# How can I find the cutoff-frequency in real experiment?

My Problem is that I can't figure out how to answer this question:

The component values in the previous measurements have been known and the cut-off frequency could be calculated. In real life, this is not always the case, as components may suffer considerable tolerances causing the cut-off frequency to diverge from its theoretical value. Assume a high-pass filter with unknown components is given and you are tasked to determine the cut-off frequency. Define methods to do so in a “real” lab scenario

I don't get any of this question. Even if there are tolerances, I can figure the output, can't I? Therefore I don't understand why I should find the method to determine cutoff-frequency.

• Note that the question says "unknown components." You only know that it is a high pass filter, but don't know that component values.
– JRE
Commented Apr 21, 2021 at 8:00
• If you are tasked to verify what the cutoff frequency is or whether it is in component tolerance, yes you have to measure what the cutoff frequency actually is with some method. And since it is a lab task, you need to think how to measure it with given equipment, as there can be multiple methods to do it. Commented Apr 21, 2021 at 8:01
• @Justme Unfortunately the Lab is online, I should simulate with LTSpice. Can you give a tip to solve this thing?
– hong
Commented Apr 21, 2021 at 8:09
• Do you know anything about the filter? Is it a first-order filter? Do you know how to setup the simulation and get a frequency domain output plot? Commented Apr 21, 2021 at 8:15
• The point of homework is to at least try doing it yourself first. How many ways of measuring the cutoff frequency you can think of, and which of them are possible in LTSpice? Commented Apr 21, 2021 at 8:19

Hong, you need two things:

• The circuit diagram under test (which type/order of highpass?)

• The definition for the cut-off freqency.

Then, perform an ac analysis with LTSpice and apply the definition-

• How is a simulator a "real" experiment though? Commented Apr 21, 2021 at 11:19
• Should be answered by the person who has created this task.
– LvW
Commented Apr 21, 2021 at 11:26
• Why? If the task is to verify the design or to implement production testing, then you can't use simulators. Commented Apr 21, 2021 at 11:27
• @Lundin The way the original question is phrased I interpret it as "describe what you would do if there were no COVID-19 so the lab was open", I guess the author of the problem is happy if OP can describe it with virtual components. OP writes in a comment that "Unfortunately the Lab is online".
– pipe
Commented Apr 21, 2021 at 17:14

It seems to be your task to figure out how to do this, and we don't solve homework for people. But your actual question here seems to be: I don't understand why I should find the method to determine cutoff-frequency.

The real life of an engineer involves not only designing things, but also verifying that your design works as intended (or more often, figuring out why it did not work as intended).

Imagine you have designed an ADC with an input filter, and the sampled data of the prototype is not what you expected. You measure the filter and realize it is 10 times higher than expected. A resistor is wrong, because manufacturing didn't get the errata you sent them, or someone took it from the wrong bin, or it wasn't soldered correctly.

Or a device that used to work comes back from the customer, they claim it doesn't work. They used it in a different country where it's colder, and you realize after verifying that you omitted to test the design over the whole temperature range promised in the manual, and it goes out of spec when it's too cold.

A lot of things outside the simulation can affect the performance of the product, and even if it's not your fault, being able to show the result on black and white goes a long way when figuring out the root cause.

• Thanks a lot. I also wanted to know the purpose of it. Because I am starter, everything is unclear. I know you don't give the answer for that but I just needed any kind of tip for RC circuit
– hong
Commented Apr 21, 2021 at 8:24

It is a mandatory practice to verify your calculations are confirmed by bench measurements. You do it to verify you did nothing wrong when determining the transfer function but also, more importantly, to see the effects of parasitics affecting the selected components themselves: the equivalent series resistance (ESR) of a capacitor or an inductor are typical offenders that you must characterize to account for their presence. Once you know how they affect the response, you can include them in the original circuit and refine the analysis.

Several ways exist to check the response of a filter. The most common one is to resort to a frequency response analyzer (FRA) which is going to sweep the input (the stimulus) while observing the output (the response). By computing the magnitude and the phase of the collected signals - $$\|\frac{V_{out}(f)}{V_{in}(f)}|\$$ and $$\arg\frac{V_{out}(f)}{V_{in}(f)}\$$ - then plotting them on a chart, you will obtain a Bode plot from which you can infer the cutoff frequency. The setup could be as below:

An oscilloscope is important to make sure the filter is not over-driven - especially an active filter - and remains linear while you sweep it.

The second method, more economic, uses a simple oscilloscope. You know that a 3-dB attenuation implies a reduction of magnitude by 29.3% of the reference point. Therefore, if a low-pass filter offers a gain of 1, or 0 dB, at low frequency, then at the cutoff frequency, the magnitude will be 0.707 or -3 dB. Modulation-wise, it means that if you inject a 1-V rms sinusoidal signal, then after a 3-dB attenuation the response is 707 mV rms:

With an oscilloscope, inject an input signal with a frequency corresponding to your reference magnitude and calibrate the vertical scale so that the output signal occupies 10 divisions. If you deal with a low-pass filter, then select a low frequency for this calibration. I have chosen 100 Hz for an expected 1-kHz cutoff point for instance. If it would be a high-pass filter, you would select a frequency above cutoff for this calibration. Then, for the low-pass filter, simply increase the frequency on the generator and observe the response on the oscilloscope screen. When the magnitude drops from 10 divisions to 7 as shown in the picture, you have your 3-dB point. With a high-pass filter, start from the flat high-frequency magnitude and go backwards by reducing the stimulus frequency.

The FRA method is obviously the most precise as it gives a complete picture of the frequency response. It can also reveal unexpected peaks or notches what the simple scope-based method won't easily do. But for simple lab. experiments aimed at training students for instance, the scope way does well and I used it many times to characterize the pole of an optocoupler.

• @hong - to emphasize what Verbal Kint said here: for now, you have an instructor to check your work. When you are a junior engineer, if you are lucky, a senior engineer will check your work. Someday when you are a senior engineer, there won't be anybody to check your work, you must learn to check your own work. For an important project I would check my work with multiple analysis methods and tests. Commented Apr 22, 2021 at 23:03