Air traffic control transponder field tester
The air traffic control transponder field inspection instrument, which integrates display control, digital processing, radio frequency and power modules, solves the problems of large size and poor adaptability of existing equipment, and realizes efficient and accurate detection of various transponders, improving the reliability and efficiency of on-site inspection.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- CHENGDU RONGCHUANG AVIATION TECH CO LTD
- Filing Date
- 2025-05-30
- Publication Date
- 2026-05-29
AI Technical Summary
Existing air traffic control transponder detection equipment is large in size, has low integration, poor radio frequency adaptation capability, and insufficient power compatibility, making it unable to effectively detect transponders of multiple modes, resulting in low detection accuracy and inconvenience in field deployment.
An air traffic control transponder field inspection instrument was designed, comprising a display control unit, a digital processing unit, an RF unit, and a power supply module. It adopts an ARM and FPGA collaborative architecture, combined with ADC and DAC modules, to support multi-level circuits and flexible power supply, enabling accurate reception and detection of various transponder signals.
It enhances the integration and flexibility of the equipment, ensures stable operation in complex field environments, improves detection accuracy and efficiency, and is suitable for rapid and accurate detection of various transponder models.
Smart Images

Figure CN224303854U_ABST
Abstract
Description
Technical Field
[0001] This utility model relates to the technical field of air traffic control transponder inspection instruments, and specifically to an air traffic control transponder field inspection instrument. Background Technology
[0002] Secondary radar is a crucial component of modern air traffic control (ATC) systems, primarily used to acquire aircraft identification codes, altitude information, and status indicators. Traditional A / C mode SSR systems, employing 12-bit response codes, have a limited identification capacity of 4096 aircraft, which is insufficient to meet the current high-density airspace identification requirements. Therefore, S-mode secondary radar was developed, employing 24-bit discrete address coding, capable of providing unique identification numbers for over ten million aircraft, significantly improving system capacity and identification accuracy.
[0003] In the daily work of airlines and maintenance units, maintenance personnel typically rely on ground support equipment to test and verify the performance of airborne transponders. However, most of the support equipment currently in use is designed for A / C mode transponders and lacks complete support for S mode transponders. Especially in field testing environments, when multiple transponder models are used together, the existing equipment has significant deficiencies in signal processing capabilities, RF interface compatibility, power supply strategies, and module integration.
[0004] Existing equipment often fails to effectively separate different transponder signals during signal transmission and reception testing, leading to signal interference and affecting identification accuracy. Furthermore, many devices are complex and bulky, hindering rapid on-site deployment; their power supply is limited and incompatible with various operating environments; and their internal modules are loosely coupled, resulting in low efficiency in inter-functional collaboration, severely restricting further performance improvements.
[0005] Therefore, there is a need for an air traffic control transponder field inspection instrument with high integration, flexible power supply support, and stable operation in complex field environments. Through optimized hardware connections and coordination between the display control module, digital processing module, radio frequency module, and power supply module, it can achieve accurate reception, modulation, and detection of various transponder signals, including Mode S, thereby improving the efficiency and reliability of transponder field inspection. Summary of the Invention
[0006] This invention addresses the problems of existing testing equipment in field use, such as large size, low integration, poor radio frequency adaptation capability, insufficient power compatibility, and limited ability to test multiple modes of transponders. It provides an air traffic control transponder field inspection instrument with a compact structure, high modular integration, strong adaptability, and the ability to accurately test multiple transponders.
[0007] This utility model is achieved through the following technical solution:
[0008] An air traffic control transponder field inspection instrument includes a display control unit, a digital processing unit, a radio frequency unit, and a power supply module; the display control unit is connected to the digital processing unit via a serial port; the digital processing unit is connected to the radio frequency unit via a communication interface; the power supply module is electrically connected to the display control unit, the digital processing unit, and the radio frequency unit respectively, and is used to provide multi-level voltage power supply.
[0009] Furthermore, the display control unit includes a serial port display screen and a physical button group; the serial port display screen is connected to the digital processing unit through a display interface, and the physical button group is connected to the digital processing unit through an I / O interface.
[0010] Furthermore, the digital processing unit includes an ARM chip, an FPGA chip, an ADC module, and a DAC module; the ARM chip is connected to the FPGA chip via an FSMC interface; the ADC module is connected to the FPGA chip via a 12-bit parallel interface; and the DAC module is connected to the FPGA chip via a 12-bit parallel interface.
[0011] Furthermore, the input terminal of the ADC module is connected to an ADC operational amplifier circuit, and the input terminal of the operational amplifier circuit is connected to the received signal output terminal of the radio frequency unit; the output terminal of the DAC module is connected to a DAC operational amplifier circuit, and the output terminal of the DAC operational amplifier circuit is connected to the modulation signal input terminal of the radio frequency unit.
[0012] Furthermore, the radio frequency unit includes a frequency source circuit, a power divider circuit, a modulation circuit, a bandpass filter circuit, a low-pass filter circuit, and an amplifier circuit; the frequency source circuit is connected to the power divider circuit, the power divider circuit is connected to the mixer and the modulation circuit respectively, the modulation circuit is connected to the low-pass filter circuit, the low-pass filter circuit is connected to the antenna through a circulator, the mixer is connected to the bandpass filter circuit, the bandpass filter circuit is connected to the amplifier circuit, and the circulator is connected to the amplifier circuit through an attenuator and a coupler.
[0013] Furthermore, the modulation circuit includes an ASK modulation module, a BPSK modulation module, and an AM modulation module, which are respectively connected to the FPGA chip via control lines.
[0014] Furthermore, the power module includes a DC / DC conversion circuit and a secondary power conversion circuit; the DC / DC conversion circuit supports 27V external power supply and 8.4V battery input, and outputs 12V voltage; the secondary power conversion circuit converts the 12V voltage into 3.3V, 1.2V and 3.0V voltages, which are supplied to the digital processing unit and the radio frequency unit respectively.
[0015] The beneficial effects of this utility model are:
[0016] (1) The air traffic control transponder field inspection instrument proposed in this utility model improves the overall integration of the system, reduces the size of the equipment, and makes it easy to carry and deploy in the field by rationally arranging the display control unit, digital processing unit, radio frequency unit and power module in an integrated device;
[0017] (2) The air traffic control transponder field inspection instrument proposed in this utility model supports the testing requirements of A / C mode and S mode transponders by designing a multi-level circuit such as frequency source, modulation, mixing, filtering and amplification. In particular, the ability to adapt to complex signal environments is improved by using multiple switchable modulation methods in conjunction with FPGA control.
[0018] (3) The air traffic control transponder field inspection instrument proposed in this utility model adopts an ARM and FPGA collaborative architecture, and is equipped with a high-speed ADC and DAC module, which can realize high-precision acquisition and generation of response signals, and ensure the accuracy and stability of data during the test process;
[0019] (4) The air traffic control transponder field inspection instrument proposed in this utility model has a power module that supports dual input of 27V external power supply and 8.4V battery, and has DC / DC and multi-level voltage regulation circuits. It can output multiple voltage levels to meet the voltage requirements of different modules and improve the flexibility and reliability of the equipment in different working scenarios.
[0020] This invention can effectively solve the problems of low detection accuracy, narrow compatibility, poor power supply flexibility and complex structure of existing field testing equipment. It is suitable for rapid and accurate testing of various types of transponders, and significantly improves the efficiency and safety of aircraft maintenance. Attached Figure Description
[0021] To more clearly illustrate the technical solutions in the embodiments of this utility model, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this utility model. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0022] Figure 1 This is a block diagram of the overall system of an air traffic control transponder field inspection instrument proposed in this utility model;
[0023] Figure 2 This invention provides a schematic diagram of the display control unit circuit for an air traffic control transponder field inspection instrument.
[0024] Figure 3 This utility model proposes a digital processing unit system framework for an air traffic control transponder field inspection instrument. Figure 1 ;
[0025] Figure 4 This invention provides a schematic diagram of the ARM circuit of an air traffic control transponder field inspection instrument.
[0026] Figure 5 This utility model proposes a digital processing unit system framework for an air traffic control transponder field inspection instrument. Figure 2 ;
[0027] Figure 6 The FPGA circuit principle of the air traffic control transponder field inspection instrument proposed in this utility model Figure 1 ;
[0028] Figure 7 The FPGA circuit principle of the air traffic control transponder field inspection instrument proposed in this utility model Figure 2 ;
[0029] Figure 8 This is a system block diagram of the ADC module of an air traffic control transponder field inspection instrument proposed in this utility model;
[0030] Figure 9 This invention relates to the schematic diagram of the ADC circuit of an ADC module for an air traffic control transponder field inspection instrument.
[0031] Figure 10 This invention provides a schematic diagram of the ADC operational amplifier circuit for the ADC module of an air traffic control transponder field inspection instrument.
[0032] Figure 11 This is a schematic diagram of the DAC circuit of the DAC module of the air traffic control transponder field inspection instrument proposed in this utility model;
[0033] Figure 12 This invention provides a schematic diagram of the DAC operational amplifier circuit for a DAC module of an air traffic control transponder field inspection instrument.
[0034] Figure 13 This is a structural diagram of the radio frequency unit of an air traffic control transponder field inspection instrument proposed in this utility model;
[0035] Figure 14 The schematic diagram of the power input circuit of the power module of the air traffic control transponder field inspection instrument proposed in this utility model;
[0036] Figure 15 The schematic diagram of the DC / DC conversion circuit of the power module of the air traffic control transponder field inspection instrument proposed in this utility model;
[0037] Figure 16 The present invention proposes a two-stage DC / DC conversion circuit principle for the power module of an air traffic control transponder field inspection instrument. Figure 1;
[0038] Figure 17 The present invention proposes a two-stage DC / DC conversion circuit principle for the power module of an air traffic control transponder field inspection instrument. Figure 2 ;
[0039] Figure 18 The present invention proposes a two-stage DC / DC conversion circuit principle for the power module of an air traffic control transponder field inspection instrument. Figure 3 . Detailed Implementation
[0040] To make the objectives, technical solutions, and advantages of this utility model clearer, the present utility model will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this utility model are only used to explain this utility model and are not intended to limit this utility model.
[0041] Example 1
[0042] This embodiment proposes a specific implementation method for an air traffic control transponder field inspection instrument.
[0043] refer to Figure 1 An air traffic control transponder field inspection instrument includes a display control unit, a digital processing unit, a radio frequency unit, and a power supply module; the display control unit is connected to the digital processing unit via a serial port; the digital processing unit is connected to the radio frequency unit via a communication interface; the power supply module is electrically connected to the display control unit, the digital processing unit, and the radio frequency unit respectively, and is used to provide multi-level voltage power supply.
[0044] It includes a display control unit, a digital processing unit, a radio frequency (RF) unit, and a power supply module; the display control unit is connected to the digital processing unit via a serial port; the digital processing unit is connected to the RF unit via a communication interface; the power supply module is electrically connected to the display control unit, the digital processing unit, and the RF unit respectively, and is used to provide multi-level voltage power supply.
[0045] refer to Figure 2In this embodiment, the display control unit, serving as the core interface for human-computer interaction, utilizes a TFT serial port display screen with a resolution of 800×480 to display the device's current operating status, parameter information, detection results, and historical data in real time. This display screen communicates with the ARM chip in the digital processing unit via a serial port, offering good compatibility and response speed. To enhance the device's ease of operation, the display control unit also includes a function keypad composed of physical buttons. This keypad is connected to the digital processing unit via an I / O interface, enabling quick operations such as parameter setting, mode switching, data reset, and starting / stopping detection. The display control unit supports switching between multiple operating modes and can dynamically display different status information and configurable parameters according to the current operating mode. For example, during S-mode transponder detection, the interface displays key parameters including the target address code, response delay, and frequency deviation; during A / C mode detection, it switches to displaying the response code, query frequency point, and other corresponding content. Simultaneously, users can adjust parameters such as frequency settings, operating level, and signal type in real time via button input and receive feedback through the screen.
[0046] refer to Figure 3 In this embodiment, the digital processing unit, as the core control module of the air traffic control transponder field inspection instrument, mainly consists of an ARM chip, an FPGA chip, an analog-to-digital converter (ADC), a digital-to-analog converter (DAC), a power management chip, and a clock circuit. The digital processing unit is responsible for core functions such as protocol parsing, message encoding / decoding, RF module control, and waveform signal generation, and is a key component for realizing the transponder testing process.
[0047] refer to Figure 4 The ARM chip uses a GD32 series microcontroller as the system's main control device, responsible for tasks such as external interface communication, protocol processing, and instruction scheduling. The ARM chip has abundant peripheral interface resources, providing the following main interface configurations:
[0048] Serial port interface: used for data communication with a host computer or other external devices;
[0049] FSMC interface: used for high-speed data exchange with FPGA chip to realize command distribution, signal acquisition and waveform processing;
[0050] SPI interface: On one hand, it connects to the RF module to achieve precise control of modulation mode, frequency parameters, etc.; on the other hand, it connects to the FLASH chip for data reading, writing, and storage.
[0051] Display interface: Used to connect to a serial display screen to output real-time parameters, status information and test results;
[0052] IO interface: Used to connect to physical button groups, receive user input commands, and realize human-computer interaction control.
[0053] refer to Figures 5-7 The FPGA chip works in conjunction with the ARM chip, primarily for high-speed data processing and control logic implementation. The FPGA integrates functions such as timing control of received signals, sampling data buffering, response waveform generation, and time slot management. The ADC module connects to the FPGA via a 12-bit parallel interface, converting analog signals received by the RF unit into digital signals for transmission to the FPGA for processing. Similarly, the DAC module connects to the FPGA via a 12-bit parallel interface, converting digital waveforms generated by the FPGA into analog signals for output to the RF modulation channel. Furthermore, the digital processing unit integrates a stable local clock circuit to ensure synchronization between data processing and signal timing control. A power supply chip is also configured to convert the external input voltage to the different voltage levels required by the ARM, FPGA, ADC, and DAC devices, ensuring stable system operation.
[0054] refer to Figures 8-10 In this embodiment, the analog-to-digital converter (ADC) in the digital processing unit converts the video envelope signal output from the RF receiving module into a digital signal, and transmits the converted digital signal to the FPGA for further demodulation and decoding. The video envelope signal is a pulse-modulated signal with a pulse width of approximately 0.5 μs, and its bandwidth is relatively narrow, therefore the sampling rate requirement for the ADC is not high. In this embodiment, an ADC chip with a maximum sampling rate of 40 Msps and a resolution of 12 bits is selected, which can meet the requirements of signal fidelity and time resolution in this project, while achieving a good balance between system resources and cost.
[0055] To improve the conversion performance and input signal matching of the ADC chip, an amplifier driving scheme is adopted in the analog input front-end circuit design of the ADC chip. This scheme includes a high-bandwidth, low-noise operational amplifier, forming a front-end analog signal conditioning circuit with impedance matching and filtering functions. This effectively suppresses high-frequency noise and improves the dynamic range of the input signal, ensuring that the ADC input signal has good amplitude and stability. The ADC chip is connected to the FPGA chip through a 12-bit parallel data interface, enabling high-speed transmission of sampling results to the internal logic unit of the FPGA in a stable data format for timing analysis, amplitude determination, and subsequent data decoding and recognition processing.
[0056] refer to Figures 11-12 In this embodiment, the digital-to-analog converter (DAC) in the digital processing unit is used to convert the digital modulation waveform generated by the FPGA into an analog signal, and after conditioning, send it to the radio frequency unit to drive the modulation circuit to modulate the radio frequency carrier.
[0057] The DAC module employs a 12-bit resolution DAC chip with a sampling rate that meets the system's waveform output requirements. This DAC chip connects to the FPGA chip via a 12-bit parallel interface, receiving digital waveform data output from the FPGA and achieving high-precision, high-speed digital-to-analog conversion. The FPGA chip has preset digital baseband waveforms in various modulation formats, allowing selection of different modulation methods such as ASK, BPSK, and AM according to testing requirements.
[0058] To further improve the amplitude stability and load-driving capability of the analog output signal, a dedicated DAC operational amplifier circuit is connected to the output of the DAC module. This operational amplifier circuit is constructed using a high-speed, high-bandwidth, low-distortion operational amplifier, possessing good linearity and gain control capabilities, and performs buffering, filtering, and amplitude amplification processing on the analog signal output by the DAC.
[0059] The output of the DAC operational amplifier circuit is directly connected to the modulation signal input of the radio frequency unit, which drives the modulation circuit to modulate the radio frequency signal according to the preset modulation format, thereby generating and transmitting the test signal.
[0060] In a preferred embodiment, regarding power supply design, the main power-consuming components in the DAC module are the DAC chip itself and the subsequent operational amplifier circuit. Both support a single 3V power supply; therefore, this embodiment adopts a unified 3V single power supply scheme, which not only meets electrical performance requirements but also simplifies the system power architecture and improves the overall consistency and reliability of the power supply design. Furthermore, the digital interface power supply DVDD of the DAC chip has the same voltage as the bank connected to the FPGA chip and is powered by the FPGA, thereby ensuring logic level compatibility and communication stability.
[0061] refer to Figure 13 In this embodiment, the radio frequency unit is used to complete the radio frequency signal transmission and reception tasks of the air traffic control transponder field inspection instrument in various operating modes. Its main functions include: modulation and transmission of 1030MHz radio frequency signals, modulation and transmission of 1090MHz radio frequency signals, reception and demodulation of 1090MHz radio frequency signals, and support for multiple modulation methods (ASK, BPSK, AM).
[0062] The radio frequency unit includes modules such as frequency source circuit, modulation circuit, power divider circuit, filter circuit, amplifier circuit, attenuator, coupler, circulator, mixer, AGC amplifier, and logarithmic amplifier.
[0063] When the device is operating in ADS-B OUT mode, the digital processing unit outputs a 1090MHz baseband modulation signal through the DAC. This signal is sent to the radio frequency unit for ASK modulation, then modulated by the carrier provided by the 1090MHz frequency source, and finally output to the circulator and transmitted through the antenna.
[0064] When the device is operating in normal interrogation mode, the frequency source circuit generates a 1030MHz carrier signal. After the modulation circuit completes ASK / BPSK modulation, the modulated 1030MHz radio frequency signal is sent to the antenna for transmission through a filter and amplifier. After the interrogation signal is transmitted, the system quickly switches to receive mode.
[0065] In receive mode, the antenna receives a 1090MHz response signal, which is then input to the receive link via a circulator. The received RF signal is first power-limited by a 20dB attenuator to prevent large signals from damaging subsequent circuits; then, a portion of the power is sampled by a coupler as a control reference for the AGC circuit. The main signal path enters the AGC amplifier and is mixed with the local 1030MHz frequency signal to generate a 60MHz intermediate frequency signal. This intermediate frequency signal is then filtered and processed by a logarithmic amplifier to obtain the video envelope signal, which is then sampled by the ADC and transmitted to the digital processing unit for subsequent demodulation.
[0066] In S-mode operation, the RF unit supports BPSK modulation in addition to ASK modulation. The modulation circuit includes dedicated ASK modulation module, BPSK modulation module and AM modulation module, which can switch the modulation mode according to the control signal of the digital processing unit to adapt to the protocol requirements of different transponders.
[0067] Furthermore, the RF received power measurement function accurately measures the signal strength by sampling the video signal output from the RF unit using an ADC and then calculating it in conjunction with preset calibration parameters such as antenna gain and cable loss. The RF signal transmit power adjustment function regulates the operating state of the AM modulation module through the analog control voltage output from the DAC, thereby achieving adjustable control of the signal amplitude.
[0068] refer to Figures 14-18 In this embodiment, the power module is used to provide a stable, low-noise multi-stage voltage power supply for each functional unit of the air traffic control transponder field inspection instrument, ensuring the normal operation of the whole machine in different working modes. The power module includes two parts: a DC / DC power conversion circuit and a secondary power conversion circuit.
[0069] The DC / DC power conversion circuit design supports two input methods: an external +27V DC power input and an internal 8.4V polymer battery power supply. This section uses a DC / DC converter chip with a wide input voltage range, which can stably convert the input voltage to a 12V DC output voltage for use by subsequent power supplies. To ensure normal operation under battery power, the input voltage range of the DC / DC power conversion circuit is designed to be compatible with inputs below 12V and 7V, meeting the power supply requirements of the polymer battery as its voltage gradually decreases during discharge.
[0070] The secondary power conversion circuit further converts the 12V voltage into the operating voltage required by each chip. Its voltage distribution is as follows:
[0071] In the digital power supply section, the main control MCU and peripheral interface circuits are powered by 3.3V, which is obtained from the 12V input voltage through a low dropout linear regulator (LDO) or a high-efficiency DC-DC chip; the FPGA core voltage is 1.2V, which is generated from the 3.3V power supply through a dedicated LDO voltage regulator; some analog circuits or I / O ports of the FPGA are powered by 2.5V, which is also obtained from the 3.3V power supply through an LDO.
[0072] In the analog power supply section, since the ADC and DAC chips are quite sensitive to power supply noise, a two-stage low-noise voltage conversion design is adopted to improve the system's measurement accuracy and signal integrity. The first stage converts the 12V or 8.4V input to 3.3V; the second stage converts the 3.3V to 3.0V through a high-performance low-noise LDO regulator to power the ADC and DAC analog circuitry.
[0073] In this embodiment, the digital and analog power supply circuits are designed separately to avoid mutual interference. Meanwhile, all multi-voltage output circuits are equipped with overcurrent, overtemperature, and short-circuit protection mechanisms to ensure stable and reliable operation of the system power supply even in complex electromagnetic environments.
[0074] The foregoing has shown and described the basic principles, main features, and advantages of this utility model. Those skilled in the art should understand that this utility model is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this utility model. Various changes and modifications can be made to this utility model without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claims. The scope of protection of this utility model is defined by the appended claims and their equivalents.
Claims
1. A field inspection instrument for air traffic control transponders, characterized in that, It includes a display control unit, a digital processing unit, a radio frequency (RF) unit, and a power supply module; the display control unit is connected to the digital processing unit via a serial port; the digital processing unit is connected to the RF unit via a communication interface; the power supply module is electrically connected to the display control unit, the digital processing unit, and the RF unit respectively, and is used to provide multi-level voltage power supply.
2. The air traffic control transponder field inspection instrument according to claim 1, characterized in that, The display control unit includes a serial port display screen and a physical button group; the serial port display screen is connected to the digital processing unit through a display interface, and the physical button group is connected to the digital processing unit through an I / O interface.
3. The air traffic control transponder field inspection instrument according to claim 1, characterized in that, The digital processing unit includes an ARM chip, an FPGA chip, an ADC module, and a DAC module; the ARM chip is connected to the FPGA chip via an FSMC interface; the ADC module is connected to the FPGA chip via a 12-bit parallel interface; and the DAC module is connected to the FPGA chip via a 12-bit parallel interface.
4. The air traffic control transponder field inspection instrument according to claim 3, characterized in that, The input terminal of the ADC module is connected to an ADC operational amplifier circuit, and the input terminal of the operational amplifier circuit is connected to the received signal output terminal of the RF unit; the output terminal of the DAC module is connected to a DAC operational amplifier circuit, and the output terminal of the DAC operational amplifier circuit is connected to the modulation signal input terminal of the RF unit.
5. The air traffic control transponder field inspection instrument according to claim 1, characterized in that, The radio frequency unit includes a frequency source circuit, a power divider circuit, a modulation circuit, a bandpass filter circuit, a low-pass filter circuit, and an amplifier circuit. The frequency source circuit is connected to the power divider circuit, which is connected to both the mixer and the modulation circuit. The modulation circuit is connected to the low-pass filter circuit, which is connected to the antenna via a circulator. The mixer is connected to the bandpass filter circuit, which is connected to the amplifier circuit. The circulator is connected to the amplifier circuit via an attenuator and a coupler.
6. The air traffic control transponder field inspection instrument according to claim 5, characterized in that, The modulation circuit includes an ASK modulation module, a BPSK modulation module, and an AM modulation module, which are respectively connected to the FPGA chip via control lines.
7. The air traffic control transponder field inspection instrument according to claim 1, characterized in that, The power module includes a DC / DC conversion circuit and a secondary power conversion circuit; the DC / DC conversion circuit supports 27V external power supply and 8.4V battery input, and outputs 12V voltage; the secondary power conversion circuit converts the 12V voltage into 3.3V, 1.2V and 3.0V voltages, which are supplied to the digital processing unit and the radio frequency unit respectively.