Filter FM and a dash of VCO linear FM research

It's time to hook up the FM inputs on the low pass filter.

I have an option to use both linear and exponential FM.

The most common option is exponential (v/oct) as this is readily available by mixing oscillator output with filter cutoff CV.

I found a nice post earlier about the use of both types but cannot find it right now, but here is a thread about linear FM at least:

https://modwiggler.com/forum/viewtopic.php?t=119415

FM off

I did initially design the FM input with two SPST (on/off) switches. This allows me to disconnect the input completely, as I was unsure how far down I could get the VCA to go.

Now I've done some calculations:

At 0V, the VCA has -80dB attenuation. That means that a 5V input signal would give a 0.5mV output.

If we've set the modulation to 1V/octave, 1 semitone would be 83.3mV, in which case 0.5mV = 0.6 cent. The input is bipolar (+/-5V) so the total change is 1.2cents.

For VCO tuning/tracking, I've assumed that a relative pitch change of about 3cent is at the limit of human hearing - and that's for VCOs. I think it is probably quite safe to use the VCA as a switch in this case. 

That leaves me with two options 

- either I use a DG413 as an SPDT switch, switching between lin and log - that saves me a single digital control signal. 

- or I use only exponential FM, in which case I don't need a switch at all.

I am currently breadboarding this. Both lin and exp FM works fine, but +/-5V linear FM seems to saturate something so the wave is cut off in some way. I will do a recording of it and add soon. Then I have to simulate the same to see what is actually going on. If I cannot make it work well I will just go for an exponential FM only.

Filter out: DCO1 is filtered, DCO2 modulates filter cutoff. Before red line: Linear FM, after: Exponential (v/oct) FM

Self resonance and exponential FM settings

Self resonancce and exponential FM output

Self resonance and linear FM output

Observations

Lin FM makes the filter "flatline". when the CV (DCO2) is low enough, the filter reaches a zero Hz cutoff, but the CV still goes lower, meaning the cutoff stays at 0Hz for some time - the filter does not support "through zero" modulation. 

PS: The output flatlines when input CV is positive, this is because the reference current is negative and any positive cv "negates" the reference current. Once the sum reaches 0 we cannot go any higher and the output flatlines.

Linear FM: When DCO2 is above a certain level,  the output "flatlines", presumably because cutoff reaches 0Hz before DCO2 reaches its peak.

Some measurements of linear FM CV vs I_abc

I_ref without any modulation is -12V / 1.2MOhm = -10uA (NB: mislabeled as -15V in captures)

With a +/-5V CV and a 120k input resistor, we will get 5V/120kOhm = 41.7uA, or approximately +/-4x the original I_ref. But since we cannot use an I_ref > 0, we get a flat line when the input from the linear FM CV reaches +10uA.

Cutoff CV: 0V, Lin FM CV: +/-5V

Cutoff CV: 2.5V, Lin FM CV: +/-5V

Cutoff CV: 3.5V, Lin FM CV: +/-5V

Cutoff CV: 4.5V, Lin FM CV: +/-5V

In my simulation I have written that we should use an input resistor that is approximately 10x the one used for the reference current, as that is what Yusynth.net uses for his VCO. That is not true.

Yusynth generates his reference current from a 5V source through a 1M resistor, giving a reference current of 5uA. For the linear FM input, he uses a 100k resistor, so a +/-5V input gives a +/-50uA output, which is 10x the normal reference current.

I, on the other hand, has used a CV that gives 4x reference current.

Cutoff CV: 0V, Lin FM CV: +/-5V, but this time we use a 50k lin CV input resistor

Calculations

To get a better feeling of the lin FM range I've done some simulations on the filter circuit. Here is the Frequency CV vs cutoff frequency vs I_control vs A/Hz (through a single cell):

1.0V:    10Hz    259nA    25.9nA/Hz

1.5V:    37Hz    1.03uA    27.8nA/Hz    

2.0V:    150Hz    4.18uA    27.8nA/Hz

2.5V:    604Hz    16.4uA    27.15nA/Hz

3.0V:    2.3kHz    63.6uA    27.7nA/Hz

3.5V:    8.2kHz    223uA    27.2nA/Hz

4.0V:    22.4kHz    639uA    28.5nA/Hz

4.5V:    42kHz    1.3mA    31.0nA/Hz

1.3mA is the highest possible value before we reach a flat top.

If we disregard the first and the last two (>= 4.0V) as we already know that they are not tracking that well, we get an average of 27.5nA/Hz

From my previous work I have that: 
${\mathrm{<br>}}_{}$R_linfm is often selected so that I_linfm = I_ref when linfm CV is at its highest (often 5 or 10V), which means that the frequency can be modulated by +/- 100% (the reference current will be between 0V$\mathrm{ 0V\; and\; 2\; *\; I\_ref).}$

This is only true as long as we do not use through zero modulation. 

Also, looking at the Yusynth VCO with its 10x FM, this is clearly not what everyone does.

What are others doing. VCOs:

Rene Schmitz: 

https://www.schmitzbits.de/vco2.html

VCO 1-3: 15V / 1M ref current, 5V / 220k lin FM (15uA vs 23uA, ca 1.5x mod)

VCO 4 (TZFM) 15V / 470k ref current, 5V / 220k lin FM (32uA vs 23uA, or 0.72x mod)

Yusynth VCO

https://yusynth.net/Modular/EN/VCO/index.html

5V / 1M ref current, 5V / 100k lin FM (5uA vs 50uA, or 10x mod)

CEM3340

Pin 13 on the CEM3340 is the reference current summer. The datasheet has a 1.5M resistor to 15V and a 1M + 0.1uF cap to lin FM. In the last paragraph of the datasheet it says "The value of the input resistor should be selected so that the maximum peak to peak input signal produces a plus and minus current equal to the reference current". This is exactly what I have written in my own research on VCOs, so I guess this is where I got it from (?).

15 / 1.5M ref current, 5V / 1M lin FM (10uA vs 5uA, or 0.5x mod. Or, could it be they expected a +/-10V lin FM CV? In that case they follow their own doubling rule.

Ian Fritz

https://ijfritz.byethost4.com/sy_cir2.htm

6.9V / 690k ref current, 5V / 100k lin FM (10uA vs 50uA, or 5x mod)

https://ijfritz.byethost4.com/sy_cir16_teezer.htm

Hard to tell as lin FM is done differently

MFOS

https://hackaday.io/project/47158/gallery#ecedc0e5555ada3907345e3c0c4cda3d

A bit hard to tell, lin FM enters through the middle of a voltage divider??

12V / 1M ref current, 5V / (1M || 100k) lin FM (1M til summer) 

JJ Clark

https://electro-music.com/wiki/pmwiki.php?n=Schematics.XR2207VCOByProfessorJamesJClark

12V / 68k ref current (!), 5V / 10k lin FM (176uA vs 500uA, or 2.8x mod)

Thomas Henry

https://electro-music.com/wiki/pmwiki.php?n=Schematics.ACD4046BasedVCOByThomasHenry

15V/1.5M ref current, 5V / 100k lin FM (with AC/DC switch) (10uA vs 50uA, or 5x mod)

Lots of VCOs here: 

https://electro-music.com/wiki/pmwiki.php?n=Category.VCO

Ken Stone CGS48 VCO and VCF-ish thingie with built in VCO

https://electro-music.com/wiki/pmwiki.php?n=Schematics.Bi-N-TicFilterByKenStone

https://sdiy.info/wiki/CGS_VCO

15V/150k ref current, 5V/100k lin FM (100uA vs 50uA, or 0.5x mod)

Linear FM and "amplitude" in Hz

As described in more detail here, increasing the base frequency also increases the "amplitude" of the modulation (if you think about the FM as a bipolar signal). The higher you get the larger the change is. 

So, what to choose

That's the hard question, isn't it... Right now I'm having a hard time understanding why anything more than a 0-to-doubling of the reference current is used on a non-through-zero FM VCO/VCF. Once we go lower than 0 the average frequency starts to drop and the VCO goes flat. I guess that's an effect as well, but why do we want it? And why on earth would we want 10x the input as is the case on the Yusynth VCO? Hmm.... I guess the only way of finding out would be a proper test.

Update: After a little thinking I think (...) I will try this: Select an R_linfm that gives a I_linfm that is 4x the reference current. That way I can just divide the CV by four (= shift right 2) to get an I_linfm equal to I_ref, meaning that the output of the exponential divider will never be below 0. 

Juno filter FM

Incidently, for the juno filter with a 10uA I_ref, this whould mean a 125k resistor. My current design uses a 120k, which gives a 41.7uA max, or 10.4uA after division by 4. This is very close to the ideal. One could argue that a 130k would be better, making us not quite reach I_ref, but again, it's better to test. It is also possible that a 5V input to the VCAs does not give exactly a unity gain, so 120k, being a standard resistor value, may be good enough anyway.

VCO lin FM

As for the VCO, we have a slight issue. My current design expected a 15V input using a 1.5M resistor, giving a 10uA I_ref. Now, hopefully, I'll be able to tune away the difference, but selecting the proper R_linfm depends on whether I match it with the current design or with a possible updated/corrected design. Anyway, here are the two options:

For 10uA, I could use the same 120k or 130k resistor as for the juno VCF.

For 12V / 1.5M = 8uA i will need 32uA. The correct value would be 156k. The closest standard value is 150k which gives 33.3uA - again, a little high (3.5% vs 4% for the juno filter) but it may work anyway.

Jupiter 6 filter lin FM

This uses the same expo converter as the juno filter. Right now they both use 15V and 1.5M R_ref, giving an I_ref of 10uA. As I've already redone the Juno filter for 12V with a 1.2M R_ref I will probably do the same with the JP6 version. That means that I can use a 120-130k R_linfm here as well.

Moog filter lin FM

The current 15V version has a 1M R_ref, giving I_ref = 15V / 1MOhm = 15uA 

If we switch to an 800k version (or 820k perhaps) for the 12V version, we will keep the I_ref the same.

I_linfm would then be 60uA and we would need an 83.3k resistor.

If we continue using the 1M R_ref, I_ref would be 12uA. I_linfm would be 48uA and we would need a 104k resistor