of cesium atoms can be ensured by raising the temperature of the cesium oven.

Due to the vacuum environment inside the cesium beam tube, cesium exists in liquid form in the cesium oven [18]. As the temperature increases, a portion of cesium transforms into a gaseous state, forming a saturated vapor pressure P inside. The research results of C.B. Alcock et al. indicated that the saturated vapor pressure P can be expressed as a polynomial of temperature T: [19]

$$logP\left(atm\right)=A+B{·T}^{-1}+C·logT+D·T{·10}^{-3 }$$

(1)

Here, A, B, C, and D are all constants.

From Formula (1), it can be seen that it is only when the temperature is stable enough that the saturated vapor pressure inside the cesium bubble can stabilize, thereby forming a relatively uniform cesium atomic beam for use in the later stage. That is to say, the stability of the cesium oven temperature directly affects the signal-to-noise ratio of the clock transition signal, and will further affect the output signal indicators of the cesium beam frequency standards.

Similarly, not limited to small cesium clocks, temperature is an important physical quantity in many situations where a hot atomic beam is required, which can directly affect many parameters, such as the velocity distribution, divergence angle, and flow rate of the atomic beam [20,21,22]. Therefore, a temperature control system with both high precision and wide range has good application prospects.

This paper is structured as follows: We present the fundamental cesium oven design in Section 2. In Section 3, the hardware design, including the sensors, the electric bridges, and the power amplification, is presented. We describe the software design in Section 4, including the digital filter, the temperature conversion, and the digital PID (proportional, integral, differential) operation. The experimental results and discussion are stated in Section 5. The conclusions are summarized in Section 6.

2. Design

The cesium oven is a very crucial component in time-keeping cesium beam frequency standards, and its design has a direct impact on the performance of this frequency standard. The main components of the cesium oven include the cesium reservoir, the jet tube, the sealing valve, the resistance heater, and the heating control system. The basic structure of the cesium oven is shown in Figure 1. Its volume is approximately 18.4 cm³. The upper “flat” cylindrical material is solid oxygen-free copper, with temperature control sensors and heating tubes placed in the reserved holes within it; the lower “thin” cylinder is a hollow stainless steel, with the cesium bulb placed inside, and the thin wire at the bottom is the ionization electrode.

To ensure the stability of the number of cesium atoms, it is necessary to set the upper temperature limit to approximately 140 °C and the lower temperature limit to around 20 °C, which is room temperature. At the same time, considering the nominal resistance value of the bridge circuit used for temperature measurement, the temperature control range is set from 20.77 °C to 141.16 °C, the temperature control accuracy is set to ±0.005 °C, which means the temperature change does not exceed 10 mK, and the temperature resolution must be set to above 0.5 mK.

Due to the complex shape and large volume of the controlled object, digital temperature control is adopted to avoid the drawbacks of analog temperature control, which is prone to oscillation during long integration times. The system structure diagram is shown in Figure 1.

The output voltage of the bridge reflects the real-time changes in temperature. This voltage, after being filtered and amplified by the signal conditioning circuit, is converted into a digital quantity by an analog-to-digital converter. The controller then performs PID calculations based on these data, and the result is converted into a voltage signal. This signal, after being amplified by a power amplifier, controls the cesium oven temperature in real-time through the heating element.

Due to the large temperature control range and high temperature resolution, a 24-bit ADC (analog-to-digital converter) is used. The ADC chip selected is ADS1232, which has a PGA (programmable gain amplifier) that can amplify the bridge signal internally, reducing the complexity of the signal conditioning circuit. The controller chosen is from the STM32L series. The DAC (digital-to-analog converter) chip selected is DAC8531, which has a 16-bit conversion precision.

Additionally, since the target temperature range is above room temperature and only heating is required, the entire system can be powered by a single power supply. At the same time, because the resistance of the heating element is relatively high, to ensure the control current, the system uses a +24 V power supply and converts it to the +12 V and +3.3 V required by the chips.

3. Hardware Design

3.1. Sensors and Wheatstone Bridges

Although there are many types of temperature sensors available, there are not many that can achieve a resolution of 0.5 mK. After comparison, a 10 K NTC (negative temperature coefficient) thermistor was chosen as the temperature sensor. It was installed in a pre-drilled hole in the cesium oven, near the heating element. This was because the cesium oven was in a vacuum environment and was insulated from the installation base by a heat-insulating ceramic, which provides good thermal insulation. As long as the temperature of the heating element is kept constant, the temperature of the cesium oven can be constantly maintained.

The bridge circuit is shown in Figure 2 [23]. To ensure accuracy, the bridge power supply uses a high-precision, low-temperature-drift reference voltage source instead of the power supply voltage. The other resistors on the bridge use 0.1% precision, low-temperature-drift metal film resistors. These measures can improve the accuracy of the bridge’s output voltage. Changes in temperature cause changes in the resistance value of the thermistor, which in turn causes changes in the output voltage of the bridge.

According to the specific configuration of the bridge and the relationship between the thermistor resistance value and temperature, it can be expressed as follows [24]:

$$R_T=R_{T_0}{e}^{B\left({\displaystyle \frac{1}{T}}-{\displaystyle \frac{1}{T_0}}\right)}$$

(2)

Here, $R_T$ is the resistance value of the thermistor at temperature T, $R_{T_0}$ is the resistance value of the thermistor at temperature T₀, and B is a constant related to the manufacturing process.

When the temperature varies between 20.77 °C and 141.16 °C, the thermistor resistance changes between 12 kΩ and 0.39 kΩ, and the bridge output varies between −585 mV and +585 mV. The reason for processing the bridge voltage into a differential output is that the subsequent analog-to-digital conversion chip ADS1232 requires a differential signal input to maximize the measurement range. Additionally, since the ADS1232 has an internal Programmable Gain Amplifier, the bridge output is directly filtered and then input into the ADS1232 for the conversion to a digital quantity.

3.2. Power Amplification

The controller performs PID calculations based on the difference between the actual temperature and the set temperature, and the result of the calculation is converted into an analog signal. This analog signal, as shown in Figure 3, changes the current through the heating element via the power amplification circuit, thereby controlling the temperature of the cesium oven in real-time.

The output of the front-end digital-to-analog conversion is driven by an operational amplifier to control the heating power through the power transistor. The Darlington transistor TIP122 was chosen for its amplification factor of 1000 and a maximum output current of up to 5 A, which meets the amplification requirements. Based on the heating requirements of the cesium oven and the results of preliminary experiments, a 5.1 Ω power resistor was selected as the sampling resistor, which can control the maximum heating current to around 500 mA. This maximum heating current is the optimal value obtained after comprehensive consideration of factors such as heating speed, power supply capacity, and cooling conditions.

Other circuits include power supply, the minimum system of the controller, and serial communication, etc., which are quite common and need not be elaborated. Since this circuit is a module of the entire machine, all controls are implemented through serial port commands, and common human–machine interaction functions such as keyboards and screens have not been designed.

4. Software Design

4.1. Digital Filtering

Analog signals are inevitably subject to interference, and although filtering can reduce its impact, it cannot be completely eliminated. Therefore, the digital quantity obtained from analog-to-digital conversion needs to be filtered before it can be used as the basis for digital PID calculations. We adopted a filtering scheme of limiting amplitude plus averaging, which has achieved very good filtering effects.

Within a control cycle, 50 continuous samples are taken, and the data obtained from these 50 samples are sorted. Then, the 10 largest data points and the 10 smallest data points are discarded, and only the arithmetic mean of the middle 30 data points is taken to obtain the final digital quantity that reflects the temperature.

4.2. Temperature Conversion

Based on the relationship between temperature and the resistance of the thermistor, the configuration of the Wheatstone bridge, the gain of the PGA, and the reference voltage of the ADS1232, the real-time temperature of the cesium oven can be calculated. Since the ADS1232 has a differential input, the most significant bit of its output digital quantity defines the polarity of the input voltage; that is, the magnitude relationship between the positive and negative input ends. Depending on the different most significant bits, we adopted a process as shown in Figure 4 for the conversion between digital quantity and temperature.

Within a control cycle, 50 continuous samples are taken, and the data obtained from these 50 samples are sorted. Then, the 10 largest data points and the 10 smallest data points are discarded, and only the arithmetic mean of the middle 30 data points is taken to obtain the final digital quantity that reflects the temperature.

4.3. Digital PID Operation

Digital PID control primarily calculates the error based on the difference between the set temperature and the actual temperature, and then converts this error into an analog signal output through a DAC to drive the heating wire and heat the cesium oven. The PID method originated from analog circuits, but performing PID calculations using digital methods can also achieve excellent control effects. In digital technology-based temperature control systems, digital PID calculations are the core of the program and directly affect the final temperature control results.

The basic PID control law can be expressed as [25]

$$u(t)=K_P\left[e\left(t\right)+{\displaystyle \frac{1}{T}}\int e\left(t\right)dt+T_d{\displaystyle \frac{de\left(t\right)}{dt}}\right]$$

(3)

where $u\left(t\right)$ is the control quantity, $e\left(t\right)$ is the control deviation, $K_P$ is the proportional gain, and $T_d$ is the derivative time.

Digital PID operation involves discretizing the differential equation represented by Equation (4), which comes in three forms: position form, increment form, and velocity form. Based on the characteristics of the temperature control circuit, an increment form PID operation has been designed. To facilitate programming, the incremental PID operation can be simplified to

$$∆u(k)=K_P\left[∆e\left(k\right)+{\displaystyle \frac{T}{T_i}}e(k)+{\displaystyle \frac{T}{T_d}}{∆}^{2}e(k)\right]$$

(4)

The flow chart of operation is shown in Figure 5.

The overall working process involves continuously repeating sampling and filtering, converting the bridge voltage, calculating real-time temperature, PID operation, and converting the error signal into an analog quantity. It is worth mentioning that in the digital temperature control process, in addition to the reasonable setting of PID parameters, the setting of the control period $\tau$ is also very important. At the same time, the system determines whether there are any instructions based on the serial port interrupt and responds to serial port instructions when necessary. The overall working process involves continuously repeating sampling and filtering, converting the bridge voltage, calculating real-time temperature, PID operation, and converting the error signal into an analog quantity. It is worth mentioning that in the digital temperature control process, in addition to the reasonable setting of PID parameters, the setting of the control period is also very important. At the same time, the system determines whether there are any instructions based on the serial port interrupt and responds to serial port instructions when necessary.

4.4. System Flow

After implementing the above software, hardware modules and algorithms, it is also a challenge to ensure that the system works in a coordinated manner and that the temperature control effect always meets the design requirements under changing external conditions. We use time-division multiplexing to schedule program execution reasonably, execute various functions at regular intervals, and put the controller into sleep mode during idle time without computing and communication functions to save power consumption. Ultimately achieving a balance between temperature control accuracy, system power consumption, and timely response.

5. Experimental Results and Discussion

After the completion of the system’s software and hardware debugging, we tested its temperature control effect. By connecting the leads of the sealed cesium beam tube through the terminal block, the thermistor and heating element pre-installed on the cesium oven were connected to the circuit. Multiple temperature working points were set for long-term testing. The temperature control module is in Figure 6, and the results are shown in Figure 7.

As shown in Figure 7, the experiment focuses on temperature control, with a target set at 60 °C. The data presented in the table illustrate the temperature readings recorded during the experiment, highlighting the system’s performance in maintaining the desired temperature. The readings show a range of values around the target temperature, specifically between 59.9995 °C and 60.0005 °C. This tight range indicates that the temperature control system is functioning effectively, with minimal fluctuations around the set point. The precision of the measurements reflects the system’s capability to maintain stability, which is crucial for applications requiring exact temperature control. Throughout the experiment, the temperature readings consistently hover around 60 °C, demonstrating the system’s responsiveness to any deviations. For instance, if the temperature slightly drops to 59.9995 °C, the control mechanism quickly adjusts to bring it back to the target. Similarly, if the temperature rises to 60.0005 °C, the system effectively regulates the heating element to prevent overshooting. The data further suggest that the temperature control system employs a feedback loop, likely utilizing a PID control algorithm. This algorithm continuously monitors the temperature and makes real-time adjustments to maintain the set point. The tight control around 60 °C not only indicates the effectiveness of the control strategy, but also ensures that the system can adapt to external disturbances, such as changes in ambient temperature or variations in the heating element’s performance. In conclusion, the experimental data demonstrate that the temperature control system is highly effective in maintaining a stable temperature of 60 °C, with minimal fluctuations. This level of precision is essential for applications where temperature stability is critical, ensuring optimal performance and reliability in various operational contexts.

As shown in Figure 7, the experimental data provided outlines the temperature control around a target of 110 °C. The recorded temperatures demonstrate minor deviations from the set point, oscillating within a narrow margin. The values range from 109.998 °C to 110.002 °C, indicating a high degree of precision in the temperature control system. The data suggest that despite slight fluctuations, the system promptly corrects any deviations, maintaining temperatures remarkably close to the desired 110 °C. This consistency is vital for applications where precise temperature control is essential, such as in scientific research, material processing, or any industrial application with thermal sensitivity. The accompanying time stamps, increasing in a sequence likely representing seconds, suggest that these temperature readings were captured at regular intervals. This regular data capture is typical for systems employing feedback control mechanisms to adjust the temperature in real-time. The system’s ability to swiftly respond to temperature changes and maintain the set point with minimal deviation is a testament to the effectiveness of its control algorithms and components.

6. Conclusions

This work presents a high-precision temperature control system for the cesium oven in time-keeping cesium beam frequency standards. The system utilizes a 24-bit ADC for temperature measurement with a resolution greater than 0.5 mK and employs a digital PID algorithm to ensure the accurate computation of error signals. A 16-bit DAC enhances the resolution of control current adjustments. The designed system achieves temperature stability within a range of 120 °C, maintaining fluctuations below 4 mK. The experimental results validate the effectiveness of this system, demonstrating its significant value for guiding temperature control in cesium ovens for time-keeping applications. This advancement in temperature control is crucial for enhancing the performance and reliability of time-keeping cesium beam frequency standards used across various critical industries.