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phase shifters and frequency shifters
MUFF WIGGLER Forum Index -> Modular Synth General Discussion  
Author phase shifters and frequency shifters
crippletoe
Hi all!
Does anyone here knows whether there is a difference between "frequency shifters" (a la Bode/Moog) and phase shifters (for example, the old Roland system 100m or the newer system 500 module).
If there is a difference and its not just different names for the same principals, can you explain what is technically the difference?


Cheers and thanks!
Dave Peck
Yes, they are indeed different modules with very different sounds. A frequency shifter changes the numeric ratio of the harmonics to the fundamental in the waveform, which tends to result in metallic ring modulator like sounds at higher ratios, although it can sometimes sound a bit like a phase shifter at very slight settings.

An example of what a frequency shifter does to the sound:

Let's say you have a sawtooth waveform with a fundamental frequency of 100 Hz and the normal spectrum of harmonics at regular mathematical multiples, 200 Hz, 300 Hz, 400 Hz, 500 Hz etc. These are MULTIPLES of the fundamental frequency, occurring at 2x, 3x, 4x, 5x the fundamental frequency of 100 Hz.

Running that wave through a frequency shifter and setting the module to 'add 50 Hz' will give you a waveform that still has the 100 Hz fundamental, but now the frequency of each harmonic in that waveform has "50" added to it (250 Hz, 350 Hz, 450 Hz, 550 Hz etc.). A sort of numeric offset has occurred, and now all of the harmonics no longer have the original 2x, 3x, 4x, 5x mathematical ratio to the 100 Hz fundamental (or to each other). This changes the timbre of the waveform. The exact nature of that change depends on the setting, and therefore the new frequencies of the harmonics.
337is
Dave Peck

Your replies are always so helpful and clear. Thank you for being a seemingly endless resource of useful information. applause
cornutt
A phase shifter uses something called an "all pass filter", which is a filter with a cutoff frequency that is outside of the audio range. The filter doesn't attenuate any frequencies, but what it does is create a phase shift that depends on frequency, so that high frequencies are phase shifted either more or less than low frequencies, depending on how the filter is wired. When this is added back to the dry signal, it creates a peak and a notch in the frequency response. Making the circuit voltage controlled and driving it with an LFO produces the characteristic sweeping sound. Most phasers have multiple stages of filters for a more complex response.
Jari Jokinen
Dave Peck wrote:
...Running that wave through a frequency shifter and setting the module to 'add 50 Hz' will give you a waveform that still has the 100 Hz fundamental, but now the frequency of each harmonic in that waveform has "50" added to it (250 Hz, 350 Hz, 450 Hz, 550 Hz etc.)...

A normal Frequency Shifter has two outputs. Frequencies for the Sum Output in the above scenario would be 150Hz, 250Hz, 350Hz etc. Frequencies for the Difference Output would be 50Hz, 150Hz, 250Hz etc.

The fundamental won't be intact. It gets the same "treatment" as the other partials.
Dave Peck
337is wrote:
Dave Peck

Your replies are always so helpful and clear. Thank you for being a seemingly endless resource of useful information. applause


Aw shucks, thanks!
Dave Peck
Jari Jokinen wrote:

A normal Frequency Shifter has two outputs. Frequencies for the Sum Output in the above scenario would be 150Hz, 250Hz, 350Hz etc. Frequencies for the Difference Output would be 50Hz, 150Hz, 250Hz etc.

The fundamental won't be intact. It gets the same "treatment" as the other partials.


Ah, you are correct! The sum output would include a fundamental of 150 Hz and the difference output would include a fundamental of 50 Hz, no 100 Hz fundamental at these outputs.
Dcramer
Ok you smarty pantses, I've always been confused by this:
I get what a ring mod does, and amplitude mod, and frequency mod.
But what's going on inside the circuit of a frequency shifter to make it work? hmmm.....
Leverkusen
Dcramer wrote:
Ok you smarty pantses, I've always been confused by this:
I get what a ring mod does, and amplitude mod, and frequency mod.
But what's going on inside the circuit of a frequency shifter to make it work? hmmm.....


A frequency shifter is basically two ring modulators where the original signal is canceled out in the end. So you just get the new side bands, which then get seperated.

You can aproximate the effect by using two ring modulators with phase inverted sine waves as modulators when you carefully dial everything in and sum the signals.
sersch
Leverkusen wrote:
A frequency shifter is basically two ring modulators where the original signal is canceled out in the end. So you just get the new side bands, which then get seperated.

The separation is the important & technically tricky part in a Frequency Shifter, as it involves carefully adjusted allpass filters for phaseshifting:

• A Ring Modulator produces the sum and the differences of all frequencies of its two input signals, and then outputs both sums and differences simultaneously at one output jack.

• A Frequency Shifter also produces the sum and the differences of all frequencies of its two input signals, but it has a separate output jack just for the sum signal (upshift), and another output jack just for the difference signal (downshift).
BananaPlug
I've kind of decided that even a perfect one would probably not become a mainstay in a system.

The problem with freq shifters is that all the sub circuits need to be lined up very precisely. Those I've encountered had at least one disappointing flaw. Haven't tried a digital one that would be more stable but, sound?

Someday I'll take a look and see what the latest crop is like.
Graham Hinton
cornutt wrote:
A phase shifter uses something called an "all pass filter", which is a filter with a cutoff frequency that is outside of the audio range.


An all pass filter doesn't have a cutoff frequency, call it a centre frequency instead. That is definitely inside the audio range. The phase angle of any filter varies around the centre/cutoff frequency with most of it happening within +/- 2 octaves.

Dcramer wrote:
I get what a ring mod does, and amplitude mod, and frequency mod.


The best way to understand what is happening in the frequency domain is to use trig identities, but most people glazed over when/if they did them at school.

Quote:

But what's going on inside the circuit of a frequency shifter to make it work?


There are two ways of doing it, both use techniques used in radio engineering.

One way is to use a multiplier with an audio input and a high frequency input, above the audio range. This will create sum and difference frequencies, aka sidebands, around that high frequency, say 50kHz +/- the 20kHz audio range. These are easily separated by a filter as they don't overlap in range. Then one of the sidebands is multiplied again with a different high frequency and the lower sideband will be back in the audio range. The frequency shift is the difference between the two high frequencies used, e.g. 50kHz up, then 49.9kHz down results in a 100Hz shift upwards.

The other way requires two multipliers and two inputs that have a 90 degree phase difference version. One could be an audio signal fed through a 90 degree phase shift network, the other could be a sine generator with sine and cosine outputs. One from each pair is multiplied separately to get two sets of sum and difference frequencies, but with a different phase relationship, then these are combined to cancel out either the upper or the lower sideband. I've shown this diagramatically and mathematically here (about halfway down the page).

I said "multiplier" rather than "ring modulator" because most "ring modulators" are really linear 4 quadrant multipliers. A real diode ring modulator creates more distortion products.

The first method is easier to do (it's how AM radio works), but requires accurate HF oscillators and wider bandwidth circuitry. The second method is better for small shifts and remains in the audio range, but depends on the quality of the phase shift network. These comprise two chains of all pass filters staggered across the audio range such the final outputs have a 90 degree phase difference. Good ones are quite a lot of circuitry.
cornutt
BananaPlug wrote:


The problem with freq shifters is that all the sub circuits need to be lined up very precisely. Those I've encountered had at least one disappointing flaw. Haven't tried a digital one that would be more stable but, sound?


The Encore one is a hybrid... as I understand it, the generation of the necessary quadrature sine waves is digital, but everything else in the audio signal path is analog. I have one and it works well. One use for it is that with a small amount of shift, it can create an effect that is like really intense phasing, but not quite like flanging.
cornutt
Graham Hinton wrote:
cornutt wrote:
A phase shifter uses something called an "all pass filter", which is a filter with a cutoff frequency that is outside of the audio range.


An all pass filter doesn't have a cutoff frequency, call it a centre frequency instead. That is definitely inside the audio range. The phase angle of any filter varies around the centre/cutoff frequency with most of it happening within +/- 2 octaves.


I knew that was not quite right as I was writing it... there's an aspect of the math in it that I don't understand. I've seen it described as having one real pole and one imaginary pole. I need to read up on that more.
Dr. Sketch-n-Etch
Here's how a frequency shifter works:

1) You put an audio signal through a phase displacement network which creates two copies of the audio signal, in which every frequency in the two copies is shifted 90 degrees. If you put a sine wave into this device, and scan the frequency over the entire audio range, you should get an unchanging circular Lissajous figure on your scope. If this audio signal is "c" for carrier, then you get sin(w_c*t) and cos(w_c*t) where w_c is the frequency of the carrier (or a bunch of discrete frequencies making up the audio signal as per Fourier's theorem).

2) You create sin and cos (90-degree shifted sin) waves in a quadrature oscillator. Let's call these "m" for modulator, so you have sin(w_m*t) and cos(w_m*t) where w_m is the frequency of the modulator. Again, putting these two waves into a scope in X-Y mode will give a perfectly circular Lissajous figure.

3) You feed sin(w_c*t) and sin(w_m*t) into one four-quadrant multiplier (or ring-mod) and cos(w_c*t) and cos(w_m*t) into another four-quadrant multiplier. This is where the magic happens. By trigonometry:

sin(w_c*t)*sin(w_m*t) = 1/2 [cos(w_c - w_m)t - cos(w_c + w_m)t] = A

cos(w_c*t)*cos(w_m*t) = 1/2 [cos(w_c - w_m)t + cos(w_c + w_m)t] = B

You will notice that, by multiplying the two sines and cosines together, you get waves at the sum and difference frequencies, but not at the original carrier or modulator frequencies. (Of course, this is easier said than done and requires some very precise multipliers.)

4) Now, by the magic of algebra, if you put these two multiplied outputs through two amplifiers, one simple summer:

A + B = cos(w_c - w_m)t = Diff

and one which adds the second output to the inverse of the first:

B - A = cos(w_c + w_m)t = Sum

Now the Diff output is only the difference frequency, and the Sum output is only at the sum frequency. This is frequency shifting. Every frequency in the carrier, w_c, is shifted up or down by the frequency of the modulator, w_m. This gives some very strange-sounding results.
Navs
A phase shifter makes you sound like Duran Duran. A frequency shifter makes you sound like Stockhausen.

Dr. Sketch-n-Etch wrote:
some maths we don't understand
hihi

You can patch one like this:

http://navsmodularlab.blogspot.de/2012/04/potd-swings-roundabouts.html

And here's what it sounds like:

https://navs.bandcamp.com/track/swings-and-roundabouts
mskala
Dr. Sketch-n-Etch wrote:
Here's how a frequency shifter works:

1) You put an audio signal through a phase displacement network which creates two copies of the audio signal, in which every frequency in the two copies is shifted 90 degrees.


That's the classic Bode design, but others are possible. In particular, you can do it this way using more radio-like techniques:

* modulate a carrier above the audio range, like 200kHz, with the audio input signal. You get two sidebands, corresponding to carrier+audio and carrier-audio.

* use a sharp low-pass or high-pass filter to pass just one of the sidebands.

* demodulate it back into the audio range, using a second high-frequency oscillator slightly offset from the first.

The hard part is filtering out the undesired sideband, and carrier feed-through, especially if you have very low frequencies in the audio. However, it does eliminate some of the issues associated with trying to create a quadrature signal, and it allows the carrier oscillators to run in narrower proportional frequency ranges (which can make them easier to build). There are other variations sometimes used in radio, too. There, people don't often want an audio-to-audio frequency shifter as a standalone device, but when they do single-sideband modulation and demodulation (which basically is frequency shifting with a large enough shift to go between audio and RF or IF) they often use circuits that could be adapted for audio-to-audio.
crippletoe
Thanks everyone for all of this amazing information (as well as different views on that information). I am an improved man.

Love.
Dr. Sketch-n-Etch
mskala wrote:
Dr. Sketch-n-Etch wrote:
Here's how a frequency shifter works:

1) You put an audio signal through a phase displacement network which creates two copies of the audio signal, in which every frequency in the two copies is shifted 90 degrees.


That's the classic Bode design, but others are possible. In particular, you can do it this way using more radio-like techniques:

* modulate a carrier above the audio range, like 200kHz, with the audio input signal. You get two sidebands, corresponding to carrier+audio and carrier-audio.

* use a sharp low-pass or high-pass filter to pass just one of the sidebands.

* demodulate it back into the audio range, using a second high-frequency oscillator slightly offset from the first.

The hard part is filtering out the undesired sideband, and carrier feed-through, especially if you have very low frequencies in the audio. However, it does eliminate some of the issues associated with trying to create a quadrature signal, and it allows the carrier oscillators to run in narrower proportional frequency ranges (which can make them easier to build). There are other variations sometimes used in radio, too. There, people don't often want an audio-to-audio frequency shifter as a standalone device, but when they do single-sideband modulation and demodulation (which basically is frequency shifting with a large enough shift to go between audio and RF or IF) they often use circuits that could be adapted for audio-to-audio.


Yeah, I tried the "Weaver" technique, and found it to be virtually impossible to implement. The "Bode" technique is pretty straightforward, as long as the PDN works properly and the multipliers are suitably accurate.
Dr. Sketch-n-Etch
Navs wrote:
Dr. Sketch-n-Etch wrote:
some maths we don't understand
hihi


Yeah, I never said that. I would never say that. There's no electronics math that I don't understand (at least, none that I've encountered so far). I eat Laplace transforms for breakfast, and was born knowing trig.
mskala
Dr. Sketch-n-Etch wrote:
Yeah, I tried the "Weaver" technique, and found it to be virtually impossible to implement. The "Bode" technique is pretty straightforward, as long as the PDN works properly and the multipliers are suitably accurate.


If I were building one I might use LM13700s just to annoy you, but the fact is, the smart way to do it now would be with DSP. We're all dinosaurs here.
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