in Inverting Schmitt Trigger, Given R2=10kΩ, Vref=4.5V and the output saturation voltage of the op-amp is 9V. Determine the value of R1 to achieve a hysteresis band of 3.0V. Express your answer in kohms
The hysteresis band for an inverting Schmitt trigger is given by the formula:
H = (R1 + R2) * (Vref / Vsat)
Where:
H = Hysteresis band
R1 = resistance connected between the inverting input and the output of the op-amp
R2 = feedback resistance connected between the non-inverting input and the output of the op-amp
Vref = reference voltage
Vsat = output saturation voltage of the op-amp
Plugging in the given values:
H = 3.0V
R2 = 10kΩ
Vref = 4.5V
Vsat = 9V
Rearranging the equation to solve for R1:
R1 = (H * Vsat) / (Vref) - R2
Substituting the values:
R1 = (3.0V * 9V) / (4.5V) - 10kΩ
R1 = (27V^2) / (4.5V) - 10kΩ
R1 = 6kΩ - 10kΩ
R1 = -4kΩ
Since the resistance value cannot be negative, it seems there might be an error in the given parameters or calculations. Please double-check the given values and ensure the calculations are correct.
To determine the value of R1 in the Inverting Schmitt Trigger circuit, we need to consider the hysteresis band and the voltage divider formed by R1 and R2.
The hysteresis band is the voltage difference between the upper and lower threshold voltages. In this case, the hysteresis band is 3.0V.
The upper threshold voltage (VUT) is given by VUT = Vref + (R1 / (R1 + R2)) * (VDD - Vref), where VDD is the supply voltage. In this case, VDD is the output saturation voltage of the op-amp, which is 9V.
The lower threshold voltage (VLT) is given by VLT = Vref - (R1 / (R1 + R2)) * Vref.
Since we know Vref = 4.5V, VUT = 9V, and VLT = (VUT - Hysteresis Band), we can rearrange the equations above to solve for R1:
VLT = Vref - (R1 / (R1 + R2)) * Vref
VUT - Hysteresis Band = Vref + (R1 / (R1 + R2)) * (VDD - Vref)
Substituting the given values:
4.5V - (R1 / (R1 + 10kΩ)) * 4.5V = 9V - 3.0V
(1 - (R1 / (R1 + 10kΩ))) * 4.5V = 6V
Now, let's simplify the equation:
1 - (R1 / (R1 + 10kΩ)) = (6V / 4.5V)
1 - (R1 / (R1 + 10kΩ)) = 1.333
Rearranging the equation:
(R1 / (R1 + 10kΩ)) = 1 - 1.333
(R1 / (R1 + 10kΩ)) = -0.333
Now, let's solve for R1:
cross-multiplying the equation:
-0.333 * (R1 + 10kΩ) = R1
-0.333R1 - 3.333kΩ = R1
-0.333R1 - R1 = 3.333kΩ
-1.333R1 = 3.333kΩ
R1 = (3.333kΩ / -1.333)
R1 ≈ -2.5kΩ
Since resistance cannot be negative, it seems there may be an error in the given problem. Please double-check and provide the correct values if available.