Electrical Measurements. OBJECTIES: This experiment covers electrical measurements, including use of the volt-ohmmeter and oscilloscope. Concepts including Ohm's Law, Kirchoff's Current and oltage Laws, the rules for combining resistors, and operational amplifiers are reviewed. A/C circuit waveforms are also measured. Signal Generator olt- Ohmmeter (OM) Oscilloscope esistors Op-amp Bread Board Oscilloscope Signal Generator DC Power Source Assorted esistors olt-ohmmeter (OM) Bread Board Operation Amplifier
. INTODUCTION: Three quantities are studied in this experiment; voltage, current and impedance. oltage or electro-motive force (emf) is the potential for work. It is a relative value. oltage is the difference in potential between two points. Current is electrical flow through a single point. Two devices are used in this lab to make measurements: the oscilloscope and volt-ohm meter (OM) or multimeter. Chapter 9 discusses both of these in detail. In performing this lab, however, it is important to remember that the OM should be treated as a number of different devices. The ohmmeter, ammeter, DC voltmeter and AC voltmeter all use different circuits which means each will have its own error and uncertainty. Impedance is the resistance to flow. Impedance can be supplied by resistors, capacitors or inductors. For this lab, only resistors are used. The quantities covered so far are related by Ohm s law (). E = I () Where: E is the potential in volts (), I is the current in amperes (A), is the resistance in ohms () Note: When combining resistors, the resulting values can be found using two equations. For resistors combined in parallel, the equivalent resistance is the inverse of the sum of the inverses as shown in (). For resistors connected in series, or cascaded, the equivalence is the sum as shown in (3). eq = eq n i i = = AC signals are measured in this lab using an oscilloscope. The properties that identify the signal are shape, frequency, and amplitude. Using the oscilloscope to view the signal amplitude vs. time, the all these can be measured. With the scanning frequency properly set, the shape of the waveform can be displayed. The Y-axis of the screen corresponds to the amplitude in volts, allowing it to be measured. Measuring the distance between identical points in two consecutive cycles gives the period, T, of the waveform in seconds per cycle. This gives the frequency by changing to cycles per second. When giving the amplitude of a signal, it is important be specific. In the case of a sinusoidal wave (4), the amplitude most easily measured via oscilloscope is peak-to-peak or. n i= i t sin f t t) = sin ( Where: is the time-varying voltage, o is the voltage amplitude, Ω is the angular frequency in radians per second, f is the frequency in cycles per second, φ is the phase angle, and t is the independent time variable. Amplitude can also be indicated by oot Mean Square (MS). Calculated using (5), this is an indication of the usable energy available from an AC signal. where T is the period. MS = T T ( t) dt MS (6) In the case of a sin wave as in (4), this reduces to (6), which is the value normally given by multimeters. () (3) (4) (5)
Operational Amplifiers (OP-AMP) The basic purpose of an electronic device is to increase the size of a signal. Besides voltage, the input signal parameter to be increased may also be current or power. A linear amplifier not only increases the signal s level but also produces an output signal that is a faithful reproduction of the input. The op-amp is a device that lends itself to the construction of very good linear amplifiers, as well as many nonlinear circuits. The schematic used in this lab is presented in the following figure: i o Figure Schematics of the noninverting operational amplifier. The circuit is called a noninverting amplifier because its output is always the same polarity as its input signal. In addition, notice that the input signal is connected directly to the op-amp s noninverting input. The closed-loop voltage gain for the noninverting amplifier is G (7) The output voltage is then G i (8) i (9) and the output voltage will always be greater than the input voltage. Also, since the input signal is applied to the opamp s noninverting input, the output voltage is always in phase with the input for AC signals. 3. POCEDUE:. The lab instructor will set the function generator to produce different signals, one at a time. Use one of the oscilloscopes to find the shape, period and amplitude of the signal. Use the scaling knobs to fill as much of the screen as possible with one full wavelength. emember that the ½ least count uncertainty depends on the current scale settings. ecord your results in Table.. Use the signal generator, oscilloscope, and digital multimeter to generate and measure the parameters in Table. AC current will be simulated using a sinusoidal signal. An offset voltage in some cases will be also applied. First, you will have to use the oscilloscope functions to display and measure peak-to-peak voltage pp, rms voltage rms for the AC current and for the DC current the average voltage avg. For the same signal, you will have to measure the rms voltage rms using the multimeter and record the values in Table. For the offset case, you will have to decoupling the AC current from the DC current when you measure the AC parameters. Second, knowing the input voltage as peak-to-peak value calculate the MS value. 3. Design and test an electrical circuit. 3
Green (+5) To source White (-5) LM 458 Op-Amp ed (+5) To source red black red Ground (black) To source output voltage Figure Schematic of a noninverting op-amp circuit. Wire color code: White (-5 ) Green (+5 ) ed (+5 ) Black (ground) The op-amp electric circuit experiment should be conducted as follows: a) Assemble potentiometer set-up shown above b) Adjust potentiometer to give an output voltage in the range of +5 m to +6 m. ecord this value in the Table. c) Assemble noninverting op-amp set-up as shown above using the potentiometer s output voltage as the op-amp s input voltage. Using the color code identify the resistors and use the combination that will give you a gain of. d) Measure the op-amp s output voltage using a multimeter and record this value in the Table. e) Disconnect power source and use the resistors combination that will give you a gain of 5 f) Connect power source, measure the op-amp s output voltage using a multimeter and record this value in the Table. g) Adjust the potentiometer to give an output voltage in the range of + m to + m. ecord this value in the Table. h) epeat steps c) through f) 4
Table Output voltages for potentiometer and operation amplifier. output voltage [m] Gain Op-amp s output voltage [m] Gain 5 Op-amp s output voltage [m] Measured Calculated Measured Calculated Table Characteristics of the signals Type Amplitude (p-p) [] Period [sec] Frequency [Hz] Type Amplitude(p-p) [] Period [sec] Frequency [Hz] Figure 3 LM458 op-amp connection diagram 5
Table 3 oltage measurements Freq [Hz] Signal generator DC AC Ampl (p-p) [] Offset [] Oscill Mult Oscill Mult avg [] rms [] pp [] rms [] rms [] Calculated rms value rms [] 4. EPOT AND ANALYSIS EQUIEMENTS: 4. Theory. Explain the workings of the cathode-ray oscilloscope.. 3. 4. Explain how Equations () and (3) can be determined using Kirchoff s oltage and Current Laws. Begin with Ohm s Law and show step-by-step derivation. What is MS voltage? How does this compare to peak-to-peak voltage? Explain how an op-amp works. 4. esults and Analysis. List the waveforms measured, including signal type, peak-to-peak voltage amplitude, period, and frequency. Use sketches or drawings if necessary to describe the shapes.. 3. If there are any differences in the voltage measurements, between the values measured using the oscilloscope versus the input values from the signal generator and the values measured with the multimeter, try to explain why are these differences and what are the possible reasons. If we select a voltage of 4 m as input for the op-amp and a gain factor of 5 what would be the output voltage knowing that the power source for the op-amp is 5? 5. SUPPLEMENTAY MATEIAL: The values of resistors used in this lab need to be identified with esistors Color Code. The on-line esistors Color Code calculator is available at http://webhome.idirect.com/~jadams/electronics/resist/resist_calc.htm. For your own reference you may use the following guide obtained from http://webhome.idirect.com/~jadams/electronics/resistor_codes.htm 6
esistor Color Code Guide esistor Color Code Chart st. & nd Color Band Digit it epresents Multiplier BLACK X BOWN X To determine the value of a given resistor look for the gold or silver tolerance band and rotate the resistor as in the photo above.(tolerance band to the right). Look at the st color band and determine its color. This maybe difficult on small or oddly colored resistors. Now look at the chart and match the "st & nd color band" color to the "Digit it represents". Write this number down. Now look at the nd color band and match that color to the same chart. Write this number next to the st Digit. The Last color band is the number you will multiply the result by. Match the 3rd color band with the chart under multiplier. This is the number you will multiply the other numbers by. Write it next to the other numbers with a multiplication sign before it. ED X OANGE 3 X, or K YELLOW 4 X, or K GEEN 5 X, or K BLUE 6 X,, or M IOLET 7 Silver is divide by GAY 8 Gold is divide by Tolerances Example : x,. To pull it all together now, simply multiply the first numbers (st number in the tens column and nd in the ones column) by the Multiplier. WHITE 9 Gold= 5% Silver=% None=% Example: First color is red which is Second color is black which is third color is yellow which is, Tolerance is silver which is % Therefore the equation is: x, =, Ohms Last updated: August, 7