Image Processing Reference
In-Depth Information
where
τ ri is the rise delay of the i-th stage,
τ fi is the fall delay of the i-th stage, and V LSDi is the
LSD supplying the i-th stage.
The output signal of the ring oscillator used to measure the external part of the chip has
aperiodof T osc , which is the sampling period of the ring oscillator. The T osc is the total
summation of all of the rise and fall delays of all the stages; that is,
5
i = 1 τ ri +
5
i = 1 τ fi ,
=
T osc
(2)
5
i = 1 f f ( V LSDi )+
5
i = 1 f r ( V LSDi ) .
=
(3)
Since we can only measure the period of the ring oscillator T osc and its inverse frequency( f osc ),
we must calculate the voltage from (3) in order to determine the LSD. However, it is impossible
to solve (3) because there are many combinations of V LSDi that satisfy (3). Therefore, the
measured LSD, V LSDm , is defined as the constant voltage which provides the same period
T osc ,
=
(
V LSDm )
T osc
f
.
(4)
The period T osc is thus the time resolution of the V LSDm .
In this scheme, the LSD is calculated from a measured period T osc or a measured frequency
f osc . The measured LSD denoted as V LSDm is therefore an average value. Since the voltage
fluctuation is integrated through the period T osc , the time resolution is determined by the
period T osc .
Next the tracking of the LSD is discussed. There is a limitation in the tracking because the
measurement of the voltage fluctuation is done by a ring oscillator as mentioned above, and
the local voltage fluctuation is averaged out at the period of the ring oscillator. When the
voltage fluctuation has a high-frequency element, the reproduction is difficult. In addition, a
single measurement is too rough to track the target voltage fluctuation. However, although
the voltage fluctuation is synchronized to the system clock, in general, since the ring oscillator
oscillates asynchronously to the system frequency, the sampling points are staggered with
each measurement. It is well known that averaging multiple low-resolution samples yields
a higher resolution measurement if the samples have an appropriate dither signal added to
them (Gray,et al., 1993).
For example, Fig. 7 (a) illustrates the case where the supply voltage fluctuation frequency
is 150 MHz, which is about half the frequency of the ring oscillator. In this case, a single
measurement cannot track the original fluctuation, but a composite of all measured voltages
follows the power supply fluctuation. Another example is shown in Fig. 7 (b). In this case,
since the frequency of the power supply fluctuation is similar to the frequency of the ring
oscillator, the measured voltage V LSDm is almost constant. These examples show that this
scheme tracks the LSD as an averaged value during the period of T osc . Therefore, as shown in
these examples, a rounding error occurs even when the frequency of the LSD is the half that
of the VMON frequency. Thus, for precise tracking, the frequency of the ring oscillator should
be designed to be more than 10 times higher than that of the LSD. In general, the frequency
of the power-supply voltage fluctuation can be classified into three domains; a low-frequency
domain (
MHz), a middle-frequency domain (
100 MHz), and a high-frequency domain
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