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Subelement E8
SIGNALS AND EMISSIONS
Section E8A
AC waveforms: sine, square, sawtooth and irregular waveforms; AC measurements; average and PEP of RF signals; pulse and digital signal waveforms
What type of wave is made up of a sine wave plus all of its odd harmonics?
  • Correct Answer
    A square wave
  • A sine wave
  • A cosine wave
  • A tangent wave

A sine wave plus all its odd harmonics can be mathematically represented by

sin(θ) + sin(3θ)/3 + sin(5θ)/5 + ...

but this is equivalent (differing only by amplitude, and k = a constant multiple of pi) to

(4/pi) X [sin(kθ) + sin(3kθ)/3 + sin(5kθ)/5 + ...]

which, according to An Introduction to Harmonic Analysis (by Yitzhak Katznelson, Dover Publications, 1976), is the Fourier Expansion of a square wave, making answer (A) the correct one.

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What type of wave has a rise time significantly faster than its fall time (or vice versa)?
  • A cosine wave
  • A square wave
  • Correct Answer
    A sawtooth wave
  • A sine wave

A cosine wave, square wave, and sine wave all have symmetric rise-and-fall patterns because they are all sums of their sinusoid harmonics, according to Hugh L. Montgomery and Robert C. Vaughan (Multiplicative Number Theory, Cambridge, 2007, p. 536-537).

But a sawtooth wave is an asymmetric triangular wave, because its rise time differs from its fall time, making it the correct one.

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What type of wave is made up of sine waves of a given fundamental frequency plus all its harmonics?
  • Correct Answer
    A sawtooth wave
  • A square wave
  • A sine wave
  • A cosine wave

A square wave consists of the fundamental and odd harmonics because it is symmetric.

A sine and cosine wave consist of only the fundamental frequency, so there are no harmonics.

A sawtooth wave consists of the fundamental, odd, and even harmonics. Only asymmetric waves contain even harmonics and this is the only answer which is an asymmetric wave.

*Hint - Sawtooth wave = all harmonics (Sawz-All)

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What is equivalent to the root-mean-square value of an AC voltage?
  • The AC voltage found by taking the square of the average value of the peak AC voltage
  • The DC voltage causing the same amount of heating in a given resistor as the corresponding peak AC voltage
  • Correct Answer
    The DC voltage causing the same amount of heating in a resistor as the corresponding RMS AC voltage
  • The AC voltage found by taking the square root of the average AC value

According to Fundamentals of Electric Circuits (McGraw-Hill, 2012, p. 467), the RMS (root-mean-square) of a sinusoidal AC voltage is essentially the square root of the arithmetic mean (averages) of the squares of the original values, which, after performing the actual calculation of

Vrms = lim (T->∞) SQRT(integral(0 to T)(V(t)^2)dt / T)

yields Vrms = Vp/SQRT(2),

which is a useful quantity because it is identical to the value of DC voltage that is applied across a resistor to result in the same amount of output power that would heat the resistor, resulting in answer (C).

Because Vrms = Vp/SQRT(2), and the average peak AC value is Vp, the square of the average peak AC value is Vp^2, which does not equal Vp/SQRT(2), eliminating answer (A).

Also, the amount of heat in a given resistor as the corresponding peak AC voltage is

Pp = (Vp^2)/R, but the Prms = (Vrms^2)/R =

((Vp/SQRT(2))^2)/R = (Vp^2)/2R =

((Vp^2)/R)/2 = Pp/2,

or only half the heat given off by using the peak value, which eliminates answer (B).

Finally, the average AC value, because of its symmetric (positive and negative) nature, is zero, and the square root of zero is zero, so answer (D) is also incorrect.

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What would be the most accurate way of measuring the RMS voltage of a complex waveform?
  • By using a grid dip meter
  • By measuring the voltage with a D'Arsonval meter
  • By using an absorption wavemeter
  • Correct Answer
    By measuring the heating effect in a known resistor

The term “RMS” stands for “Root-Mean-Squared”. Most books define this as the “amount of AC power that produces the same heating effect as an equivalent DC power”.

By Ohm's Law (\(V=IR\)), Voltage, Intensity (or Current) and Resistance are related. To know voltage, it is sufficient to know current and resistance. By having a complex waveform, there will not be any easy formula to convert AC voltage to RMS Voltage. By measuring the heating effect in a known resistor, we would find the current passing through it, with which we could find the RMS voltage applied to the circuit.

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What is the approximate ratio of PEP-to-average power in a typical single-sideband phone signal?
  • Correct Answer
    2.5 to 1
  • 25 to 1
  • 1 to 1
  • 100 to 1
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What determines the PEP-to-average power ratio of a single-sideband phone signal?
  • The frequency of the modulating signal
  • Correct Answer
    The characteristics of the modulating signal
  • The degree of carrier suppression
  • The amplifier gain

PEP is Peak Envelope Power. it's the highest power passed to the antenna from the transmitter.

PEP-to-average power ratio is determined by the waveform shape made by the voice, thus the characteristics of the modulating signal

Hint: average speech [KQ4AEY]

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What is the period of a wave?
  • Correct Answer
    The time required to complete one cycle
  • The number of degrees in one cycle
  • The number of zero crossings in one cycle
  • The amplitude of the wave
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What type of waveform is produced by human speech?
  • Sinusoidal
  • Logarithmic
  • Correct Answer
    Irregular
  • Trapezoidal
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Which of the following is a distinguishing characteristic of a pulse waveform?
  • Regular sinusoidal oscillations
  • Correct Answer
    Narrow bursts of energy separated by periods of no signal
  • A series of tones that vary between two frequencies
  • A signal that contains three or more discrete tones
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What is one use for a pulse modulated signal?
  • Linear amplification
  • PSK31 data transmission
  • Multiphase power transmission
  • Correct Answer
    Digital data transmission

A pulse width modulated signal can be used to encode data for transmission whereby the width of the pulses can be encoded to a specific value.

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What type of information can be conveyed using digital waveforms?
  • Human speech
  • Video signals
  • Data
  • Correct Answer
    All of these choices are correct
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What is an advantage of using digital signals instead of analog signals to convey the same information?
  • Less complex circuitry is required for digital signal generation and detection
  • Digital signals always occupy a narrower bandwidth
  • Correct Answer
    Digital signals can be regenerated multiple times without error
  • All of these choices are correct
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Which of these methods is commonly used to convert analog signals to digital signals?
  • Correct Answer
    Sequential sampling
  • Harmonic regeneration
  • Level shifting
  • Phase reversal

Analog-->Digital, which is to "sample" the signal.

Sampling a signal actually involves recording an amplitude value at a specific point in time and storing the value off as a time:value in a lookup table. This long standing technology extends over many technologies include Compact Disks, MP3 files, etc... The higher the sampling rate, the higher the resolution. With today's resolution, I'm amazed as how some people can still tell the difference between music recorded on vinyl (analog) and CDs (digital).

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What would the waveform of a stream of digital data bits look like on a conventional oscilloscope?
  • A series of sine waves with evenly spaced gaps
  • Correct Answer
    A series of pulses with varying patterns
  • A running display of alpha-numeric characters
  • None of the above; this type of signal cannot be seen on a conventional oscilloscope

The waveform of a stream of digital data bits would look like a series of pulses with varying patterns on a conventional oscilloscope. (E8A15)

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