Without exception, the SNR in dB always refers to the ratio of the power between the signal and noise. When we refer to the SNR (signal-to-noise ratio), we usually measure it in dB. When S21 is -3dB, the voltage level of the signal coming out is 70% of the voltage going in. What happens to the voltage level?Ī value of -3dB is always a 50% drop in power, but the ratio of output voltage to input voltage is 10 -3/20 = 70%. But, this is a 50% drop in the power level. This is what most of us learn early in our engineering career: -3 dB down is a 50% drop. This is a pretty good value for most digital interconnect structures.Ī value of an output power of -3 dB means that the ratio of output to input power is 10 -3/10 = 0.5. Because power scales as S11², the power reflected is 1% the incident power, which is 10 -20/10 = 1%. I also explained that S-parameters, a ratio of voltages, need a factor of 20 when converted into dB.Īn S11 with a value of -20 dB means a reflected voltage signal that is 10 -20/20 = 10% the incident voltage signal. I explained why we use a factor of 10 when describing the ratio of powers, but a factor of 20 when describing the ratio of voltages. On the previous page, I introduced the dB (decibel) scale to measure the ratio of two powers as dB=10log(P1/P0). On the next page, we look at some of the subtle aspects of the dB scale, like how much voltage is 10dBm and do we use 10 or 20 when describing an impedance in the dB scale. The power associated with the voltages is V² and the value of the S-parameter in dB is = 20 x log (V OUT /V IN ). This means that to describe an S-parameter in dB, we use the factor of 20 to relate the log of the ratio of the output voltage from some port compared to the input voltage. The factor of 20 lets us convert to the log of the ratio of the voltages.Īn S-parameter is always the ratio of two voltages. The value in dB is really about the ratio of the powers of the two quantities we are comparing. ![]() ![]() Whenever we describe the ratio of two things that are not powers, but amplitudes, we use a factor of 20 to get back to the original ratio. Now, we see where the factor of 20 comes from. We can pull the square terms out of the log and get 10 x log (V1²/V0²) = 10 x 2 x log(V1/V0) = 20 x log (V1/V0). We can describe the ratio of the power generated by two voltages if they were across the same resistor, as dB = 10 x log (P1/P0) = 10 x log (V1²/V0²). To use the dB scale to describe a voltage, we have to convert the voltages into powers, and take the ratio of the powers that are related to the voltages.įor example, the power dissipated in a resistor by a voltage, V1, is V1²/R. When we want to compare two quantities that are not powers, we have to somehow convert them into powers so we can use the dB scale. When we use 1mW as the reference power level, we often designate the dB as dBm to identify that the reference power is 1mW. When we use a reference power of 1W of power, we can measure any other power in dB of power. Over the past 85 years, the dB scale has been adapted to describe not just the log of the ratio of sound power, but the log of the ratio of any two powers. On the dB scale, loudness ranges from 0dB as the TOH up to 140dB for the space shuttle. To give it a little larger range, rather than referring to the Bel directly, by convention, we’ve expanded the scale by 10x and use units of 1/10th a Bel, which is called a deciBel, or dB for short.Ī dB is always, without exception, by definition, 10x the log of the ratio of the powers: in units of dB = 10 x log(P1/P0). For all its awesome power, 14 just doesn't seem like a very large number. Its loudness is log(10 7 /1) = 7 Bels.īut on this scale of Bels, the loudness of a Space Shuttle launch at the orbiter is only 14 Bels. A vacuum cleaner is about 10 million times the TOH. This is a sound level of log (100/1) = 2 Bels. A whisper is a power about 100 times the TOH. When there is such a large dynamic range, it is more convenient to describe the values in terms of the log of the ratio of the power levels to a reference level.įor sound, the TOH is used as the reference. There are 15 orders of magnitude between the threshold of hearing and the rupture level. Using 900,000 gallons of water per minute. Sound suppression system for the Space Shuttle, Even with this system, the sound level power at the position of the Orbiter was about 100W/m².įigure 1. This is why a 900,000 gallon per minute of water sound suppression system was installed on the launch pad (Figure 1). This amount of sound power reflecting off the launch pad could have easily damaged the Space Shuttle. ![]() It only got larger closer to the launch pad. The Saturn V produced 100W/m² of sound level power about 1 mile from the launch pad. The loudest recorded man-made sound is from rocket launches.
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