外文翻译---波形合成电路的分析与设计

附录二：英文原文

The Analysis and Design ofWaveform Generator

Xue lian ,Wang Fan ,Zheng Jin-fa

Engineering and CommerceCollege, South-CentralUniversity for Nationalities, WuhanHubei

430065

Abstract: In this paper, the sinusoidal waves in different frequency were synthesized into square wave according to the method of Fourier series. Firstly, the needed sinusoidal waves were achieved through the square wave generation circuit, the frequency division circuit and the filter circuit; then, after the sinusoidal waves’ phase position were shifted and synthesized, the square wave was generated. This circuit in this method was more cheaper than other circuits (eg: DDS). Keywords: Waveform Generator;SinusoidalWave;Filter;Phase PositionShift

1 waveform synthesis system overview

This is designed to simulate the process of signal synthesis. For a square wave signal by Fourier series spread knowable, it can decompose the amplitude of the more specific for unlimited odd harmonics, so in turn as long as infinite multiple odd harmonic component, the amplitude and the harmonic proportion in a particular superposition, also will certainly get a square wave signal. This paper is the simulated the base wave and three harmonic harmonic component synthesis process of square wave signal. Theoretically speaking, the harmonic components, synthetic waveform will more close to the standard square bobo shape.

This system begin with a square wave oscillator to generate a frequency of 60KHz pulse signal, again into separate frequency device 10KHz to get a frequency for handling of square wave signal and a frequency of square wave signal for 30KHz, then respectively through the filter processing for the sine signal and 30KHz 10KHz to close-spaced 10KHz sine wave as base wave component, 30KHz sine wave as three times, through modulation circuit harmonics of adjust them respectively in fengfeng value, can satisfy 2V 6V and Fourier series spread coefficient ratio; Put the sine signals into 10KHz to phase shifter phase adjuster, and after 30KHz sinusoidal signal together into addition circuit synthesis, namely complete signal stack. It can be inferred that the output signal is adder an approximate square-wave signal, and frequency for probably 10KHz. System unit circuit as shown in figure 1 below.

Figure 1 system structure diagram

2 the hardware circuit design

2.1 square wave generating circuit design

According to the above analysis, the 60kHz should be produced for pulse frequency. Square wave can use digital circuit generation, also can use analog circuits produce. As digital circuits produce waveform amplitude, needs to be smaller using simulated circuit to amplify; And compared with mixed-signal circuit pure analog circuits to complex, therefore, in this the paper only with analog circuits to generate square wave. The basic principle is: through the voltage comparator produce high level; Through the feedback loop and delay link to the electric frequency periodically height variations. Principle chart as figure2shows, diagram hysteretic comparator output voltage, threshold voltage; Oscillation period for. Through calculating formula by cycle that change, C, R1 ifss can be obtained with R2 ratio required pulse frequency. But this several variables in actual circuit will be some constraints, in choosing device parameters through actual adjustment should be determined. Select devices, it is suggested that resistance, so that circuit using metal film resistors the heat generated by the noise is small; Choose op-amp should consider when it's passband, passband more hours, it is difficult to achieve square-wave requirements, so we chose the frequency performance was good OPA820 op-amp.

Front generated for square can't use, this latter stage, still need to pass the follow-up processing, should first except negative voltage isolation, here with a diode, so after diode for the voltage after subtracting tube voltage half before diode pressure drop. Thus square wave amplitude will more small, in order to achieve the minimum separate frequency circuit requirements, should be the voltage waveforms were pressurization. In proportion with pressor circuit USES amplifier, get the voltage amplitude moderate. Then after the voltage level for use, but in order to reduce load after each level circuit, the influence of wavelet produce circuit with load ability raise circuit, finally take a shot extremely follow device. To this, square wave generator can be expected to reach, could plug in the latter stage circuit.

Figure 2 square wave generating circuit principle diagram

2.2. Points frequency circuit design

This points to the former stage frequency circuits are produced, into a square 60KHz 390v for 1/2, frequency respectively. 30KHz And the square wave signal 10KHz. This treatment can easily think of using digital counter solve. The counter is commonly used sequential circuits to pulse, it not only can count, can also used for the points frequency, timing, produce beats pulse, etc. This paper use of its points frequency characteristics, a N disables counter can will it input clock signal, points for occupies emptiescompared frequency for 1 / N, frequency for input signal 1 / N output the clock signal. So in order to get the 30KHz square wave signal, the 60KHz

square can be as the clock signal, access a secondary system, the output to a counter 390v for 1/2, frequency of square wave signal 30KHz. But for the square wave signal acquisition 10KHz, can let 60KHz square wave signal through a ternary counter, corresponding to output a occupies emptiescompared to 1/3, frequency of square wave signal for 20KHz, then the signal as the input signal, access a binary counter, you will get a 390v for 1/2, frequency for the

10KHz square. The 60KHz pulse signal coming through three digital counter processing, gain satisfaction 1/2 390v requirements of 30KHz 10KHz and pulse signal.

For digital counter choice is the key to realizing points frequency. If using common integrated counter 74LS \ HC163, such as (74LS \ HC161) constitute the counter, required disables 390v will appear uncertain situation, need separate frequency, adding in 390v regulating circuit, which makes the circuit is not stable and structure is more complex. And use trigger level could be behind the counter 390v good control, so the system USES a JK flip-flop composition counter, T flip-flop and D flip-flop also can choose. Then need to consider the choice to TTL and COMS device, because the system to treat signal in frequency 10KHz above all, if digital devices is easy to cause the conversion rate is too low counter can not work normally, the output signal distortion, so this paper chose conversion rate faster TTL devices. Final determination by two 74LS109 (double integration JK flip-flop) cascade form a ternary counter and two secondary system counter. Points frequency circuit fig.03 shows.

Figure 3 points frequency circuit principle diagram

2.3 filter and modulation circuit design

Filter circuit 10KHz mainly completes 10KHz sine wave, 30KHz square to the transformation of 30KHz sine pulse to. Ideal square wave is contains all the odd frequency components, as long as the signal through specific center frequency of frequency selective network, very easy to obtain the required frequency sine wave. Considering the effect of grade synthetic after, this system directly choose the integrated bart hepworth fourth-order low-pass filter, simply switched capacitor TLC04ID appropriate choices the chip 1, 2 wide capacitance resistance can determine the filtering frequency selective of center frequency, formulas for the f = 1/1.69 RC. This filter order number is higher, frequency selective effect is good, can get the corresponding frequency better sine wave.

If the yankees 10KHz sinusoidal signal as 30KHz sine wave, three times as a signal of harmonic,

synthetic a 10KHz by square wave signal, then Fourier decomposition knowable, 30KHz 10KHz sinusoidal signal and the extent of the sine signals for 1:3 than needed. Because the former stage two sine signal filtered in fengfeng value is required for 5V, both by the 30KHz 10KHz and amplitude circuit of sine wave 6V respectively in fengfeng value for adjustment and 2V.

For the sine signals, need 10KHz from fengfeng value 5V 6V, so to boost processing operation circuit whetherisolated selects the proportion. And for 30KHz sinusoidal line number from fengfeng value 5V, need to, so the antihypertensive treatment 2V chose simple resistance points after, to prevent voltage circuit of the resistor network level circuit influence, plus a voltage behind need comparators. The operation circuit in the attenuation, because the sine separate frequency filtering line number after all contains 2.5 V dc component, if direct capacitive coupling effect by every straight, this paper adopts the bad amplifier single power supply in isolation, after can be reached capacitance straight requirements and the large pendulum space signal. For single power supply amp, need in signal input plus bias circuits, the resistance bias is adopted. For the selection of operational amplifiers, it is LM358 can meet the requirements. Treatment can output excluding dc component 10KHz fengfeng value of 30KHz 6V sine signals and 2V sine signals in fengfeng value. As shown in figure 4 10KHz sinusoidal voltage regulation circuit shown.

Figure 4 filter and modulation circuit

2.4 move and addition circuit design

In order to strengthen the synthetic effect, need to treat synthetic signal phase shifting processing. Because analog synthesis signal only two, so just click on one of the signal can be adjusted. This paper introduces the design of 10KHz sine signals in the phase adjuster phase shifting circuit. By a RC network and a voltage followed sensor into the RC network, including by large resistance (R 100K adjustable, makes the signal phase in 30 °~ 90 can °range adjustment, voltage comparator to prevent the latter stage of the phase shifting circuit circuit interference.

Addition to finish last is that the circuit of signal synthesis. Because the system in the former stage of the signal amplitude ratio has adjust appropriate and circuit amplification operations in addition, no fixed proportion of input and output signal circuit amplitude adjustment, so here are the simplicity of a single integrated amp LM358 constitute addition circuit can well satisfy synthetic requirements. As shown in figure 5 shows addition circuit.

Figure 5 addition circuit

2.5 measurement circuit design

The measurement circuit is used for measuring system of internal all sine signals, which is separate from the RMS ahead of a wave synthesis circuit happened digital measurement unit. RMS is characterization of the ac signal amplitude is an important parameter for sine signal, the RMS for its peak / 2, i.e. only if the peak namely can get sine wave get their RMS. So in the measurement of the system as a circuit, let sine signals obtained through a peak detection circuit and the peak, its peak appears as a relatively constant straight flow, again this straight flow through the AD into the corresponding digital quantity, into SCM processing, namely the RMS, such as signal with LCD display. To last

For peak detection circuit design, because the peak in 2 are sinusoidal wave between 6V, to a larger extent to directly through the most simple, so a diode and capacitance series circuit, which diode rectifier role play half wave, and capacitance is keep peak voltage. Ideally if diode conduction voltage of 0V, then signal peak can accurately performance, and the actual in capacitance of the diode's conduction pressure drop not negligible, crunches the peak voltage equals conduction pressure drop and the original signal peak, this also is the measurement circuit in the main error, so the measurement circuit adopts the following measures to overcome this error: (1) choose conduction pressure drop of smaller diode (ge tube, 1N5189);

(2) using software compensation, decrease diode conduction pressure drop. Capacitance the ceramics capacitor can choose 105. Peak check circuit figure 6 shows.

AD chose successive comparison type, which has meet the advantages such as high speed, low consumption, eight precision measurements of the enough to satisfy the design requirements. Measuring signal amplitude 3V only in 1 ~ between only one range, so measurement (0 ~ 5V) can complete, will meet the positive reference voltage input termination VCC, its negative reference voltage grounding can. SCM chose AT89C51, in dealing with AD transform results, the program adopted average filtering algorithm, so can reduce the error, procedures set AD turned to the decimal data retention. Finally SMC162 with LCD display of RMS data given.

Figure 6 test circuits

3 system functional testing

Completed by two power system current supply for a + 5v respectively, the single power and a + 5v double power supply. Power supply reference each module circuit analysis.

By above each function module circuit can complete this system. The Chinese wave to create, produce 60KHz 3v circuit, the peak of square wave, through two separate frequency circuit the signal frequency measured respectively, 30KHz and 10KHz are 5-v square-wave peak; In through a low-pass filter to get 30KHz and 10KHz, are 5-v sine wave peak; Two signal amplitude modulation circuit by respectively after treatment 30KHz corresponding 6V 10KHz corresponding 2V,; Phase shifting to 10KHz to after two circuit fine-tuning signal into synthesis circuit, will the out-port USES an oscilloscope checked to see observed fong as shown in figure 7 difform.

Finally, using measuring circuit measurements in the system, and the measurement error at various levels in sine wave within 5%.

Figure 7 test waveforms

references

[1] TongShiBai. Analog electronic technology foundation. Beijing: higher education press, 2006 (4th edition)

[2] WuDaZheng with linear system analysis. Signal. Beijing: higher education press, 2005 (4th edition)

附录三：英文翻译

波形合成电路的分析与设计

薛莲 汪帆 郑锦发

中南民族大学工商学院电信系，湖北 武汉 430065

薛莲 (1981年11月——) 女，汉族，山东淄博，中南民族大学工商学院电信系教师，讲师，工学硕士。

摘要：本文根据傅里叶级数展开方法，将各频率正弦波合成为方波。首先，通过方波产生

电路、分频电路、滤波电路获取所需频率的正弦波；再通过移相电路、加法电路将正弦波合成为方波。与其他方式（如DDS ）相比，此种方法具有成本低廉、可靠性高等特点。

关键词：波形合成器；正弦波；滤波；移相

1 波形合成系统概述

本设计是为了模拟信号合成的过程。对于一个方波信号，由傅里叶级数展开可知，它可以分解为无限多个特定幅度的奇次谐波，那么反过来只要无限多个奇次谐波分量，且这些谐波的幅度按特定的比例叠加，也就一定可以得到一个方波信号。本文就是模拟了基波和三次谐波谐波分量合成方波信号的过程。理论上来说，谐波分量越多时，合成的波形就会越趋近于标准的方波波形。

本系统首先用一个方波振荡器产生一个频率为60KHz 的方波信号，再送入分频器处理得到一个频率为10KHz 的方波信号和一个频率为30KHz 的方波信号，然后分别通过滤波器处理为10KHz 的正弦信号和30KHz 的正弦信号，把10KHz 的正弦波作为基波分量，30KHz 的正弦波作为三次谐波，通过调幅电路调节它们的峰峰值分别为6V 和2V ，即可满足傅里叶级数展开的系数比；再把10KHz 的正弦信号送入移相器进行相位调节后，和30KHz 的正弦信号一起送入加法电路进行合成，即完成信号的叠加。可以推断，加法器的输出信号为一个近似方波的信号，且频率大概为10KHz 。系统单元电路如图1所示。

图1 系统结构框图

2 硬件电路设计

2.1方波发生电路设计

根据前面的分析，应该产生频率为60kHz 的方波。方波可以用数字电路产生，也可以用模拟电路产生。由于数字电路产生的波形振幅较小，还需要应用模拟电路进行放大；而用数模混合电路相比纯模拟电路要复杂，因此，在此本文仅用模拟电路来产生方波。其基本原理是：通过电压比较器产生高低电平；通过反馈回路和延时环节使高低电频周期性的交替变化。原理图如图2所示，图中滞回比较器的输出电压

Z U μ

=±，阈值电压

1

12T Z R

U U R R ±=±

?+；振荡周期为132ln 122T C R R R ??

=+ ?

???

。由周期计算式可知通

过改变R 3，C ，R 1与R 2比值可以得到所需频率方波。但是这几个变量在实际电路中会存在一

些约束，在选择器件参数时应该通过实际调节来确定。选择器件时，建议电阻使用金属膜电阻，这样电路产生的热噪声就小；选运放时要考虑它的通频带，通频带较小时，很难达到方波要求的频率，因此我们选择了性能很好的运放OPA820。

前面所产生的方波还不能为后级所利用，为此，还需经过后续处理，首先应该隔除负向电压，在这里用一个二极管，这样经过二极管后的电压为二极管前电压一半减去管压降。如此一来方波幅度将更小，为了达到分频电路要求的最小电压，应该将波形进行升压。升压电路采用同相比例放大器，得到幅度适度的电压。这时的电压可以为后级所利用，但为了减小后级电路负载对方波产生电路的影响，提高电路带负载能力，最后再接一个射极跟随器。到此，方波发生电路就可以达到预期要求，可以接上后级电路。

图2 方波发生电路原理图

2.2．分频电路设计

此处的分频电路是将前级产生的60KHz 方波，变为一个占空比为1/2，频率分别为30KHz 和10KHz 的方波信号。这个处理可以很容易想到用数字计数器解决。计数器是常用的时序电路，它不仅可以对脉冲进行计数，还可以用于分频、定时、产生节拍脉冲等。本文利用它的分频特性，一个N 进制的计数器可以将它的输入时钟信号，分频为占空比为1/N 、频率为输入信号1/N 的输出时钟信号。所以为了得到30KHz 的方波信号，可以将60KHz 的方波作为时钟信号，接入一个二级制计数器，则输出为一个占空比为1/2、频率30KHz 的方波信号。而对于10KHz 的方波信号获取，可以先让60KHz 方波信号通过一个三进制的计数器，对应输出一个占空比为1/3、频率为20KHz 的方波信号，再将此信号作为输入信号，接入一个二进制计数器，即可得到一个占空比为1/2、频率为10KHz 的方波。即将60KHz 的方波信号经过三个数字计数器处理，就获得了满足1/2占空比要求的10KHz 和30KHz 的方波信号。

对于数字计数器的选择也是实现分频的关键。如果采用常见的集成计数器如

（74LS\HC163、74LS\HC161）构成所需进制的计数器，则会出现占空比不定的情况，需要在分频后添加占空比调节电路，这就使得电路不稳定并且结构比较复杂。而采用触发器级联成的计数器则可以很好的掌控占空比，故本系统采用了JK 触发器组成计数器，T 触发器和D 触发器也同样可以选择。然后需要考虑器件TTL 和COMS 的选择，因为系统处理的信号均在10KHz 以上频率，若数字器件的转换速率太低则容易导致计数器不能正常工作，输出信号失真，故本文选择了转换速率较快的TTL 器件。最终确定采用两片74LS109（双集成JK 触发

器）级联组成一个三进制计数器和二个二级制计数器。分频电路如图3所示。

图3 分频电路原理图

2.3滤波和调幅电路设计

滤波电路主要完成10KHz方波到10KHz正弦波，30KHz方波到30KHz正弦波的转化。理想方波是包含了所有奇频分量的信号，只要通过特定中心频率的选频网络，很容易得到所需频率的正弦波。考虑到后级合成的效果，本系统直接选用了集成的巴特沃斯四阶低通开关电容滤波器TLC04ID，只需合适的选择该芯片1、2的外接电容电阻就可以确定滤波选频的中心频率，计算公式为f=1/1.69RC。该滤波器的阶数较高，选频效果好，可以得到相应频率较好的正弦波。

若把10KHz的正弦信号作为基波，30KHz正弦信号作为三次谐波，合成一个10KHz的方波信号，则由傅里叶级数分解可知， 10KHz的正弦信号和30KHz的正弦信号的幅度比需要为1:3。由于前级滤波后两个正弦信号峰峰值均为5V，则需通过调幅电路把10KHz和30KHz 正弦波的峰峰值分别调为6V和2V。

对于10KHz的正弦信号，需要从峰峰值5V到6V升压处理，故选用了同向比例运算电路。而对于30KHz的正弦线号，需要从峰峰值5V到2V的降压处理，故选用了简单的电阻分压电路，而防止后级电路对电阻网络的影响，后面需要加上一个电压比较器。在此调幅的运算电路中，由于分频滤波后的正弦线号均含有2.5V的直流分量，若直接采用电容耦合隔直效果不好，本文采用了运算放大器单电源供电后，在进行电容隔直则可以达到要求，并且信号的复摆空间较大。对于单电源供电运放，需要在信号输入端加上偏压电路，故采用了电阻偏压。对于运算放大器的选取，这里采用LM358即可满足要求。处理后即可输出不含直流分量的10KHz峰峰值6V正弦信号和30KHz峰峰值2V正弦信号。10KHz正弦波调压电路如图4所示。

图4 滤波和调幅电路

2.4移相和加法电路设计

为了加强合成效果，需要对待合成信号进行移相处理。因为模拟合成信号只有两个，所以只需对其中一个信号进行调节即可。本文设计了针对10KHz 正弦信号进行相位调节的移相电路。由一个RC 网络和一个电压跟随器组成，其中RC 网络中R 采用大电阻100K 可调，使得信号的相位可以在30°~90°范围内调节，电压比较器防止后级电路对移相电路的干扰。 加法电路即是为了完成最后的信号合成。由于系统在前级对信号的幅度比例已调节合适且电路放大运算比例固定，不用在加法电路进行输入输出信号的幅度调节，所以这里采用简单的单个集成运放LM358构成加法电路就可以很好的满足合成要求。加法电路如图5所示。

图 5 加法电路

2.5测量电路设计

测量电路是用来测量系统内部的所有正弦信号的有效值，它是独立于前面波形发生合成电路的一个数字测量单元。有效值是表征交流信号幅值的一个重要参量，对于正弦信号，其，即只要得到正弦波的峰值即可以得到其有效值。因此在系统的测量电路中，先让正弦信号通过一个峰值检测电路得到其峰值，并且该峰值表现为一个相对恒定的直流量，再把该直流量通过AD 转化为对应的数字量，送入单片机进行处理，即运算为信号的有效值，最后用LCD 给以显示。

对于峰值检测电路的设计，由于正弦波峰峰值均在2~ 6V 之间，幅度较大，故直接采用最简单的一个二极管和电容串联回路，其中二极管起到半波整流作用，而电容则为保持峰值电压。理想情况下若二极管的导通电压为0V ，则信号峰值可以精确的表现在电容上，而实际二极管的导通压降不可忽略，会使得实际峰值电压等于导通压降加上原信号峰值，这也是本测量电路的主要误差所在，故本测量电路采用以下办法克服该误差：（1）选用导通压降较小的二极管（锗管，1N5189）；（2）采用软件补偿，减掉二极管的导通压降。电容选用105的瓷片电容即可。峰值检查电路如图6所示。

AD 选用了逐次比较型的TLC549，它具有速度较高、功耗低等优点，8位的精度足够满足本设计的测量要求。测量信号幅度只在1~3V 之间，所以测量只需一个量程（0~5V ）即可完成，将TLC549的正向参考电压输入端接VCC,将其负向参考电压接地即可。单片机选用了AT89C51，在处理AD 转换结果时，程序采用了平均滤波算法，这样可以减小AD 转误差，程序设定对数据保留两位小数。最后用LCD SMC162对有效值数据给以显示。

图6 测试电路

3系统功能测试

系统供电由两个电源完成，分别为一个+5v的单电源和一个±5V的双电源。供电参考各模块电路分析。

由以上各个功能模块电路即可完成本系统。其中方波产生电路，产生60KHz，3v的峰值的方波，经过分频电路测得两个信号的频率分别为30KHz和10KHz，峰值均为5v的方波；在通过低通滤波器得到30KHz和10KHz，峰值均为5v的正弦波；两个信号经过调幅电路处理后幅度分别为30KHz对应2V，10KHz对应6V；对10KHz进行移相电路微调后，将两个信号送入合成电路，将输出端用示波器检查，看观察到方波波形如图7。

最后用测量电路测量系统内的各级正弦波，测量误差可以在5%以内。

图7 测试波形

参考文献

[1]童诗白.模拟电子技术基础.北京：高等教育出版社，2006（第四版）

[2]吴大正.信号与线性系统分析.北京：高等教育出版社，2005（第四版）