I/Q Mixing

Started by rickman June 17, 2017
Why is I/Q mixing done in receivers prior to the ADC rather than using a 
single mixer and converting to complex from a real data stream.  Is there 
some aspect of the signal that is lost if the signal is not down converted 
with an I/Q local oscillator?

-- 

Rick C
On 17.6.17 09:30, rickman wrote:
> Why is I/Q mixing done in receivers prior to the ADC rather than using a > single mixer and converting to complex from a real data stream. Is > there some aspect of the signal that is lost if the signal is not down > converted with an I/Q local oscillator?
It is a simple question of sample rate. The lower IF is easier to sample and convert. There are digital receivers that sample the raw RF and do the quadrature mixing numerically and then decimate the sample rate for further processing. -- -TV
Tauno Voipio wrote on 6/17/2017 12:44 PM:
> On 17.6.17 09:30, rickman wrote: >> Why is I/Q mixing done in receivers prior to the ADC rather than using a >> single mixer and converting to complex from a real data stream. Is there >> some aspect of the signal that is lost if the signal is not down converted >> with an I/Q local oscillator? > > > It is a simple question of sample rate. The lower IF is easier > to sample and convert. > > There are digital receivers that sample the raw RF and do the > quadrature mixing numerically and then decimate the sample rate > for further processing.
I guess I didn't ask the question correctly. The analog mixing could be done singly rather than as an I/Q pair, then in the digital domain convert to complex sampling. The sample rate of one ADC would need to be twice the sample rate of using separate ADCs, but otherwise would be the same. -- Rick C
rickman wrote on 6/17/2017 2:03 PM:
> Tauno Voipio wrote on 6/17/2017 12:44 PM: >> On 17.6.17 09:30, rickman wrote: >>> Why is I/Q mixing done in receivers prior to the ADC rather than using a >>> single mixer and converting to complex from a real data stream. Is there >>> some aspect of the signal that is lost if the signal is not down converted >>> with an I/Q local oscillator? >> >> >> It is a simple question of sample rate. The lower IF is easier >> to sample and convert. >> >> There are digital receivers that sample the raw RF and do the >> quadrature mixing numerically and then decimate the sample rate >> for further processing. > > I guess I didn't ask the question correctly. The analog mixing could be > done singly rather than as an I/Q pair, then in the digital domain convert > to complex sampling. The sample rate of one ADC would need to be twice the > sample rate of using separate ADCs, but otherwise would be the same.
I figured I didn't need to mention the very efficient method of converting real to complex, but just in case... This can be used by considering the conversion to be a matter of mixing down by fs/4. So the real sample sequence represents a signal that ranges from 0 to fs/2 while the same signal shifted down has a frequency range of -fs/4 to fs/4. The carrier sequence is very simple (1,0), (0,1), (-1,0), (0,-1)... There are no multiplies needed other than by -1 which is just a negation. When the zeros are considered the math becomes a matter of inverting half the samples and moving them around to form the complex sequence. If there is a FIR filter, it is very easy to incorporate this into the FIR. -- Rick C
On 17.6.17 21:03, rickman wrote:
> Tauno Voipio wrote on 6/17/2017 12:44 PM: >> On 17.6.17 09:30, rickman wrote: >>> Why is I/Q mixing done in receivers prior to the ADC rather than using a >>> single mixer and converting to complex from a real data stream. Is >>> there >>> some aspect of the signal that is lost if the signal is not down >>> converted >>> with an I/Q local oscillator? >> >> >> It is a simple question of sample rate. The lower IF is easier >> to sample and convert. >> >> There are digital receivers that sample the raw RF and do the >> quadrature mixing numerically and then decimate the sample rate >> for further processing. > > I guess I didn't ask the question correctly. The analog mixing could be > done singly rather than as an I/Q pair, then in the digital domain > convert to complex sampling. The sample rate of one ADC would need to > be twice the sample rate of using separate ADCs, but otherwise would be > the same.
So, you have a conventional superheterodyne front-end and digitize the IF. It is a method used in many current ham radio transceivers. The normal front-end filtering requirements apply, as in superheterodynes with conventional front-ends. Also, you need an IF filter before the samplers. The quadrature sampling is an old trick used in many of the semi-digital radios. -- -TV
On Sat, 17 Jun 2017 14:03:58 -0400, rickman wrote:

> Tauno Voipio wrote on 6/17/2017 12:44 PM: >> On 17.6.17 09:30, rickman wrote: >>> Why is I/Q mixing done in receivers prior to the ADC rather than using >>> a single mixer and converting to complex from a real data stream. Is >>> there some aspect of the signal that is lost if the signal is not down >>> converted with an I/Q local oscillator? >> >> >> It is a simple question of sample rate. The lower IF is easier to >> sample and convert. >> >> There are digital receivers that sample the raw RF and do the >> quadrature mixing numerically and then decimate the sample rate for >> further processing. > > I guess I didn't ask the question correctly. The analog mixing could be > done singly rather than as an I/Q pair, then in the digital domain > convert to complex sampling. The sample rate of one ADC would need to > be twice the sample rate of using separate ADCs, but otherwise would be > the same.
It's more complicated than that. Consider a signal "out there" that consists of two sine waves at F1 and F2, and an undesired signal "out there" that is a sine wave at some frequency F3 which we don't know and don't control, except that it's not F1 or F2. With I/Q mixing you can choose a carrier frequency F0 = (F1+F2)/2, and you end up with a pair of complex signals at +(F1+F2)/2 and -(F1+F2)/2. This is called "direct conversion", and it can work great. With simple signals there's no concept of "negative frequencies" (or, depending on how you hold your mouth, there's no way to distinguish a negative frequency from a positive one). So if you try to use the same F0 as above, you end up with two signals, at the same frequency, added together and indistinguishable from one another. So, you can't use direct conversion. You can, instead, use a superheterodyne process: choose F0 to be lower than the lower of F1 and F2, or higher than the higher of F1 and F2. Then you get a signal out that has two signals at frequencies F1 - F0 and F2 - F0, or F0 - F1 and F0 - F2. However, if F0 < F1, and F3 = 2F0 - F1, then F1 - F0 = F0 - F3, and the received signal has the desired signal and the undesired signal sitting right on top of each other. The second, undesired, signal is called an "image". To fix this, you have to use a filter at RF that passes the band including F1 and F2, but sharply attenuates energy at F3 -- actually, at any F3 that might be an issue. Now add to this that reasonably low-noise mixers and low distortion mixers don't mix with sine waves -- they generally switch, which effectively means that they're mixing the incoming signal with a square wave, which has content at F0, 2F0, 3F0, etc. And yes, there's not _much_ content at 2*F0 or 4*F0, etc., but it's there, and it can cause issues. And there's certainly energy at 3F0, 5F0, etc. So RF filter design, and frequency downconversion schemes (in multi-stage superheterodyne receivers) is not at all trivial. It's often MUCH easier to just take the signal in at the antenna, thump it down to baseband with an I/Q mixer, and proceed from there. But not always, so there will still be superheterodyne stages in radios, probably for years to come. -- www.wescottdesign.com
On Sat, 17 Jun 2017 14:15:01 -0400, rickman wrote:

> rickman wrote on 6/17/2017 2:03 PM: >> Tauno Voipio wrote on 6/17/2017 12:44 PM: >>> On 17.6.17 09:30, rickman wrote: >>>> Why is I/Q mixing done in receivers prior to the ADC rather than >>>> using a single mixer and converting to complex from a real data >>>> stream. Is there some aspect of the signal that is lost if the >>>> signal is not down converted with an I/Q local oscillator? >>> >>> >>> It is a simple question of sample rate. The lower IF is easier to >>> sample and convert. >>> >>> There are digital receivers that sample the raw RF and do the >>> quadrature mixing numerically and then decimate the sample rate for >>> further processing. >> >> I guess I didn't ask the question correctly. The analog mixing could >> be done singly rather than as an I/Q pair, then in the digital domain >> convert to complex sampling. The sample rate of one ADC would need to >> be twice the sample rate of using separate ADCs, but otherwise would be >> the same. > > I figured I didn't need to mention the very efficient method of > converting real to complex, but just in case... > > This can be used by considering the conversion to be a matter of mixing > down by fs/4. So the real sample sequence represents a signal that > ranges from 0 to fs/2 while the same signal shifted down has a frequency > range of -fs/4 to fs/4. The carrier sequence is very simple (1,0), > (0,1), (-1,0), (0,-1)... There are no multiplies needed other than by > -1 which is just a negation. When the zeros are considered the math > becomes a matter of inverting half the samples and moving them around to > form the complex sequence. > > If there is a FIR filter, it is very easy to incorporate this into the > FIR.
If you are sampling the RF directly, yes, this would work well. And it dodges a bunch of problems with I/Q mixers that arise because the channels aren't matched perfectly in amplitude and phase response. I, for one, was assuming that you were talking about the case where you've got a signal in the air that's at a significantly higher frequency than your sample rate, and you need to bring it down before you can run it into an ADC. -- www.wescottdesign.com
On Sat, 17 Jun 2017 14:15:01 -0400, rickman wrote:

> rickman wrote on 6/17/2017 2:03 PM: >> Tauno Voipio wrote on 6/17/2017 12:44 PM: >>> On 17.6.17 09:30, rickman wrote: >>>> Why is I/Q mixing done in receivers prior to the ADC rather than >>>> using a single mixer and converting to complex from a real data >>>> stream. Is there some aspect of the signal that is lost if the >>>> signal is not down converted with an I/Q local oscillator? >>> >>> >>> It is a simple question of sample rate. The lower IF is easier to >>> sample and convert. >>> >>> There are digital receivers that sample the raw RF and do the >>> quadrature mixing numerically and then decimate the sample rate for >>> further processing. >> >> I guess I didn't ask the question correctly. The analog mixing could >> be done singly rather than as an I/Q pair, then in the digital domain >> convert to complex sampling. The sample rate of one ADC would need to >> be twice the sample rate of using separate ADCs, but otherwise would be >> the same. > > I figured I didn't need to mention the very efficient method of > converting real to complex, but just in case... > > This can be used by considering the conversion to be a matter of mixing > down by fs/4. So the real sample sequence represents a signal that > ranges from 0 to fs/2 while the same signal shifted down has a frequency > range of -fs/4 to fs/4. The carrier sequence is very simple (1,0), > (0,1), (-1,0), (0,-1)... There are no multiplies needed other than by > -1 which is just a negation. When the zeros are considered the math > becomes a matter of inverting half the samples and moving them around to > form the complex sequence. > > If there is a FIR filter, it is very easy to incorporate this into the > FIR.
If you are sampling the RF directly, yes, this would work well. And it dodges a bunch of problems with I/Q mixers that arise because the channels aren't matched perfectly in amplitude and phase response. I, for one, was assuming that you were talking about the case where you've got a signal in the air that's at a significantly higher frequency than your sample rate, and you need to bring it down before you can run it into an ADC. -- www.wescottdesign.com
On Sat, 17 Jun 2017 14:15:01 -0400, rickman wrote:

> rickman wrote on 6/17/2017 2:03 PM: >> Tauno Voipio wrote on 6/17/2017 12:44 PM: >>> On 17.6.17 09:30, rickman wrote: >>>> Why is I/Q mixing done in receivers prior to the ADC rather than >>>> using a single mixer and converting to complex from a real data >>>> stream. Is there some aspect of the signal that is lost if the >>>> signal is not down converted with an I/Q local oscillator? >>> >>> >>> It is a simple question of sample rate. The lower IF is easier to >>> sample and convert. >>> >>> There are digital receivers that sample the raw RF and do the >>> quadrature mixing numerically and then decimate the sample rate for >>> further processing. >> >> I guess I didn't ask the question correctly. The analog mixing could >> be done singly rather than as an I/Q pair, then in the digital domain >> convert to complex sampling. The sample rate of one ADC would need to >> be twice the sample rate of using separate ADCs, but otherwise would be >> the same. > > I figured I didn't need to mention the very efficient method of > converting real to complex, but just in case... > > This can be used by considering the conversion to be a matter of mixing > down by fs/4. So the real sample sequence represents a signal that > ranges from 0 to fs/2 while the same signal shifted down has a frequency > range of -fs/4 to fs/4. The carrier sequence is very simple (1,0), > (0,1), (-1,0), (0,-1)... There are no multiplies needed other than by > -1 which is just a negation. When the zeros are considered the math > becomes a matter of inverting half the samples and moving them around to > form the complex sequence. > > If there is a FIR filter, it is very easy to incorporate this into the > FIR.
That's a fair summary of an article I posted to this newsgroup in 1999. Here's an archive of the original in google groups: https://groups.google.com/d/msg/comp.dsp/f4Y0HgRWLw4/Bj2OsU7fozYJ and here 'tis in Grant Griffin's website: https://dspguru.com/dsp/tricks/complex-downconverters-at-fs-over-4/ Regards, Allan
Tim Wescott wrote on 6/17/2017 4:39 PM:
> On Sat, 17 Jun 2017 14:15:01 -0400, rickman wrote: > >> rickman wrote on 6/17/2017 2:03 PM: >>> Tauno Voipio wrote on 6/17/2017 12:44 PM: >>>> On 17.6.17 09:30, rickman wrote: >>>>> Why is I/Q mixing done in receivers prior to the ADC rather than >>>>> using a single mixer and converting to complex from a real data >>>>> stream. Is there some aspect of the signal that is lost if the >>>>> signal is not down converted with an I/Q local oscillator? >>>> >>>> >>>> It is a simple question of sample rate. The lower IF is easier to >>>> sample and convert. >>>> >>>> There are digital receivers that sample the raw RF and do the >>>> quadrature mixing numerically and then decimate the sample rate for >>>> further processing. >>> >>> I guess I didn't ask the question correctly. The analog mixing could >>> be done singly rather than as an I/Q pair, then in the digital domain >>> convert to complex sampling. The sample rate of one ADC would need to >>> be twice the sample rate of using separate ADCs, but otherwise would be >>> the same. >> >> I figured I didn't need to mention the very efficient method of >> converting real to complex, but just in case... >> >> This can be used by considering the conversion to be a matter of mixing >> down by fs/4. So the real sample sequence represents a signal that >> ranges from 0 to fs/2 while the same signal shifted down has a frequency >> range of -fs/4 to fs/4. The carrier sequence is very simple (1,0), >> (0,1), (-1,0), (0,-1)... There are no multiplies needed other than by >> -1 which is just a negation. When the zeros are considered the math >> becomes a matter of inverting half the samples and moving them around to >> form the complex sequence. >> >> If there is a FIR filter, it is very easy to incorporate this into the >> FIR. > > If you are sampling the RF directly, yes, this would work well. And it > dodges a bunch of problems with I/Q mixers that arise because the > channels aren't matched perfectly in amplitude and phase response. > > I, for one, was assuming that you were talking about the case where > you've got a signal in the air that's at a significantly higher frequency > than your sample rate, and you need to bring it down before you can run > it into an ADC.
I don't get why you thought that. I clearly said, "using a single mixer". But whatever. -- Rick C