EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 1A/DDSPData Receivers• Digital data receivers– Equalization– Data detection– Timing recovery• NRZ data spectra– Eye diagrams• Transmission line response• Think of it as another example for a 247 project …EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 2A/DDSPDigital Data Receivers• Way back in Lecture 1, we looked briefly at the digital communication problem• Everyone wants to send bits as far as they can, as fast as they can, through the cheapest possible media, until recovery of those bits is a complex signal processing problemCheap, noisyChannelDataTransmitterClockInputDataInputClockOutputDataOutputDataReceiverEECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 3A/DDSPDigital Data Receivers• Also, since nobody wants to invest in a separate channel to send a clock alongside the data, timing recovery is a second key responsibility of digital data receivers• Today, data detection / timing recovery is the biggest mixed-signal processing market there isCheap, noisyChannelDataTransmitterClockInputDataInputClockOutputDataOutputDataReceiverEECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 4A/DDSPDigital Data Receivers• We’ll examine digital communications using high-speed digital video over coaxial cable as our underlying example– 300Mb/s over distances of 200m– It illustrates many key principles of data detection and timing recovery [2, 3]EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 5A/DDSPNRZ Data Spectrum• NRZ (Non Return to Zero) data is a complicated-sounding name for a very simple two-level transmission scheme– The data transmitter produces two output levels, and holds the appropriate binary level for a full bit period– We’ll assume the two levels are +1 and –1• What’s the spectrum of random NRZ data?EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 6A/DDSPIdeal NRZ Data Spectrum• We looked at random 1b sequences in Lecture 15 (slides 15.4-15.5)– Random sequences yield white noise• An ideal NRZ data transmitter convolves (in time) digital data impulses with a zero-order hold function (slides 12.11-12.12)– The resulting spectrum is the product of the digital data’s white spectrum and the zero-order hold’s sinx/x response: H(f) = Te-jπfTsin(πfT)πfTEECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 7A/DDSPIdeal NRZ Data SpectrumAm [dBWN]0-30-60-900 400300200100 50030EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 8A/DDSPIdeal NRZ Data Spectrum• Communication channels are not “sampled data” systems– The digital data is passed through a ZOH• Let’s look at 300Mb/s NRZ data– Expect nulls at multiples of 300MHz (from sinc)EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 9A/DDSPIdeal NRZ Data SpectrumAmplitude (dBWN)40-40-2002010710810101091011 [Hz]zeroes atm*300MHzLog frequency scale!EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 10A/DDSPIdeal NRZ Data SpectrumAmplitude (dBWN)40-40-2002010710810101091011 [Hz]-20dB/decadeslopeH(f) = Te-jπfTsin(πfT)π f TEECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 11A/DDSPIdeal NRZ Data Spectrum• Averaging can provide a better indication of long term bin amplitudes– 30 averages here produce a DFT plot based on 900 unique transmitted bits– Results conform much more closely to the sinx/x response• We’ll return to our more customary linear frequency scale for DFT plots at 1GHz and below…EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 12A/DDSPIdeal NRZ Data SpectrumAmplitude (dBWN)40-40-200200 250 750500 1000 [MHz]300Mb/s NRZ data30000 point, 300GHz DFT30 averagesEECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 13A/DDSPNon-Zero Transition Times • The zero-order hold NRZ spectrum assumes zero transition times between binary levels• All real-world NRZ data drivers take some time to switch from one level to the other– How does this change the ideal NRZ data spectrum?EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 14A/DDSPNon-Zero Transition Times• We’ll shape the edge rate of the ideal NRZ signal via a low pass filter• The low pass filter we’ll use is a Gaussian LPF, commonly used in digital signal analysis applications [4]• A Gaussian filter’s magnitude response is given by:( )56.2 222srisefftefH ≈=−σσEECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 15A/DDSPNon-Zero Transition Times• Let’s check the effect of a Gaussian Filter– Set the 10% to 90% rise times (and fall times) of the NRZ signal to 100psec– 100psec transitions times are still very fast relative to our 3.3nsec data period• The filtered NRZ data spectrum appears in red on the following slide …EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 16A/DDSPIdeal vs. Filtered Data SpectraAmplitude (dBWN)40-40-2002010710810101091011 [Hz]300Mb/s NRZ data30000 point, 300GHz DFT30 averages0 risetime100psec risetimeEECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 17A/DDSPIdeal vs. Filtered Data Spectra• The frequency at which the ideal and filtered NRZ spectra begin to diverge (by 6.8dB, in fact) is called the “knee frequency”, fknee– Knee frequencies depend only on transition times, not NRZ data rates– There’s not enough energy above fkneeto have much effect on even the simplest data receiver (a CMOS inverter)• For digital signals with 10/90 transition times:risekneetf21=EECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 18A/DDSPIdeal vs. Filtered Data SpectraAmplitude (dBWN)40-40-2002010710810101091011 [Hz]tR=100psecfknee=5GHz0 risetime100psec risetimeEECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 19A/DDSPNRZ Data in the Time-Domain20 nsec/div0.8 V/divtR=100psecEECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 20A/DDSPIsolated +1 Data Bit1 nsec/div0.8 V/divtR=100psecEECS 247 Lecture 25: Digital Data Receivers © 2002 B. Boser 21A/DDSPFiltered NRZ Data • In high-speed communications applications, the transition times are usually comparable to the bit period– Then, filtered outputs reach the full +1 and –1 levels only if ≥2 consecutive data bits are identical– Isolated +1 and –1 pulses yield smaller swings• Let’s see what happens when tR=3nsec …– fknee= 167MHz EECS 247 Lecture 25: Digital Data
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