Power measurements in (WPT) systems

Laurens Swaans &James Lo March 2017

CONFIDENTIAL

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Questions to answer

o What is a power measurement?

o Why is power important?

o Where do we measure power?

o How to measure AC power?

o What model to use?

o What do the signals look like?

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What is a power

measurement?

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What is power measurement?

o Power: – Indication of the energy usage per time unit (rate of work)

– Expressed in Joule per second (SI), or Watt (more common)

– Electrical power: 𝑃 𝑡 = 𝑣 𝑡 ∙ 𝑖 𝑡

o DC power – 𝑃𝐷𝐶 = 𝑉𝐷𝐶 ∙ 𝐼𝐷𝐶

o AC power – Instantaneous power: 𝑃 𝑡 = 𝑣 𝑡 ∙ 𝑖 𝑡

– RMS values power: 𝑃 𝑡 = 𝑉𝑅𝑀𝑆 ∙ 𝐼𝑅𝑀𝑆 ∙ cos𝜑 • RMS= Root Mean Square 𝜑 = the phase shift between voltage and current

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Why is power important?

VS

o Burning 1kg of coal vs 1kg of TNT

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Why is power important?

o Burning 1kg of coal vs 1kg of TNT – the coal has a lot more energy than the TNT, but

– the TNT has a lot more power than the coal • It takes much longer to burn all the coal than all the TNT

o Energy is accumulated power over time – The heat generated until all coal is burned up, or

– All power into the battery of a phone until it is fully charged

o Power is the amount of energy per time unit – The pressure waves generated by the TNT explosion, or

– The charge-speed of your phone while charging (% per minute)

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Why is power important?

o Foreign Object Detection (FOD)

Receiver coil

Transmitter coil

Magnetic flux

Received Power 𝑃𝑅𝑋

Power loss < 250mW 𝑃𝐿 = 𝑃𝑇𝑋 − 𝑃𝑅𝑋

Power loss > 250mW 𝑃𝐿 = 𝑃𝑇𝑋 − 𝑃𝑅𝑋

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Where do we measure power?

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A simple model

o In Wireless Power Transfer (WPT) systems: – Transmitter input: 𝑇𝑥𝐼𝑁

– Transmitter output: 𝑇𝑥𝑂𝑈𝑇

– Receiver input: 𝑅𝑥𝐼𝑁

– Receiver output: 𝑅𝑥𝑂𝑈𝑇

V Power

Transmitter Power

Receiver

Load

𝑇𝑥𝐼𝑁 𝑇𝑥𝑂𝑈𝑇 𝑅𝑥𝐼𝑁 𝑅𝑥𝑂𝑈𝑇

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Conventional powers

o TxIN: – External DC power supply: 𝑃 = 𝑉𝐷𝐶 ∙ 𝐼𝐷𝐶

– Mains connected transmitter: 𝑃 = 𝐴𝑉𝐺 𝑉 𝑡 ∙ 𝐼 𝑡

o RxOUT: – Battery or other DC load: 𝑃 = 𝑉𝐷𝐶 ∙ 𝐼𝐷𝐶

o System efficiency: 𝜼𝑺𝒀𝑺 =𝑹𝒙𝑶𝑼𝑻

𝑻𝒙𝑰𝑵

– Note the possibility to distinguish between energy efficiency and power efficiency V

Power Transmitter

Power Receiver

Load

𝑇𝑥𝐼𝑁 𝑇𝑥𝑂𝑈𝑇 𝑅𝑥𝐼𝑁 𝑅𝑥𝑂𝑈𝑇

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WPT characteristic powers

o TxOUT: – AC power generated by the coil: 𝑃 = 𝐴𝑉𝐺 𝑉 𝑡 ∙ 𝐼 𝑡

o RxIN: – AC power generated by the coil: 𝑃 = 𝐴𝑉𝐺 𝑉 𝑡 ∙ 𝐼 𝑡

o Efficiencies: – Antenna: 𝜼𝑨𝑵𝑻 =

𝑹𝒙𝑰𝑵

𝑻𝒙𝑶𝑼𝑻

– Transmitter: 𝜼𝑻𝒙 =

𝑻𝒙𝑶𝑼𝑻

𝑻𝒙𝑰𝑵

– Receiver: 𝜼𝑹𝒙 =

𝑹𝒙𝑶𝑼𝑻

𝑹𝒙𝑰𝑵

AC power measurements enables these

V Power

Transmitter Power

Receiver

Load

𝑇𝑥𝐼𝑁 𝑇𝑥𝑂𝑈𝑇 𝑅𝑥𝐼𝑁 𝑅𝑥𝑂𝑈𝑇

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How to measure AC power?

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AC power in resistive loads

o Power dissipation occurs in “resistive” loads – “resistive” means: voltage and current are in phase

– Voltage: 100kHz, 1V amplitude

– Current: 100kHz, 0.5A amplitude

– Double frequency

– Always positive

– Power: • 200kHz, 0.5W amplitude • Average P(t): 0.25W

• RMS: 𝑉𝑅𝑀𝑆 ∙ 𝐼𝑅𝑀𝑆 =1

2∙0.5

2 =0.25W

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AC power in reactive loads

o Power dissipation in WPT systems? – TxOUT and RxIN are not really “resistive”, not really “reactive”

– Voltage and current are not exactly in phase • Amount of phase shift depends on the impedance

o Power measurements when 𝛗 ≠ 𝟎 – 𝑃 = 𝐴𝑉𝐺 𝑉 𝑡 ∙ 𝐼 𝑡 still holds true

– But also: 𝑃 = 𝑉𝑅𝑀𝑆 ∙ 𝐼𝑅𝑀𝑆 ∙ 𝑐𝑜𝑠 𝜑 (for sinusoidal signals)

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How to measure AC power?

o AC power comparison

Differences caused by sampling frequency (10MHz)

ϕ AVG RMS Diff

0 0.249 0.249 0

18 0.237 0.237 7.6e-5

36 0.201 0.202 2.3e-4

54 0.146 0.147 3.2e-4

72 0.077 0.077 2.3e-4

90 3.5e-17 1.5e-17 2.0e-17

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AC power in reactive loads

o Power dissipation in WPT systems – TxOUT and RxIN are not really “resistive”, not really “reactive”

– Voltage and current are not exactly in phase • Amount of phase shift depends on the impedance

o Power measurements when 𝛗 ≠ 𝟎 – 𝑃 = 𝐴𝑉𝐺 𝑉 𝑡 ∙ 𝐼 𝑡 still holds true

– But also: 𝑃 = 𝑉𝑅𝑀𝑆 ∙ 𝐼𝑅𝑀𝑆 ∙ 𝑐𝑜𝑠 𝜑 (for sinusoidal signals)

o So we look at the “resistive part” of a “complex load” – This can be modeled as a resistor in parallel or series with the power transfer coil

– The phase shift depends on the ratio between resistance and reactance

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What model(s) to use?

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A simple model again

V Power

Transmitter Power

Receiver

Load

𝑇𝑥𝐼𝑁 𝑇𝑥𝑂𝑈𝑇 𝑅𝑥𝐼𝑁 𝑅𝑥𝑂𝑈𝑇

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Typical WPT model Transmitter parameters

Vin: input voltage

Cp: Series resonance capacitor on primary side

Lp: Primary winding

Rp: ESR of Tx

Receiver parameters Cs: Series resonance capacitor on secondary side

Ls: Secondary winding

ZL: Receiver loading

Rs: ESR of Rx

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What signals to expect?

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First simulation

o Invertor: – Transient: 10V, 160kHz

– Bode: 50kHz-250kHz

o Transmitter: – Qi TPT#2

o Receiver: – Qi TPR#1B

o Loading: – ZL=10Ω

o Coupling: – k=0.5

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Now…analyze the system

o Let the computer run through the complete load range

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Now…analyze the system

o Now add different couplings to the mix

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Now…analyze the system

o ..and different frequencies

thank you