How to Plot the Frequency Response of a Circuit

有许多参数和行为可以集中在对电路的分析中。一个这样的行为，即我喜欢简化亮起是电路的频率响应。这意味着对于施加到电路的一些输入AC信号，该电路的响应（或输出）对于不同的频率间隔来表现不同。
分析频率响应的一种常用方式是考虑给定输入频率的“增益”。还称为传递函数，增益通常定义为输出电压与输入电压的比率：

所以，如果你用电吉他插入放大器的话，你将会从你的拳头到你的扬声器体验大量的收益。超级rad，右边？

Kim Thayil of Soundgarden throwing it down with some high gain. Photo from Mesa Boogie athttp://mesaboogie.com/amplitudes/2011/August/soundgarden-kim-thayil-san-francisco-ca-july-21-2011.html

Purely resistive circuits generally do not exhibit varying behavior with a change in input frequency, that is, until you get into extremely high frequency circuits. However, energy-storage elements like capacitors and inductors introduce varying behavior that is dependent on an input signal’s frequency. A common application that takes advantage of this varying behavior is a “filter.” Filter circuits generally contain some combination of capacitors and/or inductors. We call them filters because these circuits output voltage only for a defined range of input frequencies, usually with a gain of about 1 and attenuated gain outside that range. For example: if Kim Thayil up there needs more bass frequencies coming out of his speakers for some gnarly riff, the knob he would be turning would be increasing the gain on a low-pass filter (LPF). An LPF allows only lower frequency voltages to the output, attenuating higher frequencies. That’s how Kim cranks up the bass without turning all the other frequencies up, and brings in the thunder!

The frequency where attenuation begins is known as the cutoff frequency. For a simple RC circuit, here is Example 11.6 fromDigilent的真实模拟电路分析课程介绍：

The cutoff frequency in Hertz (cycles per second) can be determined by the formula:

R and C are the resistor and capacitor values of your filter in ohms and farads, respectively. For the example LPF circuit, the cutoff frequency would be about 3Hz, not very practical. Frequencies greater than that will be logarithmically attenuated such that as input frequency approaches infinity, gain approaches zero (no output). Check out Chapter 11 in Digilent’s Real Analog course at https://reference.blog.digilentinc.com/learn/courses/real-analog-chapter-11/start for more awesome, mathy, and graphical nerd-stuff on frequency response and filtering. You’ll dig it.

所以，所有这些频率发生了什么？LPF如何表现如何？我们如何弄清楚这些东西？您可以在早上开始工作两三个路线，但是，一条路线可能更有效地利用您的宝贵时间。相同的概念适用于电路分析技术和工具。
假设你已经设计了一个滤波电路和need to determine the output response for various input frequencies. There is always the “brute-force” route, which includes: using an oscilloscope to measure input and output voltages to calculate gain and the time difference between peaks to calculate phase for individual input frequencies, plotting the data, then interpolating the results. This process can be exhaustive, will be approximative at best, and just might ruin any fun you were having.

Using the circuit from Example 11.6 with a 1kohm resistor and a 10nF capacitor, we can calculate a theoretical cutoff frequency of about 15.9kHz. Using the Oscilloscope on the模拟发现2，我们可以测量导致此频率和超出此频率的增益和相位，以验证其过滤属性。使用1V正弦波输入，我们可以以低频开始，逐渐增加频率，同时调整时间轴以获得可观察和可测量的波形。提示：这是一个漫长而繁琐的方式。

50Hz:

100Hz:

200Hz：

500Hz：

1KHz：

2kHz：

5kHz:

10kHz:

15kHz:

20khz：

50kHz:

100khz：

200khz：

500khz：

1MHz:

Well, this is certainly a low pass filter with a cutoff frequency around 15kHz. Have fun plotting data and fitting a curve to it.

我不得不使用类似的方法，我的第一个实验室表征双极结晶体管（BJT），它有点让我讨厌我的实验室教授。很高兴知道这是一个选择，但它与蜜蜂覆盖的乐趣很有趣。

输入网络分析仪。

The Analog Discovery 2 is loaded with a high-precision, quick response, and customizable Network Analyzer that can plot the gain and phase for your filter over a specified range of frequencies in a matter of seconds.
将示波器的任意波形发生器和通道1应用于电路的输入，以及示波器的通道2到输出。

Using the free, complimentary software, WaveForms, click “Run” in the Network Analyzer window and watch Bode plots of your circuit’s output gain and phase generate as the Analog Discovery 2 sweeps the input frequency. Dang, that’s nice. There is no need to specify any parameters coming from the Wave Generator, although it may be helpful to specify the start and stop frequencies for your input sweep and the sample rate for data precision in the Network Analyzer window.

光标可用于确定测量的截止频率（对于该电路的约15.5kHz，接近我们的理论计算），以所选择的频率相位，以及更包括差分测量。还产生奈奎斯特图和尼科尔斯图来确定系统电路的稳定性。收集的数据也可以导出与其他分析软件一起使用，例如Matlab。
If you find that your physical circuit is not meeting a design requirement or not responding the way you want it to, make your design modifications and run the Network Analyzer again to determine the new frequency response of your circuit.

工作聪明，不难。网络分析仪是口袋大小，USB连接，多功能模拟发现2的众多工具之一，是更好的解决方案来学习频率响应。除非你是贪婪的惩罚。