SIGMA-DELTA
CONVERSION USED
FOR MOTOR CONTROL
Jens Sorensen
Analog Devices
Visit analog.com
TECHNICAL ARTICLE
Abstract
Ʃ-Δ analog-to-digital converters are widely used in motor drives
where high signal integrity and galvanic isolation are required.
While the Σ-Δ technology itself is well understood, the converters
are often used in ways that fail to unlock the full potential of the
technology. This article looks at Σ-Δ ADCs from an application
point of view and discusses how to get the best performance in a
motor drive.
Introduction
When it comes to isolated phase current measurement in a 3-phase motor
drive, there are several technologies to choose from. Three popular methods
are outlined in Figure 1; an isolated sensor, such as a Hall effect or current
transformer, combined with an amplifier, a resistive shunt combined with an
isolation amplifier, and a resistive shunt combined with an isolating Σ-Δ ADC.
Figure 1. Common current measurement technologies for 3-phase motor drives.
This article focuses on the highest performing method—Σ-Δ conversion.
Typically, Σ-Δ ADCs target variable frequency motor drives and servo
applications where high signal quality and galvanic isolation are required.
Along with the ADC comes demodulation and filtering, which are typically
handled by an FIR filter such as a 3
rd
-order sinc filter
(
sinc3
)
.
A Σ-Δ ADC has the lowest possible resolution of 1 bit, but through oversam-
pling, noise shaping, digital filtering, and decimation, very high signal quality
can be achieved. The theory behind Σ-Δ ADCs and sinc filters is well under-
stood and well documented,
1, 2
so it will not be discussed in this article. Rather,
the focus will be on how to get the best performance in a motor drive and how
to utilize the performance in the control algorithms.
Phase Current Measurement with Σ-Δ ADCs
When a 3-phase motor is fed by a switching voltage source inverter, the
phase current can be seen as two components: an average component and
a switching component, as seen in Figure 2. The top signal shows one phase
current, the middle signal shows high-side PWM for the inverter phase-leg,
and the lower signal shows the sample synchronizing signal from the PWM
timer, PWM_SYNC. PWM_SYNC is asserted at the beginning and the center
of a PWM cycle and so it aligns with the midpoint of the current and voltage
ripple waveforms. For simplicity, it is assumed all three phases run with a duty
cycle of 50%, which means there is only one rising slope and one falling slope
of the current.
Figure 2. Phase current assumes average value at the beginning and center of
the PWM period.
For control purposes, only the average component of the current is of interest.
The most common way to extract the average component is to sample the
signal synchronized to PWM_SYNC. In these instances, the current assumes
its average value so if there is tight control of the sampling instant, under
sampling is possible without suffering from aliasing.
With conventional successive approximation
(
SAR
)
ADCs, sampling is done
by a dedicated sample-and-hold circuit giving the user tight control of the
sampling instant. Σ-Δ conversion, on the other hand, is a continuous sampling
process and other means of extracting the average value of the current are
Motor
Control
Algorithm
ADC
AC Motor
i
u
, i
v
, i
w
U
V
W
Σ
Sinc3
Average Current
Phase Current
PWM_SYNC
TimeT
SW
/2
T
SW
|
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