Frequency, Time Period, and Wavelength Frequency of an AC signal is a simple matter of how many cycles the signal goes through in a second. (Cycles Per Second, or Hertz). An AC signal will start from zero volts, increase to some maximum positive voltage, decrease back to zero, increase to some maximum negative voltage, and return to zero. This is one cycle. If the signal is 60 Hz, it is making 60 cycles per second. Each cycle, obviously, takes 1/60 th of a second, or 0.0166666 Seconds. This is the Time Period of a 60 Hz signal. The time it takes for the signal to make one complete cycle. If this electricity is traveling at the speed of light (186,000 miles per second, or 300,000 km per second) the distance it would travel in one Time Period is the Wavelength. This is true whether we are talking about current flow through a wire, or a magnetic field moving through space. At 186,000 miles per hour for 0.016666 seconds, we have a Wavelength of about 3100 miles for a 60 Hz signal. It would make sense that the higher the frequency, the shorter the time period, and the shorter the wavelength. As the frequency of our cell phones has increased, the antenna has gotten shorter. At 2.4 GHz systems, the antenna is a stub built inside the case of the phone, and is hardly noticeable at all. AC characteristics If we again consider our AC signal going from zero, to some peak positive level, back to zero, to some peak negative level, returning to zero, we should consider how much power we actually have available. If we take an incandescent lamp, working at 120 V DC, how much voltage, AC, do we have to apply to get the lamp to light to the same brightness as 120 V DC? If we were to draw a graph of our power available from AC, we would see a signal starting from zero, increasing to some peak maximum, decreasing to file://///winnt/departments/slot%20department/tr...nce/basic%20electricity/ac%20and%20frequency.htm (1 of 7) [5/16/2003 3:07:59 PM]
zero, increasing to the peak again, and returning to zero. (Polarity doesn t matter.) Most of the time our signal is far below the peak value. How much effective power do we have? As long as we are talking about a sine-wave signal, like our line power, we find that the effective power is Peak x 0.707, (or Peak / 1.414). The Peak value then can be calculated as Effective x 1.414, (or Effective / 0.707). It therefore takes 170 Volts (Peak) to get the brightness of the lamp on AC to the same brightness as 120 VDC. This Effective value is sometimes called the RMS (Root Means Square), or effective, value. Don t confuse this with the Average. Average is 0.636 of the Peak value. Keeping in mind that our signal goes both positive to this Peak value, then negative to this Peak value, our signal actually goes +170, then 170, for a total of 340 Volts (Peak to Peak), to get the same effective power we would from 120 V DC. We rate the line voltage in the effective (RMS) value. We can rate Voltage, Current, Power, or anything else that follows a sine wave, by these Peak-to-Peak, Peak, RMS, or Average, values. As long as we are talking about a sine wave, the formulas are the same. (Not all signals we will see are sine waves.) Peak x 2 = Peak-to-Peak Peak-to-Peak / 2 = Peak Peak x 0.707 = RMS or Peak / 1.414 = RMS Peak x 0.636 = Average or Peak / 1.57 = Average RMS x 1.414 = Peak or RMS / 0.707 = Peak Frequency spectrum of electromagnetic radiation file://///winnt/departments/slot%20department/tr...nce/basic%20electricity/ac%20and%20frequency.htm (2 of 7) [5/16/2003 3:07:59 PM]
(Shorter wavelength, higher frequency) (Longer wavelength, lower frequency) The range of available frequencies for electromagnetic radiation is, in deed, quite broad. Below 500,000 Hz, we have Long Wave radio, used for maritime radio. Around 1,000,000 Hz (1 MHz, or 1 Mega-Hertz), we have AM radio. Between 2 MHz and 88 MHz we have Short Wave radio. Around 100 MHz we have FM radio. Between 100 MHz and 300 MHz, we have television. Between 300 MHz and 600 MHz, we call it Micro Wave. Most of today s cell phones and satellite communications come in to play from 600 MHz to 3,000 MHz (or 3 GHz, Giga-Hertz). Above 3 GHz few people venture except the military. Even military systems top out around 150 GHz, but that is not the end of the story. Above the hundreds of GHz range is the area we perceive as heat. Above heat, we get into Infrared. This is still only electromagnetic radiation. Above Infrared there is a very narrow spectrum of electromagnetic radiation that the rods and cones inside our eyes perceive as visible light. At the low end we see red, then orange, yellow, green, blue, and violet. Above violet is a wide region of Ultraviolet. Above this range we have little more than solar noise. This is a broad range made up of radiation attributed to subatomic particles (X-Rays). The wavelengths correspond to dimensions smaller than atoms. Above this we reach the limits of our knowledge, and in our ignorance we call electromagnetic radiation beyond this Cosmic Radiation. For the curious, the question comes up, is there a maximum frequency? If an electron must travel from atom to atom to create an electromagnetic field, then the maximum frequency would be the wavelength equal to the distance file://///winnt/departments/slot%20department/tr...nce/basic%20electricity/ac%20and%20frequency.htm (3 of 7) [5/16/2003 3:07:59 PM]
between two atoms. Since our atoms vary in size from about 0.50 Angstroms to just over 2.0 Angstroms. Given this, our maximum frequency would be somewhere around 1.0 to 5.0 with 18 zeros after it. If we try to consider a higher frequency, can we get so high a frequency that the electron is not making a complete orbit around the atom? Can we extend this to the idea that we can get an electron to oscillate so fast it is actually not moving at all? For you Trekies, I often get the question about Sub-Space Transmitters. Where is the frequency of Sub-Space Transmitters? In the imagination of the authors, only. Many aspects of science we find in movies and television exists only to support the plot of the program. Such concepts are more Science Fantasy, than Science Fiction. Knowledge of these truths only makes the movies a little less entertaining. Sorry, Captain Kirk. Scotty will never be able to Beam you up. file://///winnt/departments/slot%20department/tr...nce/basic%20electricity/ac%20and%20frequency.htm (4 of 7) [5/16/2003 3:07:59 PM]
1. What is the formula for Ohm s Law to find Current? 2. What is the formula for Ohm s Law to find Voltage? 3. What is the formula for Ohm s Law to find Resistance? file://///winnt/departments/slot%20department/tr...nce/basic%20electricity/ac%20and%20frequency.htm (5 of 7) [5/16/2003 3:07:59 PM]
4. What do we multiply together to find Watts? 5. What is the Peak value for an RMS voltage of 120 V? 6. What is the RMS value for a Peak current of 1 Amp? 7. What is the effective power of your Stereo that is rated at 100 Watts, Peak-to-Peak? 8. What do radio waves, microwaves, heat, light, and cosmic waves have in common? 9. What is the approximate wavelength of an AM radio station? 10. What is the approximate wavelength of an FM radio station? 1. What is the formula for Ohm s Law to find Current? I = E/R 2. What is the formula for Ohm s Law to find Voltage? E = I x R 3. What is the formula for Ohm s Law to find Resistance? R = E/I 4. What do we multiply together to find Watts? Volts and Amps 5. What is the Peak value for an RMS voltage of 120 V? About 170 V 6. What is the RMS value for a Peak current of 1 Amp? About 0.707 Amps file://///winnt/departments/slot%20department/tr...nce/basic%20electricity/ac%20and%20frequency.htm (6 of 7) [5/16/2003 3:07:59 PM]
7. What is the effective power of your Stereo that is rated at 100 Watts, Peakto-Peak? 100 / 2 = 50 Watts, Peak. 50 x.707 = about 35 Watts. 8. What do radio waves, microwaves, heat, light, and cosmic waves have in common? They are all electromagnetic radiation. 9. What is the approximate wavelength of an AM radio station? 1 MHz = 982 ft. 10. What is the approximate wavelength of an FM radio station? 100 MHz = 9.82 ft, 3.27 yards or about 117 inches file://///winnt/departments/slot%20department/tr...nce/basic%20electricity/ac%20and%20frequency.htm (7 of 7) [5/16/2003 3:07:59 PM]