Rf and if digitization in Radio Receivers: Theory, Concepts, and Examples
Practical Specifications for Real ADCs
tải về 0.99 Mb. Chế độ xem pdf
|
Chương-3, tham-số-hiệu-năng, OFDM vs OFDMA
| 2.3.2 Practical Specifications for Real ADCs
The SNR in a real ADC can be determined by measuring the residual error. Residual error is the combination of quantization noise, random noise, and nonlinear distortion (i.e., all of the undesired components of the output signal from the ADC). The residual error for an ADC is found by using a sinusoidal input into the ADC. An estimate of the input signal is subtracted from the output of the ADC; the remaining signal is the residual error. The mean squared (MS) power of the residual error then is computed. The SNR then is found by dividing the mean squared power of the input signal by the mean squared power of the residual error. 2
(ENOB). This specification is defined as the number of bits required in an ideal ADC so that the mean squared noise power in the ideal ADC equals the mean squared power of the residual error in the real ADC. The spurious free dynamic range (SFDR) is another useful specification for ADCs. One definition of the SFDR assumes a single tone sinusoidal input into the ADC. Measurement of this SFDR is made by taking the Fast Fourier Transform (FFT) of the output of the ADC. This provides the frequency spectrum of the output of the ADC and is plotted as the ADC output power in dB vs. frequency. The SFDR is then the difference between the power in the sinusoidal input signal and the peak power of the largest spurious signal in the ADC output spectrum. An example of determining the SFDR from the ADC output spectrum is shown in Figure 5. In this idealized ADC output spectrum, the input signal is a 10-MHz sinusoid. Various spurious responses are shown. The SFDR is 50 dB. SFDR allows one to assess how well an ADC can detect simultaneously a very small signal in the presence of a very large signal. Hence, it is an important specification for ADCs used in radio receiver applications. A common misconception is that the SFDR of the ADC is equivalent to the SNR of the ADC. In fact, there is typically a large difference between the SFDR and the SNR of an ADC. The SNR is the ratio between the signal power and the power of the residual error. The SFDR, however, is the ratio between the signal power and the peak power of only the largest spurious product that falls within the band of interest. Therefore, the SFDR is not a direct function of bandwidth; it does not necessarily change with a change in bandwidth, but it may. Since the power of the residual error includes quantization noise, random noise, and nonlinear
2 The SNR is often (and more accurately) called the signal-to-noise plus distortion ratio (SINAD) when distortion is included with the noise (as in this case). 13
distortion within the entire 0 to f s /2 band, the power of the residual error can be much higher than the peak power of the largest spurious product. Hence, the SFDR can be much larger than the SNR [5]. A practical example of this can be seen from the specifications for the Analog Devices AD9042 monolithic ADC. With a 19.5-MHz analog input signal, 1 dB below full scale (the full- scale input is 1 V p-p ), the typical SFDR specification is 81 dB while the SNR specification is 66.5 dB (from −40 - +85 °C) [12].
Figure 5. Example ADC output spectrum showing the spurious free dynamic range. The SFDR specification is useful for applications when the desired signal bandwidth is smaller than f s /2. In this case, a wide band of frequencies is digitized and results in a given SNR. The desired signal then is obtained by using a narrowband digital bandpass filter on this entire band of frequencies. The SNR is improved by this digital-filtering process since the power of the residual error is decreased by filtering. The SFDR specification for the ADC is important because a spurious component still may fall within the bandwidth of the digital filter; hence, the SFDR, unlike the SNR, does not necessarily improve by the digital-filtering process. However, several techniques are available to improve the SFDR. Dithering (discussed in Section 2.2) improves the SFDR of ADCs. Additionally, postdigitization-processing techniques such as state variable compensation [13], phase-plane compensation [14], and projection filtering [15] have been used to improve SFDR.
10 0
-10
-10 -30
-40
-50
-60
-70
-80
-90
-100
0 2 4 6 8 10 12 14 16 18 20 SFDR= 50dB
Frequency (MHz) P o
er ( d B m ) 14
For an ideal ADC, and in practical sigma-delta (ΣΔ) converters, the maximum SFDR occurs at a full-scale input level. In other types of practical ADCs, however, the maximum SFDR occurs at input levels at least several dB below the full-scale input level. This occurs because as the input levels approach full-scale (within several dB), the response of the ADC becomes more nonlinear and more distortion is exhibited. Additionally, due to random fluctuations in the amplitude of real input signals, as the input signal level approaches the FSR of the ADC, the probability of the signal amplitude exceeding the FSR increases. This causes additional distortion from clipping. Therefore, it is extremely important to avoid input signal levels that closely approach the full- scale level in ADCs. Prediction of the SFDR for practical ADCs is difficult, therefore measurements are usually required to characterize the SFDR. In the preceding discussion on SFDR, a sinusoidal ADC input signal was assumed. However, intermodulation distortion (IMD) due to multitone inputs is important in ADCs used for wideband radio receiver applications. To characterize this IMD due to multitone inputs, another definition of the SFDR could be used. In this case, the SFDR is the ratio of the combined signal power of all of the multitone inputs to the peak power of the largest spurious signal in the ADC output spectrum. A current example of test equipment to generate multitone inputs produces up to 48 tones. The noise power ratio (NPR) specification is useful in applications such as mobile cellular radio, where the spectrum of a signal to be digitized consists of many narrowband channels and where adjacent channel interference can degrade system performance. Particularly, the NPR provides information on the effectiveness of an ADC in limiting crosstalk between channels [13]. The NPR is measured by using a noise input signal into the ADC. This noise signal has a flat spectrum that is bandlimited to a frequency that is less than one-half the sampling frequency. Additionally, a narrow band of frequencies is removed from the noise signal using a notch filter. This noise spectrum is used as the input signal to the ADC. The frequency spectrum of the output of the ADC then is determined. The NPR then is computed by dividing the power spectral density of the noise outside the frequency band of the notch filter by the power spectral density of the noise inside the frequency band of the notch filter [5]. When using an ADC in a bandpass-sampling application where the maximum input frequency into the ADC is actually higher than one-half the sampling frequency, the full-power analog input bandwidth is an important specification. A common definition (although not universal) of full-power analog input bandwidth is the range from DC to the frequency where the amplitude of the output of the ADC falls to 3 dB below the maximum output level. This assumes a full-scale input signal to the ADC. Typically, the ADC is operated at input frequencies below this bandwidth. Aside from full-power analog input bandwidth, it is important to examine the behavior of the other specifications such as SNR, SFDR, and NPR at the desired operating frequencies since these specifications typically vary with frequency. In addition to the SNR, SFDR, and NPR of real ADCs being a function of frequency, they are also a function of input signal amplitude. Table 1 provides a summary of the important ADC specifications for radio receiver applications. 15
Table 1. Summary of ADC Specifications for Radio Receiver Applications Specification Application Definition Signal-to-Noise Ratio (SNR) Desired Signal BW Equal to f s /2
MS Signal Power MS Power of Residual Error Spurious Free Dynamic Range (SFDR) Desired Signal BW Less Than f
/2
MS Signal Power Peak Power of the Largest Spurious Product
Noise Power Ratio (NPR) Desired Signal Spectrum Contains Many Narrowband Channels Power Spectral Density of Noise * Outside Freq. Band of Notch Filter Power Spectral Density of Noise Inside Freq. Band of Notch Filter
Full-Power Analog Input BW Bandpass Sampling Range from DC to Frequency Where Output Amplitude Falls to 3 dB Less Than Maximum** * With an input signal having a bandlimited, flat noise spectrum and a narrow band of frequencies removed by a notch filter. **For a full-scale input signal. When testing an ADC, it is important to ensure that all quantization levels are tested. For single tone inputs, the relationship between the input signal frequency and the sampling rate must be chosen so that the same small set of quantization levels is not tested repeatedly. In other words, the samples should not always occur at the same amplitude levels of the input signal. For example, using an input frequency of f
/8 is a poor choice since the same eight amplitude levels are sampled every period of the input signal (assuming that the input signal and the sampling clock are phase coherent) [16]. The histogram test can be used to ensure that all quantization levels are tested. In the histogram test, an input signal is applied to the ADC and the number of samples that are taken at each of the 2 B quantization levels are recorded. In an ideal ADC this histogram is identical to the probability density function of the amplitude values of the input signal. Comparing the histogram to the probability density function of the input signal gives an indication of the nonlinearity of the ADC. An examination of the histogram reveals whether all of the different quantization levels are being tested. When no samples are recorded for a given quantization level, this level is either not being tested by the testing procedure (input signal and sampling rate) or the ADC is exhibiting a missing code. A missing code is a quantization level that is not present in the output of a real ADC that is present in the output of an ideal ADC. Missing codes are fairly rare in currently available ADCs in general and do not occur in ΣΔ converters.
tải về 0.99 Mb. Chia sẻ với bạn bè của bạn:
|