analog switching demodulator technologies "walsh function"

[SArepairman]

I read this on a website;

PerkinElmer Instrument’s analog lock-in amplifiers use an
alternative and more sophisticated type of switching
demodulator which replaces the single analog switch with an
assembly of several switches driven by a Walsh function. This
may be thought of as a stepped approximation to a sinewave.
Careful selection of components allows such a demodulator to
offer all of the advantages of the switching demodulator with
one additional benefit, which is the complete rejection of the
responses at the third and fifth harmonics and reduced
responses for higher orders.

Does anyone know what an "assembly of several switches driven by a Walsh function." is in context of making an analog multiplier circuit?

I know you can perform a multiplication either by using a multiplier or by using a switch (for the purposes of a lock in amplifier).
What does this superior walsh function switch arrangement look like?

I was going to build a circuit out of op amps and a analog switch in the typical configuration but this has gotten me curious.

[KJDS]

From my minimal understanding, it is part of the method to used to digitally demodulate complex modulated signals, however I can imagine that just as using a double balanced mixer offers advantages over a single balanced, and an image reject mixer offers further advantages still, then using walsh codes and multiple switches can offer similar advantages.

I can't say any more than that without doing some research, and it's Friday evening, therefore my priorities are fish and beer rather than maths.

[branadic]

This is what I would have expected while reading that quote too. It's a number of switches driven by the Walsh function, that means each switch is driven by a seperate signal as explained by the Walsh function, a number of frequencies each one multiple of a fundamental frequency that drives switch 1.
The german wiki explains the Walsh function very well:

http://de.wikipedia.org/wiki/Walsh-Funktion

the english wiki does not.

[SArepairman]

I really don't understand that. The switching method (single switch) lock in amplifier makes sense to me.

I am having trouble understanding how multiple switches could even help. If you have two signals (your phase/frequency reference and your input) how the hell does adding more switches help? Would that just not result in switches operating in parallel and causing problems due to charge injection etc).

What are these additional switches connected to? Typically you have one switch that connects to a reference wave form... does this method some how use harmonics of the reference wave form?

I am sorry but that page of math equations just caused my brain to over heat. 

I think I will just find some kind of multiplication IC and be done with this tom foolery.

[Rufus]

I am having trouble understanding how multiple switches could even help. If you have two signals (your phase/frequency reference and your input) how the hell does adding more switches help?

The switches have different gains and the outputs are summed. You could make a multiplying DAC by having switches with power of 2 gain ratios controlled by each 'DAC bit' and you could feed the DAC a digital sine wave to get something only sensitive to the fundamental.

Walsh functions are an easily generated set of digital patterns which controlling switches of appropriate gain can generate any repetitive waveform including the sine wave needed for your requirement.

[Marco]

So what is the advantage of this over mixing? Dynamic range?

[SArepairman]

So what is the advantage of this over mixing? Dynamic range?

"with one additional benefit, which is the complete rejection of the
responses at the third and fifth harmonics and reduced
responses for higher orders."

I would still like to see a schematic for a practical circuit that uses this technique.
So we now know that there are multiple switches with different gains switched on at the right time.
How do we determine the gains and when to switch them? What is  the procedure for deciding these things?

somehow I missed this which is most illuminating:
http://www.milton.arachsys.com/nj71/index.php?menu=2&submenu=2&subsubmenu=5&page=2

BUt I would love if someone linked a walsh demodulator circuit or schematic of a machine that uses one





Also, I still don't understand by what you mean by gain of switches. The demodulator circuit I am familar with uses a comparator, square wave reference signal and some op amps. What are you gaining exactly>?

[Rufus]

Also, I still don't understand by what you mean by gain of switches. The demodulator circuit I am familar with uses a comparator, square wave reference signal and some op amps. What are you gaining exactly>?

This http://www.wiseguysynth.com/larry/schematics/walsh/walsh.pdf paper provides the basics and has a practical sine wave generator circuit. Instead of feeding the walsh function patterns at logic levels into the summing amplifier you control switches with those signals to feed + or - your unknown signal into the amplifier.

The output of the amplifier is the unknown signal multiplied by an approximate sine wave of 1/16th the frequency of the walsh generator clock.

[SArepairman]

Also, I still don't understand by what you mean by gain of switches. The demodulator circuit I am familar with uses a comparator, square wave reference signal and some op amps. What are you gaining exactly>?

This http://www.wiseguysynth.com/larry/schematics/walsh/walsh.pdf paper provides the basics and has a practical sine wave generator circuit. Instead of feeding the walsh function patterns at logic levels into the summing amplifier you control switches with those signals to feed + or - your unknown signal into the amplifier.

The output of the amplifier is the unknown signal multiplied by an approximate sine wave of 1/16th the frequency of the walsh generator clock.

But it seems to me that there will be multiple open switches when you describe it that way.
Can you draw a rudimentary paint diagram of how the circuit would look like? I am having alot of difficulty understanding this.

[Rufus]

Also, I still don't understand by what you mean by gain of switches. The demodulator circuit I am familar with uses a comparator, square wave reference signal and some op amps. What are you gaining exactly>?

This http://www.wiseguysynth.com/larry/schematics/walsh/walsh.pdf paper provides the basics and has a practical sine wave generator circuit. Instead of feeding the walsh function patterns at logic levels into the summing amplifier you control switches with those signals to feed + or - your unknown signal into the amplifier.

The output of the amplifier is the unknown signal multiplied by an approximate sine wave of 1/16th the frequency of the walsh generator clock.

But it seems to me that there will be multiple open switches when you describe it that way.
Can you draw a rudimentary paint diagram of how the circuit would look like? I am having alot of difficulty understanding this.

The phase sensitive detector on page 2 of this http://courses.washington.edu/phys431/lock-in/lockin.pdf document uses one change over switch to multiply the unknown signal by a square wave +/- 1.

Several switches driven by walsh functions feeding a summing amplifier with the appropriate gain for each switch will multiply the unknown by an approximate sine wave +/- 1.

[SArepairman]

so the input signal would be attenuated with additional amplifiers (i.e. to have a gain of +-0.5, +-0.4, +-0.3 ... ) and each of these inverted/non inverted amplifiers pairs would be connected to a switch connected to point A so that at any time half of the amplifiers would be connected to point A?'

So for instance the amplifiers of +1, -0.5, -0.4, 0.3 could be connected while 0.4, -1, +0.5, -0.3 would be disconnected (i did not follow the timing diagrams here but is my reasoning correct)?

This method demands many op amps.

and in addition to this the reference signal would be fed into the frequency divider block to time all the switches, which seems easy enough in a CPLD.

[Rufus]

So for instance the amplifiers of +1, -0.5, -0.4, 0.3 could be connected while 0.4, -1, +0.5, -0.3 would be disconnected (i did not follow the timing diagrams here but is my reasoning correct)?

This method demands many op amps.

You need one op-amp to multiply the unknown by -1, SPDT switches switch between unknown and -unknown. The output of the switches feed the summing junction of an op-amp through a resistor which sets the gain for that switch. You only need 2 op-amps for any number of walsh functions and switches.

[SArepairman]

So for instance the amplifiers of +1, -0.5, -0.4, 0.3 could be connected while 0.4, -1, +0.5, -0.3 would be disconnected (i did not follow the timing diagrams here but is my reasoning correct)?

This method demands many op amps.

You need one op-amp to multiply the unknown by -1, SPDT switches switch between unknown and -unknown. The output of the switches feed the summing junction of an op-amp through a resistor which sets the gain for that switch. You only need 2 op-amps for any number of walsh functions and switches.

OH. Thats easy!