Can

http://img194.imageshack.us/img194/1452/schimitttrigger2.jpg

some one explain to me how to analysis these schmitt trigger op amp circuits?
I want to calculate the Upper trigger voltage(UTP) and the Lower trigger voltage (LTP) of these circuits, but i don't know how to start and how to analysis the circuit.

Hope someone can show some calculations and explain it to me please, thanks alot.

 

To find threshold voltage you just need assume that opamp is in saturation, its doesn't mater if its is positive saturation or negative sat.
And then you need to find the voltage on non-inverting input.
And if Vin = voltage on non-inverting input, this Vin is equal threshold voltage.

 

thx for replying.
I dn't know how to solve the three parallel resistors to drive the equations. I know how to drive equations for utp and ltp for a simple schmitt trigger, but these two circuit has a resistor connected between the +ve terminal and ground, i just don't know how to solve it.

Can you explain in more detail, or show me some calculations please. thanks so much.

 

For example of a second digram.

For positive saturation voltage on non-inverting input V"+" is equal:
We can write nodal equation:
V"+"/R2 = (Va - V"+")/R1 + (Vo - V"+" )/R3 = V"+"/2.2KΩ = (13V - V"+")/40.6KΩ + (15V - V"+" )/3.9KΩ
and solve for V"+"

\(V_"+" = \frac {Va*R2*R3 + Vo*R1*R2} {R1*R2 + R1*R3 + R2*R3} =5.66399V \)

For negative sat the equation look the same but now Vo = 0.
So V"+"_neg = Va * R2||R3 / ( R1 + R2||R3 ) = 0.435295V

The equation for the first schema look the same but now
Vo = 12V or -12V, and Va =10V
So for positive sat :
V = 7.64706V
and for negative sat
V = 0.588235V

 

Take Ohm's law for each of the resistors and Kirchoff's Current Law for the + node. Assume a voltage V+ as an uknown quantity for your equations.

You now have 4 equations with 4 uknown variables to solve.
Get 'em tiger!

 

Of course you can use superposition to find V+ voltage.
Then we have very simply voltage divider :

\( V+ = \frac{ Va*R2||R3}{R1+ R2||R3} + \frac {Vo * R1||R2}{R3 + R1||R2}\)

 

Thx for all the replies.
I get it now, i was used kirchoff current law before, but i got the current direction wrong, hence i can not get the right answer. Thx very much for all your helps.

One more question. How can i analysis the circuit if the same circuit , but with Vin at the +ve terminal and offset(Va) at the -ve terminal?

 

show as the schematics