Figure 3 - 13 shows the time domain of the samples used to calculate the composite triple beat for the MZ and DPMZ modulators. Thirty tones of equal amplitude and equal frequency spacing are chosen. The power level was selected to match the desired operating range to optimize the composite triple beat suppression, under the Newman phase distribution. The correlated phases are also shown but at the same power level (if the phases were really correlated, then the desired operating level would be about 7.5 dB lower). This was chosen to illustrate the pulse train that occurs with correlated phases. An arbitrary number of samples was chosen (1024), and the samples cover one complete period. Notice that for the correlated phases, at the beginning and the end of the sample train, there is a peak 3 - 4 times greater than the peak amplitude in the Newman phase case, but that for most of the time, the correlated phases has a lower peak than the Newman phases. It is desirable to minimize the maximum signal excursion from the bias point. Only deterministic pulse trains are analyzed. It is assumed that an uncorrelated pulse train would appear slightly better than the Newman condition for most, but not all, random seeds!
Figure 3 - 14 shows the power sweep of a standard Mach-Zehnder modulator with the canonical link parameters from Table 3-1. In this case the noise bandwidth was taken to be 6 MHz. The assumption is that each channel is spaced by 6 MHz and filtered to its spacing.
And that the noise bandwidth from the other 29 channels does not contribute. This gives a
16 Here “two-tones” refers to the fact that this distortion term arises from only two of the N tones. Intermodulation distortion of the type (2f1 ± f2) will be referred to as two-frequency, while intermodulation of the form (f1 ± f2 ± f3) will be referred to as triple beat.
noise level of -93.4 dBm. The signal from the two-tone test is also shown, that is slope 1.
For the input power levels of interest, the signal strength for all cases (two-tone, Newman phases CTB and correlated phases CTB) have the same signal level. When the correlated phases CTB is at the same level of the signal this assumption breaks down. The three distortion terms have the same slope since they are all based on third-order products. The CTB crosses the noise level at a lower power level.
Figure 3 - 13: Time-domain samples of 30 tones in a Mach-Zehnder modulator; when the phases are correlated, a pulse is formed, when the phases are related by the Newman condition, the peaks are nearly optimally averaged.
CATV channels generally need 52 dB of suppression, see Ref. [3.20]. The two-tone dynamic range is 64.7 dB, nearly 13 dB more than required. However, the Newman CTB dynamic
range is 53.7 dB, and the correlated CTB dynamic range is 46.7 dB. Thus this simple link model is barely good enough for 30 channels. Note that modern CATV experiments that use a simple MZM external modulator may have better link parameters than are assumed in Table 3-1.
Figure 3 - 14: Power sweeps of 30 tones in a MZM.
The two-tone results are shown for comparison, including two-tone SFDR, noise level, and signal level.
The Newman CTB dynamic range is about 11 dB worse than the two-tone SFDR, and the correlated CTB is 7.5 dB worse still.
Figure 3 - 15 shows the same 30 channel measurement but with a linearized modulator: the DPMZM. The DPMZM successfully nulls both the Newman phase CTB and correlated phase CTB. The two-tone dynamic range is 75.4 dB at the 6 MHz noise level. The Newman CTB dynamic range is 62.4 dB and the correlated phase CTB is 54 dB. Of course, the correlated phase case is not generally analyzed, because it is so bad, and, if designed for,
systems are generally highly overbuilt. An interesting negative effect is that the difference between the two-tone case and the Newman phase dynamic range is 13 dB, while it was only 11 dB for the Mach-Zehnder modulator. There is not an obvious answer for this, though it is clear from the plot that the shape of the two curves does not match as closely as it did in the standard Mach-Zehnder modulator plot.
Figure 3 - 15: 30 tone CTB in a linearized modulator.
The modulator choice is the DPMZM.
This leads to the basic question: Is 9 dB worth it? Calculations were run for 90, 120, 150, 180, 210, 240, 270, and 300 channels with the DPMZ (not plotted). The 300 channel calculations give 54 dB dynamic range for the Newman phase relationship. The increase in the number of channels leads to an equivalent reduction in the dynamic range, in this range of operation.
Therefore, linearized modulators offer great potential for increasing the bandwidth of CATV, or other sub-carrier systems.
The author speculates that a very high bandwidth system could be built using sub-octave modulators. Recall from noise scaling that as the system bandwidth increases, the ability to reduce shot noise becomes a more significant contribution to the reduction in dynamic range.
Many sub-carrier systems are in the 1 - 10 MHz per channel range. At this noise bandwidth, a well-optimized sub-octave modulator would yield a significantly higher dynamic range.
However the trick would be in building a sub-carrier system that is sub-octave. For example consider a system of 1000 5 MHz channels in which the lowest channel starts at 5 GHz. The author did not get to an in-depth analysis of the sub-octave modulators in sub-carrier systems.
It is left as a subject for future work.
C h a p t e r 4
BANDWIDTH OF LINEARIZED ELECTROOPTIC MODULATORS
Abstract
Many schemes have been proposed to make high dynamic range analog r-f photonic links by linearizing the transfer function of the link's modulator, as described in the previous chapter.
This chapter studies the degrading effects of finite transit time and optical and electrical velocity dispersion on such linearization schemes. The majority of the linearization techniques, but not all, experience a reduction in dynamic range with increasing frequency far more severe than the corresponding reduction in gain. However, much of the lost dynamic range in some of these modulators may be regained by segmenting and rephasing the r-f transmission line. Additionally, this chapter addresses some novel properties of the gain function of directional coupler-based modulators.