Math Bridge: Read Motor Current Without Aliasing

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Math BridgeActuatorsStruggle-friendly runway

How can a 20 kHz motor ripple pretend to be 400 Hz?

One thread from current and a sense resistor to ADC resolution and aliasing.

Max, the actuators guideMax guides
The one targetSeparate current resolution from sample timing.
The chapter case0.18, 0.60, 1.80 A; 20 kHz; 1.2 kHz.
What it buys youDetect stalls without trusting a false wobble.

See the relationship before changing it

The figure reads from left to right. The blue card is motor current. The middle card applies this page's rule. The green card is sense-amplifier output. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only motor current, so the numeric fixture does not switch without explanation.

Motor current changes sense-amplifier output An input card leads through the rule sense output = current x 0.1 ohm x gain 10 to the sense-amplifier output result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Larger motor current makes more sensed voltage until headroom clips.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 0.6 A.

  2. 2

    Name the relationship. sense output = current x 0.1 ohm x gain 10

  3. 3

    Substitute with units. 0.60 x 0.1 x 10 = 0.60 V

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change motor current

Try Predict the direction of sense output = current x 0.1 ohm x gain 10. Test another motor current, then compare sense-amplifier output.

0.6 A
Chapter baseline
Sense-amplifier output

Observe Larger motor current makes more sensed voltage until headroom clips. Reset motor current to 0.6 and compare sense-amplifier output.

Explain Larger motor current makes more sensed voltage until headroom clips.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only motor current moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only motor current. It is not a field prediction.

1. Current becomes a voltage

A small resistor develops V=IR. An amplifier multiplies that voltage so the ADC can distinguish normal running from load and stall.

Max: The resistor tells you how much current flows. The sample clock tells you whether you saw the ripple honestly.

2. Build the measurement chain

1

SenseVsense=IcoilRsense.

2

AmplifyVout=GVsense.

3

DigitiseAn N-bit ADC has q=Vref/2^N.

3. Ask the time question separately

fs≥2fpwm; k=round(fpwm/fs); falias=|fpwm−kfs|

If sampling is too slow, the switching ripple does not disappear. Its samples fit a slower false pattern.

4. Try the ADC sampling rate

Vout=IRsenseG; q=Vref/2^N; falias=|fpwm−round(fpwm/fs)fs|

TryRaise the sample rate from the chapter's 1,200 Hz example toward the 40 kHz Nyquist floor.

No-load output
Loaded output
Stall output
10-bit ADC step
Ideal ADC SNR
Nyquist floor
Apparent ripple
Nyquist met?

ObserveAt 1,200 Hz, the three currents become 0.180, 0.600, and 1.800 V, the ADC step is 3.22 mV, but 20 kHz ripple folds to 400 Hz.

ExplainThe ADC has enough voltage resolution to separate the regimes. It still needs at least 40 kHz sampling, or an analogue filter plus a justified slower measurement contract, to avoid a false low-frequency ripple.

Technical boundaries.

This ideal chain

resistor tolerance
Needs separate evidence
heating
Needs separate evidence
amplifier offset/bandwidth/saturation
Needs separate evidence
ADC acquisition time
Needs separate evidence
switching edges
Needs separate evidence
common-mode limits
Needs separate evidence
anti-alias filtering
Needs separate evidence
motor commutation
Needs separate evidence
sensor calibration
Needs separate evidence

Use field evidence or a deeper model before release.

5. Reproduce the 400 Hz fold

round(20,000/1,200)=17. Therefore |20,000−17×1,200|=400 Hz. That slow-looking wobble came from fast switching, not a 400 Hz mechanical fault.

6. Verify a stall rule

Capture raw current with timestamps. Record the PWM clock, sample clock, analogue filter, ADC range, startup duration, loaded baseline, stall threshold, and independent motion evidence.

7. Check yourself

What voltage represents the 600 mA loaded case?
Answer: 0.600×0.1×10=0.600 V.
Why is 3.22 mV resolution not enough by itself?
Answer: Fine voltage steps cannot prevent time-domain aliasing.
Does a 400 Hz trace prove a 400 Hz motor event?
Answer: No. With these clocks it can be the alias of 20 kHz switching.
Honesty boundary.

These are the chapter inputs, worked results, and named teaching assumptions.

180 mA
Current or responsivity value
600 mA
Current or responsivity value
1.8 A
Current or responsivity value
0.1 Ω
Resistance or impedance value
gain 10
Percentage, ratio, or gain
0.180 V
Voltage or voltage-step value
0.600 V
Voltage or voltage-step value
1.800 V
Voltage or voltage-step value
10-bit
Digital resolution or converter setting
3.3 V
Voltage or voltage-step value
3.22 mV
Voltage or voltage-step value
20 kHz
Frequency, sample rate, or event rate
40 kHz
Frequency, sample rate, or event rate
1,200 Hz
Frequency, sample rate, or event rate
400 Hz
Frequency, sample rate, or event rate

They do not define a production stall detector by themselves.

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