The Power Meter
Peter J. Kindlmann
EE325
The Basic Premise
A standard 120V circuit feeds a complex load, eg. a load with both reactive and non-linear properties such as a transformer power supply. (We do assume the V-I properties of the load are symmetrical.) A current-sensing resistor Rs develops a differential voltage vd suitably small to keep the operation of the differential pair Q1, Q2 acceptably linear. (Rs, to which the other circuit potentials are tied, is inserted into the neutral side of the line which differs from ground by at most a few volts.) An emitter resistor RE controls emitter bias current during the negative half-cycle of the line voltage, with bias current consistent with classical Ebers-Moll transconductance control behavior.
The average power P(t) = <V(t).I(t)>
For the diff. amplifier, deltaIc = Ic2 - Ic1 = gm.vd, where gm = 1/2(IE/VT)
(the 1/2 because the current defined by IE is split between the two transistors.)
Since vd = I(t).Rs and IE = V(t)/RE, we obtain
<Ic> = 1/4(Rs /RE )(1/VT)P(t)
where another factor of 1/2 accounts for (so-called "two-quadrant") transconductance multiplication only during one line voltage half-cycle.
Our intended output <deltaIc> can be directly indicated by a d'Arsonval meter, or processed further. In either case we do need to arrange for collector supply voltage to keep the transistors happy. For further processing we will want deltaIc as single-ended output, obtained in the usual way by using a current mirror as an active differential amplifier collector load.
Further Evolution (project possibilities)
kW-hour Measurement
Although it is useful to know the power in watts, it is usually even more useful to know energy consumption over a, say, 24-hour period. This implies a much longer integration interval than can be trusted to analog signal processing.
A most convenient approach to integration is current-to-frequency conversion (a close relative of voltage-to-frequency (V/f) conversion), with pulses accumulated in a counter of suitable modulus. A direct indication of frequency, say as counts/sec, can serve as indication of power <P(t)>.
Measurement Isolation
Because of requirements for electrical safety, circuitry directly connected to the power line is not the favorite of instrument designers. To improve one's options for connections to the rest of the world, e.g. computer data-acquisition systems, the output portion of the power meter should be isolated from the power line.
Pulses from the current-to-frequency (I/f) converter could be coupled through
Finally, it is possible to use opto-isolators suitable for linear operation (a rare subset of opto-isolators) to configure a two-quadrant (even four-quadrant) transconductance multiplier that provides isolation and eliminates all active components on the power line side. Some recently available optocouplers make this option increasingly attractive.