Math Bridge: Shunt Burden and Cycle Current

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Math BridgeEnergy & PowerStruggle-friendly runway

How can the meter change the sleep cycle it is measuring?

Start with charge in each state. Then test whether one shunt can see sleep without collapsing the radio rail.

Battery Bruno, the energy and power guideBattery Bruno guides
The one targetMeasure a whole duty cycle without changing the device's behaviour.
The chapter case130 mA boot, 5 mA warm-up, 120 mA radio, and 10 µA sleep.
What it buys youA defensible average-current result and a safe range-switching plan.

A field team faces an unresolved physical question: How can the meter change the sleep cycle it is measuring? They must answer it before changing cycle time on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is cycle time. The middle card applies this page's relationship. The green card is cycle charge (mc). 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 added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

Cycle time changes cycle charge (mc) An input card leads through the page relationship to the cycle charge (mc) result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. The same Ohm's-law multiplication controls both outcomes. There is no free shunt value: sensitivity and burden trade against each other.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for cycle time is 1.

  2. 2

    Name the relationship. Q=0.130x0.100+0.005x0.250+0.120x0.050+0.000010x900=0.02925 A·s T=900.4 s Iavg=0.02925/900.4=32.5 uA 20 log10(0.120/0.000010)=81.6 dB

  3. 3

    Substitute the chapter fixture. Set cycle time to 1. The page ledger gives cycle charge (mc) as 29.25.

  4. 4

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

Predict, then change cycle time

Try Predict the direction of cycle charge (mc). Move one control, calculate, then check your prediction.

1
Chapter baseline
Cycle charge (mC)

Observe The same Ohm's-law multiplication controls both outcomes. There is no free shunt value: sensitivity and burden trade against each other. Reset the control to 1 and compare cycle charge (mc).

Explain Only cycle time moves here. The other chapter fixtures remain fixed.

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 cycle time moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only cycle time. It replays the chapter fixture; it is not a field prediction.

1. Start with the physical story

Current tells us how quickly charge moves. A short, high-current radio burst and a long, tiny sleep current both matter. To compare them fairly, multiply each current by its time. That product is charge. A shunt meter adds a resistor to the supply path, so it also creates a voltage drop that the unmeasured device did not have.

Battery Bruno: Keep the units beside every number. They show whether a result is charge, energy, voltage, time, or a ratio.

2. Name every algebra move

1

Find charge in every stateMultiply each state current by its duration: Q=I×t.

2

Add the chargesQtotal is the sum of boot, warm-up, radio, and sleep charge.

3

Add the timesTtotal is one complete wake-to-wake cycle.

4

Divide charge by timeIavg=Qtotal/Ttotal.

5

Test the measurementVburden=I×Rshunt at both the smallest and largest currents.

6

Compare the extremes20 log10(Imax/Imin) expresses the current span in decibels.

3. Reproduce the chapter case

Q=0.130×0.100+0.005×0.250+0.120×0.050+0.000010×900=0.02925 A·s
T=900.4 s
Iavg=0.02925/900.4=32.5 µA
20 log10(0.120/0.000010)=81.6 dB

At 10 Ω, sleep produces 100 µV, but the radio peak loses 1.20 V. At 1 Ω, the peak burden falls to 120 mV while sleep produces only 10 µV. That is why the chapter changes range between states.

4. Try one real input

TryMove the control and predict which outputs should change before reading them.

Cycle time
Cycle charge (mC)
Average current
Current span
Radio burden
Sleep signal
Rail during radio

ObserveIncreasing the shunt makes the sleep signal easier to see, but it removes more voltage during the radio burst. Average current and dynamic range do not change because they belong to the workload, not the meter.

ExplainThe same Ohm's-law multiplication controls both outcomes. There is no free shunt value: sensitivity and burden trade against each other.

Technical boundaries.

This is a small formula ledger, not a complete source qualification.

Catalog currents
The state currents are example values; measure the actual board.
Meter bandwidth
A slow meter may miss a short radio peak even with a safe shunt.
Battery behaviour
This ledger does not include cell resistance or regulator loss.

Correct, not complete: the ledger proves the arithmetic and the shunt trade-off, not field battery life.

5. Use the result in the design

Choose a safe high-current range first, capture the peak, then use a lower-current range for sleep. Join the records by state and calculate average current from charge, not from a casual screen average.

6. Record the evidence state

Keep the board, firmware, rail voltage, shunt or meter range, state currents, state times, sample rate, and any brownout or reset. A changed range is part of the evidence, not a hidden detail.

7. Check yourself

Why is the cycle 900.4 seconds, not 900?
Answer: Boot, warm-up, and radio add 0.4 seconds to the configured 900-second sleep.
Why can a larger shunt falsify the result?
Answer: Its burden voltage lowers the device rail and can alter or reset the radio state being measured.
Why not average the four current numbers directly?
Answer: The states last for very different times, so each current must be weighted by its duration.
Honesty boundary.

The arithmetic uses the chapter's named or clearly labelled catalog-typical inputs.

Catalog currents
The state currents are example values; measure the actual board.
Meter bandwidth
A slow meter may miss a short radio peak even with a safe shunt.
Battery behaviour
This ledger does not include cell resistance or regulator loss.

Correct, not complete: the ledger proves the arithmetic and the shunt trade-off, not field battery life.

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