Concept explainers
Consider the Schmitt trigger in Figure 15.30(a). (a) Derive the expressionfor the switching point and crossover voltages as given in Equations (15.76)and (15.77). (b) Let
(a)
To derive: the expression for the switching point and crossover voltages
Answer to Problem 15.49P
The switching voltage
The upper crossover voltage of Schmitt trigger is
The lower crossover voltage of Schmitt trigger is
Explanation of Solution
Given:
Consider the Schmitt trigger as shown below.
Calculation:
In an ideal op-amp, the inverting and non-inverting terminal currents are zero. And the inverting and non-inverting node voltages are equal. Given circuit can be represented as
Applying Kirchhoff’s current law at inverting node:
Applying Kirchhoff’s current law at non-inverting node:
Assuming
Therefore, the switching voltage
When
The upper crossover voltage off Schmitt trigger is
Therefore, the upper crossover voltage of Schmitt trigger is
When
The lower cross over voltage of Schmitt trigger is
Therefore, the lower crossover voltage of Schmitt trigger is
Conclusion:
The switching voltage
The upper crossover voltage of Schmitt trigger is
The lower crossover voltage of Schmitt trigger is
(b)
The values of
Answer to Problem 15.49P
The resistor values are
The reference voltage is
Explanation of Solution
Given:
The crossover voltages are
The minimum resistance is to be
Calculation:
Let
The minimum resistance is to be
The crossover voltages are
Substitute
Substitute
Substitute
Choose
Therefore, the resistor values are
Substitute
Substitute
Conclusion:
Therefore, the resistor values are
(c)
To find: the currents in the resistors when
Answer to Problem 15.49P
When
When
Explanation of Solution
Given:
Consider the Schmitt trigger as shown below.
Calculation:
The current in the resistor is given by
( i ) When
The current in the resistor is
Therefore, the current is
( ii ) When
The current in the resistor is
Therefore, the current is
Conclusion:
Therefore,
When
When
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Chapter 15 Solutions
Microelectronics: Circuit Analysis and Design
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