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GVSU EGR 214 - Integrating Amplifier – An Application of Capacitor Experiment #8

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Integrating Amplifier – An Application of Capacitor Experiment #8 by Thao Lai April 13, 2004 Engineering 214 Circuits Analysis I Lab Section 1 Partner: Kevin LaBeau Instructor: Dr. BlauchAbstract The relationship between voltage and current for capacitance will be verified and applied to a specific integrating amplifier circuit. The analysis will be broken into hand calculations, verification using PSpice Schematics Software and on an oscilloscope, verified through the actual building and measuring of the circuit. The results of this experiment will either verify or disprove the voltage-current relationship for capacitance in a circuit with an integrating amplifier. 1.0 Introduction The elements or components of any circuit are related through various proportions. Some components, such as resistors, are just multiplied by the value of the current flowing through them to result in a voltage across the resistor. This laboratory will examine the relationship between voltages and currents when dealing with the component of a capacitor. The capacitor, identified as “C”, will be connected in an integrator circuit that resembles the one shown in Figure 1. Figure 1: Integrating Amplifier Circuit to be analyzed2.0 The Voltage-Current Relationship for Capacitors A capacitor is a device that temporarily stores charge in a circuit. It consists of two metallic plates separated and insulated from each other by a dielectric. The amount of charge that is stored is proportional to the voltage across the capacitor. The relationship between the voltage and charge of the capacitor is separated by a constant known as the capacitance. In an equation, the relationship can be expressed as, CvCq ×= (1) with q representing the charge in coulombs, C being the relationship constant known as capacitance, and Cv being the voltage going across the capacitor in the circuit. Current is the change in charge over a change in time, which can be expressed as, dtdqi = (2) By substituting the charge in equation (1) into the charge of equation (2), the relationship becomes, dtdCvdtdvCiCC×+×= (3) However, the capacitor in this laboratory will have a constant capacitance value, so equation (3) becomes, dtdvCiC×= (4) In the circuit shown in Figure 1, the 100kΩ resistor provides DC feedback to stabilize the output voltage of the op-amp. So it is possible to just ignore that resistor and use Kirchoff’s Current Law at the negative input node of the op-amp. The application of KCL there looks like,0=−−dtdvCRvOS ∫+−= kdtRCvvSO (5) If the function generator displays the input signal as a square wave such as the one displayed in Figure 2, thenOv is a triangular wave representing the integral of theSv square wave, shown in Figure 3. Figure 2: vS Square Wave Figure 3: vo Triangular Wave Since the input signal has an average value of zero, the op-amp output signal also has to have an average value of zero. By selecting an appropriate integration constant, k, the average value of zero can be accounted for. Equation (5) can then be stated as, ktRCVvO+−= for 20Tt ≤≤ (6) T/2 T t vS V 0 -V T/2 T t -Vo Vo 0Equation (6) shows that the straight line slope is negative. This means that when time is zero, the output signal must start from positive Vo, so oVk =. When the time is at T/2, the output voltage signal is stopped at negative Vo. If the frequency, f, represents the inverse of time, T, Vo can be calculated to be the equation displayed in (7). ooVTRCVV +−=−2 fRCVVo4= (7) 3.0 Verification of Input and Output Voltage Relationship 3.1 Analysis and Design It was necessary to decide on a frequency around 1 kHz to calculate the ideal resistance and capacitance from equation (7). The resistance that was chosen was 3 kΩ and the capacitance chosen had a value of 100 nF. The actual value calculated for V was calculated to be 6 volts from equation (7) when the output voltage was chosen to be 5 volts. This ideal calculation is displayed below. ( )( )( )( ) volts651010030001000449=×==−VVfRCVVo (8) 3.2 Simulation and Design Verification The resulting circuit on PSpice is depicted below in Figure 2. VPULSE was used as the voltage source and a transient analysis configured to display at least 50ms of the output was used.Figure 4: Integrating Amplifier Circuit with Design Element Values Before simulation in PSpice, the actual resistance values were measured on the DMM so that they could be put into the circuit drawn, not the nominal values. Table 1 shows those values. Table 1: Resistance Values Resistor Nominal Value Measured Value R 3 kΩ 2.981 kΩ R1 100 kΩ 99.8 kΩ Once the actual resistance values were put into PSpice, the circuit was simulated. The resulting element values of the simulation can be found in Table 2 with the actual measured values from the building and measuring procedure of the laboratory. Also, the simulation of the circuit output voltage graph can be found in the Appendix. The circuit in Figure 4 was built on the CADET circuit wiring board. The square wave of the voltage source was controlled by the function generator. All of the measurements made were made on the SCOPE. There are two available channels, channel 1 which is yellow on the screen and channel 2, which is blue on the screen.The scope probes were connected to Ch1 and Ch2 inputs on the SCOPE. The Ch1 scope was connected between the function generator and the datum. The Ch2 probe was connected to pin 6 of the op-amp. The "measurements” feature on the scope was used to make the peak voltage, average voltage, and the measurements for frequency. The values of the measurements are all on Table 2. 4.0 Laboratory Measurements 4.1 Laboratory Equipment Used Without the necessary tools, this lab could not have been performed. The materials used to build and measure the circuit were an Oscilloscope Tektronix Model TDS 3012 (SCOPE), a digital multimeter (DMM), a C.A.D.E.T. Trainer Circuit Wiring Board, an Op-Amp 741, a 100k ¼ W resistor, a ¼ W resistor of a chosen resistance value, a non-polarized polyester capacitor of chosen value, and various leads and connectors. 4.2 Description of Measurements Before the circuit was built, resistors were measured for their actual resistance values, recorded


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GVSU EGR 214 - Integrating Amplifier – An Application of Capacitor Experiment #8

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