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The columns contained in this SI/PI Fundamentals section come from members of the Signal Integrity Journal community who are experts in their field and have a commitment to providing training and education in SI/PI/EMI issues for other engineers.
Signal Integrity

Signal Integrity Basics: Technical Terms

February 26, 2018

Nyquist frequency, first harmonic, clock frequency, fundamental frequency, and some other intimidating terms might be thrown at you by an SI engineer. Read on to get up to speed on these and other terms you need to know.

In the past few years, I have seen some product managers, mechanical engineers, junior signal integrity (SI) engineers or even business directors feel intimidated during a conversation when certain technical terms come up. Have you ever heard “Nyquist Frequency” or “First Harmonic” and thought, “Wow, I have no idea what he is talking about, this guy sounds very smart!”? Well, here is the good news: the concept behind those terms is not that complicated. In today’s post, I will try to explain them.

We start off by making a distinction between the bit rate, measured in bits per second, and frequency, measured in Hertz. Even though they are related, they are not the same thing. So let’s say you are transmitting 2Gbps (2 Gigabits/sec). If we plot the bit sequence 1010101010 as a function of time (horizontal axis), it should look somewhat like this:

You can try to recover this signal using one sinusoidal wave with one frequency. If you do, this is what you get:

Close, but far from good enough, you would say. So what if we add another sine wave with another frequency, and a different amplitude?

Hmm… Now we are getting closer. What if we keep on adding different frequencies with different amplitudes?

And add some more.

And if we add enough sine waves with different frequencies, eventually we can get to this:

What you just saw in the previous pictures is, roughly speaking, the concept of Fourier Transform. The idea that we can convert from frequency domain (on the right) and time domain (on the left). I left out the math that you will need to determine the frequencies and their corresponding amplitude, as that is not simple and is covered in an entire semester of senior level electrical engineering class. But I hope you can grasp the idea.

Now let’s pause for a second and go back to where we started. Remember this picture?

Yes, we needed a lot of frequencies, but without this one, it would be impossible to recover the signal. So if the bit rate (red line) is 2Gbps, what is the frequency of this sine wave (blue line)?

  • Hint 1: if the transmission rate is 2Gbps, each bit last for 0.5ns. Can you see that? Good!
  • Hint 2: The period of the sine wave, given by the distance between two maxima, is 1ns. Clear? Great!

Now, the frequency is given by 1/period, so if you do the math, you get 1GHz. That is the Nyquist frequency! We arrived at our destination. Please remain seated with your seatbelt fastened. The weather in Nyquist is 0.5 x bit rate.

That 1GHz is what the SI engineer refers to as Nyquist frequency, fundamental frequency, clock frequency or first harmonic for the 2Gbps transmission rate. As we saw, it is closely related to the bit rate, but it is not the same thing. In this example, the second harmonic is 2GHz and the third harmonic is 3GHz. Usually, we need at least up to the third harmonic to recover a signal with a minimum level of accuracy. So when you say that you are transmitting at 20Gbps, the SI engineer needs the simulation or the measurement to go up to 30GHz (remember, first harmonic is 10GHz). Next time, you already know why. No need to feel intimated anymore. You can even reply by saying “I want you to simulate all the way to 40GHz, we are transmitting at 20Gbps, fourth harmonic will give better results.” Oh my, you will sound so smart….


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