Multivibrator mathematics

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Multivibrator mathematics

Postby Proschuno » Sun May 05, 2013 8:03 pm

So my goal this summer is to try and to build a tube based VCO, and so all I have right now are just plain vacuum tubes, not thyratrons like Metasonix and other people are using right now. But a problem I am hitting is that the normal equations used in predicting the frequency f=1/ln2 *2(r1c2+r2c1) commonly used for transistors do not apply, but the equations mentioned here http://www.radarpages.co.uk/theory/ap33 ... h6p112.htm that forget the ln2 term seem to work, but it seems only a limited range of grid resistors given a set plate resistor and capacitance.

I notice the plate and grid resistances seem to combine, but the equation only mentions one resistor value for each tube independent of plate resistance, are there more accurate equations I can use?

So essentially I'm trying to see how I can get a wide range of predictable behavior out of a vacuum tube multivibrator. The tube I am using right now is a 6SN7. My goal is to eventually build my own tube based VCO which will be utilized in a synthesizer, not necessarily using a 6SN7.
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Re: Multivibrator mathematics

Postby Geek » Sun May 05, 2013 8:21 pm

There's a tube one here:
http://webpages.charter.net/dawill/tmor ... pflop.html

And PWM that can be a VCO:
http://webpages.charter.net/dawill/tmor ... erator.gif

Tim has all sorts of goodies spread throughout his site (y)
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Re: Multivibrator mathematics

Postby Impmon » Wed May 08, 2013 6:20 pm

Proschuno wrote:So my goal this summer is to try and to build a tube based VCO, and so all I have right now are just plain vacuum tubes, not thyratrons like Metasonix and other people are using right now. But a problem I am hitting is that the normal equations used in predicting the frequency f=1/ln2 *2(r1c2+r2c1) commonly used for transistors do not apply


As for any other hollow state design, this involves loadlines (attached).

If putting one of the most hideously useless VTs, the 12AV7, to use here, select some operating points:

Vpp= 150Vdc
Rl= 15K

Then read off the values:

Vp(max)= 150V
Vp(min)= 46.25V
Vgk(off)= -7V

When one side goes into saturation, the voltage drop is: 150 - 46.25= 103.75. The grid of the opposite side sees this voltage as a negative voltage, and that is more than enough to cut it off, and keep it off. To figure out how long, apply the usual capacitor discharge formula:

v(t)= V(0) * exp[-t/(RC)]

Take the log of both sides and solve for t:

t= (1/RC) * ln[v(0)/v(t)]

V(0)= 103.75
v(t)= 7.0

t= (1/RC) * 2.696

f0= 1/2t= 1 / [(1/RC)5.392]

For FM, you can exchange the grid return resistors with modualted CCS's. Drive these anti-phase for PDM. For the actual CCS's, you could use PNP transistors, or even pentodes if you supply a high enough negative rail.
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Re: Multivibrator mathematics

Postby Proschuno » Thu May 09, 2013 8:04 am

Wow! I noticed that I usually had to multiply the RC term by 4 when I divided it by 1 to get the frequency, so I could get an answer close to the frequency I was measuring.
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Re: Multivibrator mathematics

Postby Impmon » Thu May 09, 2013 10:39 am

Proschuno wrote:Wow! I noticed that I usually had to multiply the RC term by 4 when I divided it by 1 to get the frequency, so I could get an answer close to the frequency I was measuring.


It's different for every VT type, as there are no convenient relationships that apply to a wide variety of VT types. No Vbe= 0.6V, or Id= Idss(1 - Vgs/Vp)^2 (JFET current formula) and so on. Not possible for a device where every element is hanging there in (a rough approximation of) free space, all doing their own thing, totally unconnected (except by the electrons coming off the cathode). You have to use the actual plate characteristics and draw loadlines to see what is actually going on.

Every type, every operating condition, is going to give very different answers as to when the plate comes out of cutoff, and how long it will take for the timing capacitors to discharge to that voltage. I've seen various formulas for determining the frequency of plate coupled multivibrators, but they are all far from accurate, much less so than the collector coupled multivibrator formula:

f0= 1/(2ln(2)RC)
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Re: Multivibrator mathematics

Postby Proschuno » Sun May 12, 2013 9:14 pm

Alright so I applied your formulas and still nothing matches up, so I'm doing something wrong. here is what I have:

Vpp=200v
Rl= 20k

This would mean that Vmin= 65 volts, and Vg(off)= -10v.

Grid resistors are 220k each and capacitors are 1 nanofarad each.
So for your equations you mentioned, is 'R' the value of the grid resistors, or Rg+Rl?

The frequency I get on my oscilloscope is exactly 1111 hertz.

So would the given values predict this given frequency? And I am using a 6SN7 for my multivibrator right now.
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Re: Multivibrator mathematics

Postby Impmon » Mon May 13, 2013 2:31 am

Loadline (attached)

From what you've given me:

Vpp= 200Vdc
Rl= 20K
Rt= 220K
Ct= 1000pF
Vgk(off)= -12V
Vpk= 66.36V
deltaV= 200 - 66.36= 133.64

t= RCln[V(0)/V(t)]

t= (220E3)(1000E-12)ln(133.64/12.0)= 530.25uS
fo= 1/(530.25E-6)2= 942.95Hz

You're off by about 168Hz. That's under a 20% error, and so far as hollow state is concerned, that's pretty good. (Back in "the day", 20% resistors were common, 10% considered premium, and 5% "precision" -- that was before laser trimmed, metal film types with precisions of 0.1%. No such thing back then.) At least you're well within the ball park, and like any other case where hollow state is concerned, you're not gonna be spot on every time, nor will your designs never require some tweaking before finalizing that design. There's a lot of empirical work as well as theoretical.

You're always gonna have both simplifying assumptions (true for SS design as well) and the natural variations in individual device characteristics. The latter is going to have a much greater impact since hollow state devices are low gain devices, and so circuit performance is going to depend a lot more on those device characteristics. The max gain of a 6SN7 is 20. What does a BJT operating at even a modest collector current of 1.0mA give? It's a helluvalot more!

I'd say you did pretty good here, and depending on what frequency you're shooting for, adjust the values of the timing resistors and/or the timing capacitors until you have what you're after.
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Re: Multivibrator mathematics

Postby Proschuno » Mon May 13, 2013 12:10 pm

Awesome! Thanks for your help, I'm still a little new to playing with tubes, and this has really saved me a lot of trouble. I'm just curious, is there anyway to predict the behavior of the multivibrator given if I knew how the tube itself tested on a tube tester? I'm sure it's not an easy task, and building a VCO would require me to be able to tune the exponentiator for the irregularities anyway, but I'm just curious.
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Re: Multivibrator mathematics

Postby Impmon » Mon May 13, 2013 12:56 pm

You might be able to improve accuracy if you knew the actual plate current cutoff grid voltage, and the Vpk at Vgk= 0. However, VTs age with use, and the characteristics drift over time. The frequency will drift along with the characteristics. (Collector coupled multivibrators are a good deal easier to manage, especially if you run them at low voltages so the EB junction never sees a reverse break down voltage. Sometimes, the EB junction is used as a "Zener", but it's never a good idea, as it's very noisy (and Zeners are noisy enough as it is) but the junction degrades with time and reverse break down.)

Since what you eventually want is a VCO, you don't need extreme accuracy anyway, and a highly stable oscillator doesn't make a very good VCO.

In almost every case where a plate coupled multivibrator is in use, you almost always have some sort of frequency control/sync. That would include o'scope deflection time bases, the vertical and horizontal time bases for TV sets, frequency dividers, and so on.
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