Basic Electrical & Electronics Engineering — Signal Generator, NEC licence examination syllabus (Nepal Engineering Council).
Crystal Oscillators: a slice of quartz that keeps better time than anything else
Your watch, your phone's clock, every computer — all timed by a vibrating rock.
An LC oscillator drifts. Its inductor's value changes with temperature, its capacitor ages, and its Q is maybe 100 — so its frequency wanders by hundreds of parts per million. A quartz crystal has a Q in the tens of thousands and a frequency set by the physical dimensions of a mechanical resonator, not by electrical components. That's a different league of stability, and it's why nothing else is used for timekeeping.
The piezoelectric effect
Quartz is PIEZOELECTRIC:
Apply mechanical stress → a voltage appears
Apply a voltage → it physically deforms
Drive it with AC and the slice vibrates mechanically. At its
natural mechanical resonance the vibration is huge, and the
electrical impedance changes dramatically — which is what
the circuit senses.
Frequency depends on the physical THICKNESS of the slice:
f ∝ 1/t (thinner slice = higher frequency)
The equivalent circuit
Electrically the crystal behaves as:
L — series inductance (represents the vibrating mass)
C_s — series capacitance (mechanical stiffness), very small
R — series resistance (mechanical losses), very small
C_p — parallel capacitance (the metal electrodes + holder)
This gives TWO resonances:
Series resonance: f_s = 1/(2π√(L·C_s))
minimum impedance
Parallel resonance: f_p = 1/(2π√(L·C_eq))
where C_eq = C_s·C_p/(C_s + C_p)
maximum impedance
Because C_s << C_p, the two frequencies sit very close
together — typically 0.1% apart. The crystal is used in the
narrow band between them.
Why the stability is so good
🎯 Crystal vs LC, by the numbers
Q factorLC tank: 50–300. Crystal: 10 000 – 1 000 000. Q measures how sharply the resonator rejects nearby frequencies, so a crystal is thousands of times more selective.
StabilityLC: 10⁻³ to 10⁻⁴ (±100 ppm or worse). Crystal: 10⁻⁶ to 10⁻⁸ (±1 ppm or better). A temperature-compensated crystal reaches 10⁻⁹.
WhyFrequency is set by mechanical dimensions of quartz, which barely change with temperature or age — not by an inductor's permeability and a capacitor's dielectric, which drift constantly.
The costA crystal is fixed frequency — you cannot tune it more than a few hundred ppm. If you need to sweep frequency, you must use LC.
The crystal's high Q is the entire story. In the Barkhausen picture, Q determines how narrow the band is where the phase condition holds — and a Q of 100 000 means only an extremely precise frequency can satisfy it. Any drift is immediately fought by the sharply changing phase. That's mechanical precision translated into electrical precision.
Worked numerical 1 — the two resonances
A crystal has L = 3 H, C_s = 0.05 pF, C_p = 8 pF, R = 2 kΩ. Find f_s, f_p, the Q factor, and the separation between the two frequencies.
Series resonance:
f_s = 1/(2π√(L·C_s))
= 1/(2π√(3 × 0.05 × 10⁻¹²))
= 1/(2π√(1.5 × 10⁻¹³))
= 1/(2π × 3.873 × 10⁻⁷)
= 1/(2.433 × 10⁻⁶)
= 411.1 kHz
Parallel resonance:
C_eq = C_s·C_p/(C_s + C_p)
= (0.05 × 8)/(0.05 + 8) = 0.4/8.05
= 0.04969 pF (just slightly less than C_s)
f_p = 1/(2π√(3 × 0.04969 × 10⁻¹²))
= 1/(2π√(1.4907 × 10⁻¹³))
= 412.4 kHz
Separation:
Δf = 412.4 − 411.1 = 1.3 kHz
As a fraction: 1.3/411 = 0.32% — extremely close
Q factor:
Q = ω_s L/R = (2π × 411 100 × 3)/2000
= 7 749 000/2000
= 3875
Even this modest example has Q ≈ 3900, over ten times a
good LC tank.
Worked numerical 2 — frequency drift comparison
Compare the drift of a 10 MHz LC oscillator (stability 100 ppm) with a 10 MHz crystal (stability 1 ppm), over 24 hours.
LC oscillator, 100 ppm:
Δf = 10 × 10⁶ × 100 × 10⁻⁶ = 1000 Hz
Over 24 h, a clock built on it drifts:
error = 100 × 10⁻⁶ × 86 400 s = 8.64 s/day
Crystal, 1 ppm:
Δf = 10 × 10⁶ × 1 × 10⁻⁶ = 10 Hz
Clock error = 1 × 10⁻⁶ × 86 400 = 0.0864 s/day
= 86 ms/day ≈ 2.6 s/month
A typical quartz wristwatch is specified at about 15 s/month,
which corresponds to roughly 6 ppm — consistent with a small,
uncompensated crystal.
Worked numerical 3 — thickness and frequency
A quartz slice 0.5 mm thick resonates at 3 MHz. What thickness is needed for 10 MHz, and what problem does that create?
Since f ∝ 1/t:
f₁t₁ = f₂t₂
3 MHz × 0.5 mm = 10 MHz × t₂
t₂ = 1.5/10 = 0.15 mm
The slice must be three times thinner — only 150 µm, about
twice the thickness of paper.
The problem: above roughly 20–30 MHz the slice becomes so
thin it is mechanically fragile and breaks during handling.
The solution: OVERTONE operation. Drive the crystal at its
3rd, 5th or 7th harmonic, so a physically robust 20 MHz
crystal produces 100 MHz on its 5th overtone. This is how
crystals reach hundreds of MHz.
💡 Exam angle: usually 4–5 marks. The core marks are: the piezoelectric effect (both directions), the equivalent circuit with its two resonances, and the very high Q as the reason for stability. Quote figures if you can — Q of 10⁴–10⁶ and stability of 1 ppm versus 100 ppm for LC make the answer concrete. Mention the trade-off (fixed frequency, cannot be tuned) if asked for disadvantages.
Syllabus points
Crystal oscillator operation & stability
Create a free account to tick topics off, take notes as you read, watch the video lessons and get a day-by-day study plan built around your exam date.