What is Signal to Noise Ratio and How to calculate it?

As a teenager, while learning the ins and outs of car audio, I often basked in the sheer detail of every note. For me, music was intoxicating, almost as much as the fields of Science and Electronics. However, during this time, the onset of the compact disc and, of course, the car subwoofer was taking center stage.

Before the compact disc, vinyl was the clear-cut choice for audio reproduction, in terms of listening pleasure. However, many would argue that it still is, under certain conditions. Moreover, the CD was a game-changer back then, and the clarity it afforded versus the cassette tape was undeniable. Just like there was a demand for devices to play the new 4K video standard of today, the same was true for the compact disc.

Which, of course, ushered in the car audio CD receiver. With its superior clarity and ease of use, the CD receiver’s reign was complete. However, where there is capitalism, you are sure to find direct competition. This was most certainly the case for the CD receiver, and the most taunted difference the high-end car audio components could use to sway their customers was superior clarity. The clarity that they were speaking of was only achievable through their superior signal to noise ratio specifications.

The one specification that was always better than the lesser brands was their signal to noise ratio (SNR). Furthermore, even to the untrained ear, the difference in the clarity and musical presence was undeniable. So, if SNR can make that much of a difference in musical sound clarity, then its importance in signal transmission applications is exponentially more critical. Therefore, over the next few paragraphs, I will discuss SNR and how to calculate it to ensure design accuracy.

What is Signal to Noise Ratio?

In terms of definition, SNR or signal-to-noise ratio is the ratio between the desired information or the power of a signal and the undesired signal or the power of the background noise.

Also, SNR is a measurement parameter in use in the fields of science and engineering that compares the level of the desired signal to the level of background noise. In other words, SNR is the ratio of signal power to the noise power, and its unit of expression is typically decibels (dB). Also, a ratio greater than 0 dB or higher than 1:1, signifies more signal than noise.

Aside from the technical definition of SNR, the way I define it in other terms is by using a comparative. For example, say that you and one other person are inside a large room having a conversation. However, the room is full of other people who are also having conversations. Furthermore, a few of the other individuals also have similar voice patterns to you and the other individual involved in your discussion. As you can imagine, it would be difficult to decipher which person is saying what.

Why is Signal to Noise Ratio Important?

In the previous comparison, you can get a better understanding of what is meant by an unwanted signal or noise. As you can also imagine, it would be nearly impossible to understand the other party involved in your conversation. Also, in a scenario such as this, we would consider this to be a signal to noise issue or the equivalent of a signal to noise ratio that is below acceptable parameters.

Now suppose the desired signal is essential data with a strict or narrow tolerance for errors, and there are other signals disrupting your desired signal. Again, it would make the task of the receiver exponentially more challenging to decipher the desired signal. In summary, this is what makes having a high signal to noise ratio so important. Furthermore, in some cases, this can also mean the difference in a device functioning or not, and in all cases, it affects performance between transmitter and receiver.

In wireless technology, the key to device performance is the device’s ability to distinguish the applied signals as legitimate information from any background noise or signals on the spectrum. This epitomizes the definition of the standards SNR specifications are utilized to set. Furthermore, the standards I am referring to ensure proper wireless functionality, as well.

The Basics of Signal to Noise Ratio Calculations

In basic terms, SNR is the difference between the desired signal and the noise floor. Also, in terms of definition, the noise floor is the specious background transmissions that are produced by other devices or by devices that are unintentionally generating interference on a similar frequency. Therefore, to ascertain the signal to noise ratio, one must find the quantifiable difference between the desired signal strength and the unwanted noise by subtracting the noise value from the signal strength value.

Achieving your desired signal integrity can be difficult at any stage of designing.

Hypothetically speaking, if your device's radio receives a signal at -65 dBm (decibels per milliwatt), and the noise floor is -80 dBm, then the resulting signal to noise ratio is 15 dB. This would then reflect as a signal strength of 15 dB for this wireless connection. As I am sure you are aware, in terms of connectivity in wireless networks, the experts state a requirement of an SNR of at least 20 dB to say, surf the web. However, the following is SNR requirements versus SNR values:

• 5 dB to 10 dB: is below the minimum level to establish a connection, due to the noise level being nearly indistinguishable from the desired signal (useful information).

• 10 dB to 15 dB: is the accepted minimum to establish an unreliable connection.

• 15 dB to 25 dB: is typically considered the minimally acceptable level to establish poor connectivity.

• 25 dB to 40 dB: is deemed to be good.

• 41 dB or higher: is considered to be excellent.

Although SNR is routinely in use to quantify the clarity or strength of electrical signals, it can also apply to any form of signal (transmission). For example, it is in use to describe isotope levels in ice cores, biochemical signaling between cells, or audio sound clarity for car amplifiers and source units (DVD, CD, or Digital). However, with audio components, the SNR is always a positive value. For example, an SNR of 95 dB, means that the level of the audio signal is 95 dB higher than the level of the noise. Which, in turn, means that an SNR of 95 dB is better than one that is 80 dB.

How to Calculate Signal to Noise Ratio

SNR calculations can be either simple or complex, and it depends on the devices in question and your available data. So, if your SNR measurements are already in decibel form, then you can subtract the noise quantity from the desired signal: SNR = S - N. This is because when you subtract logarithms, it is the equivalent of dividing normal numbers. Also, the difference in the numbers equals the SNR. For example, you measure a radio signal with a strength of -10 dB and a noise signal of -50 dB. -10 - (-50) = 40 dB.

As I stated earlier, calculating SNR can be involved, as well. So, for complex calculations, you divide the value of the desired signal by the amount of the noise and then take the common logarithm of the result, i.e., log (S ÷ N). After this, if the signal strength measurements are in watts (power), you will then multiply by 20. However, if they are units of voltage, then you will multiply by 10.

Furthermore, for power, SNR = 20 log (S ÷ N) and for voltage, SNR = 10 log (S ÷ N). Also, the resulting calculation is the SNR in decibels. For example, your measured noise value (N) is 2 microvolts, and your signal (S) is 300 millivolts. The SNR is 10 log (.3 ÷ .000002) or approximately 62 dB.

Signal to Noise Ratio Formula and Channel Capacity

Signal to noise ratio affects all wireless networks, and this includes Bluetooth, Wi-Fi, 4G, 4G LTE, and 5G, since their operation is dependent on radio signals. Also, since they function through the use of radio signals, each of the mentioned communication methods has a maximum channel capacity. Furthermore, as the SNR increases, so does the channel capacity.

Overall, the channel capacity, the bandwidth, and the signal to noise ratio, all affect the maximum capacity of communications channels. Moreover, this discovery belongs to Claude Shannon, and he makes this correlation during World War II. In today’s fields of electronics and science, engineers and scientists alike, refer to it as Shannon's Law or the Shannon-Hartley theorem.

According to Shannon’s Law, the following formula depicts this correlation that forms the capacity dependent relationship:

C = W log2(1 + S/N)

Within this formula:

C equals the capacity of the channel (bits/s)

S equals the average received signal power

N equals the average noise power

W equals the bandwidth (Hertz)

The Shannon-Hartley theorem shows that the values of S (average signal power), N (average noise power), and W (bandwidth) sets the limit of the transmission rate.

Achieving technical designs with demanding signal challenges is rewarding in the current evolving industry. 

The importance of accurately calculating the signal to noise ratio is imperative to the ultimate goal of efficient and accurate designs. Furthermore, computing the SNR will also provide insight into design functionality and design performance. The time to realize that a design is not feasible is before the manufacturing phase. Therefore, it is essential to assess design parameters through calculations as well as simulation.

Thankfully, with Cadence’s suite of design and analysis tools, you’ll be sure to have your designers and production teams working together towards implementing proper techniques to calculate the signal to noise ratio in all of your PCB designs. Allegro PCB Designer is the layout solution you’ve been looking for, and it can unquestionably facilitate the implementation of effective signal to noise ratio strategies into your current and future PCB designs. 

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts. To watch videos about related topics or see what's new with our suite of design and analysis tools, subscribe to our YouTube channel.