LAB 4_ Internal Impedance (1)

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LAB 4: INTERNAL IMPEDANCE OF INSTRUMENTS; INFLUENCE OF INSTRUMENTS ON CIRCUITS Lab Course: ECE291 Written By: Anna Chang, Abdallah Bereka, Shricharan Kulavanikerpuram Subramaniam Date of Submission: 10/13/2022 Instructor: Dr. Hongya Ge . Introduction Ⅰ

1 The purpose of this lab is to demonstrate the difference between “ideal” instruments and real instruments. Ideal instruments are assumed to have no internal resistance, but there is a small internal resistance on digital voltmeters, ammeters, and voltage sources. Through calculating the difference between the voltage output and the voltage measured, the internal resistance of the device will be calculated and observed. . Pre-Lab Ⅱ 1. Knowing that to measure voltage you need to connect a voltmeter between two points of a circuit and that the voltmeter should have little effect on the circuit, what do you think is the value of the voltmeter internal resistance, high or low? What is the resistance of an ideal voltmeter which does not influence a circuit at all (does not draw any current)? A real voltmeter can be represented by a circuit consisting of an ideal voltmeter and a resistor representing its internal resistance. Draw the schematic of that circuit, indicating terminals which represent leads used for voltage measurements. Write an equation for finding the unknown voltmeter internal resistance Rint if you know the value of the resistor R and the voltage Vs in experiment 1.1 of this laboratory( Fig 4.1). a. The value of the internal resistance should be high since there should barely be any current flowing through the voltmeter. The resistance of an ideal voltmeter is infinite. b. R internal = [V output *R L ]/(V output -V measured ) c. [Figure 1] Schematic diagram of ideal voltmeter with infinite internal resistance 2. Draw an equivalent circuit of a real ammeter, consisting of an ideal instrument and the internal resistance. Again, a good instrument should have a minimal effect on a circuit being measured. Remember that, unlike a voltmeter, an ammeter is connected in series with the measured circuit. So, an ideal ammeter should not resist current flow and should not develop any voltage across its terminals.

2 a. [Figure 2] Schematic diagram of ideal voltmeter with infinite internal resistance 3. An ideal voltage source gives voltage which is independent of current. A real source can be represented by an ideal source and the internal resistance, on which a voltage drop develops as the current flows. Thus a real voltage source gives lower voltage with a load (e.g. a resistor) than without a load. Write an equation for finding the unknown waveform generator internal resistance R. Hint if you know the value of the load resistor RL and the voltages measured in experiment 1.3 of this laboratory a. R internal = [V output *R L ]/(V output -V measured ) . Experimental Procedure: Ⅲ 1. Internal Resistance of Digital Voltmeters 1. Measure the internal resistance of the digital voltmeters at your bench in the DC mode on two different ranges by setting the DC power supply first to 0.3 V (low voltage). 2. Measure the internal resistance of the digital voltmeters at your bench in the DC mode on two different ranges by setting the DC power supply first to 20 V (high voltage). 3. Measure the internal resistance of the digital voltmeters at your bench in the DC mode using the waveform generator supplying a sine wave with a frequency of 100 Hz, with the amplitude of a 5V. [Figure 3] Schematic diagram of circuit to solve given in the lab book 2. Internal Resistance of Digital Ammeters

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3 1. To measure the DC resistance of a digital ammeter do not use an analog voltmeter. It will not show well the very small voltage drop you expect to measure. Use an oscilloscope instead. i. NOTE: Use a 1kΩ resistor in series with the ammeter to protect it from excessive current [Figure 4] Schematic diagram of circuit to solve given in the lab book 3. Low Impedance Circuit 1. Make a simple voltage divider to attenuate signals by a factor of 2. 2. Use two equal resistors of about 10 k and measure their values with a digital ohmmeter. 3. Determine the attenuation of the divider by measuring the input and the output voltage (use the same instrument for both). 4. Make the following measurements: (a) with DC using a digital voltmeter, (b) with AC (a sinewave signal of about 100 Hz) using a digital voltmeter and an oscilloscope. 4. High Impedance Circuit 1. Make a simple voltage divider to attenuate signals by a factor of 2. 2. Use two equal resistors of about 200 k and measure their values with a digital ohmmeter. 3. Determine the attenuation of the divider by measuring the input and the output voltage (use the same instrument for both). 4. Make the following measurements: (a) with DC using a digital voltmeter, (b) with AC (a sinewave signal of about 100 Hz) using a digital voltmeter and an oscilloscope.

4 [Figure 5] Schematic diagram of circuit to solve given in the lab book Equipment List: ● Multimeter ● Power supply (set to 12V and 6V) ● Wires ● 3 resistors of different values ● Breadboard ● Multisim . Results: Ⅳ Voltage Resistor (Ω) Measured Voltage Internal Resistance (Ω) 0.3 V 1k 0.2997 V 1*10^6 20 V 1k 19.984 V 1.25*10^6 [Figure 4] Table of measured voltages and internal resistance of digital voltmeters Frequency Voltage Resistor (Ω) Measured Voltage Internal Resistance (Ω) 100 Hz 5 V 1k 3.355 V 0.02*10^6 [Figure 5] Table of measured voltages and internal resistance of a waveform generator

5 Voltage Measured Current Resistor (Ω) Internal Resistance (Ω) 1 V 0.6621 mA 1k 2959.45 5 V 3.3595 mA 1k 609.57 [Figure 6] Table of measured currents and internal resistance of a digital ammeter Output Voltage Resistor (Ω) Measured Voltage Internal Resistance (Ω) 5V 0 3.5269 0 5V 1k 3.355 0.02*10^6 [Figure 7] Table of measured voltages and internal resistance of a waveform generator with and without a load resistance Instrument for 10k R Measured Voltage Internal Resistance (Ω) DC → Digital Voltmeter 2.4952 V 5.2*10^6 AC → Digital Voltmeter 1.7459 V 0.8*10^6 Oscilloscope 5.4 V 0.135*10^6 [Figure 8] Table of attenuation with low impedance using two identical resistors that act as voltage dividers for different instruments. Instrument Used for 200k R Measured Voltage Internal Resistance (Ω) DC Digital Voltmeter 2.4756 V 20.29*10^6 AC Digital Voltmeter 1.5877 V 1.76*10^6 Oscilloscope 4.9 V 9.8*10^6 [Figure 9] Table of attenuation with high impedance using two identical resistors that act as voltage dividers for different instruments. R L Voltage Drop

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6 10k 7.8263 V [Figure 10] Table of the Measured Voltage across the Load Resistor . Questions and Discussion Ⅴ In this experiment, it has been proved that measurements provided by the digital multimeter or the oscilloscope are marginally off due to the internal resistance in the instruments. The internal resistance is really high as we have proved through the experiment to protect the instruments from overvoltage and to provide marginally close readings. In the first part of the experiment we used the multimeter as a voltmeter to provide the readings when connected to a DC voltage source with different voltages (0.3V, 20V). The result was high internal resistance in both situations and the voltage readings were slightly different. In 1.3 of the lab we have used the wave generator as the voltage source and we have come to realize that the internal resistance was also high. It can be derived from theory that there must be no influence from the measuring tools needed to calculate precise numbers on an electric circuit.As for part (2) of the lab we are comparing the impedance between the oscilloscope and the multimeter and based on the results the range of impedance for the oscilloscope is between 1 mega Ohm and 10 megaOhm. Due to the sinewave we had (V input = V measured *sqrt 2) to give the real voltage and based on that we have calculated the internal resistance for the Oscilloscope. As such, it can be derived that the resistance of the tool has to be infinite, or equivalent to the behavior of an open circuit to not change or throw off any values generated by the circuit. As resistance increases,current decreases as stated by I = V / R, so the resistance has to be a number high enough to make the voltage across the measurement tool 0. Our measurement partially supports this conclusion. The measurements that do not align with our assumption of high resistance can be chocked up to potential errors in our circuit construction, design, and errors within the generating of voltage and the internal workings of our circuit itself. . Conclusion Ⅵ As per experiment, we have come to conclude that the instruments have high impedance to act as an open circuit providing the most accurate readings. But there is a marginal difference and that is due to the fact that we can’t have a perfect reading unless we have an infinite internal resistance(making an ideal circuit).