ultra-wideband FM

The received analog PWM can be converted to analog pulse amplitude modulation (PAM) with theoretically any value (not just some few discrete quantized values). Those PAM pulses are copies of those pulses at the sampler output at the Tx end (with some inaccuracy).

Gating those very short PAM pulses (with the rest of the pulse cycle time as zero) into an analog LPF will restore the original bandlimited signal at the Tx end.

Thus no oversampling required.

Yes, of course. PWM could be perfectly converted to/from regular PAM by means of sample holds and/or integrate and dumps. As you noted, the keyword is "accuracy". I am not sure what is feasible at 300+ MHz.

VLV

Why not PWM?

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I've done a _lot_ better than 60dB. Ok, those ones weren't over fiber but transformers and coax. The transformers were the limiting factor but it simply was not necessary to use a 20x carrier.

For simple loops, yes. But even if the PWM was a GHz that ain't considered impossible these days. You'd have to make the controlled oscillator out of inverters though. Maybe even accept a non-constant frequency. The FCC patrol isn't out there on those fibers :-)

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How about doing some math before breaking physical laws?

It doesn't matter.

There is no feedback from far side, hence timing distortions are all yours.

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

My client wasn't interested in math, only results counted. And they got those delivered :-)

It does matter. At some point excessively high PWM rates cost real money.

Correct. But a fiber has a bandwidth from here to the Klondike. There will be PWM errors due to finite rise and fall times in transmitters and detectors but those can to a large extent be compensated for if you also register the peak amplitudes and provide a correction factor.

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Take 400MHz and you'll be fine. You don't need 3GHz here, it would be a waste of resources and money.

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So does FM, however, the Bessel function drops of quite rapidly even with a high modulation index.

Are you referring to aliasing around zero frequency ?

Looking at the problem purely in time domain, for 60 dB headroom, you should be able to measure the pulse width with an accuracy of about

1/1000 of the pulse period.

Clearly, the transmission system (transmitter, fiber and receiver) is going to need a significantly larger bandwidth than the pulse repetitions frequency, in order to have sufficiently short pulse rise and fall times, so that the it can be reliably determined, when the threshold level is crossed during the pulse edges.

For an infinite bandwidth, the pulses would be really square and it would not be a problem, when the threshold level is crossed in each direction, even in the presence of strong amplitude noise.

With a limited bandwidth and hence not so steep edges, the stability of the threshold levels become critical and any amplitude noise will alter the threshold crossing time and hence the measured period, i.e. producing jitter (and amplitude noise after PWM->PAM conversion).

While the transmission system performance depends on the system bandwidth and the additive amplitude noise, but I still do not understand why oversampling would be required.

This is where clamped or peak amplitude measurement comes in. That allows to correct for threshold drift in a system where the link budget varies a bit. In a fiber system that's usually caused by connectors not being 100% clean and plumb, polarization issues, and so on. Or when a fiber radius is allowed to move.

Don't worry, I don't either, so that makes two of us. I hope Vladimir won't have our degrees pulled :-)

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It depends.

No. Think a little bit how PWM differs from FM.

OK, looking at the problem purely in time domain:

Think of PWM as if it is PCM which goes through the boxcar filter with the variable length (0...100% duty). The length of the filter varies with the instant amplitude of the signal. This creates nonlinear distortions.

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

doing so would be like 10 bits per pulse, so for 150MHz signal bandwidth you'd only need 300MHz pulse rate.

making a 1/1000 cycle at 300MHz is 300GHz

if I remember correctly a theoretical 3rd order deltasigma moulator at

16x oversampling can make 60dB SNR thats "only" 16*300MHz = 4.8GHz

-Lasse

It would not be very smart to let this run 0%...100%. If you reduce the gain and place an offset onto it then you can, for example, go from

25%...75%. Much less BW-demanding and it preserves the chance to correct errors based on amplitude differences. Which is one of the key parameters here because you LD and PD and the electronics around them can't be of infinite BW and cost.

The real cat's meouw would be if the source signal allow the introduction of the occasional sync preamble, where you could have a 0V ref level and a max volt ref level.

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Another one. Used it before (on cables) and totally forgot. Probably because I didn't have a margarita yesterday.

Send it plain old AM but in sampled blocks. A higher amplitude (higher than the signal will ever be) is sent inbetween samples, or once every so many samples. This is also sampled but then used on the receive side just like the black porch signal is on an analog TV receiver. It is used to adjust the gain to a possibly varying attenuation over the fiber. The falling edge of these high amplitude reference pulses are also used to sync-lock the sampler on the receive side.

In order to get amplitude variations out of the laser diode you could use it's back facet photodiode as a feedback element. This is the diode that is normally used for a "governor" to avoid distroying the laser diode, and it still should be. Photodiodes are very linear devices and whatever happens after the fiberoptics connector is calibrated out at the receive side.

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Some back of the envelope calculations:

Assuming 333 MHz sampling rate (3 ns pulse repetition time), thus for

60 dB (10 bit) accuracy, the pulse width would have to be measured with 3 ps accuracy.

A square wave low pass limited to about 300 MHz would have a rise and fall time in the order of 1 ns. To reach the 60 dB goal, the threshold stability and amplitude noise would have to be less than 1/300 of the pulse amplitude.

With 3 GHz bandwidth, the slope would be 100 ps and to reach 3 ps accuracy, the amplitude accuracy requirement would be 1/30 of the pulse amplitude.

With 30 GHz bandwidth and 10 ps slopes, the amplitude error and noise could be as high as 1/3 of the pulse amplitude.

Thus, a practical system would require something between 3-30 GHz but definitely not 300 GHz BW.

That would fall into the same ballpark.

That's only 50dB SNR. I guess John's fiber isn't going across the Atlantic :-)

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By the way Tim; you should put up a site with [pointers to] current versions of SciLab and matching versions of your exercizes from your book.

I recommend against on/off of the laser. Use bright/dim instead and servo versus temperature etc., to stay above critical current for dim and below max output for bright. And use "square wave" drive to the LD modulator. Hello fast edges.

Who knows? JL has yet to discuss the bandwidth of the modulating signal. Sorry, but i just reading the thread.

Well the old C-band satellite television system used 70 MHz FM IF per channel for a modulating signal of NTSC or similar. Some of the later models used 140 MHz FM IF. Used to be able to get parts.