Vankka J. - Digital Synthesizers and Transmitters for Software Radio (2000)(en)
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fundamental
/
), while spurious responses due to the D/A-converter clock feedthrough noise and dynamic non-linearities generally roll off much more slowly with the frequency. Nevertheless, the first and second images may still meet the system SNDR requirements. The SNDR degradation can be compensated by using a more accurate D/A converter.
and 
The NRZ and RTZ pulses are optimized for signals near DC. For frequencies near 
, the RZ2c pulse shows the largest gain. In the case when the frequencies are near 2 
, the RZ2 pulse results in the smallest loss of gain. Depending on the image frequency, different D/A converter pulse shapes give the largest gain. In order to be able to make the RZ, RZ2 and RZ2c pulses, a higher sampling frequency than 
is required. Large voltage steps in these pulses cause clock jitter and waveform fall/rise asymmetry sensitivity. In this chapter, the filters were designed to precompensate the distortion from the NRZ pulse shape.
/4 and the I and Q signals are both compensated by using real FIR filters. After pre-compensation, signals are down-converted back to the baseband. The block diagram of this method is shown in Figure 13-4 (c).
, which is shown in Figure 13-2.
. The measured second image of the WCDMA signal.
FIR Filters for Compensating D/A Converter Frequency Response |
265 |
Distortion |
|
In the first case, the pre-compensation is carried out in IF by using a real linear phase FIR filter. The sampling frequency is 76.8 MHz, the signal frequency is 19.2 MHz and the center frequency of the image is located at 96 MHz. The output signal of the D/A converter is pre-compensated so that the droop in the second image is cancelled. The magnitude response of the precompensation filter at 19.2 MHz f
/4) is obtained from (13.2), where f
is 76.8 MHz and f is 96 MHz (5/4 f
) ± 2.5 MHz. If a D/A converter pulse shape other than the NRZ is used, then the magnitude response of the precompensation filter is obtained from the inverse of (13.3), (13.4), or (13.5).
In the second case, the pre-compensation is performed in the baseband, where the sampling frequency is 30.72 MHz. Because the frequency response is not symmetric with respect to zero frequency, the precompensation FIR filter has to be complex. The pre-compensation located in the baseband allows the pre-compensation filter to run at a lower computational rate.
The third way to compensate discussed in this chapter is to up-convert the baseband signal to f
/4, using the complex multiplier ejn /2 . In this special case, when the IF center frequency is equal to a quarter of the sampling rate, considerable simplification is achieved, since the sine and cosine signals representing the complex phasor degenerate into two simple sequences [1 0 –1 0 …] and [0 1 0 –1 …], thus eliminating the need for high-speed digital multipliers and adders to implement the mixing functions. The only operations involved are sign inversions and the interchanging of real and imaginary parts. After the upconversion, two real filters compensate I- and Q-signals separately, and the compensated signal is down-converted back to the baseband with the e-jn /2 complex multiplier. In this case, the sampling frequency is the same as in the complex filter case.
Table 13- 1. Three implementations
|
|
Real FIR |
Complex |
Quadrature |
|
|
|
in the IF |
FIR |
in the f /4 |
|
|
|
|
|
s |
|
Number of Taps |
5 |
5 |
7 |
||
Sampling |
Fre- |
76.8 |
30.72 |
30.72 |
|
quency (MHz) |
|
||||
|
|
|
|
||
Number of Les |
|
135 |
456 |
416 |
|
LEs utilized (%) |
7 |
26 |
24 |
||
Max Clock |
Fre- |
131.57 |
125 |
75.18 |
|
quency (MHz) |
|
||||
|
|
|
|
||
Peak Error of |
the |
±0.0278 |
±0.0325 |
±0.0374 |
|
Compensation (dB) |
|||||
|
|
|
|||