4 Analogtodigital converter 华科Word格式.docx

1、The values are usually stored electronically in binary form, so the resolution is usually expressed in bits. the number of discrete values available, or levels, is usually a power of two. For example, an ADC with a resolution of 8 bits can encode an analog input to one in 256 different levels, since

2、 28 = 256. The values can represent the ranges from 0 to 255 （i.e. unsigned integer） or from -128 to 127 （i.e. signed integer）, depending on the application.（分辨率也可以用电压单位伏特来表示）Resolution can also be defined electrically, and expressed in volts. The voltage resolution of an ADC is equal to its overall

3、 voltage measurement range divided by the number of discrete intervals as in the formula: Where:Q ： resolution in volts per step （volts per output code）, EFSR ： the full scale voltage range = VRefHi VRefLo, M ： the ADCs resolution in bits, and N ： the number of intervals, given by the number of avai

4、lable levels （output codes）, which is: N = 2M 下面具3个例子：Some examples may help:Example 1 Full scale measurement range = 0 to 10 volts ADC resolution is 12 bits: 212 = 4096 quantization levels （codes） ADC voltage resolution is:（10V - 0V） / 4096 codes = 10V / 4096 codes 0.00244 volts/code 2.44 mV/code E

5、xample 2 Full scale measurement range = -10 to +10 volts ADC resolution is 14 bits: 214 = 16384 quantization levels （codes） （10V - （-10V） / 16384 codes = 20V / 16384 codes 0.00122 volts/code 1.22 mV/codExample 3 Full scale measurement range = 0 to 8 volts ADC resolution is 3 bits: 23 = 8 quantizatio

6、n levels （codes） （8 V 0 V）/8 codes = 8 V/8 codes = 1 volts/code = 1000 mV/code This type of ADC can be modeled mathematically as:（实际系统中，AD分辨率由性噪比决定）In practice, the useful resolution of a converter is limited by the best signal-to-noise ratio that can be achieved for a digitized signal. An ADC can r

7、esolve a signal to only a certain number of bits of resolution, called the effective number of bits （ENOB）. One effective bit of resolution changes the signal-to-noise ratio of the digitized signal by 6 dB, （如果分辨率被AD限制，那么前置运放的信噪比将起很大作用）if the resolution is limited by the ADC. If a preamplifier has b

8、een used prior to A/D conversion, the noise introduced by the amplifier can be an important contributing factor towards the overall SNR.1.2 Response type（线型非线性）1.2.1 Linear ADCsMost ADCs are of a type known as linear, although analog-to-digital conversion is an inherently non-linear process （since t

9、he mapping of a continuous space to a discrete space is a piecewise-constant and therefore non-linear operation）. The term linear as used here means that the range of the input values that map to each output value has a linear relationship with the output value.1.2.2 Non-linear ADCsIf the probabilit

10、y density function of a signal being digitized is uniform, then the signal-to-noise ratio relative to the quantization noise is the best possible. Because this is often not the case, its usual to pass the signal through its cumulative distribution function （CDF） before the quantization. This is good

11、 because the regions that are more important get quantized with a better resolution. In the dequantization process, the inverse CDF is needed.This is the same principle behind the companders used in some tape-recorders and other communication systems, and is related to entropy maximization. （Never c

12、onfuse companders with compressors!）For example, a voice signal has a Laplacian distribution. This means that the region around the lowest levels, near 0, carries more information than the regions with higher amplitudes. Because of this, logarithmic ADCs are very common in voice communication system

13、s to increase the dynamic range of the representable values while retaining fine-granular fidelity in the low-amplitude region.An eight-bit a-law or the -law logarithmic ADC covers the wide dynamic range and has a high resolution in the critical low-amplitude region, that would otherwise require a 1

14、2-bit linear ADC.1.3 Sampling rate（如何确定采样频率）The analog signal is continuous in time and it is necessary to convert this to a flow of digital values. It is therefore required to define the rate at which new digital values are sampled from the analog signal. The rate of new values is called the sampli

15、ng rate or sampling frequency of the converter.A continuously varying bandlimited signal can be sampled （that is, the signal values at intervals of time T, the sampling time, are measured and stored） and then the original signal can be exactly reproduced from the discrete-time values by an interpola

16、tion formula. The accuracy is limited by quantization error. However, this faithful reproduction is only possible if the sampling rate is higher than twice the highest frequency of the signal. This is essentially what is embodied in the Shannon-Nyquist sampling theorem.（奈奎斯特采样定理）Since a practical AD

17、C cannot make an instantaneous conversion, the input value must necessarily be held constant during the time that the converter performs a conversion （called the conversion time）. An input circuit called a sample and hold performs this taskin most cases by using a capacitor to store the analog volta

18、ge at the input, and using an electronic switch or gate to disconnect the capacitor from the input. Many ADC integrated circuits include the sample and hold subsystem internally.（采样保持电路）1.3.1 AliasingFor example, a 2kHz sinewave being sampled at 1.5kHz would be reconstructed as a 500Hz sinewave. Thi

19、s problem is called aliasing.Matlab演示：second_nyqst.mdl 。To avoid aliasing, the input to an ADC must be low-pass filtered to remove frequencies above half the sampling rate. This filter is called an anti-aliasing filter, and is essential for a practical ADC system that is applied to analog signals wi

20、th higher frequency content.（可以用作下变频或带通采样）Although aliasing in most systems is unwanted, it should also be noted that it can be exploited to provide simultaneous down-mixing of a band-limited high frequency signal。1.3.2 IF/RF （bandpass） sampling（信号有正频率，和负频率，采样是按照采样频率将它们在频谱上进行搬移）Real signals have Fou

21、rier spectra with symmetry about zero. That is, they have a negative-frequency spectrum that is a mirror image of the positive-frequency spectrum. Sampling effectively shifts both sides of the spectrum by multiples of the sampling frequency. The criterion to avoid aliasing is that none of these shif

22、ted copies of the spectrum overlap.画图解释采样是将被采样信号进行频谱周期搬移。In the case of a bandpass （non-baseband） signal, with low and high band limits fL and fH respectively, the condition for an acceptable sample rate is that shifts of the bands from fL to fH and from fH to fL must not overlap when shifted by all

23、 integer multiples of sampling rate fs. This condition reduces to the constraint:,for some n satisfying:The highest n for which the condition is satisfied leads to the lowest possible sampling rates.（n最大的时候采样率最低）Important signals of this sort include a radios intermediate-frequency （IF） or radio-fre

24、quency （RF） signal.（中频或射频采用这个）If n 1, then the conditions result in what is sometimes referred to as undersampling, bandpass sampling, or using a sampling rate less than the Nyquist rate 2fH obtained from the upper bound of the spectrum. （n1的时候，就不满足普通的奈奎斯特频率要求了）Alternatively, for the case of a given

25、 sampling frequency, simpler formulae for the constraints on the signals spectral band are given below.（举个容易理解的例子）Example:Consider FM radio to illustrate the idea of undersampling. In the US, FM radio operates on the frequency band from fL = 88 MHz to fH = 108 MHz. The bandwidth is given by The samp

26、ling conditions are satisfied for Therefore, n can be 1, 2, 3, 4, or 5. The value n = 5 gives the lowest sampling frequencies interval and this is a scenario of undersampling. In this case, the signal spectrum fits between and 2 and 2.5 times the sampling rate （higher than 86.488 MHz but lower than

27、108110 MHz）.（被采样信号，卡在2 到 2.5倍采样频率之间）A lower value of n will also lead to a useful sampling rate. For example, using n = 4, the FM band spectrum fits easily between 1.5 and 2.0 times the sampling rate, for a sampling rate near 56 MHz （multiples of the Nyquist frequency being 28, 56, 84, 112, etc.）.Wh

28、en undersampling a real-world signal, the sampling circuit must be fast enough to capture the highest signal frequency of interest. （信号采集频率应该快到采集最高频的信号）Theoretically, each sample should be taken during an infinitesimally short interval, but this is not practically feasible. （每次采集时间应该无限短，不过不实际）Instea

29、d, the sampling of the signal should be made in a short enough interval that it can represent the instantaneous value of the signal with the highest frequency. （实际上，足够短就行，不需要无限短）This means that in the FM radio example above, the sampling circuit must be able to capture a signal with a frequency of 108 MHz, not 43.2 MHz. Thus, the sampling frequency may be only a little bit greater than 43.2 MHz, but the input bandwidth of the system must be at least 108 MHz. Similarly, the accuracy of the sampling timing, or apertur