ECE 2006 University of Minnesota Duluth Lab 7 A. Dommer Page 1 January 2005 EQUIVALENT EQUIPMENT CIRCUITS INTRODUCTION The student will analyze the internal properties of the equipment used in lab. The input resistance of the oscilloscope and digital multimeter when used as a voltmeter will be measured. The output resistance of the function generator will similarly be determined. The student will also determine the Thevenin and Norton equivalent a complex circuit using SPICE. BACKGROUND When an electrical instrument is connected to a circuit to provide power or take measurements it becomes part of the circuit. Often the resistance of the connected instruments is neglected as they have been designed to not interfere with most circuits. Even though electricity flows through multiple elements inside of the instrument, these components may be modeled as a simple resistor or resistor and source. To determine the internal resistance of an instrument it is usually only necessary to vary a single component of an exterior connected circuit. Enough measurements are available throughout the exterior circuit to provide information for basic circuit analysis techniques to calculate the internal properties of an instrument. Root Mean Square (RMS) The current and voltage in alternating current (AC) systems is not constant. Thus, one cannot easily apply ohm’s law to a circuit with an AC source. If one thinks of a resistive element, current traveling forward will heat the element up just as much as current traveling backwards. Taking the average of the absolute value of an AC waveform will result in the DC equivalent. If one desires to use ohm’s law to analyze an circuit with an AC source, RMS values for voltage and current must be calculated or measured. Thevenin and Norton Equivalents Thevenin’s theorem states that a two terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTH in series with a resistor RTH where VTH is the open-circuit voltage VOC at the terminals and RTH is equivalent to the resistance at the terminals when all independent sources are turned off. RTH VTHECE 2006 University of Minnesota Duluth Lab 7 A. Dommer Page 2 January 2005 Figure 1: Input Resistance Measurement IN Norton’s theorem states that a two terminal circuit can be replaced by an equivalent circuit consisting of a current source IN in parallel with a resistor RN, where IN is the short -circuit current ISC through the terminals and RN is the input or equivalent resistance at the terminals when the independent sources are turned off. Mathematically these relationships can be described as follows: VTH = VOC IN = ISC RIN = RTH = RN = ( VTH / IN ) PROCEDURE Determining the internal resistance of the oscilloscope Connect the oscilloscope directly to the DC power supply. In this manner the circuit in Figure 1 is constructed with the variable resistance Rv set to 0 volts and Ri denoting the internal resistance of the oscilloscope. Adjust the DC power supply until the oscilloscope measures 8 volts. VPS = _______ Volts Select a nominal 10 M resistor and measure its resistance using the digital multimeter. RV = ________ Ohms RNECE 2006 University of Minnesota Duluth Lab 7 A. Dommer Page 3 January 2005 Using the nominal 10 M resistor as RV, construct the circuit displayed in Figure 1 and measure the voltage across the oscilloscope terminals Vi. Vi = _________ Volts Knowing three of the four variables of the circuit displayed in Figure 1, calculate the internal resistance of the oscilloscope, denoted as Ri in the figure. Include calculation in lab report. Oscilloscope Internal Resistance = Ri = _________ Ohms Determining the internal resistance of the multimeter used as a voltmeter Set the multimeter to measure voltage and connect directly to the DC power supply. In this manner the circuit in Figure 1 is constructed with the variable resistance Rv set to 0 volts. Adjust the DC power supply until the multimeter reads 16 volts. Make sure the multimeter is set to measure DC, not AC voltages. VPS = _______ Volts Record the measured value of the nominal 10 M resistor used in the previous section. RV = ________ Ohms Using the nominal 10 M resistor as RV, construct the circuit displayed in Figure 1 and measure the voltage across the multimeter terminals Vi. Vi = _________ Volts Knowing three of the four variables of the circuit displayed in Figure 1, calculate the internal resistance of the multimeter, denoted as Ri in the figure. Include calculation in lab report. Multimeter Internal Resistance = Ri = _________ OhmsECE 2006 University of Minnesota Duluth Lab 7 A. Dommer Page 4 January 2005 Figure 2: Output Resistance Measurement Measuring the output resistance of the function generator Connect the digital multimeter directly to the function generator. In this manner the circuit in Figure 2 is constructed with the load resistance RL set to 0 volts. We will neglect the internal resistance of the voltmeter for the purposes of this experiment and assume that the circuit is open, thus VO is equal to Vfg with RL removed. Adjust the function generator to a sinusoidal frequency of 50Hz. Adjust the amplitude until the digital multimeter displays 1.6 volts. Make sure the digital multimeter is set to measure AC RMS, not DC. Vfg = _________ Volts RMS Select a nominal resistor of about 50 and measure its resistance using the digital multimeter. RL = __________ Ohms Using the 50  resistor as RL, construct the circuit displayed in Figure 2 and measure the voltage displayed on the digital multimeter VO. VO = __________ Volts RMS Knowing three of the four variables of the circuit displayed in Figure 2, calculate the output resistance of the function generator, denoted as RO in the figure. Include calculation in lab report. Function Generator Output Resistance = RO = _________ OhmsECE 2006 University of Minnesota Duluth Lab 7 A. Dommer Page 5 January 2005 Figure 3: DC Circuit for SPICE Analysis Norton and Thevenin Analysis by means of SPICE Assume that the circuit represented in Figure 3 can only be analyzed by taking measurements at the open terminals represented by the voltage Va. Create a PSPICE schematic to measure the open circuit voltage VOC at the open terminals of the circuit displayed in Figure 3. VOC = ___________