REV. A

ADE7757

–11–

The HPF in Channel V1 has an associated phase response that

is compensated for on-chip. Figures 11 and 12 show the phase

error between channels with the compensation network acti-

vated. The ADE7757 is phase compensated up to 1 kHz as

shown. This will ensure correct active harmonic power calcula-

tion even at low power factors.

FREQUENCY – Hz

0.30

0.25

0.20

0.15

0.10

0.05

0

–0.05

–0.10

0

100

200

300

400

500

600

700

800

900

1000

Figure 11. Phase Error between Channels (0 Hz to 1 kHz)

FREQUENCY – Hz

0.30

0.25

0.20

0.15

0.10

0.05

0

–0.05

–0.10

40

45

50

55

60

65

70

Figure 12. Phase Error between Channels (40 Hz to 70 Hz)

Digital-to-Frequency Conversion

As previously described, the digital output of the low-pass filter

after multiplication contains the real power information. However,

since this LPF is not an ideal “brick wall” filter implementation,

the output signal also contains attenuated components at the

line frequency and its harmonics, i.e., cos(h t) where h = 1, 2,

3, . . . and so on.

The magnitude response of the filter is given by

|H f

+

|

.

1

1

445

2

2

f

(5)

For a line frequency of 50 Hz, this would give an attenuation

of the 2

(100 Hz) component of approximately 22 dB. The

dominating harmonic will be at twice the line frequency (2 )

due to the instantaneous power calculation.

Figure 13 shows the instantaneous real power signal at the output

of the LPF that still contains a significant amount of instanta-

neous power information, i.e., cos(2 t). This signal is then passed

to the digital-to-frequency converter where it is integrated

(accumulated) over time in order to produce an output frequency.

The accumulation of the signal will suppress or average out any

non-dc components in the instantaneous real power signal. The

average value of a sinusoidal signal is zero. Thus, the frequency

generated by the ADE7757 is proportional to the average real

power. Figure 13 shows the digital-to-frequency conversion for

steady load conditions, i.e., constant voltage and current.

LPF

F1

F2

DIGITAL-TO-

FREQUENCY

CF

DIGITAL-TO-

FREQUENCY

MULTIPLIER

F1

TIME

CF

TIME

V

I

0

FREQUENCY (RAD/s)

2

COS (2 )

ATTENUATED BY LPF

V

I

2

LPF TO EXTRACT

REAL POWER

(DC TERM)

INSTANTANEOUS REAL POWER SIGNAL

(FREQUENCY DOMAIN)

Figure 13. Real Power-to-Frequency Conversion

As can be seen in the diagram, the frequency output CF is seen

to vary over time, even under steady load conditions. This fre-

quency variation is primarily due to the cos(2 t) component in

the instantaneous real power signal. The output frequency on

CF can be up to 2048 times higher than the frequency on F1

and F2. This higher output frequency is generated by accumu-

lating the instantaneous real power signal over a much shorter

time while converting it to a frequency. This shorter accumula-

tion period means less averaging of the cos(2 t) component.

Consequently, some of this instantaneous power signal passes

through the digital-to-frequency conversion. This will not be a

problem in the application. Where CF is used for calibration

purposes, the frequency should be averaged by the frequency

counter, which will remove any ripple. If CF is being used to

measure energy, for example in a microprocessor based applica-

tion, the CF output should also be averaged to calculate power.

Because the outputs F1 and F2 operate at a much lower fre-

quency, a lot more averaging of the instantaneous real power

signal is carried out. The result is a greatly attenuated sinusoidal

content and a virtually ripple-free frequency output.