Rainbow-electronics LM3813 User Manual download pdf (Page 11)

PWM Output and Current

Accuracy

Offset

The PWM output is quantized to 1024 levels. Therefore, the

duty cycle can change only in increments of 1/1024.

There is a one-half (0.5) quantization cycle delay in the

output of the PWM circuitry. That is to say that instead of a

duty cycle of N/1024, the duty cycle actually is (N+

⁄

)/1024.

The quantization error can be corrected for if a more precise

result is desired. To correct for this error, simply subtract

1/2048 from the measured duty cycle.

The extra half cycle delay will show up as a DC offset of

⁄

bit if it is not corrected for. This is approximately 1.1 mA for 1

Amp parts, and 11 mA for 7 Amp parts.

Jitter

In addition to quantization, the duty cycle will contain some

jitter. The jitter is quite small (for example, the standard

deviation of jitter is only 0.1% for the LM3812/13-1.0). Sta-

tistically the jitter can cause an error in a current sample.

Because the jitter is a random variable, the mean and stan-

dard deviation are used. The mean, or average value, of the

jitter is zero. The standard deviation (0.1%) can be used to

define the peak error caused from jitter.

The “crest factor” has often been used to define the maxi-

mum error caused by jitter. The crest factor defines a limit

within which 99.7% of the samples fall. The crest factor is

defined as

0.3% error in the duty cycle.

Since the jitter is a random variable, averaging multiple

outputs will reduce the effective jitter. Obeying statistical

laws, the jitter is reduced by the square root of the number of

readings that are averaged. For example, if four readings of

the duty cycle are averaged, the resulting jitter (and crest

factor) are reduced by a factor of two.

Jitter and Noise

Jitter in the PWM output appears as noise in the current

measurement. The Electrical Characteristics show noise

measured in current RMS (root mean square). Arbitrarily one

could specify PWM jitter, as opposed to noise. In either case

the effect results in a random error in an individual current

measurement.

Noise, just like jitter, can be reduced by averaging many

readings. The RMS value of the noise corresponds to one

standard deviation. The “crest factor” can be calculated in

terms of current, and is equal to

3 sigma (RMS value of the

noise).

Noise will also be reduced by averaging multiple readings,

and follows the statistical laws of a random variable.

Accuracy of 7A Versions

The graph of Figure 7 shows two possible responses to a 7A

current step. The flat response shows basically a 7A level

with some noise. This is what is possible with a good thick

trace and a good thermal connection to the IC on the sense

pins.

The second trace that asymptotically approaches a higher

value shows what can happen under extremely poor thermal

conditions. Here a very small wire connects the IC to the

current source. The very small wire does not allow heat in

the sense resistor to dissipate. Hence, as the sense resistor

heats up, a temperature difference between the sense ele-

ment and the die gets larger, and an error develops. Even-

tually the temperature difference reaches steady state,

which accounts for the under-damped exponential response.

Accuracy versus Noise

The graph shown in Figure 8 illustrates the typical response

1 Ampere current gauges. In this graph, the horizontal

axis indicates time, and the vertical axis indicates measured

current (the PWM duty cycle has been converted to current).

The graph was generated for an actual current of 500 mA.

The difference between successive readings manifests itself

as jitter in the PWM output or noise in the current measure-

ment (when duty cycle of the PWM output is converted to

current).

The accuracy of the measurement depends on the noise in

the current waveform. The accuracy can be improved by

averaging several outputs. Although there is variation in

successive readings, a very accurate measurement can be

obtained by averaging the readings. For example, on aver-

aging the readings shown in this example, the average

current measurement is 502.3 mA (Figure 8). This value is

very close to the actual value of 500 mA. Moreover, the

accuracy depends on the number of readings that are aver-

aged.

10012223

FIGURE 7. Transient Response to 7 Amp Step Current

10012226

FIGURE 8. Typical Response of LM3812-1.0/LM3813-1.0

LM3812/LM3813

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Rainbow-electronics LM3813 User Manual Page 11

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