[sdiy] Newbie question regarding the 4069 VCO

[René Schmitz]

Hi James,

James Howe wrote:

> To that end I've been studying the 4069 VCO found at  
> http://www.uni-bonn.de/~uzs159/vco4069.html and reading the various  
> e-mails sent to this list concerning how it works.  Overall I 
> understand  how it works, the integrator generates a ramp, the Schmitt 
> trigger resets  the ramp generating a sawtooth, etc.  What I don't fully 
> understand is why  it works the way it does.  I'd also like to 
> understand more about why  certain components were selected.  Why the 
> particular transitors, why the  1N4148 diode, etc.  I'm trying to work 
> though these things myself but I  know it would help me a great deal if 
> people could sort of walk through  the various design aspects, why 
> certain values/components were selected,  and in general how it works 
> from a lower level.

Well, lets start with the input stage (the question in your private 
mail...).

You're right that its a voltage divider, dimensioned so that a 1V input 
is scaled down to about 17mV. (ln(2)*kT/q) The NTCs do vary the upper 
leg of the voltage divider so that the scale factor is temperature 
dependant, cancelling the voltage dependance of the exponential. (Its 
only approximative, because the NTCs have a ~exp(-T) law, while actually 
1/T would be required. But in the neighborhood of 25°C its good enough.)

How the individual CVs is summed, can be understood if you consider that 
the upper leg of the divider is much larger than the lower, and that the 
base draws very little current. So you can say that the current through 
the both upper legs, must flow through the trimmer and 1.5K. Since the 
division ratio is so high, this means that the voltage at the transistor 
base is moving only very little. That means that the large 110k resistor 
combination approximates a current source. That means you can view this 
node as roughly a current summing node.

For the exponential convertor, I recommend to read my expo tutorial. It 
doesn't cover this special circuit. The math however does apply as well. 
(A few signs will change, but the general concept is the same.)

The integrator behaves the same as the textbook version with an opamp. 
Just think of the invertor as an opamp running on single supplies, with 
its + input tied to Vb/2. The invertor input being the - terminal.

The specialty here is the way how the integrator gets reset. Normally 
you would have a switch (BJT FET or the like) to short the cap 
terminals, and discharging it. Here we push current into the invertor 
summing node, forcing the integrator to work into the other direction.
The diode current and the expo current have opposite direction.
The extra resistor in series with the cap is a so called franco 
compensation resistor. Its purpose is to compensate the finite reset 
time of the VCO. Resulting in better high frequency response.
Its action is that the expo current generates a voltage drop across it, 
so that the schmitt trigger sees a slightly higher voltage than that of 
the cap. So the higher the current, the earlier the schmitt trigger 
fires. "Earlier" in both timing and voltage sense. Dimensioning is 
Rcomp*C =t(reset).
The diode is necessary to bypass the resistor during the reset portion 
of the cycle, so that the resistor is only in effect during the ramp 
portion of the wave.

The schmitt trigger can be understood by considering that the decision 
threshold of the gate input is halfway between the supply. The voltage 
of that node is dependant on both the input, and the state of the 
schmitt triggers output. When the transition region is approached, the 
moving output moves the node voltage into the direction of change that 
is due to the input voltage. This is positive feedback. (Sort of like 
the spring action on a microswitch.) So there is a region where the 
output state is dependant on the previous state.
It can be best understood if you calculate the voltages at the input 
node for various input voltage combinations. Its a voltage divider 
again. (Ok, to really explain it, I would need to make an 
asciimatic-animation...)

As for the various choices of components. Well, 1N4148 is everyones 
small signal diode. The BC548s and 559s are just what I consider 
"standard" small signal transistors. (I'm in Europe.) There is no 
reasoning whatsoever about them. No need to hunt them down, since any 
other small signal transistors will work.
Same goes for the various voltage dividers, the values are fairly 
arbitrary, for example using 100k and 220k instead of 10k and 22k in the 
schmitt trigger would give the same results, since the dividier *ratio* 
is the same. The only thing is that they shouldn't load the gates too 
much. Too small values wouldn't work, and too high values do give 
problems with stray capacitances. This was only picked out of a stomach 
feeling.
The dimensioning of the input divider has the same considerations, also 
the NTCs only come in E6 or E12 values, so that limits the choices. I 
wanted to stay close to 100k, since thats considered the standard input 
impedance. But somewhere near 20 or 50k would work as well.

Hope this helps.

Cheers,
  René

-- 
uzs159 at uni-bonn.de
http://www.uni-bonn.de/~uzs159