INPUT TERMINAL of the integrator B.The output of the integrator is a triangular wave and it is feedback as input to the comparator A through a voltage divider R2R3. Analysis:Just before switching occurs from +Vsat to −Vsat, the voltage at point P is zero.This means the −Vramp must be developed across R2 and +Vsat must be developed across R3. i.e.\( - \FRAC{{{V_{ramp}}}}{{{R_2}}} = - \frac{{ + {V_{sat}}}}{{{R_3}}} \cdots \left( i \right)\)\( - {V_{ramp}} = \frac{{{R_2}}}{{{R_3}}} + {V_{sat}} \cdots \left( {ii} \right)\) Similarly, +Vramp, the output of integrator at which the output of comparator switches from −Vsat to +Vsat, is given by:\( + {V_{ramp}} = - \frac{{{R_2}}}{{{R_3}}}\left( { - {V_{sat}}} \right) \cdots \left( {iii} \right)\)The peak to peak output amplitude of a triangular wave is:\({V_0} = + {V_{ramp}} - {V_{ramp}} = 2\frac{{{R_2}}}{{{R_3}}}{V_{sat}} \cdots \left( {iv} \right)\)Where Vsat = | + Vsat| = | − Vsat|.Equation (iv) represents the amplitude of triangular wave decreases with an increase in R3.The time is taken by the output to swing from −Vramp to +Vramp (or from +Vramp to −Vramp) is equal to half the period (T/2).This time can be calculated from the integrator output equation as follows:\({V_0} = - \frac{1}{{{R_1}{C_1}}}\mathop \smallint \limits_0^{\frac{T}{2}} \left( { - {V_{sat}}} \right)dt = \frac{{{V_{sat}}}}{{{R_1}{C_1}}}\left( {\frac{T}{2}} \right)\)\(\frac{T}{2} = \frac{{{V_0}}}{{{V_{sat}}}}{R_1}{C_1}\)\(\frac{T}{2} = 2{R_1}{C_1}\left( {\frac{{{V_0}}}{{{V_{sat}}}}} \right)\)Substituting V0 from equation (iv) in the above equation.\(T = \frac{{4{R_1}{C_1}{R_2}}}{{{R_3}}}\)We know that the frequency is inversely proportional to the time.\(f = \frac{{{R_3}}}{{4{R_1}{C_1}{R_2}}}\)Thus the frequency of oscillation increases with an increase in R3.

"> INPUT TERMINAL of the integrator B.The output of the integrator is a triangular wave and it is feedback as input to the comparator A through a voltage divider R2R3. Analysis:Just before switching occurs from +Vsat to −Vsat, the voltage at point P is zero.This means the −Vramp must be developed across R2 and +Vsat must be developed across R3. i.e.\( - \FRAC{{{V_{ramp}}}}{{{R_2}}} = - \frac{{ + {V_{sat}}}}{{{R_3}}} \cdots \left( i \right)\)\( - {V_{ramp}} = \frac{{{R_2}}}{{{R_3}}} + {V_{sat}} \cdots \left( {ii} \right)\) Similarly, +Vramp, the output of integrator at which the output of comparator switches from −Vsat to +Vsat, is given by:\( + {V_{ramp}} = - \frac{{{R_2}}}{{{R_3}}}\left( { - {V_{sat}}} \right) \cdots \left( {iii} \right)\)The peak to peak output amplitude of a triangular wave is:\({V_0} = + {V_{ramp}} - {V_{ramp}} = 2\frac{{{R_2}}}{{{R_3}}}{V_{sat}} \cdots \left( {iv} \right)\)Where Vsat = | + Vsat| = | − Vsat|.Equation (iv) represents the amplitude of triangular wave decreases with an increase in R3.The time is taken by the output to swing from −Vramp to +Vramp (or from +Vramp to −Vramp) is equal to half the period (T/2).This time can be calculated from the integrator output equation as follows:\({V_0} = - \frac{1}{{{R_1}{C_1}}}\mathop \smallint \limits_0^{\frac{T}{2}} \left( { - {V_{sat}}} \right)dt = \frac{{{V_{sat}}}}{{{R_1}{C_1}}}\left( {\frac{T}{2}} \right)\)\(\frac{T}{2} = \frac{{{V_0}}}{{{V_{sat}}}}{R_1}{C_1}\)\(\frac{T}{2} = 2{R_1}{C_1}\left( {\frac{{{V_0}}}{{{V_{sat}}}}} \right)\)Substituting V0 from equation (iv) in the above equation.\(T = \frac{{4{R_1}{C_1}{R_2}}}{{{R_3}}}\)We know that the frequency is inversely proportional to the time.\(f = \frac{{{R_3}}}{{4{R_1}{C_1}{R_2}}}\)Thus the frequency of oscillation increases with an increase in R3.

">

The equation of frequency of oscillation of a triangular wave generator is given as(1) \({f_0} = \frac{{3{R_1}{C_1}{R_2}}}{{{R_3}}}\)(2) \({f_0} = \frac{{4{R_1}{C_1}{R_2}}}{{{R_3}}}\)(3) \({f_0} = \frac{{{R_3}}}{{3{R_1}{C_1}{R_2}}}\)(4) \({f_0} = \frac{{{R_3}}}{{4{R_1}{C_1}{R_2}}}\)

General Knowledge General Awareness in General Knowledge 9 months ago

  457   0   0   0   0 tuteeHUB earn credit +10 pts

5 Star Rating 1 Rating

Triangular Wave Generator:It consists of a comparator (A) and an integrator (B) as shown in the figure:The output of comparator A is a square wave of amplitude ±Vsat and is applied to the inverting (-) INPUT TERMINAL of the integrator B.The output of the integrator is a triangular wave and it is feedback as input to the comparator A through a voltage divider R2R3. Analysis:Just before switching occurs from +Vsat to −Vsat, the voltage at point P is zero.This means the −Vramp must be developed across R2 and +Vsat must be developed across R3. i.e.\( - \FRAC{{{V_{ramp}}}}{{{R_2}}} = - \frac{{ + {V_{sat}}}}{{{R_3}}} \cdots \left( i \right)\)\( - {V_{ramp}} = \frac{{{R_2}}}{{{R_3}}} + {V_{sat}} \cdots \left( {ii} \right)\) Similarly, +Vramp, the output of integrator at which the output of comparator switches from −Vsat to +Vsat, is given by:\( + {V_{ramp}} = - \frac{{{R_2}}}{{{R_3}}}\left( { - {V_{sat}}} \right) \cdots \left( {iii} \right)\)The peak to peak output amplitude of a triangular wave is:\({V_0} = + {V_{ramp}} - {V_{ramp}} = 2\frac{{{R_2}}}{{{R_3}}}{V_{sat}} \cdots \left( {iv} \right)\)Where Vsat = | + Vsat| = | − Vsat|.Equation (iv) represents the amplitude of triangular wave decreases with an increase in R3.The time is taken by the output to swing from −Vramp to +Vramp (or from +Vramp to −Vramp) is equal to half the period (T/2).This time can be calculated from the integrator output equation as follows:\({V_0} = - \frac{1}{{{R_1}{C_1}}}\mathop \smallint \limits_0^{\frac{T}{2}} \left( { - {V_{sat}}} \right)dt = \frac{{{V_{sat}}}}{{{R_1}{C_1}}}\left( {\frac{T}{2}} \right)\)\(\frac{T}{2} = \frac{{{V_0}}}{{{V_{sat}}}}{R_1}{C_1}\)\(\frac{T}{2} = 2{R_1}{C_1}\left( {\frac{{{V_0}}}{{{V_{sat}}}}} \right)\)Substituting V0 from equation (iv) in the above equation.\(T = \frac{{4{R_1}{C_1}{R_2}}}{{{R_3}}}\)We know that the frequency is inversely proportional to the time.\(f = \frac{{{R_3}}}{{4{R_1}{C_1}{R_2}}}\)Thus the frequency of oscillation increases with an increase in R3.

Posted on 28 Nov 2024, this text provides information on General Knowledge related to General Awareness in General Knowledge. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

Take Quiz To Earn Credits!

Turn Your Knowledge into Earnings.

tuteehub_quiz

Tuteehub forum answer Answers

Post Answer

No matter what stage you're at in your education or career, TuteeHub will help you reach the next level that you're aiming for. Simply,Choose a subject/topic and get started in self-paced practice sessions to improve your knowledge and scores.