# Multiplier circuit measures real power in high-frequency PWMs

Applications which require the precise monitoring or regulation of dissipated load power, such as motors or servos, can make use of a circuit that measures real power by finding the product of the voltage and current consumed by the load. This task becomes more difficult when the voltage and current waveforms are high frequency, as is the case in pulse width modulated (PWM) motor drive applications. The control signals used for PWM motor drive can be several hundreds of kilohertz in frequency. In many such cases, a measure of the average or RMS power output is more useful than just the high frequency, instantaneous power waveform that is be produced by a power-measuring circuit. An LT1256 gain-controlled amplifier, along with an LTC1968 high-bandwidth RMS-DC converter, can produce both instantaneous and true RMS power outputs from fast-changing voltages and currents.

**Figures 1 through 5** show the power circuit measuring the dissipated load power in an H-bridge PWM motor driver. **Figure 1** shows the H-bridge, which is a network of four switches set up to look like the letter H.

__Click to Enlarge Image__Figure 1: A typical H-bridge block diagram, with two sets of switches that regulate the voltage across the load, a brushless DC motor

The duty cycle of a square-wave input signal dictates the average voltage delivered to the load, here, a brushless DC motor. Therefore, varying the duty cycle varies the speed and direction of the motor shaft. The amount of current consumed by the motor varies with the mechanical resistance (motor load) seen by the shaft of the motor.

The LT1995 and LT1991 precision-gain amplifiers differentially measure the voltage and current across the motor (**Figures 2 and 3**, respectively).

__Click to Enlarge Image__Figure 2: An LT1995 and a pair of LT1632’s measure up to ±50V of dynamic voltage across the DC motor.

__Click to Enlarge Image__Figure 3: The LT1991 measures the voltage across the small sense resistor with up to ±60V of common-mode input swing.

The high common-mode rejection of these amplifiers allows precise measurement of voltage and current despite a large common-mode signal (the supply voltage of the H-bridge). The LT1632 inverters attenuate the voltage signal to within the input common-mode range of the LT1995. The combination of the LT1632s and the LT1995 produces an output voltage, ΔV, that is 0.1x the voltage across the load.

The LT1991 has a high common-mode range (±60V), but only in a gain-of-1 configuration, so the LT1013 amplifier provides gain to the output of the LT1991. The combination of the LT1991 and the LT1013 produces an output voltage, VI, that is 10x the voltage across the sense resistor. The gains of the voltage and current sections (0.1x and 10x, respectively) are picked arbitrarily to give an easy mathematical relationship, and can be changed to fit the application.

The low-pass RC network at the output of the LT1991 attenuates the 100kHz (and harmonic) feedthrough, further increasing the high-frequency common-mode rejection of the circuit. No useful information is lost in the filtering, since the high inductance of the motor windings significantly limits the bandwidth of the motor current (how much depends on the specific motor, but it won’t be anywhere close to 100kHz). Smaller sense resistors generate much smaller current-sense voltages and limit the dynamic range of the circuit, so the gain of the LT1013 can be increased if necessary. At higher gains (greater than 100), the LT1013 should be replaced with a higher-bandwidth amplifier.

**Figure 4** shows the separate voltage and current signals being combined by the LT1256 to produce the instantaneous power of the circuit.

__Click to Enlarge Image__Figure 4: Both AC and DC components are in the resulting audio signal of a DC-biased amplifier

The LT1256 is set up in a multiplication configuration, with a gain of 1.25 on one amplifier, and a gain of –1.25 on the other amplifier. The voltage at the VC pin, controlled by the output of the LT1013, linearly selects a voltage gain within that range. The input range of the VC pin is set by the LT1790 voltage reference and the other half of the LT1013 to be ±1.25V. The gain of the LT1256 is equal to the voltage on the VC pin (e.g. –0.5 V at the VC pin means a gain of –0.5). In other words, the expression for the LT1256 circuit is (referring to **Figure 1**):

LT1256_{OUTPUT} = V • I for –1.25V ≤ I ≤ 1.25V

The instantaneous power waveform is attenuated by 10 and input to the LTC1968, which gives a DC output proportional to the RMS power (**Figure 5**).

__Click to Enlarge Image__Figure 5: The LTC1968 RMS-DC converter, which maintains excellent performance up to 500kHz, converts the instantaneous power waveform from Figure 4 to a DC output.

The input to the LTC1968 is attenuated because the LTC1968 requires an output voltage of less than 1V to maintain good accuracy. The overall gain of the circuit is:
P_{INST} ΔV • V_{I}

P_{RMS} (DC) = 0.1 •ΔV • V_{I}

The RMS output voltage with respect to the power consumed by the motor is:

P_{RMS} (DC) = (A_{V} • R_{SENSE} • A_{V,1013} • 100) mV/W_{RMS}

Where

A_{V,1632} = Attenuation of LT1632’s (V/V),

A_{V,1013} = Gain of LT1013 (V/V)

R_{SENSE} = Value of sense resistor (Ω)

**Circuit bandwidth and voltage ratings**

The bandwidth of the voltage measurement section (LT1632 and LT1995) is 8.7MHz, giving good fidelity with a 100kHz square-wave input. The common-mode voltage (H-bridge supply voltage) is limited by the LT1632’s output swing to slightly less than 45V. A greater attenuation can be chosen for the LT1632 to extend this range (replacing the 10kΩ resistors with 100kΩ resistors will give an additional 10x attenuation and increase the common-mode input range to 450V).

The current measurement section (LT1991 and LT1013) has a bandwidth of 10kHz, limited by the RC low-pass filter (LPF) network. This bandwidth is chosen because DC motors have large winding inductances, and therefore any 100kHz current ripple is likely to be caused by the large common-mode voltage experienced by the LT1991. Even the LT1991, with its well-matched resistors, only has 40dB of CMRR at 100kHz. Therefore, picking the LPF bandwidth is a trade-off between passing the actual current ripple and attenuating the spurious common-mode signal from the LT1991. The common-mode voltage is limited to 60V by the LT1991’s input voltage range, but can be extended by using precision matched resistor divider networks at both inputs. The LT1013’s useful output range is limited to {{1.25V by the LT1256’s VC pin, so the current through the motor should be limited to (0.125 • R_{SENSE}). For higher currents, a smaller sense resistor would be necessary.

**Circuit waveforms**

**Figure 6a** shows the voltage, current, and instantaneous power waveforms produced by the power measurement circuit.

__Click to Enlarge Image__Figure 6a: Power measurement circuit waveforms with 60% duty cycle PWM drive, 0.1 sense resistor, and light motor resistance. Trace 1 is the voltage, Trace 2 is the current, and Trace 3 is the instantaneous power.

Trace 1 (top) is the differential voltage across the motor, after a gain of 0.1V/V. Trace 2 (middle) is the current through the motor, with a gain of 1V/A. Trace 3 (bottom) is the instantaneous real power dissipated in the motor, with a gain of 0.1V/W. These power measurement circuit waveforms are performed with a 60% duty cycle PWM drive, 0.1Ω sense resistor, and light motor resistance. RMS power dissipation, as measured with a high-impedance voltmeter, is 5.9mV (590mW). **Figure 6b** shows the same three waveforms, but with more load (resistance) on the motor shaft.

__Click to Enlarge Image__Figure 6a: Heavy motor resistance with 60% duty cycle and 0.1Ω sense resistor. Trace 1 is the voltage, Trace 2 is the current, and Trace 3 is the instantaneous power.

The heavy motor resistance is shown with a 60% duty cycle and 0.1 ohm sense resistor. Here too, Trace 1 is the voltage, Trace 2 is the current, and Trace 3 is the instantaneous power. Notice that the average motor current has increased (in an absolute sense) with a heavier load. RMS power dissipation, as measured with a high-impedance voltmeter, is 20mV (2 Watts).

Not surprisingly, the average power dissipated in the motor increases due to the increased motor current.

**Circuit accuracy**

The gain accuracy of power measurement circuit depends on the accuracy of the LT1256 and the resistors in Figure 4. The LT1256 has a maximum 3% gain error over the commercial (0deg C to 70deg C) temperature range. The use of 0.1% metal film resistors or matched resistor networks, for the gain setting and voltage attenuation in the circuit, yields better than 4.5% gain error over temperature.

The power measurement circuit presented here is capable of measuring the power dissipated in a high-frequency PWM-driven motor or any other high-frequency power measurement application. In lower-frequency applications, the LTC1966 or LTC1967 may be substituted for the LTC1968.

**About the Author**

**Cheng-Wei Pei** is an applications engineer at Linear Technology Corp.

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