AC Magnitude and Pha
Objectives:
Today's experiment provides practical experience with the meaning of magnitude and pha in a linear circuits and the u of phasor algebra to predict the respon of a linear system to a sinusoidal input. Using the digital oscilloscopes, we can better understand the true implications of amplitude and pha.
Pre Lab:
∙ Read and understand Hambley Sections 5.1 through 5.4 ∙ For v(t) = 160 Cos (180πt+ 60) determine: ∙ 1. V max
∙ 2. The pha angle θ.
korres∙ 3. The angular frequency ω. ∙ 4. V rms
∙ 5. The phasor voltage V
Part A: RC Circuit Measurements
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Procedure:
1. Set the output impedance of the function generator to Hi-Z mode.
2. Using any method, t the waveform generator for 500mV pk-pk using a 250 Hz sine wave.
3. Measure the 1k Ω resistor using the Fluke 45 as an Ohmmeter. Measure the 1μF capacitor using the
universal bridge on the instructor’s table. Enter the values on the data sheet.
4. Construct the RC circuit illustrated in Figure 1. U the BNC to “micrograbber” cables to make
component connections,(remember to check that the amplification factor for CH1 and CH2 are 1x). When using the probes, u common n precautions to avoid damaging the nsitive contacts and clips.
Figure 1. The first positive peak for v 1 occurs before the first positive peak of v 2 so v 1 leads v 2. The
difference in time determines the pha difference between v 1 and v 2: ︒-=-3602
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1x T
t t ϑ. You can also look at the ti me difference between zero crossings if it’s hard to tell exactly where the peaks of the sine waves occur.
Figure 2: The RC Circuit
新东方考研词汇5. The display itlf has a natural coarness, which can be reduced by lecting the Average
function. Try to u as few samples as possible to avoid long delays while moving from one display to another. Set both channels to the same Volts/Division tting. Averaging is a way to pull a repetitive signal out of the background noi. It works better than a bandwidth limit or brightness control becau the bandwidth is not reduced. The simplest averaging is smoothing (number of averages = 1). The oscilloscope acquires the signal every 5 ns. The smoothing function us two acquisitions to display one signal. The Average function (number of averages >1) requires a stable trigger. The trigger is what tells the scope when to display the signal. It is constantly acquiring the signal, but doesn’t let you e it until the signal meets some criteria you t using the trigger controls.
6. Which channel appears to display the greater peak magnitude? U the measure function to
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determine the Voltage pk-pk amplitudes for both channels, and record in the data sheet.
7. AC Phasor analysis can determine the Complex Gain as a function of radian frequency.
U measured values of your resistor and capacitor components to determine theoretical gain. Measure the frequency in Hz using your oscilloscope and calculate the radian frequency. Record the frequency, radian frequency, and theoretical gain value on your data sheet. Show all calculations in your lab report.
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RC
j C j R C j Gain ωωω+=+==
11/1/112V V
dreadnought8. Calculate the ratio of the CH1 and CH2 pk-pk measurements to determine the measured gain and
record on your data sheet.
NOTE: If the displayed wave is extremely jumpy, the problem is generally faulty leads or an
ungrounded probe. If you cannot remedy the problem, ask for assistance.
9. We can also measure the pha. Position the time cursors on corresponding zero crossings (or peaks)
of the CH-1 and CH-2 waveforms. Determine the time difference ∆t between the waves. Indicate which channel arrives at the reference point first--this channel is said to "lead". Record the values on the data sheet.
10. The measure function displays the wave periods. Record the period on the data sheet.
11. The pha shift, θ, is related to the time shift, Δt, that you obrve on the oscilloscope . T is the
remonstrate1
Using the voltage divider rule, )(
12L j R L
j V V ωω+=. Dividing through both sides by V1 yields the
complex gain for the circuit: L
j R L
j V V Gain ωω+==12. This gain is sometimes called the “transfer
function” since if we know the input voltage Phas or V1, we can determine the output voltage magnitude and pha at any frequency. Try changing the frequency of the function generator signal, V1. What happens to the amplitude of the output waveform V2 when you decrea the frequency? When you increa it?
6. 7. 8. 9.
Data Sheet
Part A: RC Circuit Measurements初学者怎么学习化妆
Nominal 1kΩ resistor value____________ Nominal 1μF capacitor value____________ Which channel has the great peak magnitude? CH-1 CH-2 (Circle One)
CH-1 ___________________ CH-2 ____________________much
f ______________ ω ______________
Theoretical Gain ____________________ Measured Gain ____________________
Theoretical Pha ____________________
∆t ______________________ Which channel leads? __________
T________________________ Measured Pha ____________________
Part B: RL Circuit Measurements
Nominal 470Ω resistor value____________ Nominal 1 mH inductor value__________ Which channel has the great peak magnitude? CH-1 CH-2 (Circle One)
CH-1 ___________________ CH-2 ____________________
f __________ ω ______________
Theoretical Gain ____________________ Measured Gain ____________________
Theoretical Pha ____________________
∆t ______________________ Which channel leads? __________
T________________________ Measured Pha ____________________
Your Name_____________________________ Lab Instructor___________________ Partner Name___________________________ Date___________________________
