1 / 26

AC Sources

AC Circuits. AC Sources. Often, electrical signals look like sines or cosines AC power, Radio/TV signals, Audio Sine and cosine look nearly identical They are related by a phase shift Cosine wave is advanced by /2 (90 degrees) compared to sine We will always treat source as sine wave.

alexalexander
Télécharger la présentation

AC Sources

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. AC Circuits AC Sources • Often, electrical signals look like sines or cosines • AC power, Radio/TV signals, Audio • Sine and cosine look nearly identical • They are related by a phase shift • Cosine wave is advanced by /2 (90 degrees) compared to sine • We will always treat source as sine wave Frequency, period, angular frequency related • This symbol denotes an arbitrary AC source

  2. RMS Voltage • There are two ways to describe the amplitude • Maximum voltage Vmax is an overstatement • Average voltage is zero • Root-mean-square (RMS) voltage is probably the best way • Plot (V)2, find average value, take square root • We can do something similar with current House current (US) is at f = 60 Hz and Vrms = 120 V Vmax = 170 V

  3. Amplitude, Frequency, and Phase Shift We will describe any sort of wave in terms of three quantities: • The amplitudeAis how big it gets • To determine it graphically, measure the peak of the wave • The frequency is how many times it repeats per second • To determine it graphically, measure the period T • Frequency f = 1/T and angular frequency  = 2f • The phase shift is how much it is shifted earlier/latercompared to basic sine wave • Let t0 be when it crosses the origin while rising • The phase shift ist0(radians)

  4. Our Goal • Feed AC source through an arbitrary circuit • Resistors, capacitors, inductors, or combinations of them • We will always assume the incoming wave has zero phase shift ? • We want to find current as a function of time • For these components, can show angular frequency  is the same • We still need to find amplitude Imax and phase shift  for current • Also want instantaneous power P and average powerP consumed • Generally, maximum current will be proportional to maximum voltage • Call the ratio the impedance, Z

  5. Degrees vs. Radians • All my calculations will be done in radians • Degrees are very commonly used as well • But the formulas look different • Probably best to set your calculator on radians and leave it there

  6. Resistors R = 1.4 k • Can find the current from Ohm’s Law • The current is in phase with the voltage VoltageCurrent Impedance vector: • A vector showing relationship between voltage and current • Length, R is the ratio • Direction is to the right,representing the phase shift of zero 1.4 k

  7. Power in Resistors R = 1.4 k • We want to know • Instantaneous power • Average Power

  8. Capacitors C= 2.0 F • Charge of capacitor is proportional to voltage • Current is derivative of charge • Current leads voltage by /2 • We say there is a –/2 phase shift: Impedance vector: • Define the impedance* for a capacitor as: • Make a vector out of it • Length XC • Pointing down for  = –½ 1.3 k *We will ignore the term “reactance”

  9. Power in Capacitors C= 2.0 F We want to know • Instantaneous Power • Average Power • Power flows into and out of capacitor • No net power is consumed by capacitor Only resistors contribute to the average power P consumed

  10. Capacitors and Resistors Combined • Capacitors and resistors both limit the current – they both have impedance • Resistors: same impedance at all frequencies • Capacitors: more impedance at low frequencies

  11. Inductors • Voltage is proportional to change in current • Integrate this equation L= 4.0 H • Current lags voltage by /2 • We say there is a +/2 phase shift Impedance vector: • Define the impedance for an inductor as: • Make a vector out of it • Length XL • Pointing up for  = +½ 1.5 k

  12. Impedance Table

  13. Adding Impedances Graphically • Suppose we have 2+ items in series • Resistors, Capacitors, Inductors • We can get the total impedance and phase shift by adding the impedances graphically 1.4 k 1.4 k 60 Hz170 V The impedance and phase shift of two components in series can be found by adding the vector sum of the two separate impedances • Each impedance is represented by a 1.4 k vector pointing to the right • The length of the combination is 2.8 k • The total impedance is denoted Z • The total arrow is to the right, so phase shift is 0 1.4 k 1.4 k Z = 2.8 k

  14. Adding Impedances Graphically (2) We can add different types of components as well • The resistor is 1.4 k to the right • The capacitor is 1.3 k down • The total is 1.9 k down-right 1.4 k 2.0 F 1.4 k  60 Hz170 V 1.3 k 1.9 k • The current is then the voltage over the impedance • The phase can be found from the diagram

  15. RLC AC Circuits L C R • For this rather general circuit, find • Impedance • Phase shift • Current • Average power f Vmax • Find the angular frequency  • Find the impedance of the capacitor and inductor • Find the total impedance Z • Find the phase shift  • Find the current • Find the average power consumed XC XL R  Z

  16. Power in RLC AC Circuits 6. Find the average power consumed L C R Only resistors contribute to the average power P consumed f Vmax • Most power is delivered to resistor when Imax is maximized • When Impedance is minimized • The “resistor” might well represent some useful device • Like a speaker for a stereo

  17. Frequency and RLC Circuits Low pass filter High pass filter L C • Impedance tends to be dominated bywhichever component has largest impedance • At low frequencies, that’s the capacitor • At high frequencies, that’s the inductor • At intermediate, that’s the resistor • If the circuit includes a capacitor, it blocks low frequencies • If the circuit includes an inductor, it blocks high frequencies R f Vmax

  18. A Sample Circuit 1000 F 0.1 mH 10  f Vmax = 5 V • What frequencies make it through the capacitor? • What frequencies make it through the inductor? • These inequalities compatible if:

  19. A Sample Circuit (2) Power Phase Shift 1000 F 0.1 mH 10  f Vmax = 5 V • At low frequencies, blocked by capacitor • At high frequencies, blocked by inductor • At intermediate, power goes to resistor • Frequencies from about 16 Hz–16 kHz get through • Close to perfect for an audio system What happens if L > R2C ?

  20. The Narrow Band Filter 2.1 pF 1.54 H 2.0  f Vmax = 1 mV • At resonant frequency, capacitor and inductor cancel • Perfect for picking up WFDD – radio station in North Carolina

  21. Types of RLC Circuits High Pass Filter • Lets frequencies through if  > 1/RC Low Pass Filter • Lets frequencies through if  < R/L RLC circuit • If R2 > L/C, it is a combination of Low and High pass filter • If R2 < L/C it only lets a narrowrange of frequencies through • The smaller R2C/L, the narrower it is

  22. Comments on Phase Shifts • The phase shift represents how the timing of the current compares to the timing of the voltage • When it is positive, the current lags the voltage • It rises/falls/peaks later • When it is negative, the current leads the voltage • It rises/falls/peaks earlier

  23. Transformers N1 turns N2 turns • Let two inductors share the same volume • You can (should) give them an iron core too • The EMF’s can be calculated from the flux • The magnetic flux must be changing • Only works for AC

  24. What Transformers are Good For N1 =500 N2 =5000 V2 = ? V1 = 120 V • Their main purpose in life is to change the voltage A 120 V AC source is fed into a transformer, with N1 = 500 turns on the primary coil, and N2 = 5000 turns on the secondary. What is the voltage out of the transformer? • Voltage can increases, does that mean power increases? • When you increase voltage, you decrease current • In an ideal transformer, the product is conserved Realistic transformers are 80-95% efficient

  25. Transformers and Power Transmission Generator500 V Transmission Line 100 kV House Current 120 V • Why transmit at 10 kV, instead of 500 V or 120 V? • Transmission wires are long – they have a lot of resistance • By using a step up transformer, we increase the voltageand decrease the current • Power lost for a resistor is: • You then step it down so youdon’t kill the customer

  26. Power Supplies 20 Vripply DC 20 Vsmooth DC 21 V AC To devices 120 V AC • What if we need a different voltage for a specific device? • Use a transformer • What if we want direct current? • A diode is a device that only lets current through one direction • What if we don’t like the ripples • Capacitors store charge from cycle to cycle

More Related