1 Physics 241 Lab – Matt Leone Week 12: RLC Radios! [email protected] (email preferred), PAS 376, o. 520-621-6819 Office Hours: M & W 11:00-11:50, or by appointment. Consultation Room (PAS 372): F 12:00-12:50 http://bohr.physics.arizona.edu/~leone/phy241/phys241lab.html General Comments: • We will use the driven series RLC circuit and the process of mutual inductance to make radio receivers. • WARNING: ALWAYS CHECK THE VOLUME OF THE SPEAKER BEFORE INSERTED THE SPEAKER INTO YOUR EAR (i.e. move the speaker slowly toward the ear). • You should practice for your practical. • Be sure to practice problems for exam 3 after every meal. Lab 12 – Discussion. Reminder from lab 8 on how to measure C: In and RC circuit driven sinusoidally with angular frequency ωD, ! VC,amp="CZVsource,amp and ! VR,amp=RZVsource,amp, dividing these equations gives ! VC,ampVR,amp="CR, or after substitution and rearrangement, ! C =VR,amp"DRVC,amp. Therefore to measure a capacitor’s capacitance, set up and RC circuit and drive it sinusoidally. Measure ! "D, R, VR,amp, and VC,amp and use the above equation. Hint, it is often easiest to change the frequency so that ! VR,amp and VC,amp are the same. Be sure to use a middle ground configuration. How to measure L, very similar process: In and RL circuit driven sinusoidally with angular frequency ωD, ! VL,amp="LZVsource,amp and ! VR,amp=RZVsource,amp, dividing these equations gives ! VL,ampVR,amp="LR, or after substitution and rearrangement, ! L =RVL,amp"DVR,amp. Therefore to measure an inductor’s inductance, set up and RL circuit and drive it sinusoidally. Measure ! "D, R, VR,amp, and VL,amp and use the above equation. Hint, it is often easiest to change the frequency so that ! VR,amp and VL,amp are the same. Be sure to use a middle ground configuration.2 Resonance: In lab 11, you found that for an RLC circuit (linear & sinusoidally driven) that there is a frequency at which the current in the resistor is maximized (i.e. absorbing the most energy from the oscillating source). Specifically you should have found ! "resonance=1LC. Then you made the following plot to prove there was a resonant frequency: This is useful because an LRC circuit can be tuned to a specific resonant frequency by adjusting its C or L. If you lower the resistance of an RLC circuit and retake your measurements, the resonant frequency won’t change (since L and C don’t change). But you get a different plot: The smaller the resistance, the sharper this peak gets. This is useful because an LRC circuit with low resistance will be driven by the resonant frequency (have a large current) while ignoring other frequencies. A radio is an RLC circuit that responds only to a specific frequency. How could you make the peak as sharp as possible in an RLC circuit? Take the resistor out so that only the tiny resistance of metal wires is present.3 Modulating Waves: [Figure to right] Start with a sound wave that you would like to transmit into another (disconnected) RLC circuit. Unfortunately, this wave is alternating too slowly to induce a large voltage in the inductor of the other circuit. Remember the equation for mutual inductance, ! Vinducedin circuit 2= "dIcircuit 1dtM1 to 2, where M is a constant that describes how much the solenoids overlap. If the current doesn’t oscillate rapidly enough, then ! Vinducedin circuit 2 is small. “Gee, I wish this wave oscillated more quickly,” you might say. But then it wouldn’t be the sound wave you wanted to hear in the first place! [Figure to left] Next take a wave that oscillates quickly, radio or slightly sub-radio frequency for example. This isn’t the frequency you want to hear, but it does oscillate quickly enough to be create a large induced voltage, i.e. it oscillates quickly enough to be transmitted through the “transformer” via mutual inductance into the other circuit. [Figure to right] Combine the two waves by multiplying them together. This modulated wave has the properties of both waves: it carries information about the audio frequency component AND it oscillates quickly enough to generate a high induced voltage in the other circuit. In today’s lab, we would like to transmit a sound wave from one circuit with a “transmitting” solenoid into another “receiving” solenoid. We will use a capacitor in the second “receiving” circuit to make an RLC “receiving” circuit. By changing the capacitor of the “receiving” circuit, we can adjust its resonant frequency (see previous page). Therefore, we will be able to “tune” our “receiver” to a particular radio frequency.4 Now you would like to listen to your transmitted wave. But there is a huge problem. Whenever the wave it up, it pushes the speaker in one direction, and whenever it is down it pushes the speaker in the other direction (reversed current). The wave is oscillating up and down with the high radio frequency, much too fast for the speaker to respond to. It just sits there quivering. The trick is to add a diode to the output. This will allow only positive voltage to reach the speaker. The speaker now gets pushed out a maximum distance at the maximum amplitude of the pulse and relaxes at the minimum amplitude. This is the most crucial theory for understanding today’s lab. Possible O-scope Measurement Configurations:5 Useful Equations for RLC Circuit: Resistance-like quantities: ! Z = R2+ "L# "C( )2 ! "C=1#C ! "L=#L Time dependent behavior of components: ! VC(t) ="CZ# $ % & ' ( Vsource,ampsin)t( ) ! VL(t) = "#LZ$ % & ' ( ) Vsource,ampsin*t( ) ! Vdrive(t) = Vsource,ampcos"t +#( ) ! "= tan#1$L#$CR% & ' ( ) * . Relating resistor voltage to total circuit: ! Vsourceamplitude= IresistoramplitudeZ =VresistoramplitudeRZ ! Eenergy ofcapacitorE-field=12CV2 ! Eenergy ofinductorB-field=12LI2 ! Paverage dissipatedfrom inputby resistor=12IresistoramplitudeVresistoramplitude Note the ½ in the power loss of the resistor. This is a way to average the power loss since the current is oscillating and not constant (compare with P=IV for constant I and V).6 Lab 12 – Procedure – write on this sheet and turn it in with your write-up. 1. Here you will use a sound wave to modulate a radio frequency wave. a. Clean your ear-speaker with alcohol. b. Set your function generator to 3,600 Hz. c. Hook this output up to the speaker/diode connection of your
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