Amplitude or Peak Value What is the amplitude of this signal? The peak to peak value of this signal? Peak to Peak Value For a sine wave the peak to peak value is simply: 2(peak value) Or : (+peak value) + (-peak value)
Root Mean Square (RMS Value) RMS value of a sine wave is: 0.707 x peak voltage
Heating Effect of an AC Waveform The RMS value is the value of AC voltage that you would need to apply to a circuit to achieve the equivalent heating effect obtained from a dc power source. Therefore if you supplied this heating element with 7.07 volts DC, to achieve the same effect with AC you would need to use 10 volts. Because RMS also = (dc value) x 1.414
Frequency and Periodic Time The frequency of a waveform is a measure of how many full cycles the waveform completes in 1 second. It can be calculated as: 1/T = Frequency (Hz) Where T = periodic time Given that the periodic time for the above waveform is 20 mS (milli-seconds) Calculate the frequency of the waveform above.
Phase Shift Consider the small circuit above. V1 is an AC waveform applied as an input. The oscilloscope measures the input and output waveforms (channels A & B) We can see that that the output is not only attenuated, it is also different in phase from the input.
Phase Shift Continued When an output and input are in phase it means that the signals rise and fall at exactly the same time. If they rise and fall at different times within the cycle we say that the output is ‘phase shifted’ with respect to the input. Phase shift only occurs in AC circuits. The output may be as much as 90 degrees leading (capacitive circuits) Or 90 degrees lagging (inductive circuits)
Equation of a sine wave Instantaneous Value = Max Value x Sin(2πt +/- φ) Where f = frequency φ = phase shift in radians t = time 2πf is often written as ω because there are 2π radians in one full cycle of a sine wave. The instantaneous and maximum values can either be voltage or current With this equation you can calculate or predict precisely what the voltage or current will be in a circuit that is supplied with an AC sine wave at any given point in time. To convert radians to degrees: 360/2 π x radians = answer in degrees To convert degrees into radians: (degrees/360) x 2 π = answer in radians
Try the following problems An alternating voltage is given by: V = 75sin(200πt – 0.25) volts Find: The amplitude The peak to peak value The periodic time The frequency The phase angle in degrees and minutes relative to 75 sin200t
Exam Question (P10) The current in an ac circuit at any time is given by: I = 60sin(50πt + 0.2) amperes Find: The peak value The periodic time The frequency The phase angle in degrees and minutes The value of the current when t = 0 seconds The value of the current when t = 0.008 seconds The time when the current first reaches 60A The time when the current is first at a maximum