Lesson RLC and Filters · Filters
Low-pass and high-pass filters
Filters pass some frequencies and reject others. A low-pass filter passes lows and blocks highs; a high-pass filter does the opposite. Inductors rise in opposition as frequency rises; capacitors fall. Putting L in series or C in shunt (and the reverse) builds these classic filters.
Why filters exist
Radios, TVs, audio crossovers, EMI filters, and signal boards must separate frequencies. Without filters, every station would pile on top of every other. Resonant circuits are one filter family; L and C frequency laws build the rest.
Low-pass: pass lows, reject highs
Series inductor + load: At low f, XL is small → most voltage reaches the load. As f rises, XL rises → more drop on L, less on the load. When XL ≫ Rload (rule of thumb around 10×), the load signal is nearly gone.
Shunt capacitor across the load: At low f, XC is high → little shunt away from the load. As f rises, XC falls → capacitor steals signal from the load. When XC ≈ one-tenth of Rload, little output remains.
L and C together sharpen the rejection curve; a peak can appear near resonance before the drop.
High-pass: reject lows, pass highs
Swap the roles:
- Series capacitor with the load: high XC at low f blocks; low XC at high f passes.
- Shunt inductor across the load: low XL at low f shorts the signal away; high XL at high f leaves the load alone.
Cutoff frequency (concept)
The cutoff is where the filter begins to reject strongly (often discussed around half-power / equal reactance points in teaching). You do not need a deep transfer-function course to use the idea: design so the reactance crosses the load resistance near the frequency you care about.
Broadband tuning note
Practical filters often include trimmer capacitors or inductors and switched ranges so one circuit covers a band of stations or channels. Variable C is common because it tunes over a wide range.
Field examples
- Ferrite and LC filters on VFD outputs / inputs
- Bypass caps killing high-frequency noise on DC rails (low-pass idea)
- Coupling caps blocking DC while passing AC signals (high-pass idea)
- Speaker crossovers (next lessons expand)
Numbers you should be able to work cold
Rule-of-thumb crossings with load R:
- Series L low-pass: strong rejection when XL ≈ 10×R
- Shunt C low-pass: strong shunting when XC ≈ R/10
- Series C high-pass: blocking when XC high (low f)
- Shunt L high-pass: shorting lows when XL low
Example: Rload=1 kΩ, want shunt-C low-pass strong at 10 kHz:
XC≈100 Ω → C=1/(2πf XC)≈0.16 µF order-of-magnitude design start (refine with specs).
Bypass vs coupling in one sentence
Bypass (shunt C) = low-pass noise to ground. Coupling (series C) = high-pass the signal, block DC.
EMI filter reading
When you open a drive filter and see L in the line and C to ground, you are looking at low-pass thinking in hardware.
Field case
Situation. A sensor cable next to a VFD picks up noise. A tech adds a small capacitor across the analog input (shunt C). Noise drops; slow process signals still read correctly.
What happened. Low-pass action: high-frequency PWM noise shunted; low-frequency process signal mostly passed.
Applied lesson. Match the capacitor so XC is low at noise frequencies but still high at the signal frequency — otherwise you filter out the measurement itself.
### 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
Low-pass and high-pass filters 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
Noise on signals; loss of desired high or low content
Where to look
Series L, shunt C (low-pass); series C, shunt L (high-pass)
Likely causes
- Wrong cutoff
- open/shorted filter part
- miswired topology
What to measure
- Output vs frequency if possible
- component values
- noise spectrum
What not to do
- Add huge shunt C that kills legitimate signal bandwidth
Checklist
- I explain low-pass vs high-pass goals
- I know series L and shunt C favor low-pass
- I know series C and shunt L favor high-pass
- I use XL↑ with f and XC↓ with f
- I can give a field example of each
- I respect cutoff vs signal bandwidth