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On Tue, 2 Nov 1999, Thomas Hudson wrote:

and triangles waveforms, such as this one I selected at random from the

web:

http://www.xavax.com/efm/synth/cbook/pics/lfo1a_sd.gif

This circuit has two sections, a "comparator" and an "integrator".

If you remember calculus classes, then integration should at least sound

familiar. (A comparator can also be considered a differentiator with no

"interval" between points (series cap C=0), for those who have dealt with

the math).

Differentiation is essentially taking a sum value of parameter/variable

apart to find the rate-of-change between the (numeric) parts. Integration

is essentially taking a bunch of individual numeric "parts" and summing

them together over a range. These two principles are the complement of

each other.

Now, how does helps us in the synth world:

Looking at the schematic, note that the author provided two

LFOs-on-one-quad op-amp. Either one suits this explanation. I'll talk

about the "upper" circuit.

The op-amp on the left is the basic integrator. what it does is average

the change in voltage over a period of time by storing the "instantaneous"

value of the voltage on the capacitor and feeding it back to the input to

be added to the next "instantaneous" voltage. Since integration is the

summation of all intervals in a range, by definition this circuit is an

integrator.

Here is what that integrator sees during a single input period T at some

frequency, say, 1Hz.

+V t=0 _______t=T=1 __t=0 t=T=1 second

| --__

0V | --__

_______| --__

-V

Input (pin 6) Output (pin 7)

Notice that the output goes ∗negative∗ because the postitive-going input

is going to the negative (inverting) op-amp terminal. Remember this.

(AC circuit analysis says that one of the conditions for the above

grpahs to be valid is that the circuit has been running a "long time";

e.g., we're not looking at the power-up state. Pretend this LFO has

been running for 10 seconds).

The thing to observe here is that even though input square wave cycle

has a sharp step halfway through, the output is the ∗average∗ of every

input that can be summed up between t=0 and t=T. This is how a voltage

ramp is created.

Now, to get the integrator to reverse the slope and complete the

triangle, something is needed to change the sign of the value being fed

into the integrator. This is what the comparator is for. The comparator

is the op-amp on the right side of the circuit diagram. This op-amp

compares the ramp from the integrator with zero volts (see the + input

connected to ground? --zero volts) and each time the ramp goes above zero,

it causes the comparator output to go to a postive voltage. This is what

creates the negative-going ramp as seen above.

Now here is the trick: This positive voltage goes back to the MINUS

input of the integrator, which means that the integrator is generates a

down-ramp. Eventually, this down-ramp voltage will go below zero. When

the comparator sees this drop below zero, its output changes quickly to a

negative voltage. The negative voltage goes back to the integrator just

like the positive voltage did, but remember, it is going into the minus

input.

Two minuses make a plus, so now the integrator does this:

+V _______ t=T t=0 __ t=T

t=0 | __--

0V | __--

| __--

-V |_______ --

The two outputs end up strung together: /\/\/\/\/

The side benefit is that the comparator is generating square waves at

the same rate: __--__--__--__--

Extra info: the "rate" control sets how much voltage is allowed back to

the intergrator to be changed into triangles. This change rate of

integration for a given cycle.

The diode and voltage divider resistor create a square wave output in

the range of 0~5V.

There are other caveats to consider when conveeting pulses to triangles,

such as that an integrator is also a 1st-order low-pass filter.

Hope this helps,

--Crow

/∗∗/

> Can you give more details about how this is done. I'm not anThe best example is to look at a simple LFO circuit that provides pulse

> electronics whiz, but I have a project where I would like to

> convert pulses to triangles.

and triangles waveforms, such as this one I selected at random from the

web:

http://www.xavax.com/efm/synth/cbook/pics/lfo1a_sd.gif

This circuit has two sections, a "comparator" and an "integrator".

If you remember calculus classes, then integration should at least sound

familiar. (A comparator can also be considered a differentiator with no

"interval" between points (series cap C=0), for those who have dealt with

the math).

Differentiation is essentially taking a sum value of parameter/variable

apart to find the rate-of-change between the (numeric) parts. Integration

is essentially taking a bunch of individual numeric "parts" and summing

them together over a range. These two principles are the complement of

each other.

Now, how does helps us in the synth world:

Looking at the schematic, note that the author provided two

LFOs-on-one-quad op-amp. Either one suits this explanation. I'll talk

about the "upper" circuit.

The op-amp on the left is the basic integrator. what it does is average

the change in voltage over a period of time by storing the "instantaneous"

value of the voltage on the capacitor and feeding it back to the input to

be added to the next "instantaneous" voltage. Since integration is the

summation of all intervals in a range, by definition this circuit is an

integrator.

Here is what that integrator sees during a single input period T at some

frequency, say, 1Hz.

+V t=0 _______t=T=1 __t=0 t=T=1 second

| --__

0V | --__

_______| --__

-V

Input (pin 6) Output (pin 7)

Notice that the output goes ∗negative∗ because the postitive-going input

is going to the negative (inverting) op-amp terminal. Remember this.

(AC circuit analysis says that one of the conditions for the above

grpahs to be valid is that the circuit has been running a "long time";

e.g., we're not looking at the power-up state. Pretend this LFO has

been running for 10 seconds).

The thing to observe here is that even though input square wave cycle

has a sharp step halfway through, the output is the ∗average∗ of every

input that can be summed up between t=0 and t=T. This is how a voltage

ramp is created.

Now, to get the integrator to reverse the slope and complete the

triangle, something is needed to change the sign of the value being fed

into the integrator. This is what the comparator is for. The comparator

is the op-amp on the right side of the circuit diagram. This op-amp

compares the ramp from the integrator with zero volts (see the + input

connected to ground? --zero volts) and each time the ramp goes above zero,

it causes the comparator output to go to a postive voltage. This is what

creates the negative-going ramp as seen above.

Now here is the trick: This positive voltage goes back to the MINUS

input of the integrator, which means that the integrator is generates a

down-ramp. Eventually, this down-ramp voltage will go below zero. When

the comparator sees this drop below zero, its output changes quickly to a

negative voltage. The negative voltage goes back to the integrator just

like the positive voltage did, but remember, it is going into the minus

input.

Two minuses make a plus, so now the integrator does this:

+V _______ t=T t=0 __ t=T

t=0 | __--

0V | __--

| __--

-V |_______ --

The two outputs end up strung together: /\/\/\/\/

The side benefit is that the comparator is generating square waves at

the same rate: __--__--__--__--

Extra info: the "rate" control sets how much voltage is allowed back to

the intergrator to be changed into triangles. This change rate of

integration for a given cycle.

The diode and voltage divider resistor create a square wave output in

the range of 0~5V.

There are other caveats to consider when conveeting pulses to triangles,

such as that an integrator is also a 1st-order low-pass filter.

Hope this helps,

--Crow

/∗∗/