Lesson RLC and Filters · Field and integration
RLC integrated
Close the RLC course by locking the contrasts: series vs parallel resonance, lead vs lag from net reactance, and filter families from low-pass to crossover. If you can choose the right model for a symptom — max current vs min current, pass vs notch — you are ready for three-phase power topics next.
Master contrast table
| Topic | Remember |
|---|---|
| Series RLC Z | √[R²+(XL−XC)²] |
| Series resonance | XL=XC → min Z, max I, high EL & EC |
| Parallel RLC | Cancel IL and IC; IT from remainder |
| Parallel resonance | Max Z, min line I, circulating tank current |
| Low-pass | Series L / shunt C |
| High-pass | Series C / shunt L |
| Bandpass | Pass a window |
| Notch | Reject a window |
| T / pi | Steeper multi-section filtering |
Formula set to keep
XL = 2πfL XC = 1/(2πfC) fr = 1/(2π√(LC)) PF = P/VA (sign from lead/lag)
Decision tree for symptoms
High line current + high voltages on L and C? Think series resonance or near-cancellation in series.
Low line current but hot L/C? Think parallel tank circulating current.
Noise at high frequency on a DC rail? Think missing or wrong low-pass bypass.
Need to remove one interfering tone? Think notch.
Need woofer/tweeter split or steep EMI roll-off? Think crossover / T / pi.
Link backward and forward
You arrived from capacitive and inductive AC courses with XC and XL. You leave toward three-phase power, where motors, transformers, and capacitor banks meet on wye and delta systems — still the same VAR story, now on three lines.
Integration drill (mental)
- Name whether the circuit is series-dominant or parallel-dominant.
- Say whether net XL or XC wins.
- Predict lead or lag.
- Say whether fr is a friend (filter) or foe (accidental).
- List two meters you will use (clamp, DMM, PF meter, analyzer).
If you can do that aloud on a rooftop, the course worked.
Numbers you should be able to work cold
Drill set:
- Series Z with XL=80, XC=20, R=15 → Z=√(15²+60²)=61.8 Ω
- fr for L=0.05 H, C=20 µF → ≈159 Hz
- Parallel: IL=6 A, IC=6 A, IR=2 A → IT=2 A (resonant cancel)
- Low-pass vs high-pass part placement in one sketch from memory
Oral exam for a helper
Ask them to explain why series resonance can show EL≫ET, and why parallel resonance can show hot parts with quiet line clamps. Correct answers mean the course stuck.
Forward glance
Three-phase systems host the same L and C on three wires. PF banks become three-phase banks; resonance becomes a system study. Keep this vocabulary.
Field case
Situation. Final checkout after teaching a helper: a parallel PF bank, a VFD line filter (pi), and a noisy analog input. Helper correctly says: bank → parallel VAR cancel; filter → low-pass multi-section; analog → add shunt C carefully for low-pass noise control without killing bandwidth.
What happened. Concepts transferred without mixing topologies.
Applied lesson. Integration is language plus measurement, not memorizing every schematic variant.
### Teaching pause — say this out loud
Before you leave this lesson, explain the main idea to an imaginary first-month helper in under one minute. If you need the book open to do it, reread How it works once more. Field diagnosis only helps after the concept is yours.
Also sketch the key diagram from memory (triangle, wye/delta, filter shape, or charge curve — whichever this lesson used). Labels beat artistic skill.
### Why this lesson matters on Monday morning
RLC integrated is not trivia. You will meet it when a meter reading looks “impossible,” when a replacement part is almost right, or when a helper asks why the book uses √3 or lead/lag. Master the model here so the next call is pattern recognition, not panic.
Common Monday uses: verify a nameplate against clamps, explain a PF or capacitor change to a customer, or catch a miswired series/parallel or wye/delta assumption before energizing.
In the field
Symptom
Mixed power and signal complaints on one site
Where to look
Separate power RLC from signal filters first
Likely causes
- Multiple unrelated issues blamed on “bad power”
What to measure
- PF/VARs on power
- spectrum on signals
- thermal on filters
What not to do
- Apply one capacitor “fix” to every symptom
Checklist
- I can explain series vs parallel resonance in one minute
- I can sketch low-pass vs high-pass parts placement
- I can state what bandpass and notch each do
- I recognize T/pi as sharper filters
- I use fr = 1/(2π√(LC)) safely
- I know when to call for harmonic engineering help
- I am ready to apply VAR ideas on three-phase systems