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plugin-ECP214TheoryExample - Theoretical Analysis W The...

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Unformatted text preview: Theoretical Analysis W March 25, 2010 The pur . '7 ‘ =~=-e - is to analyze the inner workings of the Op—Amp Oscillator used in Lab #6, irst, the overall function of the circuit will be studied. NeWetical oscillating r is circuit will be determined based on the components Showggurfi below. \ V+ Schmitt Trigger I R1 L355?" Figure 1: - OpAmp Oscillator The voltage on the negative terminal of the Schmitt Trigger will always be (V+)/2 because the two 10kQ resistors create a voltage divider. Initially, the output voltage of the Schm-itt Trigger (V1) is zero. To , . obtain a high output voltage at node V1, the voltage across R2 must be greater than or equal to (V+)/2. (61)“? The voltage across R2 may be found using Equation 1 below. R2 2 _ R2+R3 VR V2 Equation 1 The voltage output of the Schmitt Trigger (V1) will oscillate-between V+ and CV. This oscillating output is then sent to the integrating OpAmp on the right side of Figure 1 as shown above. In order to analyze this portion of the circuit, the current through the capacitor is required. The OpAmp is considered ideal? so the current through the capacitor is the same as the current through R3. The equation for‘the current l through R3 is: Vl—Vx R3 IR = [C = Equation 2 3 Tthe voltage at the positive terminal of the Integrating OpAmp will always be (V+)/2 due to the voltage ' Ider created by the two 10k!) resistors. This will cause the output current of the OpAmp to oscillate. The current through the capacitor (It) can be used to determine the value of the capacitor as shown in Equation 3 below. 1c C =3 W Equation 3 K At this point in the analysis, the guidelines given for determining the oscillating frequency come into play. The guidelines are as follows: - Schmitt trigger voltages are at least 1v apart - the maximum current in any resistor must be greater than 20uA and less than ZOmA - 5v 5 (V+) .<. 25v dV a‘t' for the integrator must be less than 200K volts/sec and greater than 20 volts/sec Using Equation 1, Equation 2 and Equation 3, along with the limits and guidelines discussed above, the range of all the component values can be determined. See Table 1 below for the appropriate ranges of each component. Table 1: Component Value Ranges Component Value Range Finally, the theoretical oscillating frequency can be calculated in terms of the components in Table 1 69‘”) above. The known shape of the output voltage can be used to find Equation 4 below. )4” T_VXR1 CXR3XZ . 2— R2 x V Equation4 Equation 4 can then be solved for the oscillating frequency. 7i g f = - = —-——— V Equation 5 T 4XR1XR3XC Equation 5 above shows how the frequency is independent of the source voltage. To increase the frequency, R2 must be increased. On the other hand, to decrease the frequency, C, R1, or R3 must be increased. ...
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