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From: Vladimir Vassilevsky on 14 Jul 2010 12:48 Joerg wrote: > Vladimir Vassilevsky wrote: > >> >>Joerg wrote: >>>Vladimir Vassilevsky wrote: >>> >>PWM is a kind of angular modulation. As such, it creates infinite >>sidebands on both sides of the carrier. Some part of the lower sideband >>inevitably falls into the bandwidth of the useful signal. How much of >>trash gets into the signal? It depends. Ballpark: for 60dB of rejection, >>the PWM carrier should be ~ x20 times of the highest signal frequency. >> > I've done a _lot_ better than 60dB. How about doing some math before breaking physical laws? > 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. It doesn't matter. >>But, still loop cutoff ~ PWM rate/8. Or, >>if you want to really push phase margin, PWM rate/6. Consequently, the >>feedback is going to be quite shallow and it can't be the cure for all >>sins of PWM. >> > > > 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 :-) There is no feedback from far side, hence timing distortions are all yours. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
From: Joerg on 14 Jul 2010 12:54 Vladimir Vassilevsky wrote: > > > Joerg wrote: > >> Vladimir Vassilevsky wrote: >> >>> >>> Joerg wrote: >>>> Vladimir Vassilevsky wrote: >>>> > >>> PWM is a kind of angular modulation. As such, it creates infinite >>> sidebands on both sides of the carrier. Some part of the lower sideband >>> inevitably falls into the bandwidth of the useful signal. How much of >>> trash gets into the signal? It depends. Ballpark: for 60dB of rejection, >>> the PWM carrier should be ~ x20 times of the highest signal frequency. >>> >> I've done a _lot_ better than 60dB. > > How about doing some math before breaking physical laws? > My client wasn't interested in math, only results counted. And they got those delivered :-) >> 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. > > It doesn't matter. > It does matter. At some point excessively high PWM rates cost real money. > >>> But, still loop cutoff ~ PWM rate/8. Or, >>> if you want to really push phase margin, PWM rate/6. Consequently, the >>> feedback is going to be quite shallow and it can't be the cure for all >>> sins of PWM. >>> >> >> >> 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 :-) > > There is no feedback from far side, hence timing distortions are all yours. > 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. -- Regards, Joerg http://www.analogconsultants.com/ "gmail" domain blocked because of excessive spam. Use another domain or send PM.
From: Joerg on 14 Jul 2010 12:57 Vladimir Vassilevsky wrote: > > > Paul Keinanen wrote: > >> On Wed, 14 Jul 2010 09:19:12 -0500, Vladimir Vassilevsky >> <nospam(a)nowhere.com> wrote: >> >> >>> >>> Paul Keinanen wrote: >>> >>>> On Tue, 13 Jul 2010 15:44:19 -0500, Vladimir Vassilevsky >>>> <nospam(a)nowhere.com> wrote: >>>> >>>> >>>> >>>>> For ~10 bit accuracy, the PWM rate must be ~20 times higher then >>>>> the highest frequency of the signal. >>>>> >>>>> Generating 10-bit linear ramp at 2 GHz is nontrivial. >>>> >>>> >>>> Why that high ? >>> >>> If the PWM is demodulated with LPF, then it is inherently nonlinear. >>> Higher clock frequency - better linearity. >> >> >> 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). > > 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. > Take 400MHz and you'll be fine. You don't need 3GHz here, it would be a waste of resources and money. [...] -- Regards, Joerg http://www.analogconsultants.com/ "gmail" domain blocked because of excessive spam. Use another domain or send PM.
From: Paul Keinanen on 14 Jul 2010 16:16 On Wed, 14 Jul 2010 11:48:12 -0500, Vladimir Vassilevsky <nospam(a)nowhere.com> wrote: > > >Joerg wrote: > >> Vladimir Vassilevsky wrote: >> >>> >>>Joerg wrote: >>>>Vladimir Vassilevsky wrote: >>>> > >>>PWM is a kind of angular modulation. As such, it creates infinite >>>sidebands on both sides of the carrier. So does FM, however, the Bessel function drops of quite rapidly even with a high modulation index. >>>Some part of the lower sideband >>>inevitably falls into the bandwidth of the useful signal. Are you referring to aliasing around zero frequency ? >>>How much of >>>trash gets into the signal? It depends. Ballpark: for 60dB of rejection, >>>the PWM carrier should be ~ x20 times of the highest signal frequency. >>> >> I've done a _lot_ better than 60dB. > >How about doing some math before breaking physical laws? 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.
From: Joerg on 14 Jul 2010 16:28
Paul Keinanen wrote: > On Wed, 14 Jul 2010 11:48:12 -0500, Vladimir Vassilevsky > <nospam(a)nowhere.com> wrote: > >> >> Joerg wrote: >> >>> Vladimir Vassilevsky wrote: >>> >>>> Joerg wrote: >>>>> Vladimir Vassilevsky wrote: >>>>> >>>> PWM is a kind of angular modulation. As such, it creates infinite >>>> sidebands on both sides of the carrier. > > So does FM, however, the Bessel function drops of quite rapidly even > with a high modulation index. > >>>> Some part of the lower sideband >>>> inevitably falls into the bandwidth of the useful signal. > > Are you referring to aliasing around zero frequency ? > >>>> How much of >>>> trash gets into the signal? It depends. Ballpark: for 60dB of rejection, >>>> the PWM carrier should be ~ x20 times of the highest signal frequency. >>>> >>> I've done a _lot_ better than 60dB. >> How about doing some math before breaking physical laws? > > 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). > 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. > 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. > Don't worry, I don't either, so that makes two of us. I hope Vladimir won't have our degrees pulled :-) -- Regards, Joerg http://www.analogconsultants.com/ "gmail" domain blocked because of excessive spam. Use another domain or send PM. |