An NRZ signaling scheme is often used to conserve bandwidth in a baseband commu- nication system. Since the data does not return to zero in one bit period, the maximum fundamental frequency in the data is half of the data rate, and occurs when the data is alternating ones and zeros. A typical waveform of an NRZ data signal is shown in Fig. 4.3(a), and the PSD of this data signal is shown in Fig. 4.3(b). The 3 dB bandwidth, required of a lowpass filter to pass 80% of the data signal power, is about0:80BT, as
shown in Fig 4.4. Therefore, a 10 Gb/s system can, in principle, be implemented with circuits limited to a bandwidth of approximately 8 GHz, with a penalty in maximum SNR of 20%, or approximately 1 dB, by having suppressed the high frequency edges.
We would like to extract a clock signal directly from the random data. However, from Fig. 4.3(b) we see there is a spectral-null at the bit-rate. The reason for this spectral- null was discussed in detail in chapter 2. From the eye-diagram of Fig. 4.2 we notice a definite timing structure embedded in the data, despite its random nature. When the data does not change values, the signal stays either high or low, and there is no way to obtain any timing information from a constant signal. However, the cross-overs in the eye-diagram occur at integer multiples of the bit periodT. Therefore, in an NRZ data signal timing information is only contained in the transitions between different bits, and we can extract a clock by synchronizing a periodic signal with these data transitions. This procedure can be illustrated more clearly with an example.
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-1.5 -1 -0.5 0 0.5 1 1.5
0 5 10 15 20 25
Normalized Time (t / T)
Normalized Amplitude Power in Bandwidth B /32 (dB)
Normalized Frequency (f / B ) T
T
-100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0
0 1 2 3 4 5 6 7 8 9 10
(a) (b)
Figure 4.3 Random NRZ data: (a) typical time domain sample, (b) power spectral density.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Normalized 3-dB frequency (f3dB/BT)
Fractional signal power
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Normalized 3-dB frequency (f3dB/BT)
Power reduction (dB)
(a) (b)
Figure 4.4 Cumulative power in rectangular NRZ data after passing through a lowpass filter with a 3-dB frequency off3dB: (a) linear scale, (b) decibels.
168 Chapter 4
Figure 4.5 Metronome, as an analogy of a variable frequency oscillator used to recover a clock from random data.
4.1.1 Traffic Light Analogy
We could imagine ourselves trying to recover a clock from random data manually.
Imagine sitting on a park bench in Munich, just after having purchased a metronome, like the one shown in Fig. 4.5, for our piano at home. While waiting for our train, we decide to pass the time by synchronizing the metronome with the traffic-light across the street. Our goal is to find the lowest fundamental clock period used to control the traffic lights. As we are watching, we see long periods where the light stays either red or green. When the light is constant on one color, we have no idea as to the timing information controlling the traffic signal. Suddenly, the light switches to yellow, and we start our pendulum swinging; we want to try to get the pendulum to return by the time the light turns red. If the pendulum doesn’t get there in time, we speed it up by sliding the weight down on the pendulum; if there was more than one cycle of the pendulum during one yellow light, then we slow the pendulum by moving the weight higher. Over several cycles of the traffic light we get the pendulum swinging so that it has exactly one cycle on every yellow light, and has an integer, but not necessarily equal, number of cycles when the light is red or green. We will notice that the pendulum will need a slight adjustment every now-and-then because there will be drift in both the metronome, and the traffic-light timing; therefore feedback is required to keep the two clocks synchronized. Adjustments are made by measuring the position of the pendulum whenever a change occurs in the colors of light being transmitted.
This system, albeit operating at a very low data rate, is a model of a wavelength-shift- keyed (WSK) optical communication system, where different wavelengths (or colors) of light are transmitted across the same channel. In this case there are three colors transmitted, each with a distinct interpretation. In our analogy we used a PLL to extract
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the clock from the data by applying feedback to adjust a variable frequency oscillator in accordance with phase-error estimates obtained by looking at transitions in the data.
Instead of the metronome we could have used a slinky2 with a weight on the end.
We can vary the natural frequency of this harmonic oscillator by holding the slinky in different places, thus altering the effective spring-constant. We will try to match the self-resonance of the spring and mass system to the clock rate of the traffic lights.
This is analogous to pre-tuning a bandpass filter to the bit-rate of a communication system. Each time that we notice the traffic light changing colors we give the slinky a push downward. When the light stays constant, the slinky keeps oscillating, but the amplitude gets smaller due to dissipation in the spring. Then the light changes and we give the slinky another push to keep in going. This example illustrates clearly how dissipation (finiteQ) in the resonator leads to random amplitude modulation in the clock signal.
From the above analogies we see there is no mystery in extracting a clock from a system such as this. We have just outlined how the clock can be recovered from random data using either a PLL, or a BPF. Our challenge will be to design a circuit that will do this clock extraction automatically and considerably faster.