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E8A

SIGNALS AND EMISSIONS

Fourier analysis; RMS measurements; average RF power and peak envelope power (PEP); analog/digital conversion

E8A011 of 11

What technique shows that a square wave is made up of a sine wave and its odd harmonics?

Why Fourier analysis is the mathematical technique that decomposes any repetitive waveform into a sum of sine waves: a fundamental plus harmonics at integer multiples of that frequency. For an ideal square wave the result is the fundamental plus only the odd harmonics (3rd, 5th, 7th...), each with amplitude 1/n of the fundamental. That is why a square wave passed through a narrow filter comes out as a sine wave, and why digital signals with fast edges splatter energy across many harmonics.

Watch out Vector analysis deals with quantities having magnitude and direction, useful for phasors and fields but not for breaking a waveform into harmonic components; numerical and differential analysis are general math tools with no specific role here.

Fourier = frequency. Square wave = fundamental + odd harmonics only.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E8A022 of 11

Which of the following is a type of analog-to-digital conversion?

Why Analog-to-digital converters come in a handful of standard architectures: successive approximation (SAR), flash/parallel, sigma-delta, and dual-slope integrating. A SAR converter uses a comparator and an internal DAC to perform a binary search, testing the most significant bit first and working down, so an N-bit conversion takes N comparison steps. That trade of speed for simplicity makes it the most common general-purpose ADC design.

Watch out Level shifting is the tempting one, but it only moves an analog signal's DC offset so it fits a device's input range; it is a preparation step, not the conversion itself. Harmonic regeneration and phase reversal are not conversion methods at all.

ADC families to know: successive approximation, flash, sigma-delta. SAR = binary search, one bit per step.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E8A033 of 11

Which of the following describes a signal in the time domain?

Why The time domain view plots how a signal's instantaneous amplitude (voltage or current) varies as time advances, which is exactly what an oscilloscope shows with time on the horizontal axis and amplitude on the vertical axis. Fourier analysis is the mathematical bridge that converts that amplitude-versus-time record into the frequency domain, where amplitude is plotted against frequency instead, as a spectrum analyzer does.

Watch out Plotting frequency against time describes a spectrogram or waterfall display, not the basic time domain representation; a series of discrete impulses is just one particular waveform, not a general definition of the domain.

Time domain = scope: amplitude vs time. Frequency domain = analyzer: amplitude vs frequency.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E8A044 of 11

What is "dither" with respect to analog-to-digital converters?

Why An ADC has to round each sample to the nearest quantization step, and when the input is small or slowly varying that rounding error is correlated with the signal, producing harmonic distortion and "stair-step" artifacts rather than benign noise. Adding a tiny amount of random noise (typically on the order of one LSB) before conversion randomizes which step is chosen, so the error becomes uncorrelated broadband noise that the ear or a digital filter handles much better. Averaging many dithered samples can even recover detail smaller than one quantization step, effectively increasing resolution.

Watch out The choice about the converter being unable to settle describes instability or metastability in the comparator, not dither; the one about irregular step size describes differential nonlinearity, an ADC accuracy defect.

Dither = deliberate dirt: add a little noise on purpose so quantization error sounds like hiss, not distortion.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E8A055 of 11

What is the benefit of making voltage measurements with a true-RMS calculating meter?

Why RMS (root mean square) is the equivalent DC heating value of a waveform. Ordinary average-responding meters actually rectify and average the signal, then multiply by a fixed factor (about 1.11) that is only correct for a pure sine wave, so they misread square waves, pulses, SSB audio or distorted AC. A true-RMS meter squares the instantaneous samples, averages them, and takes the square root, so it reports the correct RMS value regardless of waveshape.

Watch out Converting to phasor form is tempting because phasors are drawn with RMS magnitudes, but a phasor also needs phase information that a single RMS reading does not supply, and phasors only apply to sinusoids anyway.

True RMS = true for any shape. Average-responding meters are only calibrated for sine waves.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E8A066 of 11

What is the approximate ratio of PEP-to-average power in an unprocessed single-sideband phone signal?

Why SSB voice is a varying-envelope emission: the RF envelope follows the speech waveform, so the power swings from nearly zero between syllables to full peak on vowel peaks. Averaged over normal speech, the peak envelope power runs roughly 2.5 times the average power for unprocessed audio. Speech processing (compression/clipping) raises the average toward the peak, lowering this ratio and putting more talk power on the air.

Watch out The 1-to-1 choice describes a constant-envelope signal such as key-down CW, FM, or an unmodulated carrier, where peak and average power are the same; 25 to 1 grossly overstates the peaky nature of ordinary speech.

Unprocessed SSB is about 2.5:1 PEP-to-average; add compression and it moves toward 1:1 like FM.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E8A077 of 11

What determines the PEP-to-average power ratio of an unprocessed single-sideband phone signal?

Why In SSB the RF envelope is a direct copy of the audio waveform, so the ratio between the highest instantaneous peak (PEP) and the long-term average power is set by the peak-to-average ratio of the talker's voice. Speech is very spiky, with brief loud syllables separated by quiet intervals, so an unprocessed SSB signal typically averages only a fraction of its PEP. That is why speech processing, which compresses the dynamic range, raises average power without raising PEP.

Watch out Carrier suppression is tempting, but a properly generated SSB signal has essentially no carrier to begin with, and any residual carrier does not control the voice envelope's peak-to-average behavior. Amplifier gain scales peak and average power together, leaving the ratio unchanged.

The envelope is your voice: peak-to-average comes from how you talk, and processing evens it out.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E8A088 of 11

Why are direct or flash conversion analog-to-digital converters used for a software defined radio?

Why A flash (direct conversion) ADC compares the input against a whole ladder of reference voltages at once, using 2^n - 1 comparators in parallel, so it produces a sample in a single clock cycle. That parallel architecture gives the highest sample rates of any ADC type, and by Nyquist you need a sample rate over twice the highest frequency you want to digitize. In a direct-sampling SDR that speed is what lets the converter digitize RF directly at the antenna instead of after several stages of downconversion.

Watch out Low power consumption is actually the opposite of a flash converter's weakness: all those parallel comparators running at once make it the most power-hungry ADC type, so the choice citing low power and drift is wrong, and that also rules out the all-of-these answer.

Flash = all comparators fire at once = fastest sampling. Speed is the whole point, and it costs power.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E8A099 of 11

How many different input levels can be encoded by an analog-to-digital converter with 8-bit resolution?

Why An n-bit ADC produces an n-bit binary code word, and the number of distinct codes is 2^n. With 8 bits that is 2^8 = 256 discrete levels, numbered 0 through 255. Gain in the input amplifier only scales the analog voltage range that gets mapped onto those levels; it does not create or remove codes.

Watch out The choice that says 8 confuses the bit count with the level count, and the choices involving amplifier gain confuse resolution (number of steps) with input span (volts per step).

Levels = 2^bits. 8 bits = 256, 10 bits = 1024, 12 bits = 4096.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E8A1010 of 11

What is the purpose of a low-pass filter used at the output of a digital-to-analog converter?

Why A DAC builds its output from discrete steps at the sample rate, so the waveform is really the desired signal plus copies (images) of it centered on multiples of the sampling frequency, along with the sharp-edged staircase harmonics. A low-pass reconstruction filter set just below the Nyquist frequency (half the sample rate) passes the wanted audio or baseband signal and strips off those higher-frequency sampling artifacts, smoothing the steps into a clean analog waveform.

Watch out The idea about lowering input bandwidth to increase resolution describes anti-alias filtering ahead of an analog-to-digital converter, and resolution is set by the number of bits, not by filtering; nothing in an analog output filter can sort out out-of-sequence digital codes.

DAC out = reconstruction filter: smooth the staircase, kill the images above Nyquist.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E8A1111 of 11

Which of the following is a measure of the quality of an analog-to-digital converter?

Why An analog-to-digital converter is judged by how faithfully its digital output reproduces the input waveform, so the standard figures of merit are distortion and noise numbers: total harmonic distortion, signal-to-noise ratio, SINAD, and effective number of bits. Quantization error and any nonlinearity in the converter's transfer curve create spurious products at harmonics of a pure input tone, and total harmonic distortion sums the power in those harmonics relative to the fundamental. A lower THD figure means the converter's steps track the analog input more linearly.

Watch out Peak envelope power is a transmitter output measurement, reciprocal mixing describes receiver local-oscillator phase noise mixing strong adjacent signals into the passband, and power factor applies to AC circuits with reactive loads. None of them says anything about digitizing accuracy.

ADC quality = how clean the digitized tone is: THD, SNR, SINAD, ENOB. The other three choices belong to transmitters, receivers and AC power.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

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