太赫兹功率传感器结构改进及快速测量方法研究

本文改进了WR-6 (110GHz~170GHz) 量热型功率传感器的内部结构，并采用惠斯通电桥和数字PID方式对传感器进行控制，实验结果证明该结构大大降低传感器的热时间常数，提高了响应速度。实验结果表明，相比前期采用的四线自平衡电桥功率计，新方法的测量时间减小了1倍，在20mW量程下的测量时间为15s内。

量热型功率计分为热敏电阻式和热电偶式，都是通过测热的方式将负载吸收的待测射频功率转换为可测量的直流或低频信号。目前国家功率基准采用量热的方式来定标传感器的有效效率，但市场上缺少110GHz频率以上的商用功率传感器，中国计量科学研究院研制出WR-6热敏电阻传感器并基于量热方式建立WR-6功率基准[1]。其中该功率计采用四线自平衡电桥进行直流替代[2][3]，但需要外接数字电压表且响应时间长达半分钟，在室温进行量值传递时容易受到温度的波动。

因此改进了太赫兹功率传感器结构并对直流替代加热单元进行软件PID控制以实现太赫兹功率快速测量。由于采用了更好的热补偿算法，新型热敏型功率传感器能够在室温下作为计量级功率传感器使用，这也为今后研制商用太赫兹热敏型功率计提供有益的参考。

WR-6量热型传感器采用直流替代方法，即太赫兹能量通过波导传输到吸波负载上，负载吸收太赫兹波产生热量，此时减小负载上的直流功率使得负载温度保持不变，将太赫兹功率产生的热量用直流功率的变化表示出来。如下图1所示采用了四线自平衡电桥进行直流替代的原理框图。工作端RT1与参考端RT2呈串联关系且流经二者的电流相同，且有a, c两点等电势，b, d两点等电势，所以根据欧姆定律有RT1=RT2。给传感器加入电磁波功率后，吸收元件吸收电磁波功率，电阻值发生变化，这将会导致A1和A2的输入端电压发生变化，并通过控制三极管实现对环路电流的调整，环路达到平衡。

本文将四线自平衡电桥中测温与加热功能合为一体的直流电路部分分为只负责测温的热敏电阻和只负责加热的加热电阻。

改进后功率传感器采用双线结构如图2所示，加入太赫兹功率的一端称作工作端，另一端用于对环境温度产生的影响进行补偿，被称作补偿端。为了达到良好的补偿效果，两端的热力学特性尽量做到了一致。两端均接有热敏电阻和加热电阻，热敏电阻接入功率计中的惠斯通电桥进行温度测量，补偿端的加热电阻用于进行各量程偏置功率的设置，工作端的加热电阻用于进行直流替代。

传感器采用等温法进行工作，具体工作过程如下：加入太赫兹功率前，控制系统根据量程设置通过DA给两端加热电阻输出相同加热功率，测量电桥测量两端温差，理想条件下，系统平衡时温差为0。加入太赫兹功率后，工作端的太赫兹负载吸收太赫兹功率，导致工作端温度快速上升，AD检测到电桥变化，计算机系统立刻进行PID运算并减少工作端DA输出以达到新的平衡。稳定后，工作端直流功率的变化量被称作直流替代功率，它正比于太赫兹负载吸收的功率。用工作端的直流功率来替代工作端的射频功率，这种方法不需要负载达到热平衡，只要太赫兹波负载和直流负载的温差在可接受可控制的范围内，工作端偏置电压值保持稳定，功率计的输出就稳定了。

该方法控制过程简单，但难点在于如何制造出响应时间快、负载温度均匀的传感器，同时又能保持可接受的灵敏度[5]。

为查看两端加入功率的热时间常数[4]，系统上电后分别给工作偏置和参考偏置加入相同功率等待系统平衡。

如图3可以看出在加入相同的功率下工作端和参考端响应有3%误差，该误差可以用过实验进行修正，可以认为对称性较好。直流响应的快慢决定是否能够用直流快速替代射频,改进结构在直流下的响应速度与之前相比提高一倍。更重要的是射频响应速度，射频的响应速度与之前相比提高了2倍看出改进结构对射频响应时间常数为11.6s，和改进后直流响应时间近似。由于直流和射频响应速度一致，在进行射频功率测量前加入已知直流功率进行替代能够有效查看替代效果，并对系统进行调试。

在测量系统中，将工作端与参考端负载的温差转换为电压差e(t)，输入到PID控制器中，根据PID控制策略调整工作端偏置加热电阻电压值，使两端负载温度差维持不变。PID 控制算法公式为

其中Kp为比例调节系数，Ki为积分调节系数，Kd为微分调节系数。

本文在20mW功率量程下对不同直流功率(模拟射频功率)进行直流替代。相比较保持功率传感器温度不变，作为功率指示器来说更重要的是控制输出的电压值能够快速稳定。如图4所示，在10mW直流下替代的电压值在8s能够达到平衡的95%，此时已经能够读数。读数完全稳定在15s，测量时间相比四线自平衡功率计缩短一半。如图5所示，误差放大器输出说明需要经过大约两分钟功率座的温度才能稳定。

用PID调节参考偏置电压进行不同直流下替代的效果如表1所示直流替代效果，其中响应时间表示从10%到90%的时间，可以看出直流替代的响应时间比较快。

通过改进太赫兹功率传感器实现了时间常数的减小，闭环控制中增加反馈增益实现了直流和射频功率的快速测量，相比与四线电流自平衡功率计,测量时间缩短一半,为实现量热型性太赫兹功率计快速测量提供方法。

This paper improves the internal structure of the WR-6 (110GHz~170GHz) calorimetric power sensor and utilizes the Wheatstone bridge and digital PID control to regulate the sensor. The experimental results demonstrate that this structure significantly reduces the thermal time constant of the sensor and enhances the response speed. The experimental method for determining the system gain and time constant is established, and the results indicate that compared to the previous four-wire balanced bridge power meter, the new method reduces the measurement time by half, with a measurement time of within 15 seconds for a 20mW range.

Calorimetric power sensors can be classified into thermal resistance-based and thermocouple-based sensors, both of which convert the RF power absorbed by the load into measurable DC or low-frequency signals through heat measurement. Currently, calorimetric methods are used as the national power standards for calibrating sensor effective efficiency. However, there is a lack of commercial power sensors above 110GHz frequency range. The WR-6 thermal resistance sensor has been developed by the National Institute of Metrology, China, and the WR-6 power standard based on the calorimetric method has been established [1]. The power meter in this study employs a four-wire balanced bridge for DC substitution [2][3], but it requires an external digital voltmeter and has a response time of up to half a minute, making it susceptible to temperature fluctuations during value transfer at room temperature.

Therefore, this paper proposes improvements to the terahertz power sensor structure and implements software PID control for the DC substitution heating unit to achieve fast terahertz power measurement. With a better thermal compensation algorithm, the new thermal-sensitive power sensor can be used as a metrology-grade power sensor at room temperature, providing useful references for future development of commercial terahertz thermal-sensitive power meters.

The WR-6 calorimetric sensor adopts the DC substitution method, where terahertz energy is transmitted through waveguides to the absorbing load, which generates heat. By reducing the DC power on the load to maintain a constant load temperature, the heat generated by terahertz power is represented by the change in DC power. As shown in Figure 1, a four-wire balanced bridge is used for DC substitution. The working terminal RT1 and the reference terminal RT2 are in series and carry the same current. Points a and c have the same potential, as well as points b and d, so according to Ohm's law, RT1=RT2. When electromagnetic power is applied to the sensor, the absorbing element absorbs the electromagnetic power, causing the resistance value to change. This in turn leads to variations in the input voltages of A1 and A2, and the loop current is adjusted through transistor control to achieve balance.

In this paper, the DC circuit part responsible for temperature measurement and heating function in the four-wire balanced bridge is divided into a thermal resistance solely responsible for temperature measurement and a heating resistor solely responsible for heating.

The improved power sensor adopts a dual-line structure, as shown in Figure 2. The end where terahertz power is introduced is referred to as the working end, while the other end is used to compensate for the influence of ambient temperature and is referred to as the compensation end. To achieve good compensation results, the thermodynamic characteristics of both ends are made as consistent as possible. Both ends are connected to the thermal resistance and heating resistance. The thermal resistance is connected to the Wheatstone bridge in the power meter for temperature measurement, and the heating resistance on the compensation end is used to set bias power for various ranges. The heating resistance on the working end is used for DC substitution.

The sensor operates using the isothermal method. The working process is as follows: before introducing terahertz power, the control system outputs the same heating power to the working bias and reference bias resistors based on the range setting, and measures the temperature difference between the two ends using the bridge. Ideally, the temperature difference is 0 when the system reaches equilibrium. After introducing terahertz power, the terahertz load on the working end absorbs power, causing the temperature of the working end to rise rapidly. The AD detects changes in the bridge, and the computer system immediately performs PID calculations and reduces the output of the working end DA to achieve a new equilibrium. Once stabilized, the change in DC power on the working end is referred to as the DC substitution power, which is proportional to the power absorbed by the terahertz load. By substituting the DC power of the working end for the RF power, this method does not require the load to reach thermal equilibrium. As long as the temperature difference between the terahertz load and the DC load is within an acceptable and controllable range, and the bias voltage of the working end remains stable, the output of the power meter will also remain stable.

The challenge lies in manufacturing a sensor with fast response time and uniform load temperature while maintaining acceptable sensitivity [5].

To observe the thermal time constants when power is applied to both ends [4], the system is powered on, and the same power is applied to the working bias and reference bias, waiting for system equilibrium.

As shown in Figure 3, under the same applied power, there is a 3% error in the response between the working end and the reference end. This error can be corrected through experimentation and suggests good symmetry. The response speed under DC determines the feasibility of replacing RF with DC. The improved structure exhibits twice the response speed compared to the previous one. More importantly, the response speed for RF is also improved, which is two times faster than before, indicating a time constant of 11.6s for RF response, which is nearly the same as the improved DC response time. Due to consistent response rates for DC and RF, introducing known DC power before RF power measurement allows for effective evaluation of the substitution effect and system debugging.

In the measurement system, the temperature difference between the working and reference end load is converted into a voltage difference e(t) and input to the PID controller. Based on the PID control strategy, the bias heating resistor voltage of the working end is adjusted to maintain a constant temperature difference between the two ends. The PID control algorithm equation is as follows:

where Kp is the proportional gain, Ki is the integral gain, and Kd is the derivative gain.

In this paper, DC substitution is performed for different DC powers (simulated RF powers) under a 20mW power range. For a power indicator, it is more important to control the output voltage to quickly stabilize than to maintain a constant power sensor temperature. As shown in Figure 4, at 10mW DC power, the substitution voltage reaches 95% of equilibrium within 8s, which is already readable. The reading stabilizes completely at 15s, reducing the measurement time by half compared to the four-wire balanced power meter. As shown in Figure 5, the output of the error amplifier indicates that it takes about two minutes for the power seat temperature to stabilize.

The effect of DC substitution under different DC powers using PID control for bias heating voltage adjustment is shown in Table 1. The response time represents the time from 10% to 90%, and it can be seen that DC substitution has a fast response time.

By improving the terahertz power sensor, the time constant is reduced, and closed-loop control with increased feedback gain enables fast measurement of both DC and RF powers. Compared to the four-wire balanced power meter, the measurement time is halved, providing a method for fast measurement of thermally sensitive terahertz power meters.