CN111726173A - An internal calibration system and method for transmitting and receiving duplex phased array antennas - Google Patents
An internal calibration system and method for transmitting and receiving duplex phased array antennasDownload PDFInfo
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Abstract
Translated fromChinese
Description
Translated fromChinese技术领域technical field
本发明涉及一种用于收发双工相控阵天线的内校准系统及方法，属于相控阵天线技术领域。The invention relates to an internal calibration system and method for transmitting and receiving duplex phased array antennas, belonging to the technical field of phased array antennas.
背景技术Background technique
相控阵天线发挥其优异电性能的前提是阵面幅相分布的精确控制，即要求阵列单元的幅相分布与满足指向要求的期望值保持一致。然而在实际的相控阵天线系统中，由于存在着幅度和相位误差，因此阵元的幅度和相位一致性很难得到满足。阵元幅度和相位误差的存在将导致相控阵天线的增益降低，并降低波束指向精度，从而影响相控阵天线工作性能。因此对于任何应用领域的相控阵天线，阵面幅相校准是不可避免的。The premise of the excellent electrical performance of the phased array antenna is the precise control of the amplitude and phase distribution of the array, that is, the amplitude and phase distribution of the array elements are required to be consistent with the expected value that meets the pointing requirements. However, in the actual phased array antenna system, due to the existence of amplitude and phase errors, it is difficult to satisfy the amplitude and phase consistency of the array elements. The existence of array element amplitude and phase errors will reduce the gain of the phased array antenna and reduce the beam pointing accuracy, thus affecting the performance of the phased array antenna. Therefore, for phased array antennas in any application field, the alignment of the array's amplitude and phase is unavoidable.
相控阵天线装配完成后必须对阵元的幅、相进行校准，使得天线性能达到最佳状态。但是天线在交付用户使用一段时间后，受使用环境的影响，天线的射频通道会产生相位漂移，最终导致全阵的辐射性能受到明显影响，扫描能力下降。相控阵天线在车载、机载、星载等平台上有广阔的应用前景，而部分平台要求相控阵天线能够在不拆机、无辅助设备的情况下实现对自身幅度相位的监测和校正。因此，具备在线校准的功能，是相控阵天线的核心竞争力之一。After the phased array antenna is assembled, the amplitude and phase of the array elements must be calibrated, so that the antenna performance can reach the best state. However, after the antenna is delivered to the user for a period of time, due to the influence of the use environment, the radio frequency channel of the antenna will have a phase shift, which will eventually lead to a significant impact on the radiation performance of the entire array and a decrease in the scanning capability. Phased array antennas have broad application prospects on vehicle, airborne, and spaceborne platforms, and some platforms require that phased array antennas can monitor and correct their own amplitude and phase without disassembling the machine and without auxiliary equipment. . Therefore, having the function of online calibration is one of the core competitiveness of phased array antennas.
互耦方法不需额外的校准设备，可实现天线阵列在线校准，但其需要单元间的互耦要满足对称条件或者互耦系数（幅相信息）已知，因此对天线单元方向图以及单元排布提出严格要求，或者需要对天线阵面各个天线单元间的传输系数进行精确测量，而这对于大型相控阵天线，其所需工作量是不可估量的。The mutual coupling method does not require additional calibration equipment, and can achieve online calibration of the antenna array, but it requires the mutual coupling between units to meet the symmetry conditions or the mutual coupling coefficient (amplitude and phase information) is known, so the antenna unit pattern and unit array are required. However, for large-scale phased array antennas, the required workload is immeasurable.
而另外一种互耦方法是采用耦合器在天线端口处进行信号的闭环耦合，实现信号回路，此方法优点是不需考虑互耦系数的不一致性，缺点是耦合信号不包含无源天线阵列的幅相信息，需要采用其他方法标定天线阵列的幅相特征。Another mutual coupling method is to use a coupler to perform closed-loop coupling of the signal at the antenna port to realize the signal loop. The advantage of this method is that it does not need to consider the inconsistency of the mutual coupling coefficient. The amplitude and phase information of the antenna array needs to be calibrated by other methods.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于解决上述问题，提出一种用于收发双工相控阵天线的内校准系统及方法，该系统采用耦合器在天线端口处进行信号的闭环耦合，实现了信号回路，解决了无源天线阵列幅相信息不明确的问题，其实现简便，具有很高的工程应用前景。The purpose of the present invention is to solve the above problems, and propose an internal calibration system and method for transmitting and receiving duplex phased array antennas. The problem of unclear amplitude and phase information of passive antenna arrays is easy to implement and has high engineering application prospects.
为了实现上述目的，本发明采用技术方案为：In order to achieve the above object, the present invention adopts the technical scheme as follows:
一种用于收发双工相控阵天线的内校准系统，包括定标分机、波控分机、接收射频通路和发射射频通路；An internal calibration system for transmitting and receiving duplex phased array antennas, comprising a calibration extension, a wave-controlled extension, a receiving radio frequency path and a transmitting radio frequency path;
所述定标分机包括定标激励通道、定标接收通道和通信及信号处理模块；其中，定标激励通道产生中频信号，并通过第一选通开关连接接收射频通路和发射射频通路，所述中频信号经过上变频后，在第一选通开关的选通作用下输出给接收射频通路或发射射频通路，从而为接收射频通路输出接收单载波信号，或者为发射射频通路输出发射单载波信号；定标接收通道通过第二选通开关连接接收射频通路和发射射频通路，在第二选通开关的选通作用下接收接收射频通路或发射射频通路的回路信号，并将接收到的回路信号下变频为中频信号，再经过A/D转换后输出数字回路信号给通信及信号处理模块；通信及信号处理模块与波控分机进行通信，并对定标接收通道发来的数字回路信号进行幅相解算；The calibration extension includes a calibration excitation channel, a calibration receiving channel, and a communication and signal processing module; wherein, the calibration excitation channel generates an intermediate frequency signal, and is connected to the receiving radio frequency channel and the transmitting radio frequency channel through a first gating switch, and the After the intermediate frequency signal is up-converted, it is output to the receiving radio frequency path or the transmitting radio frequency path under the gating action of the first gating switch, so as to output and receive a single carrier signal for the receiving radio frequency path, or to transmit a single carrier signal for the transmitting radio frequency path output; The calibration receiving channel connects the receiving radio frequency channel and the transmitting radio frequency channel through the second gating switch, and receives the loop signal of the receiving radio frequency channel or the transmitting radio frequency channel under the gating action of the second gating switch, and converts the received loop signal under the gating function. The frequency is converted into an intermediate frequency signal, and after A/D conversion, the digital loop signal is output to the communication and signal processing module; solve;
所述波控分机作为控制中枢，一方面与定标分机进行交互，发送校准指令和通道开关信息，接收通道编号和通道幅相信息，并对相控阵各有源通道进行幅度、相位的补偿；另一方面根据通道分时校准顺序，在某一时刻开启相应通道，并将通道设置为初始状态；The wave control extension acts as the control center. On the one hand, it interacts with the calibration extension, sends calibration instructions and channel switch information, receives channel number and channel amplitude and phase information, and performs amplitude and phase compensation for each active channel of the phased array. ; On the other hand, according to the channel time-sharing calibration sequence, open the corresponding channel at a certain time, and set the channel to the initial state;
所述接收射频通路包括顺次连接的接收定标网络组合、第一通道切换开关、多个并列的接收通道，以及接收馈电网络组合，每个接收通道的前端均设有一个耦合器；所述发射射频通路包括顺次连接的发射馈电网络组合、第二通道切换开关、多个并列的发射通道，以及发射定标网络组合，每个发射通道的后端均设有一个耦合器；第一/第二通道切换开关用于切换不同的接收/发射通道，实现待校准通道的选择，所述耦合器用于形成校准信号，每路接收/发射通道均用于实现信号的放大、滤波和幅相控制。The receiving radio frequency path includes a receiving calibration network combination connected in sequence, a first channel switch, a plurality of parallel receiving channels, and a receiving feeding network combination, and the front end of each receiving channel is provided with a coupler; The transmitting radio frequency path includes a combination of transmitting feeder networks connected in sequence, a second channel switch, a plurality of parallel transmitting channels, and a combination of transmitting calibration networks, and a coupler is provided at the back end of each transmitting channel; The first/second channel switch is used to switch between different receiving/transmitting channels to realize the selection of the channel to be calibrated. The coupler is used to form a calibration signal, and each receiving/transmitting channel is used to realize signal amplification, filtering and amplitude. Phase control.
一种收发双工相控阵天线的内校准方法，包括以下步骤：An internal calibration method for a transceiver duplex phased array antenna, comprising the following steps:
1）天线研制过程中，对天线在暗室进行外场校准，此时得到天线每个通道收发的初始幅度矩阵[A1_out]和相位矩阵[ψ1_out]，所述天线中具有如权利要求1所述的内校准系统；1) In the process of antenna development, the antenna is calibrated in the dark room outside the field, and the initial amplitude matrix [A1_out] and phase matrix [ψ1_out] of the transmission and reception of each channel of the antenna are obtained. calibration system;
2）启动内校准系统，得到每个通道收发的初始幅度矩阵[A1_in]和相位矩阵[ψ1_in]，两者相减得到内校准基准数据：[A1]=[A1_in]-[A1_out]和[ψ1]=[ψ1_in]-[ψ1_out]；将幅相矩阵[A1_out]、[ψ1_out]和[A1]、[ψ1]存储于波控分机的FLASH中；2) Start the internal calibration system to obtain the initial amplitude matrix [A1_in] and phase matrix [ψ1_in] of each channel’s transmission and reception, and subtract the two to obtain the internal calibration reference data: [A1]=[A1_in]-[A1_out] and [ψ1] ]=[ψ1_in]-[ψ1_out]; store the amplitude and phase matrices [A1_out], [ψ1_out] and [A1], [ψ1] in the FLASH of the WCS extension;
3）天线在装机初次使用时，先进行内校准，将直接测得的实时内校准幅度矩阵[A2_in]和相位矩阵[ψ2_in]分别与[A1]和[ψ1]相减，得到[A2]、[ψ2]，并存储于波控分机的FLASH中；3) When the antenna is installed and used for the first time, the internal calibration is performed first, and the directly measured real-time internal calibration amplitude matrix [A2_in] and phase matrix [ψ2_in] are subtracted from [A1] and [ψ1] respectively to obtain [A2], [ψ2], and stored in the FLASH of the wave-controlled extension;
4）天线在长期使用过程中，每次加电时先将幅度矩阵[A2]和相位矩阵[ψ2]从FLASH加载到FPGA内部RAM当中；若需要进行在线实时内校准，则将直接测得的实时内校准幅度矩阵[A3_in]、相位矩阵[ψ3_in]分别与[A1]、[ψ1]相减，得到[A3]、[ψ3]，写入到RAM当中覆盖掉[A2]、[ψ2]；若不需要进行在线实时内校准，则RAM中的数据与出厂时的内校准数据一致，都为[A2]和[ψ2]；4) During the long-term use of the antenna, the amplitude matrix [A2] and the phase matrix [ψ2] are loaded from the FLASH into the internal RAM of the FPGA each time the power is turned on; if online real-time internal calibration is required, the directly measured The real-time internal calibration amplitude matrix [A3_in] and phase matrix [ψ3_in] are subtracted from [A1] and [ψ1] respectively to obtain [A3] and [ψ3], which are written into RAM to cover [A2] and [ψ2]; If online real-time internal calibration is not required, the data in RAM is consistent with the internal calibration data at the factory, which are [A2] and [ψ2];
5）将实时内校准幅度矩阵的变化量 [ΔA]=[A3]-[A2] 作为判别天线是否正常的依据，并以实时内校准相位矩阵的变化量[Δψ]=[ψ3]-[ψ2]作为相位修正差值，对初始相位数据进行修正。5) The variation of the real-time calibration amplitude matrix [ΔA]=[A3]-[A2] is used as the basis for judging whether the antenna is normal, and the variation of the real-time calibration phase matrix [Δψ]=[ψ3]-[ψ2 ] is used as the phase correction difference to correct the initial phase data.
本发明的有益效果在于：The beneficial effects of the present invention are:
1、本发明通过外场校准方法实现了对无源天线阵列幅相数据的标定，再加上得到的射频通路的幅相数据，最终获得了相控阵天线整系统的阵面幅相分布数据。1. The present invention realizes the calibration of the amplitude and phase data of the passive antenna array through the external field calibration method, and then adds the obtained amplitude and phase data of the radio frequency channel, and finally obtains the frontal amplitude and phase distribution data of the entire phased array antenna system.
2、本发明方法与天线单元互耦方法相比，实现简便、工作量小；与现有的耦合器信号耦合方式相比，由于考虑了无源天线阵列的幅相误差，校准数据更加准确且可信。2. Compared with the antenna unit mutual coupling method, the method of the present invention is simple to implement and has a small workload; compared with the existing coupler signal coupling method, due to the consideration of the amplitude and phase errors of the passive antenna array, the calibration data is more accurate and more accurate. credible.
附图说明Description of drawings
图1是本发明实施例中内校准系统的原理框图。FIG. 1 is a schematic block diagram of an internal calibration system in an embodiment of the present invention.
图2是本发明实施例中内校准系统的工作流程图。FIG. 2 is a working flow chart of the internal calibration system in the embodiment of the present invention.
图3是本发明实施例中内校准系统的发射频点方向图。FIG. 3 is a directional diagram of a transmitting frequency point of an internal calibration system in an embodiment of the present invention.
图4是本发明实施例中内校准系统的接收频点方向图。FIG. 4 is a pattern of receiving frequency points of the internal calibration system in the embodiment of the present invention.
具体实施方式Detailed ways
下面结合附图对本发明做进一步说明。The present invention will be further described below with reference to the accompanying drawings.
如图1所示，一种用于收发双工相控阵天线的内校准系统，其由定标分机、波控分机、接收射频通路和发射射频通路组成。As shown in Fig. 1, an internal calibration system for transmitting and receiving duplex phased array antennas is composed of a calibration extension, a wave-controlled extension, a receiving radio frequency channel and a transmitting radio frequency channel.
在相控阵天线测试中，首先通过外场校准方法标定了无源天线阵列的幅相数据，弥补了采用耦合器的内校准方法的缺点。In the phased array antenna test, the amplitude and phase data of the passive antenna array are first calibrated by the external field calibration method, which makes up for the shortcomings of the internal calibration method using the coupler.
定标分机包括定标激励通道、定标接收通道、选通开关和通信及信号处理模块。其中定标激励通道产生中频信号，通过可选上变频输出接收或发射单载波信号；定标接收通道输入接收回路或发射回路信号，通过可选下变频变为中频信号，再经过A/D输出数字信号；选通开关实现对发射频率和接收频率的选择；通信及信号处理模块与波控分机进行通信，同时实现对接收回路或发射回路信号的幅相解算。The calibration extension includes a calibration excitation channel, a calibration receiving channel, a gating switch, and a communication and signal processing module. The calibration excitation channel generates an intermediate frequency signal, and receives or transmits a single-carrier signal through the optional up-conversion output; the calibration receiving channel inputs the receive loop or transmit loop signal, and converts it into an intermediate frequency signal through optional down-conversion, and then outputs it through A/D. Digital signal; gating switch realizes the selection of transmitting frequency and receiving frequency; communication and signal processing module communicates with the wave-controlled extension, and simultaneously realizes the amplitude and phase calculation of the receiving circuit or transmitting circuit signal.
波控分机作为控制中枢，一方面与定标分机进行交互，传输校准指令和通道开关信息，接收通道编号和通道幅相信息，并最终对相控阵各有源通道进行幅度相位的补偿；另一方面根据通道分时校准顺序，在某一时刻开启相应通道，并将通道设置为初始状态。As the control center, the wave-controlled extension interacts with the calibration extension, transmits calibration instructions and channel switch information, receives channel number and channel amplitude and phase information, and finally compensates the amplitude and phase of each active channel of the phased array; On the one hand, according to the channel time-sharing calibration sequence, the corresponding channel is turned on at a certain time, and the channel is set to the initial state.
射频通路分为接收射频通路和发射射频通路，接收/发射射频通路由接收/发射定标网络组合、通道切换开关、耦合器、接收/发射通道和接收/发射馈电网络组合组成，通道切换开关实现待校准通道的选择，耦合器是形成校准信号回路的关键器件，多路接收/发射通道实现信号的放大、滤波和幅相控制等功能。The radio frequency channel is divided into the receiving radio frequency channel and the transmitting radio frequency channel. The receiving/transmitting radio frequency channel is composed of the receiving/transmitting calibration network combination, the channel switch, the coupler, the receiving/transmitting channel and the receiving/transmitting feeding network combination. The channel switching switch To realize the selection of the channel to be calibrated, the coupler is the key component to form the calibration signal loop, and the multiple receiving/transmitting channels realize the functions of signal amplification, filtering and amplitude and phase control.
本系统主要包括两个环路：控制环路和信号环路。The system mainly includes two loops: control loop and signal loop.
控制环路由天线的波控分机、定标分机的通信与信号处理模块和组件的幅相控制芯片组成；The control loop is composed of the wave control extension of the antenna, the communication and signal processing module of the calibration extension and the amplitude and phase control chips of the components;
信号环路由定标分机的定标激励通道、定标接收通道、组件的放大通道、网络的合成/功分通道等组成，实现信号的产生、变频、模数/数模转换、放大、滤波、合成/功分等操作。The signal loop is composed of the calibration excitation channel of the calibration extension, the calibration receiving channel, the amplification channel of the component, the synthesis/power division channel of the network, etc. Synthesis/power division and other operations.
由于本天线内校准系统是采用射频通道内微带耦合线和定标网络作为内校准系统的基准，因此首先应对定标基准进行标定。首先采用外场校准方法得到整个系统的一组初始幅相值，再用内校准方法得到包含定标基准的一组通道幅相数据，两组数据相减，可以得到包含无源天线阵列、射频通道内微带耦合线和定标网络的幅相数据，将此数据进行存储，作为内校准的基准数据。Since the internal calibration system of the antenna adopts the microstrip coupling line and the calibration network in the radio frequency channel as the benchmark of the internal calibration system, the calibration benchmark should be calibrated first. Firstly, the external field calibration method is used to obtain a set of initial amplitude and phase values of the entire system, and then the internal calibration method is used to obtain a set of channel amplitude and phase data including the calibration reference. The amplitude and phase data of the inner microstrip coupling line and the calibration network are stored and used as the reference data for the inner calibration.
内校准系统的工作流程规划为四步：The workflow of the internal calibration system is planned in four steps:
1）天线研制过程中，对天线在暗室进行外场校准，此时得到天线每个通道收发的初始幅度矩阵[A1_out]和相位矩阵[ψ1_out]。内校准系统启动，依据图2的工作流程，得到每个通道收发的初始幅度矩阵[A1_in]和相位矩阵[ψ1_in]。两者相减得到内校准基准数据：[A1]=[A1_in]-[A1_out]，[ψ1]=[ψ1_in]-[ψ1_out]。将幅相矩阵[A1_out]、[ψ1_out]和[A1]、[ψ1]存储于波控分机的FLASH中；1) During the antenna development process, the antenna is calibrated outside the darkroom, and the initial amplitude matrix [A1_out] and phase matrix [ψ1_out] of each channel of the antenna are obtained. The internal calibration system is started, and according to the workflow in Figure 2, the initial amplitude matrix [A1_in] and phase matrix [ψ1_in] of each channel's transmission and reception are obtained. The two are subtracted to obtain the internal calibration reference data: [A1]=[A1_in]-[A1_out], [ψ1]=[ψ1_in]-[ψ1_out]. Store the amplitude and phase matrices [A1_out], [ψ1_out], [A1], [ψ1] in the FLASH of the wave-controlled extension;
2）天线在装机初次使用时，先进行内校准，将直接测得的实时内校准幅度矩阵[A2_in]、相位矩阵[ψ2_in]，分别与[A1]、[ψ1]相减，得到[A2]、[ψ2]，存储于波控分机的FLASH中；2) When the antenna is installed and used for the first time, internal calibration is performed first, and the directly measured real-time internal calibration amplitude matrix [A2_in] and phase matrix [ψ2_in] are subtracted from [A1] and [ψ1], respectively, to obtain [A2] , [ψ2], stored in the FLASH of the wave-controlled extension;
3）天线在长期使用过程中，每次加电先将幅度矩阵[A2]和相位矩阵[ψ2]从FLASH加载到FPGA内部RAM当中。若需要进行在线实时内校准，则将直接测得的实时内校准幅度矩阵[A3_in]、相位矩阵[ψ3_in]分别与[A1]、[ψ1]相减，得到[A3]、[ψ3]，写入到RAM当中覆盖掉[A2]、[ψ2]。若不需要进行在线实时内校准，则RAM中的数据与出厂时的内校准数据一致，都为[A2]和[ψ2]；3) During the long-term use of the antenna, the amplitude matrix [A2] and the phase matrix [ψ2] are loaded from the FLASH to the internal RAM of the FPGA at each power-on. If online real-time internal calibration is required, subtract the directly measured real-time internal calibration amplitude matrix [A3_in] and phase matrix [ψ3_in] from [A1] and [ψ1] respectively to obtain [A3], [ψ3], and write Enter into RAM to cover [A2], [ψ2]. If online real-time internal calibration is not required, the data in RAM is consistent with the internal calibration data at the factory, which are [A2] and [ψ2];
4）实时内校准幅度矩阵变化：[ΔA]=[A3]-[A2]，作为判别天线是否正常的依据。实时内校准相位矩阵变化：[Δψ]=[ψ3]-[ψ2]，作为相位修正差值，对初始相位数据进行修正。4) Real-time internal calibration amplitude matrix change: [ΔA]=[A3]-[A2], as the basis for judging whether the antenna is normal or not. Real-time internal calibration phase matrix change: [Δψ]=[ψ3]-[ψ2], which is used as the phase correction difference to correct the initial phase data.
考虑到通道相位测试受温度影响较大，因此可以在被测通道内设计温度监测电路，通过温度实时监测保证天线内校准在相近的温度条件下进行。Considering that the channel phase test is greatly affected by temperature, a temperature monitoring circuit can be designed in the measured channel to ensure that the calibration in the antenna is performed under similar temperature conditions through real-time temperature monitoring.
通信及信号处理模块是定标分机的核心处理部分，通信及信号处理模块主要完成AD采样、信号幅度相位的解算、RS-422通信等功能。两路中频信号经过AD采样后送入FPGA，并行同时存入FPGA内部RAM，经过RAM读写控制，一次并行读出，在FPGA内部实现各种运算、处理，求出相对幅度、相位。将计算的结果通过RS-422发送到波控主板内存储，并接收波控主板发送的指令。The communication and signal processing module is the core processing part of the calibration extension. The communication and signal processing module mainly completes functions such as AD sampling, signal amplitude and phase calculation, and RS-422 communication. The two IF signals are sampled by AD and sent to the FPGA, and stored in the internal RAM of the FPGA at the same time. After reading and writing control of the RAM, they are read out in parallel, and various operations and processing are implemented inside the FPGA to obtain the relative amplitude and phase. Send the calculated results to the wave control mainboard for storage through RS-422, and receive the instructions sent by the wave control mainboard.
通过图3、图4的内校准和外校准两种方法的方向图对比可见，两种方向图曲线几乎一致，仅在远旁瓣方向有所差别。从测试结果可以看出，本内校准系统恢复了天线的初始性能，达到了预期效果。By comparing the patterns of the two methods of internal calibration and external calibration in Figures 3 and 4, it can be seen that the curves of the two patterns are almost the same, and only differ in the direction of the far side lobes. It can be seen from the test results that the internal calibration system restores the initial performance of the antenna and achieves the expected effect.
通过以上实施例可以看出，本发明实现简便，在天线装机使用过程中，能够在线实现相控阵天线的快速高精度校准。It can be seen from the above embodiments that the present invention is easy to implement, and can realize fast and high-precision calibration of the phased array antenna online during the installation and use of the antenna.
总之，本发明通过耦合器将定标分机内产生的单载波信号在整个系统内形成信号回路，将携带有通道幅相信息的信号回传到定标分机，在定标分机内实现信号幅相信息的解算，再将通道幅相信息通过波控分机补偿到相控阵各有源通道，从而实现相控阵天线的幅相标定。本发明内校准系统的组成部分均为相控阵天线的主要组成部分，不需借助外部设备即可实现相控阵天线的快速校准。In a word, the present invention forms a signal loop in the whole system through the coupler of the single-carrier signal generated in the scaling extension, returns the signal carrying the channel amplitude and phase information to the scaling extension, and realizes the signal amplitude and phase in the scaling extension. The information is calculated, and then the channel amplitude and phase information is compensated to each active channel of the phased array through the wave control extension, so as to realize the amplitude and phase calibration of the phased array antenna. The components of the internal calibration system of the present invention are all main components of the phased array antenna, and the fast calibration of the phased array antenna can be realized without the aid of external equipment.
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