Proportional Branch - Texas Instruments UCD3138 Technical Reference Manual

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4.1.2 Proportional Branch

The Xn value is used directly as an input to the Proportional (P) branch of the filter. It is multiplied by the
16 bit signed Kp coefficient, and the 24 bit result is used as the output of the P branch. When multiplying
two signed numbers in binary arithmetic, an extra sign bit is generated. Because of this, 9 bits times 16
bits gives 24 meaningful bits, not 25.
No clamp is needed on the proportional branch. It is self-limiting, because it has no memory. It will never
exceed 24 bits. If a lower maximum output is desired from the proportional branch, it can be achieved by
reducing the value of Kp.
4.1.3 Integral Branch
There are two options for the use of Xn in the Integrator (I) input. The current Xn can be used by itself, or
the current Xn can be added with the previous Xn-1. Doing the addition provides a trapezoidal
approximation, which is sometimes considered theoretically superior to a single point. However, since the
output of the adder is also 9 bits, if the Xn and Xn-1 values add up to more than 255 or less than -256, the
output of the adder will be clamped at those values.
This will only occur at the lowest gain setting of the Error ADC. So if the lowest gain setting of the EADC is
to be used, trapezoidal approximation may cause premature saturation on the input.
The Xn value, or the Xn + Xn-1 sum is multiplied by the Ki coefficient. Note that the trapezoidal mode will
normally have double the output of the simple Xn value. This will change the overall gain of the I stage by
a factor of two. This must be taken into account if the Xn addition mode is changed.
The output of this multiplication will always fit within 24 bits. This value is then added to the existing I
value. The hardware will automatically clamp it at a 24 bit signed number, and there are high and low
clamp registers available which can be used to clamp it to lower values. There are also status register bits
that will be set if the input value exceeds the clamp.
The clamped value is fed to the next stage of the filter, and is also fed back to be added to the next Xn *
Ki value when it is calculated.
4.1.4 Differential Branch
On the Differential (D) branch, Xn-1 is subtracted from Xn. The difference between the two most recent X
values is then multiplied by Kd, giving a 24 bit signed number.
The D branch has an additional pole added after this multiplication, giving more control of the filter
response to permit better matching to the power supply plant. This D alpha branch acts as an integrator
on the output of the D stage. With each filter calculation, the 24 bit result of the previous D and D alpha
calculation is multiplied by the 9 bit Kalpha (Kα). This gives a 32 bit signed result. To match the 24 bit data
path, this must be rounded back down to 24 bits. This is the one rounding that actually takes place in the
filter before the filter output.
There is also a simple clamp to prevent the K output from going outside a 24 bit signed number. Because
of the integral element for the alpha stage, it is possible for it to exceed this range.
SNIU028A – February 2016 – Revised April 2016
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