Oscillators Questions and Answers

Answer: D

A load capacitance in series or parallel shifts the operating frequency slightly within the narrow window between the two resonances, which is how a crystal oscillator is trimmed to exactness or modulated in a phase-locked loop. Overdriving, overtone operation and selection are all separate matters. The pulling range is small precisely because the quality factor is high, so a crystal that must be tuned over any real range is the wrong component for the job.

Answer: A

A parallel-resonant crystal reaches its marked frequency only when the circuit presents the specified capacitance across it, commonly twelve or twenty picofarads, so the load capacitors are part of the frequency-determining network rather than incidental. It will oscillate with other loads but at a different frequency, drive level is set elsewhere, and overtone selection needs a tuned circuit. A component specified together with its circuit conditions has to be used with those conditions, and this is the case where it matters most.

Answer: B

The crystal is a mechanical resonator, and too much power drives it beyond its elastic limit, ageing its frequency and eventually cracking it. Too little drive is a starting problem rather than a rating, and drive does not set frequency directly. That a purely electrical component has a mechanical failure mode is easy to overlook, and it is why a series resistor limiting drive is a standard part of a crystal oscillator rather than an optional refinement.

Answer: C

Parts per million multiply the nominal frequency directly:

\[ \begin{aligned} 10 \times 10^{6} \times 50 \times 10^{-6} \\ &= 500 \ \mathrm{Hz} \end{aligned} \]

giving 500 Hz. Expressing stability in parts per million rather than in hertz lets one figure describe a crystal at any frequency, which is why data sheets use it - but converting to hertz is what tells you whether it is good enough for the application.

Answer: D

Holding the crystal at a constant temperature above the highest ambient removes the principal source of drift, taking a good crystal from tens of parts per million to a few parts in a hundred million. Starting, waveform purity and pulling range are unaffected. It costs power, warm-up time and money, which is why the technique appears in frequency standards and base stations rather than in consumer equipment - a clear case of a specification bought at a price that only some applications will pay.

Answer: A

A relaxation oscillator charges a capacitor until a threshold is crossed, then discharges it, so its waveform is a ramp or an exponential rather than a sine and its output is naturally a square wave. A resonant circuit is what the sinusoidal family uses, an active device is essential, and the frequency depends directly on the timing components. The two families differ in whether energy oscillates between two storage elements or is repeatedly dumped, and every other difference follows from that.

Answer: B

Each half is held off while a capacitor discharges through a resistor towards the supply, and the time constant of that pair sets each half period. Supply voltage cancels out of the timing to first order, which is a real advantage, and the collector resistors set the amplitude and the edge speed rather than the period. A timing that depends on a resistor and a capacitor and not on the supply is what makes the circuit usable without regulation.

Answer: C

The capacitor charges towards the supply and the switching threshold is a junction drop, so a higher supply charges faster but has further to go, and the two effects largely cancel. No current source is involved, and saturation voltage is a small correction. That a timing circuit can be made insensitive to its supply by arranging the threshold to scale with it is a recurring idea, and it is why this simple circuit outlasted more elaborate alternatives.

Answer: D

The capacitor charges through both resistors and discharges through only the second, so the high time depends on their sum and the low time on the second alone, both scaled by the capacitance. Supply and load do not enter the timing, the comparators' thresholds are fixed fractions of the supply and so cancel, and reset and control are auxiliary functions. That the mark and space are set by different resistances is why a plain 555 astable cannot reach a symmetrical square wave without a diode across one resistor.

Answer: A

Applying the standard astable relation:

\[ \begin{aligned} f &= \frac{1.44}{(R_{1}+2R_{2})C} \\ &= \frac{1.44}{21000 \times 10^{-7}} \end{aligned} \]

which gives about 686 Hz. The factor of two on the second resistor is what accounts for it appearing in both the charge and the discharge interval, and omitting it is the usual error in this calculation.