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Typical dB Applications
Frequency response is typically reported as "20 Hz to 20 kHz, +/-3 dB", often shortened to "20 - 20 kHz" with the dB limits implied. The -3 dB (half-power) point is the standard for reporting frequency response, even when you are actually measuring voltage. The equivalent voltage ratio is 0.707, which is half of the square root of 2. So a "1000 to 2000 Hz noise band" implies that at 1000 Hz (and at 2000 Hz) the noise is 3 dB softer (70.7% voltage amplitude) than at middle frequencies like 1400 Hz.
Signal-to-Noise Ratio (SNR) is expressed in dB. This is the ratio between the signal level and the system noise level. Since system noise is typically constant, the maximum SNR is obtained with the largest possible signal. That is determined by the point where distortion exceeds some specified limit. For many systems, distortion is low until the signal amplitude approaches the power supply voltage(s).
The dynamic range of a system is also given in dB. This is the ratio between the largest and smallest signals that the system can handle. For analog systems, this is often the same as the SNR. For digital systems like sound cards, the dynamic range is determined by the number of bits.
A 16-bit system should ideally have a 96 dB dynamic range. Why? Remember that every additional bit doubles the number of possible output voltages you can produce, and every time you double the voltage you add 6 dB (actually 6.02 dB) to the range. So 16 times 6 dB = 96 dB. Similarly, an 8-bit system would have a 48 dB range, and a 12-bit system would have a 60 dB range. By this reasoning, a 20-bit system should ideally have a 120 dB range, and a 24-bit system should be 144 dB. In reality the upper limit of actual systems it not much beyond 120 dB due to analog noise floor limits and other phenomena.
In an N-bit digital system, the theoretical maximum SNR is given by the ratio of the maximum sine wave signal to the quantization noise, where both are RMS values. The maximum sine wave uses the whole dynamic range of 2^N steps, half of which are positive and half negative. So its amplitude is 2^N / 2, and its RMS value is 2^N / (2 * sqrt(2)). The RMS value of the quantization noise turns out to be very close to 1 / sqrt(12) for most systems.
The ratio of these is (2^N / (2 * sqrt(2))) / (1 / sqrt(12)), which is 2^N * (sqrt(12) / 2 * sqrt(2)) or 2^N * 1.225. Expressed in dB, this is 20 * log10(2^N) + 20 * log10(1.225) or 6.02 * N + 1.76 dB. (For more information see Analog Devices tutorial MT-001 by Walt Kester, entitled Taking The Mystery Out Of The Infamous Formula, SNR = 6.02N + 1.76 dB, And Why You Should Care.)
Although technically incorrect, amplifier gain is often expressed in dB based simply upon the ratio of the output voltage over the input voltage, even when it is clear that the input resistance and output resistance are quite different. For example, an typical home audio power amplifier with a voltage gain of x20 may be referred to as 26 dB of gain, even though the input impedance is 47000 ohms and the output load is 8 ohms.
Note that amplifier gain refers only to voltage and is completely independent of power rating, which is determined by output current capability. However, an audio power amplifier is expected to produce its rated output power with typical "line" input levels of around 1 VRMS.
Attenuation is usually given in dB. Note that use of the word "attenuation" implies a reduction from the reference (input) level, or negative dB. So if you see mention of an "attenuation of 60 dB", that means the output voltage is 0.1% of the input, which might also be described as "60 dB down". Here 0 dB is the input signal level before any attenuation.
CAUTION: There is a real possibility for sign confusion when dealing with "attenuation" and "level", since that same 60 dB of attenuation might instead have been expressed as a level of -60 dB. This is usually clear from the context, but not always. The typical problem arises when you ask another person to adjust a control. You may think of it as controlling level ("volume"), and they may think of it as controlling attenuation. So what happens when you ask for "3 dB more"? Do you get 3 dB more level, or 3 dB more attenuation? You should agree on a standard, but just to be safe you may want to say something like "3 dB louder".
Distortion is often expressed in dB, as in "The distortion at the third harmonic is more than 40 dB down". This means that when the desired or input tone frequency produces an output of a certain voltage, the distortion component at 3 times that frequency is less than 1% as large.
This same approach is used with Total Harmonic Distortion (THD) and Intermodulation Distortion (IMD) by combining all the distortion components together to get a single dB value. However, note that you can't do this by simply adding all the individual component dB values. That's because the sum of logarithms is not equal to the log of their sum, and the sum of squares is not equal to the square of their sum. To do this properly you would need to add the squared component voltages together first, divide by the reference squared, and then take the log and multiply by 10:
dB(total) = 10 * log10((V1^2 + V2^2 + ... + Vn^2) / V0^2)
This gives the RMS sum of the components, expressed in dB.
However, you should rarely have to do this calculation when using Daqarta because the Sigma cursor readout in Spectrum mode will directly show the total power between cursors. The THD Meter Mini-App included with Daqarta automates this even further.
There may be times, however, when you have several discrete dB values, such as distortion peaks, that you wish to combine to get a single dB value. The RMS "Sum" of dB Values topic shows how to do this, including a macro "Mini-App" to do it automatically.
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