Need help with a circuit

[Dark Alchemist]

I need a circuit that can perform the following

if (x < -1)
x = 0
else if (x < 1)
x = sqrt(1 - (x^2))
else
x = 0

Now what I have done so far is the comparisons and have three
comparators so at a given x the appropiate values are given (1, -1, 0).
I have taken care of the square root, minus, and the square part as
well.

So, does anyone know what I use and how to do the if then else parts?
3 outputs and only one is needed at the input to the rest of the
circuit. I don't want a specialized ic for this so its just or, not,
and, xor, etc...

Thank you.

 

[Bob]

I need a circuit that can perform the following

if (x < -1)
x = 0
else if (x < 1)
x = sqrt(1 - (x^2))
else
x = 0

Now what I have done so far is the comparisons and have three
comparators so at a given x the appropiate values are given (1, -1, 0).
I have taken care of the square root, minus, and the square part as
well.

So, does anyone know what I use and how to do the if then else parts?
3 outputs and only one is needed at the input to the rest of the
circuit. I don't want a specialized ic for this so its just or, not,
and, xor, etc...

Thank you.

It seems like your equations should use a different variable name for the
output of the function. For example:
if (x<-1)
y=0
....
....
where x is the input and y is the output, right?

Also, if you look at your possible values for x then you'll see what the
"else" part really is. You're on the right track by realizing that you need
comparitors. Now, you just need to write out the truth table (for the
comparitor outputs as the input to your logic function) and then just reduce
the logic to drive your math (zero or sqrt(1-x^2)) function.

Bob

 

[Dark Alchemist]

Well, the posibilities of x would be a sine wave (for this test but
could be anything in reality).

If x <= 0 then y = 0 else if x <1 then y = sqrt(1 - x^2) is as far as I
was able to simplify it.

So, comparator A compares against 0 and comparator B compares <1 but we
do not want the compare at B if A is true.
This is as far as I got before my eyes started to glaze over, heheheh.

 

[Bob]

Suppose you had two comparators.

One would would output a high (or low if you prefer) when X<-1.
The second one's output would go true when X<1.

Do you think that this would be enough comparators to cover all input (X)
values?

Bob

 

[John Fields]

Well, the posibilities of x would be a sine wave (for this test but
could be anything in reality).

If x <= 0 then y = 0 else if x <1 then y = sqrt(1 - x^2) is as far as I
was able to simplify it.

So, comparator A compares against 0 and comparator B compares <1 but we
do not want the compare at B if A is true.
This is as far as I got before my eyes started to glaze over, heheheh.

---
If we assume that x is a voltage which varies over some range and that
you want to know when the voltage is less than or equal to 0 volts and
also when it's less than 1 volt, then you can set up two voltage
comparators like this:


+2V
| Vcc
[10.0K] |
| [10K]
+----|+\ |
| | >--+-->B
x>---+---------|-/
| | Vcc
| [10.0K] |
| | [10K]
+---------|+\ |
| | >--+-->A
+----|-/
|
GND

and your truth table will look like this:

x A B
--------+-----+-----
<=0V 0 1

0<x<1 1 1

=1V 1 0

So the logic to control your function machine would look like this:

+2V
| Vcc
[10.0K] |
| [10K]
+----|+\ |
| | >--+----+
x>---+--[10K]--------|-/ |
| | Vcc |
| [10.0K] | |
| | [10K] +--B
+--[10k]--------|+\ | and Y---+
| | | >--+-------A |
| +----|-/ |
| | |
| GND +---------E--------+
| | |
+------------------------>x| y = sqrt(1-x²) |-->y
| |
+------------------+

Where the line coming down from the AND would be an enable. When x was
less than 0V it would go low, disabling the function machine, then
when x was between 0V and 1V it would go high to enable the function
machine, and when x rose to higher than 1V it would disable it again
for as long as x remained higher than 1V.

 

[Dark Alchemist]

Hmmm, I was able to get all the way to the last part on my own but even
looking at what you did (where I see an and gate) I am lost.

So, I have two ouputs (A, B) and your logic table works. Now all I
need to do is take the A AND B = 0 or 1 in this instance. I noticed
that 0<x<1 1 1 . 1 and 1 is 1 while 0 and 1 or 1 and 0 = 0
so would it not be simpler to (A AND B) * sqrt(1-x^2)? The product of
that would be 0 or the sqrt part.

 

[Active8]

Hmmm, I was able to get all the way to the last part on my own but even
looking at what you did (where I see an and gate) I am lost.

So, I have two ouputs (A, B) and your logic table works. Now all I
need to do is take the A AND B = 0 or 1 in this instance. I noticed
that 0<x<1 1 1 . 1 and 1 is 1 while 0 and 1 or 1 and 0 = 0
so would it not be simpler to (A AND B) * sqrt(1-x^2)? The product of
that would be 0 or the sqrt part.

That's very good! But you'd need an analog multiplier that works at
DC if you go there. John simply used A && B as an enable, a much
better approach.

 

[Dark Alchemist]

Hmmm, I am not grasping beyond the and part from what he was telling
me.
We have A && B then what? From this point on is where I got lost.

 

[John Fields]

Hmmm, I was able to get all the way to the last part on my own but even
looking at what you did (where I see an and gate) I am lost.

So, I have two ouputs (A, B) and your logic table works. Now all I
need to do is take the A AND B = 0 or 1 in this instance. I noticed
that 0<x<1 1 1 . 1 and 1 is 1 while 0 and 1 or 1 and 0 = 0
so would it not be simpler to (A AND B) * sqrt(1-x^2)? The product of
that would be 0 or the sqrt part.

---
Yes, that's essentially what I've done by ANDing the comparator
outputs and giving you that AND as an enable. Not knowing what your
square-rooter-subtractor circuitry looks like, that was as far as I
could go. If you can perform the ANDing in your computational
circuitry, go for it!

 

[John Popelish]

Well, the posibilities of x would be a sine wave (for this test but
could be anything in reality).

If x <= 0 then y = 0 else if x <1 then y = sqrt(1 - x^2) is as far as I
was able to simplify it.

So, comparator A compares against 0 and comparator B compares <1 but we
do not want the compare at B if A is true.
This is as far as I got before my eyes started to glaze over, heheheh.

I am tinkering with a strictly opamp solution but I need some idea of
the DC accuracy you need, and the settling time or maximum frequency
you intend ot pass through this function. Keep in mind that at +-1
volt in, the gain is infinite.

 

[Dark Alchemist]

So, was my simplification still holding the same as the original?
Btw, thank you everyone for you help.

 

[Active8]

Hmmm, I am not grasping beyond the and part from what he was telling
me.
We have A && B then what? From this point on is where I got lost.

They turn the sqrt circuit on or off. Off would be x < 0 OR x > 1.
So when the sqrt is off, it should output zero.

My point was that if you try to do (A && B) * sqrt, the * implies
analog multiplication wheras && or AND is digital multiplication.

Now you can analog multiply sqrt with 1 or 0, the circuitry won't be
as simple, however. So use A && B as a control, i.e., an enable.

I still think that you coming up with (A AND B) * sqrt(1-x^2) was
very good. It's true.

 

[John Fields]

So, was my simplification still holding the same as the original?
Btw, thank you everyone for you help.

---
Dunno, for sure...

Modifying the circuit a little and looking at the circuit and the
truth table, we have:


+2V
| Vcc
[10.0K] |
| [10K]
+----|+\ |
| | >--+----+
x>---+--[10K]--------|-/ |
| | Vcc | +-------+
| [10.0K] | | 0V---|b |
| | [10K] +--B | _ |
+--[10k]--------|+\ | and AB------|a/b y|---y
| | | >--+-------A | |
| +----|-/ +----|a |
| | | +-------+
| GND | S1
| |
| |
| +-------+ +-------+
| 1V--|1 | +----------------+ |
| +------+ | 1-x²|--|1-x² sqrt(1-x²)|--+
+--|x x²|--|x² | +----------------+
+------+ +-------+

The blocks on the bottom are your circuits, and sqrt(1-x²) is shown as
being routed through a switch where the output (y)is either sqrt(1-x²)
or 0, depending on whether is x is <=0V, between 0V and 1V, or >1V.

The AND gate only goes true when 0V<x<1V, with the result that the
switch will be turned off when x is outside the limits, and at those
times y will be equal to 0V, like this:


x A B y
--------+-----+-----+-------------
<=0V 0 1 0

0V<x<1V 1 1 sqrt(1-x²)