or
Amateur Extra Class (2016-2020)
Subelement E8
SIGNALS AND EMISSIONS
Section E8A
AC waveforms: sine, square, sawtooth and irregular waveforms; AC measurements; average and PEP of RF signals; Fourier analysis; Analog to digital conversion: Digital to Analog conversion
What is the name of the process that shows that a square wave is made up of a sine wave plus all of its odd harmonics?
Fourier analysis
• Vector analysis
• Numerical analysis
• Differential analysis

Fourier analysis allows for a time domain signal (Anything we can measure as a function of time) to be transformed into the frequency domain. Letting anyone determine what frequency components exist in the signal.

Hint: Squares have Four(ier) sides

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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
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 does a Fourier analysis show to be made up of sine waves of a given fundamental frequency plus all of its harmonics?
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 "dither" with respect to analog to digital converters?
• An abnormal condition where the converter cannot settle on a value to represent the signal
A small amount of noise added to the input signal to allow more precise representation of a signal over time
• An error caused by irregular quantization step size
• A method of decimation by randomly skipping samples

When an analog signal is sampled by an analog to digital converter the digital value is not infinitely precise, but is truncated to a value which can be represented by the digital output. This quantization error prevents us from hearing signals less than 1 least significant bit in peak-to-peak amplitude.

If we add a small amount of uncorrelated noise to the analog signal before it is sampled, this combined signal can cause bit transitions in the output which are statistically proportional to the weak signal. This noise is called "dither" because it causes the least significant bit to fluctuate randomly. By averaging over time the dither can be eliminated and the weak signal recovered.

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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 wave meter
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?
2.5 to 1
• 25 to 1
• 1 to 1
• 100 to 1

Recall that PEP means the peak envelope power.

The peak envelope of a sinusoidal waveform is its peak-to-peak value, which is twice its peak value. After performing the integration, the average value of a sinusoidal waveform is $2 \times \frac{V_p}{\pi}$ $≈$ $0.637 \times V_p$. The ratio of the peak envelope of a sinusoidal waveform to its average value is therefore $\frac{2 \times V_p}{\left(\frac{2 \times V_p}{\pi}\right)} = \pi$, or $3.14$, which is closer to "2.5 to 1" than the other answers.

If the root mean square (RMS) value of the same waveform is considered instead of its average, the ratio of the peak envelope of a sinusoidal waveform to its RMS value is $\frac{2 \times V_p}{V_p \times \frac{\sqrt{2}}{2}}$ $=$ $2 \times \sqrt{2}$ $≈$ $2.8$, which is even closer to "2.5 to 1" than the other answers.

A true SSB signal is not a simple sinusoid, but made of many superimposed sinusoids, making this an approximation.

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What determines the PEP-to-average power ratio of a single-sideband phone signal?
• The frequency of the modulating signal
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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Why would a direct or flash conversion analog-to-digital converter be useful for a software defined radio?
• Very low power consumption decreases frequency drift
• Immunity to out of sequence coding reduces spurious responses
Very high speed allows digitizing high frequencies
• All of these choices are correct

A direct conversion or flash ADC is optimized for speed at expense of almost every other parameter. The ADC requires a comparator for every possible output code. This limits the number of output bits, since each additional bit will double the complexity of the device.

Since the output can be determined essentially as fast as a compare and a priority encoder can run; flash ADC's can be produced capable of gigahertz sampling rates. High sample rates are required for a software defined radio, since the sample rate of the ADC is often a limiting factor in the bandwidth of the radio.

** Test Tip = Remember that 'The Flash' runs at a 'Very High Speed'

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How many levels can an analog-to-digital converter with 8 bit resolution encode?
• 8
• 8 multiplied by the gain of the input amplifier
• 256 divided by the gain of the input amplifier
256

In binary encoding, the number of levels that can be encoded by a certain number of bits is 2 to the power of the number of bits.

2 bits, $2^2$ = 4 levels

6 bits, $2^6$ = $2 \times 2 \times 2 \times 2 \times 2 \times 2$ = 64 levels

For 8 bits, $2^8=256$. So an 8-bit encoded value can be one of 256 numerical values (typically 0-255). The answer is 256.

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What is the purpose of a low pass filter used in conjunction with a digital-to-analog converter?
• Lower the input bandwidth to increase the effective resolution
• Improve accuracy by removing out of sequence codes from the input
Remove harmonics from the output caused by the discrete analog levels generated
• All of these choices are correct

There are often times when signals are passed through a low-pass filter before being converted to a digital signal. The purpose of a low-pass filter being used in conjunction with a Digital-To-Analog (D2A) converter is to remove unwanted harmonics from the output caused by the discrete analog levels generated.

-KE0IPR

Hint: Filters generally limit or remove. K0LLO

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What type of information can be conveyed using digital waveforms?
• Human speech
• Video signals
• Data
All of these choices are correct

Digital waveforms convey information that has been transcribed into a digital signal. Speech, Video, and other Data are often converted to a digital format so therefore can be transmitted over a digital waveform.

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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
Digital signals can be regenerated multiple times without error
• All of these choices are correct

Digital signals have a fixed number of states. For example, binary signals can only be 0 or 1 (off or on). Because of this, digital signals can be stored, copied, and manipulated without degrading the signal. Every copy of a digital signal is identical to the original.

In contrast, analog signals are continuously variable. Whenever analog signals are stored, copied or manipulated some noise or distortion is always introduced, which degrades the signal. The difference may be very small, but any copy of an analog signal will be different from the original.

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Which of these methods is commonly used to convert analog signals to digital signals?
Sequential sampling
• Harmonic regeneration
• Level shifting
• Phase reversal

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

-xyzhangj

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).

-KE0IPR

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