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AD-03 Datasheet(PDF) 3 Page - National Semiconductor (TI) |
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AD-03 Datasheet(HTML) 3 Page - National Semiconductor (TI) |
3 / 4 page 3 http://www.national.com 3) Down convert to an I.F. of 1MHz then digitize at a rate of 1MHz. In this method, some of the advantages of digital down conversion can be retained - multiple channels can be demodulated simultaneously - and complexity is reduced from a system that down converts to baseband. From an aperture standpoint we are still seeing input slew rates an order of magnitude greater than we did in example 1, but two orders of magnitude less than those seen in example 2. 4) Place a sample and hold circuit, sampling at a rate of 1MHz, in front of the A/D in scenario 2. This results in the A/D converter seeing a very low slew rate, but the aperture errors are shifted to the sample-and-hold circuit. In many cases a sample-and-hold has much lower aperture errors associated with it than a comparable speed A/D converter. In all of the above scenarios, the digital output from the converter is at a 1 MHz rate and the digital output would be identical if the A/D converter were an ideal converter with no aperture jitter. With real world converters, there will be a vast difference in the signal to noise ratio in each of these three scenarios. The solution involving placing a sample and hold circuit in front of an A/D converter is especially interesting with many high speed, high resolution, monolithic A/D converters. Many of these devices have particularly poor aperture performance and as a result even if the input frequencies are reduced to sub-nyquist rates, the aperture error may be the dominant error source. Use of a separate sample and hold will allow for the burden of sampling the signal to be shifted to the sample and hold, reducing the sensitivity to aperture jitter in the A/D converter. Reducing Noise Through Signal Processing A/D converter outputs contain noise that has as its origins quantization noise, noise that comes from aperture related effects and noise from other sources. Often it is desirable to lump all of these together and just treat them as noise and work towards reducing them. One technique that can be used for this is simply to over- sample the input then digitally low pass filter the output. If we take the example above, where we have a 100MHz carrier modulated with a 100kHz signal, if we sample at a rate of 2MHz instead of a rate of 1 MHz, the noise is distributed over a band that is twice as wide. If the digital signal is then filtered, and the half of the band that does not contain the signal of interest is thrown away, the result is a 3dB improvement in the signal to noise level. This could be carried on as far as the speed of the converter permits with the cost being carried mainly in the power and complexity of the digital filtering hardware. Imagine sampling the signal at 1GHz, then filtering out all but the lowest 500kHz band to obtain the equivalent of 1MHz sampling: we would be able to obtain a 30dB improvement in SNR over what we would have sampling at 1MHz. Another signal conditioning method that can be used toreduce the noise both from aperture effects as well as other sources is implemented in SD A/D converters. A block diagram of a simple converter is shown in Figure 3. Figure 3 If we replace the SD A/D and D/A pair with a simple additive noise where this noise represents the noise contributed by the sampling process, both quantization noise and aperture jitter related noise, then the block diagram is modified to look like that in Figure 4. The transfer function for the signal in this system is given by: Figure 4 It can be seen from this that if H(s) is large for the frequency range in which the signal is, then the signal transfer function is near unity. The noise however, sees a different transfer function: If H(s) is large in the area of interest then the noise is attenuated in this same area. The result is that the signal to noise ratio is increased. If an analysis is done of this (which is beyond the scope of this paper) it turns out that this is a much more effec- tive method of reducing the noise than the simple over- sampling and low pass filtering that is outlined above. With a first order filter for H(s) then the SNR improvement that can be realized with Σ∆ techniques is 9dB per octave of oversampling as compared to the 3dB that we obtained above. As the order of the filter used increases the gains can be increased as well. Conclusion As digitizing systems increase in speed, aperture effects play a larger and larger role in the total error budget of the system. Techniques for analysis and prediction of the errors have been presented. Techniques for the reduction of aperture related errors have been presented. Signal In H(s) A/D D/A Digital Out + STF Hs 1H S = () + () Signal In H(s) Sampling & Quantization Noise In Out ++ NTF 1 1H S = + () |
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