Rf and if digitization in Radio Receivers: Theory, Concepts, and Examples
tải về 0.99 Mb. Chế độ xem pdf
|
Chương-3, tham-số-hiệu-năng, OFDM vs OFDMA
| 2.3 Important Specifications
In this section, theoretical signal-to-noise ratio (SNR) due to quantization noise and aperture jitter is discussed. Practical specifications for real ADCs are then presented.
For radio receiver applications where the amplitude of the desired signal falls within the ADCs FSR, and the bandwidth of the desired signal is equal to f
/2, the SNR of an ADC is a useful specification. The theoretical maximum SNR of ADCs generally is assumed to be 6B (dB), where B is the number of bits of resolution of the ADC. A more precise expression providing the maximum possible theoretical SNR can be derived based on some assumptions about the noise and the input signal. First, it is assumed that the noise present is due to quantization error only. The amplitude of this quantization noise is assumed to be a random variable uniformly
11
distributed over one quantization step. Assuming a sinusoidal input with an amplitude equal to the FSR of the ADC, the maximum possible theoretical SNR is given as
SNR = 6.02B + 1.76 + 10 log 10
s 2f max (dB) (1) where f s is the sampling frequency and f max is the maximum frequency of the input analog signal [2],[9]. The commonly stated theoretical SNR of 6B (dB) is an approximation to this equation when f s = 2f max and the 1.76 dB is neglected. From this equation, note that as the sampling frequency is increased beyond 2f
, the SNR increases. This occurs because the quantization noise power, which is a fixed amount and independent of bandwidth (P
= q 2 /12R), is spread out over an increasingly wider band as the sampling frequency is increased. This lessens the amount of the quantization noise that falls within the 0 to f s /2 band. Figure 4 shows this phenomenon. Consequently, oversampling increases the maximum possible SNR. Such oversampling is sometimes used to realize a greater maximum SNR than at first appears possible. An 8-bit ADC, with a sampling rate of 20 Msamples/s, for example, can provide 68 dB rather than 48 dB of maximum SNR for 100-kHz signals in the passband if appropriate digital filtering is used to recover the 100-kHz signal.
Figure 4. Frequency-spreading of quantization noise power due to oversampling. Besides being limited by the quantization step size (resolution), the SNR of the ADC also is limited by aperture jitter. Aperture jitter is the variation in time of the exact sampling instant. Aperture jitter can be caused externally by jitter in the sampling clock, or internally since the sampling switch does not open at precise times. Aperture jitter causes a phase modulation of the sampled signal and thus results in an additional noise component in the sampled signal [10]. The
A A
P o w er
P o w er f s = f max
P qn = q
1 R
f s
=f max
0
f
0 f
f max
fs
f s ≫ f max
P qn = q
1 R
12
maximum analog input frequency of the ADC is limited by this aperture jitter since the SNR due to aperture jitter (SNR aj ) degrades as the input frequency increases. The SNR aj is given as
SNR
aj = 20 log 10
1 2π f max t a
where t a is the aperture jitter of the ADC [2]. For sampling at f s =2f max quantization noise and the SNR due to aperture jitter can be combined to give the overall SNR [11]. tải về 0.99 Mb. Chia sẻ với bạn bè của bạn:
|