I was wondering... Say I happen to have a 100MHz DAC around... if I had a perfect anti-imaging filter, I could get 50MHz of bandwidth from it, and with realistic filters I might get 40MHz. Say I take the filtered (analog) output from the DAC and feed it to a 4x frequency multiplier. Now my top frequency is something under 200MHz (perfect filters), or say 160MHz (realistic filters). Is this a viable techniques to increase the bandwidth of my system? Although a frequency mutliplier is non-linear (just a pair of cascaded mixers "mixing with themselves" for the 4x case), isn't the Fourier spectrum of some signal I have my DACs create just the same as what it was prior to the multipliers but with relabeling any given frequency f as 4*f? For instance... if I'm sending amplitude modulated digital pulses (something like a raised cosine function that will occupy an approximately constant bandwidth), if I want the pulse to occupy 10MHz at the system's final output, it needs to occupy 2.5MHz at the input to the frequency multipliers... and hence I just feed by DAC 4 times as many samples (of the raised cosine) in time... right? Thanks for the help. This seemed quite straightforward to me, but people have been telling me that attempting to perform pulse shaping prior to a frequency multiplier is non-trivial and not encouraged. ---Joel Kolstad
Frequency multipliers: A way around Nyquist limitations?
Started by ●July 12, 2005
Reply by ●July 12, 20052005-07-12
Joel Kolstad wrote:> I was wondering... > > Say I happen to have a 100MHz DAC around... if I had a perfect anti-imaging > filter, I could get 50MHz of bandwidth from it, and with realistic filters I > might get 40MHz. > > Say I take the filtered (analog) output from the DAC and feed it to a 4x > frequency multiplier. Now my top frequency is something under 200MHz (perfect > filters), or say 160MHz (realistic filters).Not really. If you have a single frequency and you know what it is, then you can do it. That's rather uninteresting. Think about what happens when you start with a band of frequencies. For one thing, how would you multiply?> Is this a viable techniques to increase the bandwidth of my system? Although > a frequency mutliplier is non-linear (just a pair of cascaded mixers "mixing > with themselves" for the 4x case), isn't the Fourier spectrum of some signal I > have my DACs create just the same as what it was prior to the multipliers but > with relabeling any given frequency f as 4*f?No. That's the rub.> For instance... if I'm sending amplitude modulated digital pulses (something > like a raised cosine function that will occupy an approximately constant > bandwidth), if I want the pulse to occupy 10MHz at the system's final output, > it needs to occupy 2.5MHz at the input to the frequency multipliers... and > hence I just feed by DAC 4 times as many samples (of the raised cosine) in > time... right?What does multiplication mean to you? Sometimes a signal is negative and sometimes positive. What happens when you square it? Remember, you don't multiply frequencies, you multiply voltages (and get intermodulation products in the process).> Thanks for the help. This seemed quite straightforward to me, but people have > been telling me that attempting to perform pulse shaping prior to a frequency > multiplier is non-trivial and not encouraged.Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 12, 20052005-07-12
Hi Jerry, Thanks for the response... "Jerry Avins" <jya@ieee.org> wrote in message news:M_qdnRxaxvJTkEnfRVn-tQ@rcn.net...> Not really. If you have a single frequency and you know what it is, then > you can do it. That's rather uninteresting. Think about what happens > when you start with a band of frequencies. For one thing, how would you > multiply?Hmm... I see what you mean... (cos(w1*t)+cos(w2*t))^2 is certainly not DC+cos(2*w1*t)+cos(2*w2*t)... hmm... So then... why do frequency multipliers work so well for FM? My understanding is that FM transmitters usually start with some low frequency center frequency and a small (absolute) deviation around it... the output is fed to frequency multipliers until it gets up to, say, 100MHz where it's amplified and transmitted. I suppose this works as well as it does in that there's only one "instanteous" frequency? Since the signal is something like cos( (w0+f(t))*t )... ---Joel Kolstad
Reply by ●July 12, 20052005-07-12
Joel Kolstad wrote:> Hi Jerry, > > Thanks for the response... > > "Jerry Avins" <jya@ieee.org> wrote in message > news:M_qdnRxaxvJTkEnfRVn-tQ@rcn.net... > >>Not really. If you have a single frequency and you know what it is, then >>you can do it. That's rather uninteresting. Think about what happens >>when you start with a band of frequencies. For one thing, how would you >>multiply? > > > Hmm... I see what you mean... (cos(w1*t)+cos(w2*t))^2 is certainly not > DC+cos(2*w1*t)+cos(2*w2*t)... hmm... > > So then... why do frequency multipliers work so well for FM? My understanding > is that FM transmitters usually start with some low frequency center frequency > and a small (absolute) deviation around it... the output is fed to frequency > multipliers until it gets up to, say, 100MHz where it's amplified and > transmitted.Armstrong's early transmitters worked that way. One can achieve large deviations by incorporating that method along with others while starting with a a crystal oscillator.> I suppose this works as well as it does in that there's only one > "instanteous" frequency? Since the signal is something like cos( > (w0+f(t))*t )...Essentially, that's right. The idea you have isn't completely off base. If the signal you want to deal with has a relative narrow band at the high frequency, you can do what's called "sub-band sampling". The Nyquist criterion applies not to the frequency of a signal, but to its bandwidth. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 13, 20052005-07-13
Jerry Avins wrote: (snip)>>> Not really. If you have a single frequency and you know what it is, then >>> you can do it. That's rather uninteresting. Think about what happens >>> when you start with a band of frequencies. For one thing, how would you >>> multiply?Slightly different, but I have heard of optical systems with frequency multipliers, such as a red laser through a non-linear material and then separating the third harmonic of the source beam. That is to get short wavelengths where there aren't any laser materials. For a modulated source it would be more complicated, but it seems that it could still work. -- glen
Reply by ●July 13, 20052005-07-13
Joel Kolstad wrote:> Say I happen to have a 100MHz DAC around... if I had a perfect anti-imaging > filter, I could get 50MHz of bandwidth from it, and with realistic filters I > might get 40MHz.> Say I take the filtered (analog) output from the DAC and feed it to a 4x > frequency multiplier. Now my top frequency is something under 200MHz (perfect > filters), or say 160MHz (realistic filters).> Is this a viable techniques to increase the bandwidth of my system? Although > a frequency mutliplier is non-linear (just a pair of cascaded mixers "mixing > with themselves" for the 4x case), isn't the Fourier spectrum of some signal I > have my DACs create just the same as what it was prior to the multipliers but > with relabeling any given frequency f as 4*f?I haven't thought all the way through the mixer idea, you would need a balanced mixer that wouldn't allow any of the original signal through. If it did allow the original signal, then you wouldn't be able to tell that from multiplied lower frequency source. If you consider Shannon instead of Nyquist you are allowed to trade signal/noise for bandwidth. My guess is that if you do get the frequency multiplier to work the S/N decreases just enough to satisfy Shannon. It is usually done the other way, FM allows better S/N at the expense of additional bandwidth. -- glen
Reply by ●July 13, 20052005-07-13
"Joel Kolstad" <JKolstad71HatesSpam@yahoo.com> wrote in message news:11d8b33avtmo6e4@corp.supernews.com...> Hi Jerry, > > Thanks for the response... > > "Jerry Avins" <jya@ieee.org> wrote in message > news:M_qdnRxaxvJTkEnfRVn-tQ@rcn.net... >> Not really. If you have a single frequency and you know what it is, then >> you can do it. That's rather uninteresting. Think about what happens >> when you start with a band of frequencies. For one thing, how would you >> multiply? > > Hmm... I see what you mean... (cos(w1*t)+cos(w2*t))^2 is certainly not > DC+cos(2*w1*t)+cos(2*w2*t)... hmm... > > So then... why do frequency multipliers work so well for FM? My > understanding > is that FM transmitters usually start with some low frequency center > frequency > and a small (absolute) deviation around it... the output is fed to > frequency > multipliers until it gets up to, say, 100MHz where it's amplified and > transmitted. I suppose this works as well as it does in that there's only > one > "instanteous" frequency? Since the signal is something like cos( > (w0+f(t))*t )... >One problem with freq. multiplication is the increase in phase noise. FM is tolerant of this, so many FM transmitters use freq. mult. However, in other areas, simply mixing is used to change frequencies. Clay
Reply by ●July 13, 20052005-07-13
"glen herrmannsfeldt" <gah@ugcs.caltech.edu> wrote in message news:mp6dnRrfSKSUfEnfRVn-sg@comcast.com...> For a modulated source it would be more complicated, but it seems > that it could still work.Something that should have been obvious to me (my college professors would be quite dismayed...) is that running a signal through a frequency multiplier simply convolves the signal with itself in the frqeuency domain; hence you can get a pretty good qualitative idea of what's going to happen with a shaped pulse with a few quick sketches... It is still somewhat surprising to me that frequency multipliers work as well as they do for FM... for a cosine input, their Fourier spectra has all those "Bessel function harmonics" as dictated by the modulation index, and running that spectra through a frequency multiplier seems as though it's going to produce a various changes in the output spectra other than just stretching. I've been told that, in general, frequency multipliers are applicable to pretty much any signalling standard that has a constant envelope... FM, PM, FSK, perhaps even OQPSK. ---Joel
Reply by ●July 13, 20052005-07-13
glen herrmannsfeldt wrote:> Jerry Avins wrote: > > (snip) > >>>> Not really. If you have a single frequency and you know what it is, >>>> then >>>> you can do it. That's rather uninteresting. Think about what happens >>>> when you start with a band of frequencies. For one thing, how would you >>>> multiply? > > > Slightly different, but I have heard of optical systems with > frequency multipliers, such as a red laser through a non-linear > material and then separating the third harmonic of the source > beam. That is to get short wavelengths where there aren't any > laser materials. > > For a modulated source it would be more complicated, but it seems > that it could still work.Sure it works. That's what's behind heterodyning. The modulated signal is, of course, narrow band at the original frequency. The intercarrier TV sound carrier is at 4.5 MHz. I brought it out of one set into a push-push diode frequency doubler (aka full-wave rectifier) and into the retuned IF (10.7 MHz to 9) of a broadcast FM tuner. Listeners were surprised to hear how good the actually broadcast sound was. In service like that, the intermodulation products are easily removed by minimally selective filters. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 13, 20052005-07-13
Clay S. Turner wrote: ...> One problem with freq. multiplication is the increase in phase noise. FM is > tolerant of this, so many FM transmitters use freq. mult. However, in other > areas, simply mixing is used to change frequencies.Armstrong's quasi-commercial FM station at Alpine, NJ used a crystal oscillator and phase modulated the buffered output, using an integrator in the modulator chain to convert PM to FM. (The same thing can be done by amplitude modulating a balanced modulator to suppress the carrier, then injecting a large carrier component in quadrature with the suppresses one.) At this point, the deviation -- more properly, the modulation index -- is quite small. The signal qualifies as NBFM. To increase the deviation the signal is tripled, then heterodyned down, thus preserving the increased deviation. The process is repeated until the desired deviation is attained. The heterodyning frequencies* are chosen so that neither they nor their multiples combine to produce spurs that survive the filtering. Jerry ____________________________________ * Armstrong also invented the superheterodyne receiver. -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
