db

dBm是一个考征功率绝对值的值，计算公式为：10lgP（功率值/1mw）。 [例1] 如果发射功率P为1mw，折算为dBm后为0dBm。 [例2] 对于40W的功率，按dBm单位进行折算后的值应为：

10lg（40W/1mw)=10lg（40000）=10lg4+10lg10+10lg1000=46dBm。 2、dBi 和dBd

dBi和dBd是考征增益的值（功率增益），两者都是一个相对值， 但参考基准不一样。dBi的参考基准为全方向性天线，dBd的参考基准为偶极子，所以两者略有不同。一般认为，表示同一个增益，用dBi表示出来比用dBd表示出来要大2. 15。

[例3] 对于一面增益为16dBd的天线，其增益折算成单位为dBi时，则为18.15dBi（一般忽略小数位，为18dBi）。 [例4] 0dBd=2.15dBi。

[例5] GSM900天线增益可以为13dBd（15dBi），GSM1800天线增益可以为15dBd（17dBi)。 3、dB

dB是一个表征相对值的值，当考虑甲的功率相比于乙功率大或小多少个dB时，按下面计算公式：10lg（甲功率/乙功率）

[例6] 甲功率比乙功率大一倍，那么10lg（甲功率/乙功率）=10lg2=3dB。也就是说，甲的功率比乙的功率大3 dB。

[例7] 7/8 英寸GSM900馈线的100米传输损耗约为3.9dB。

[例8] 如果甲的功率为46dBm，乙的功率为40dBm，则可以说，甲比乙大6 dB。 [例9] 如果甲天线为12dBd，乙天线为14dBd，可以说甲比乙小2 dB。 4、dBc

有时也会看到dBc，它也是一个表示功率相对值的单位，与dB的计算方法完全一样。一般来说，dBc 是相对于载波（Carrier）功率而言，在许多情况下，用来度量与载波功率的相对值，如用来度量干扰（同频干扰、互调干扰、交调干扰、带外干扰等）以及耦合、杂散等的相对量值。 在采用dBc的地方，原则上也可以使用dB替代。

The difference between the actual analog value and quantized digital value due is called quantization error. This error is due either to rounding or truncation.

Many physical quantities are actually quantized by physical entities. Examples of fields where this limitation applies include electronics (due to electrons), optics (due to

photons), biology (due to DNA), and chemistry (due to molecules). This is sometimes known as the \"quantum noise limit\" of systems in those fields. This is a different manifestation of \"quantization error,\" in which theoretical models may be analog but physics occurs digitally. Around the quantum limit, the distinction between analog and digital quantities vanishes.

Contents

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1 Quantization noise model of quantization error

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2 References 3 See also

4 External links

[edit] Quantization noise model of quantization error

Quantization noise. The difference between the blue and red signals in the upper graph is the quantization error, which is \"added\" to the original signal and is the source of noise. Quantization noise is a model of quantization error introduced by quantization in the analog-to-digital conversion (ADC) process in telecommunication systems and signal processing. It is a rounding error between the analog input voltage to the ADC and the output digitized value. The noise is non-linear and signal-dependent. It can be modelled in several different ways.

In an ideal analog-to-digital converter, where the quantization error is uniformly

distributed between −1/2 LSB and +1/2 LSB, and the signal has a uniform distribution covering all quantization levels, the signal-to-noise ratio (SNR) can be calculated from

The most common test signals that fulfil this are full amplitude triangle waves and sawtooth waves.

In this case a 16-bit ADC has a maximum signal-to-noise ratio of 6.0206 · 16=96.33 dB. When the input signal is a full-amplitude sine wave the distribution of the signal is no longer uniform, and the corresponding equation is instead

Here, the quantization noise is once again assumed to be uniformly distributed. When the input signal has a high amplitude and a wide frequency spectrum this is the case.[1] In this case a 16-bit ADC has a maximum signal-to-noise ratio of 98.09 dB.

For complex signals in high-resolution ADCs this is an accurate model. For low-resolution ADCs, low-level signals in high-resolution ADCs, and for simple waveforms the quantization noise is not uniformly distributed, making this model inaccurate.[2] In these cases the quantization noise distribution is strongly affected by the exact amplitude of the signal.

dBFS

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dBFS means \"decibels full scale\". It is an abbreviation for decibel amplitude levels in digital systems which have a maximum available level (like PCM encoding).

Clipping of a digital waveform.

0 dBFS is assigned to the maximum possible level.[1]

There is a potential for ambiguity when assigning a level on the dBFS scale to a

waveform rather than to a specific amplitude, since some derive the characteristic level of the waveform from its peak amplitude value, while others use its RMS amplitude value.[2][3][4]

For the case in which the RMS value of a full-scale square wave is designated 0 dBFS, all possible dBFS measurements are negative numbers. A sine wave could not exist at a larger RMS value than −3 dBFS without clipping, by this convention.  For the case in which the RMS value of a full-scale sine wave is designated 0 dBFS, a full-scale square wave would be at +3 dBFS.

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The measured dynamic range of a digital system is the ratio of the full scale signal level to the RMS noise floor. The theoretical dynamic range of a digital system is often estimated by the equation

The value of n equals the resolution of the system in bits or the resolution of the system minus 1 bit (the measure error). This comes from a model of quantization noise

equivalent to a uniform random fluctuation between two neighboring quantization levels. Only certain signals produce a uniform random fluctuations, so this model is not always accurate.[5]

However, a signal that fluctuates randomly between two neighboring 16-bit quantization levels will measure at −96.33 dBFS when the full-scale square wave convention is used. Although the decibel (dB) is permitted for use alongside SI units, the dBFS is not.[6] The term dBFS was first coined in the early 1980s by James Colotti, an analog engineer who pioneered some of the dynamic evaluation techniques of high-speed A/D and D/A Converters. Mr. Colotti first introduced the term to industry at the RF Expo East in Boston Massachusetts in November 1987, during his presentation “Digital Dynamic Analysis of A/D Conversion Systems through Evaluation Software based on FFT/DFT Analysis\".