Analog Electronics Course Project—Waveform Superposition + Butterworth Low-Pass Filter

一、设计要求
（1）信号发生器提供两路信号，A路：幅值2V，频率150Hz的正弦波，B路：幅值1V，频率5KHz的正弦波，利用运放搭建加法电路，实现两路信号的叠加。设立测试点，测量信号求和后的波形。
（2）搭建有源低通滤波电路，对之前的求和电路进行滤波，滤除高频成分，设立测试点。
二、方案选择与论证
第一部分：利用运放搭建求和电路
在选择同相加法和反相加法时，需要考虑它们的特性和应用情况。同相加法器的输入阻抗大，输出阻抗小，这意味着一部分输入信号会被消耗在输入端，但是输出信号的稳定性较高；反相加法器的输入阻抗小，输出阻抗大，意味着较少的输入信号会被消耗在输入端，但是输出信号的稳定性较低。反相加法器的另一个缺点是其输出电压反相，这意味着在某些情况下可能需要额外的处理才能满足需求。因此，这里的两路输入信号，A路：幅值2V，频率150Hz的正弦波，B路：幅值1V，频率5KHz的正弦波，略有消耗对后级电路影响可以忽略，且可以得到稳定性较高的同相输出信号，所以在此选择同相加法电路。但是同相加法电路可能会引入一些噪声和失真，这会降低电信号的质量，降低信噪比，但这可以在后级滤波电路时解决。
第二部分：搭建有源低通滤波电路
 有源低通滤波电路是一种滤波器，它不仅仅包含无源组件（如电阻、电容、电感），还包含了有源组件，例如晶体管或者运算放大器等。它的主要形式是有源RC滤波，也被称作电子滤波器。与无源滤波器相比，有源低通滤波电路的优点在于它可以提供更好的滤波效果，并且可以通过调整有源元件的参数来改变滤波特性。一阶有源低通滤波电路是构建更高级别的二阶、高阶有源低通滤波电路的基础单元。具体来说，这种电路的工作原理是利用有源元件对输入信号进行放大，然后通过低通滤波器滤除高频噪声。由于使用了有源元件，有源低通滤波电路具有较高的增益和较低的输入阻抗，可以提供更好的滤波效果。增加滤波器的阶数可以提高其选择性（即更陡峭的频率响应），但是同时也会增加滤波器的复杂度和成本。过高的阶数可能会导致滤波器不稳定。因此，选择适当的阶数需要根据具体的应用需求进行权衡。在此选择二阶有源滤波电路。（使用一阶有源滤波器进行仿真时，波形已经有明显的失真，达不到良好的滤波效果，制作成实物的效果几乎可以肯定会很差，因此需要采用更高阶的滤波网络）。
二阶有源滤波电路主要有两种结构，分别是Sallen-key和多路反馈（KFB）。这些滤波电路使用了运算放大器作为无限增益器件，形成了无限增益多端反馈电路。二阶有源滤波电路还包括四种类型的有源滤波器，分别是巴特沃斯、贝塞尔、切比雪夫和椭圆滤波器。
一、巴特沃斯滤波器（Butterworth filter）：
优点：
1、通带内的频率响应曲线最大限度平坦，没有起伏。在通带内，信号的波形能够尽可能地保持原始状态，不会产生失真。
2、阻带内逐渐下降为零。这意味着在阻带内，信号会被完全屏蔽，不会对通带内的信号产生影响。
缺点：
1、设计时需要确定通带截止频率、阻带频率等参数。
2、巴特沃斯滤波器的阶数越高，通带内的频率响应曲线越平坦，但阻带内的衰减也会越慢，导致滤波器的性能越复杂。
二、贝塞尔滤波器（Bessel filter）：
优点：
1、在所有滤波器中线性相位特性最佳的。意味着，在通带的频率范围内，信号的相位恒定，这对于许多应用来说是非常重要的。
缺点：
1、幅频特性的选频特性较差。这意味着在通带和阻带之间的过渡区域，贝塞尔滤波器的性能可能不如其他类型的滤波器。
2、贝塞尔滤波器[5]的阻带下降较慢，可能会导致一些不必要的干扰。
三、切比雪夫滤波器（Chebyshev filter）：
优点：
1、在频域内能够更加灵活地控制通带波纹和阻带衰减，能够在保证通带内波纹最小的同时，实现在频域上的等波纹设计。
2、在需要高通或低通滤波时，具有更好的性能。它可以在频域内更精细地控制滤波效果，从而达到更精确的滤波目标。
缺点：
1、阻带衰减较差，在滤除高频或低频信号时，切比雪夫滤波器可能无法彻底阻止这些信号的渗透，从而影响滤波效果。
四、椭圆滤波器（Cauer filter）：
优点：
1、等波纹特性：椭圆滤波器的通带和阻带都具有等波纹特性，在这两个区域内，滤波器的性能良好，并且能够提供稳定的滤波效果。
2、较低的阶数：对于同样的性能要求，椭圆滤波器所需的阶数比其他类型的滤波器更低。能够在保证滤波效果的同时，减少资源消耗和计算量。
3、窄的过渡带：椭圆滤波器能获得较其他滤波器为窄的过渡带宽，在某些需要陡峭过渡带的应用中特别有优势。
4、逼近理想滤波器：椭圆滤波器的设计方法能更好地逼近理想的高通滤波器的特性，使得它能在某些需要高通滤波的应用中表现优异。
缺点：
1、 它的设计和实现比较复杂。
2、 在过渡带附近的性能较为敏感，因此在设计和调试时需要格外注意。
综上所述：在此次课程设计中选用巴特沃斯低通滤波器的方案。虽然在阻带的衰减速度相较于其它几种方案较慢，但相比与一阶的低通滤波器的频率响应陡峭程度已经有了很大的提升。（仿真中可看到明显效果）并且输入端的两路信号分别为150Hz和5KHz，相差巨大，可以通过设计好滤波网络的RC值让截止频率逼近150Hz，不会出现高频噪声影响的问题。并且通带内的频率响应曲线最大限度平坦，没有起伏。信号的波形能够尽可能地保持原始状态，不会产生失真。阻带内逐渐下降为零。这意味着5KHz的信号会被完全屏蔽，不会对通带内的信号产生影响。截止频率的计算也很简便，方便设计。
三、电路原理方框图
该电路包含两个组成部分，分别是运放搭建的加法电路和巴特沃斯低通电路。信号发生器提供两路信号，加法电路对两路信号求和A路：幅值2V，频率150Hz的正弦波，B路：幅值1V，频率5KHz的正弦波，实现两路信号的叠加。巴特沃斯低通滤波电路对前路的叠加信号进行滤波，滤除高频成分，得到A路的输入信号。
四、设计及仿真验证
4.1单元电路及元器件选用
1. Operational Amplifier (op-amp): The general-purpose op-amp LM358P is selected. It has wide applications, numerous reference cases, complete TI official reference materials, and is inexpensive. However, it should be noted that it cannot be directly replaced with a voltage comparator (such as LM393) because it lacks comparator functionality. It also lacks internal phase compensation circuitry, which may lead to circuit instability. A phase compensation capacitor can be added during the design to prevent op-amp self-oscillation, but in actual testing, it did not oscillate without it, so it was omitted here to save materials. (See the attached chip manual for details) 2. Resistors: Common 10KΩ 0603 package surface mount resistors are selected, which are small and inexpensive. (Here, I prioritize a compact and refined board design. Beginners may find soldering 0603 package surface mount resistors difficult; consider your soldering ability and choose 0805 package or through-hole resistors.)
3. Variable Resistor: A variable resistor is needed in the filter network to adjust the cutoff frequency. A common 10KΩ variable
resistor ; its resistance value can be adjusted by selecting the correct knob, making it convenient and easy to use. (All the above components can be purchased from LCSC Mall or Taobao) 4. Capacitors: To filter out the 5kHz high-frequency sine wave, theoretically the larger the capacitance, the better. However, considering factors such as actual size and price, we chose common 100nF 0603 package surface-mount capacitors, which are small and inexpensive.
5. Pin headers: Convenient for connecting to oscilloscopes and power
supplies. A BOM list is available.
 
4.2 Overall Circuit Design
Here, I used Multisim software for simulation, circuit construction, and effect testing. We can use this method in all project design processes to avoid unnecessary waste of manpower and resources.
4.3 Simulation and Result Analysis
We can see that the effect achieved by the simple first-order low-pass filter circuit is significantly distorted. Therefore, we introduce a Butterworth low-pass filter circuit here. Under similar cutoff frequencies, it can be clearly observed that the transition region of the Butterworth low-pass filter is steeper than that of the first-order low-pass filter. While a fourth-order Butterworth low-pass filter offers a flatter passband in practical applications, its frequency drop-off rate slows down with increasing order. This not only increases design complexity but also makes it prone to a bulge in the passband due to the quality factor Q if the parameters are not properly tuned. Furthermore, since the LM358 only integrates two op-amps, using a fourth-order Butterworth filter increases material consumption and may be more cumbersome to tune, potentially resulting in performance inferior to a second-order Butterworth low-pass filter. Therefore, a second-order Butterworth filter was ultimately chosen for the prototype.
Under the same measurement dimensions, significant distortion was clearly observed in the output waveform of the first-order low-pass filter, even with the cutoff frequency set close to 150Hz. It's easy to predict that under real-world interference, the waveform distortion would be even greater, which is unacceptable. In contrast, the improved Butterworth low-pass filter solution produced a completely distortion-free output waveform, ensuring the filtering quality of the prototype. The fourth-order and second-order Butterworth low-pass filters produce almost identical signal outputs in simulations, making the second-order filter the optimal choice due to its ease of debugging and material savings.
V. Hardware Fabrication and Debugging
5.1 PCB Design and Fabrication
A TVS diode could be connected to each of the two power signal inputs to absorb surge voltages. However, the power signal input requirements are not stringent in this design, so it was omitted to save materials. A phase compensation capacitor with a typical value of 22pF could be connected in parallel with the negative feedback resistor to prevent self-oscillation, but after selecting suitable components, it was found that self-oscillation did not occur, so it can also be omitted. An adjustable resistor is used in the filter network to allow for adjustable cutoff frequency. Several extra resistors and capacitors can be placed in the input and output sections as spare positions; in actual fabrication, these are left unsoldered, making it easier to avoid flying wires if needed. Pin headers are used as test interfaces in the design, especially GND; several can be placed for easier wiring. In actual testing, it was found that having only two GND interfaces was not very convenient. The remaining parts are connected according to the internal structure of the operational amplifier shown in the diagram below, based on the simulation circuit.
During the layout process, copper plating was used for both 12V power supplies to provide sufficient current carrying capacity. The signal section and power section were laid out separately to avoid interference and were grounded. Because the circuit connection here is very simple, the global routing was kept as free of vias as possible to ensure smooth wiring and avoid right-angle traces that could cause signal reflection and interference. Finally, some restricted areas were placed during copper plating to remove sharp copper areas and dead copper (islands) to avoid antenna effects. (Actually, the circuit here is very simple. For convenience, breadboards or perforated boards can also be used to build the circuit. However, it may not be as stable. If a short circuit is encountered during the defense, it will burn out... Anyway, building a board is free [doge dog head for protection]).
5.2 Hardware debugging and test results
 
show that the measured results are very close to the simulation results. When the two variable resistors are adjusted to approximately 6.4KΩ, the cutoff frequency is the theoretical value of 175.84Hz, and the filtered measurement signal has almost no distortion.
 
Special note: Due to my limited ability, the Butterworth filter circuit used here is a combination of information I found from various sources and other people's experience. This is just the simplest application; I hope it will be helpful to beginners. Criticism and corrections from experienced users are also welcome. (Doge)