Lab 0.3 — LCR Capacitor/Resistor Measurement
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Goal
Learn to use the FNIRSI LC1020E LCR meter and, more importantly, learn why a component’s measured value depends on the frequency you measure it at. You will measure the same resistors you read with the Fluke — now with an AC bridge — and measure ceramic vs. electrolytic capacitors across the meter’s four test frequencies, watching capacitance and ESR shift. This is the first place the course’s central theme appears: a real component is not its ideal symbol. Understanding ESR, dissipation factor, and frequency dependence is exactly what separates a working analog front-end (clean supplies, well-behaved filters, stable references) from a noisy one — and it is the physical foundation under every filter and decoupling decision in the firmware labs to come.
Recommended reading
- Lyons Ch. 1 — signals/systems framing; the impedance-vs-frequency idea introduced here is the practitioner’s entry point to it. → Lyons
- O-S&S Ch. 1 — signals and systems basics; a light read for the notion that a capacitor’s impedance \(Z=1/(j\omega C)\) is frequency-dependent, which is why an LCR meter must state its test frequency. → O-S&S
- The FNIRSI LC1020E manual: test-frequency selection, the R/C/L/ESR/Q/D/θ readouts, and (critically) the discharge-first warning for capacitors.
- PEI Ch. 3 — capacitors and inductors: real-world behavior, ESR, and dielectric types — the theory behind what the LCR meter is showing you.
- Course 1 Week 9 (complex analysis) underlies the complex-impedance and phase-angle \(\theta\) readings you’ll take here. → Course 1 Week 9
Equipment & parts
- FNIRSI LC1020E LCR meter (with its test leads / SMD tweezers as applicable).
- Fluke 117 DMM (for the resistor cross-check and to confirm caps are discharged).
- Resistors from Lab 0.2: 100 Ω, 1 kΩ, 10 kΩ.
- Capacitors from the kit: a small ceramic (e.g. 100 nF / 0.1 µF) and a couple of larger ceramics (e.g. 1 µF, 10 nF), plus electrolytics (e.g. 10 µF and 100 µF, rated ≥ 16 V).
- A resistor (~1 kΩ) or short jumper used only to discharge electrolytics before measuring.
Safety & don’t-break-it
- Discharge every electrolytic before you measure or handle it. A charged electrolytic can hold a voltage from a previous circuit; the LCR meter’s AC drive assumes a de-energized part, and a charged cap can corrupt the reading or stress the meter. Short its two leads through a ~1 kΩ resistor (not a bare wire — a bare short is hard on the cap) for a second, then confirm ≈ 0 V with the Fluke on DC volts. For the small caps in this kit the stored energy is negligible, but make it a universal habit now, because Module 1’s supplies and later filter caps will hold real charge.
- Observe electrolytic polarity in circuits. Electrolytics are polarized — the shorter lead / the stripe side is the negative terminal. Reversed or over-voltage electrolytics can heat, bulge, and vent. The LCR meter’s low-voltage AC test is non-destructive regardless of orientation, but ingrain the polarity habit here so you never reverse one on a powered rail later.
- Never measure L/C/R/ESR on a powered or in-circuit part. Like ohms and continuity, the LCR meter sources its own signal and assumes an isolated, de-energized component. Measure parts off the board.
- Ceramics are non-polarized and rugged; the only real hazard in this lab is a charged electrolytic, so the discharge reflex is the whole safety story.
Background
An LCR meter applies a small AC test signal at a chosen frequency \(f\) and measures the component’s complex impedance \(Z\), from which it derives R, L, or C plus the parasitics. This is fundamentally different from the Fluke’s capacitance mode (which times an RC charge) — and it’s why the LCR meter makes you pick a frequency.
Ideal reactances. For a capacitor and inductor,
\[Z_C = \frac{1}{j\omega C}, \qquad Z_L = j\omega L, \qquad \omega = 2\pi f.\]
The magnitude of a capacitor’s impedance, \(|Z_C| = 1/(2\pi f C)\), falls with frequency — so the meter needs enough signal to measure it. A large electrolytic (\(\sim100\ \mu\)F) has a tiny reactance at 100 kHz and is best measured at 100 Hz or 1 kHz; a small ceramic (\(\sim\)nF) has a huge reactance at low frequency and reads best at 10 kHz or 100 kHz. That is why the LC1020E offers 100 Hz / 1 kHz / 10 kHz / 100 kHz.
What the readouts mean.
- R — resistance (the real part of \(Z\) for a resistor).
- C / L — the capacitance or inductance the meter fits to the measured reactance.
- ESR — equivalent series resistance: the small real resistance in series with an ideal capacitor (lead/plate/electrolyte losses). Modeled as \(Z = \text{ESR} + \frac{1}{j\omega C}\). ESR is large and frequency-dependent for electrolytics, tiny for ceramics — it is what makes a decoupling cap “good” or “bad.”
- D — dissipation factor, the ratio of lost to stored energy per cycle: \(D = \tan\delta = \omega\, C\cdot\text{ESR}\) for a capacitor. Lower is better.
- Q — quality factor, \(Q = 1/D\). High Q = low loss.
- θ — the phase angle of \(Z\). An ideal capacitor is \(-90°\); ESR pulls it toward \(0°\), and the departure from \(-90°\) is exactly \(\delta\) (so \(D=\tan\delta\)).
Why measured C drifts with frequency. A real capacitor is not a pure \(C\): dielectric absorption, ESR, and lead inductance make the fitted value depend on \(f\). Class-2 ceramics (X7R/Y5V) and electrolytics show the largest drift; C0G/NP0 ceramics are nearly flat. Observing this drift is the point of the lab.
Procedure
Part A — Cross-check resistors against the Fluke.
- Power on the LC1020E, select R mode, and set the test frequency to 1 kHz.
- Measure 100 Ω, 1 kΩ, 10 kΩ. Compare each to the value you recorded with the Fluke in Lab 0.2 — they should agree within tolerance. (For a pure resistor, frequency barely matters, so you’ll see little change across test frequencies — a useful contrast with the caps.)
Part B — Ceramic capacitor across frequency.
- Select C mode. Take the 100 nF ceramic. Because it’s non-polarized, orientation doesn’t matter. Measure and record C, ESR, D (or Q), θ at each frequency in turn: 100 Hz → 1 kHz → 10 kHz → 100 kHz.
- Note how C stays relatively flat (a small ceramic is well-behaved) while ESR and the readable digits are best at the higher frequencies where \(|Z_C|\) is small enough to measure cleanly. Repeat for a second ceramic (1 µF or 10 nF).
Part C — Electrolytic capacitor across frequency.
- Discharge the 10 µF electrolytic (1 kΩ across its leads for a second), confirm ≈ 0 V on the Fluke, then connect it to the LCR meter observing polarity where the meter marks it (many meters don’t require polarity for the low-voltage test, but keep the habit).
- In C mode, record C, ESR, D/Q, θ at 100 Hz, 1 kHz, 10 kHz, 100 kHz. Watch the electrolytic’s ESR fall then behave nonideally, and its fitted C drop noticeably at high frequency — the opposite of the well-behaved ceramic. Repeat for the 100 µF electrolytic (best measured at 100 Hz / 1 kHz).
Part D — Fluke vs. LCR on one cap.
- Measure the 100 nF ceramic with the Fluke’s capacitance function and compare it to the LC1020E’s 1 kHz reading. Note that the Fluke gives one number with no frequency context, while the LCR meter shows you the frequency dependence explicitly.
Deliverable & expected results
A bench note (docs/lab-0-3.md) with: the resistor cross-check, and a small table of C/ESR vs. frequency for one ceramic and one electrolytic. Fill Predicted from the marked/nominal value; Measured stays “…” until you’re on the bench.
| Component | Quantity | Predicted (nominal) | Measured @100 Hz | Measured @1 kHz | Measured @10 kHz | Measured @100 kHz |
|---|---|---|---|---|---|---|
| 100 nF ceramic | C | 100 nF (±10–20%) | … | … | … | … |
| 100 nF ceramic | ESR | low (< 1 Ω, small) | … | … | … | … |
| 10 µF electrolytic | C | 10 µF (±20%) | … | … | … | … |
| 10 µF electrolytic | ESR | moderate (≈ ohms) | … | … | … | … |
| 100 µF electrolytic | C | 100 µF (±20%) | … | … | … | … |
Also record for a couple of caps: Q or D and θ at 1 kHz (predict \(\theta \approx -90°\) for a good ceramic, further from \(-90°\) for the electrolytic).
Analysis & reconciliation
For the resistors, the LCR and Fluke should agree within the parts’ ±5% tolerance — any residual difference is measurement method (AC bridge vs. DC ohms) and lead resistance. For the capacitors, reconcile two things by hand. First, confirm the reactance magnitude at your chosen frequency, \(|Z_C| = 1/(2\pi f C)\) — e.g. a 100 nF cap at 1 kHz is \(\approx 1.6\text{ k}\Omega\), at 100 kHz only \(\approx 16\ \Omega\) — which explains why small caps read cleaner at high frequency and large caps at low frequency. Second, check the loss relationship \(D=\tan\delta = \omega C\cdot\text{ESR}\) against the meter’s D and ESR readings: they should be self-consistent. The expected story is that the ceramic’s C is nearly flat and its ESR/D small, while the electrolytic’s C sags and ESR rises as frequency climbs — the physical reason electrolytics are poor high-frequency decouplers and why real designs pair a bulk electrolytic with a small ceramic. If a cap reads wildly off, verify it was fully discharged and that the leads make solid contact.
Going further
- Measure an inductor from the kit (if present) in L mode and watch Q rise with frequency — the inductor dual of the capacitor’s behavior.
- Put a small ceramic and an electrolytic in parallel and measure the combination — a preview of the bulk-plus-bypass decoupling network you’ll build for the STM32 supply in later modules.
- Log C and ESR vs. frequency for one electrolytic and plot the curves; you’ll recognize this ESR-vs-frequency shape again when you characterize the RC filters in Module 1 and the anti-alias filter in Module 4.