Amps x Volts = Watts

Analog topologies abound for converting current to voltage, voltage to current, voltage to frequency, and frequency to voltage, among other conversions.

Figure 1 joins the flock while singing a somewhat different tune. This current, voltage, and power (IVW) DC power converter multiplies current by voltage to sense wattage. Here’s how it gets off the ground.

Figure 1 The “I*V = W” converter comprises voltage-to-frequency conversion (U1ab & A1a) with frequency (F) of 2000 * Vload, followed by frequency-to-voltage conversion (U1c & A1b) with Vw = Iload * F / 20000 = (Iload * Vload) / 10 = Watts / 10 where Vload < 33 V and Iload < 1.5 A.

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The basic topology of the IVW converter comprises a voltage-to-frequency converter  (VFC) cascaded with a frequency-to-voltage converter (FVC). U1ab and A1a, combined with the surrounding discretes (Q1, Q2, Q3, etc.), make a VFC similar to the one described in this previous Design Idea, “Voltage inverter design idea transmogrifies into a 1MHz VFC”

The U1ab, A1a, C2, etc., VFC forms an inverting charge pump feedback loop that actively balances the 1 µA/V current through R2. Each cycle of the VFC deposits a charge of 5v * C2, or 500 picocoulombs (pC), onto integrator capacitor C3 to produce an F of 2 kHz * Vload (= 1 µA / 500 pC) for the control signal input of the FVC switch U1c. 

The other input to the U1c FVC is the -100 mV/A current-sense signal from R1. This combo forces U1c to pump F * -0.1 V/amp * 500 pF = -2 kHz * Vload * 50 pC * Iload into the input of the A1b inverting integrator.

 The melodious result is:

Vw = R1 * Iload * 2000 * Vload * R6 * C6

or, 

Vw = Iload * Vload * 0.1 * 2000 * 1 MΩ * 500 pF = 100 mV/W.

The R6C5 = 100-ms integrator time constant provides >60-dB of ripple attenuation for Vload > 1-V and a low noise 0- to 5-V output suitable for consumption by a typical 8- to 10-bit resolution ADC input. Diode D1 provides fire insurance for U1 in case Vload gets shorted to ground.

Stephen Woodward’s relationship with EDN’s DI column goes back quite a long way. Over 100 submissions have been accepted since his first contribution back in 1974.

Related Content

• Voltage inverter design idea transmogrifies into a 1MHz VFC
• A simulated 100-MHz VFC
• A simple, accurate, and efficient charge pump voltage inverter for $1 (in singles)
• 100-MHz VFC with TBH current pump

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