SI9961A Datasheet, PDF (7/9 Pages) Vishay Siliconix – 12-V Voice Coil Motor Driver

Si9961A
Vishay Siliconix
If a unit step voltage is applied to the above transfer function
and the inverse Laplace transform is taken, the output result is:
V_O + A
p ) (x * p) x e^{*x t}
x
Where t = time
As we can see, if x = p (i.e. if the VCM pole and compensation
amplifier zero = the transconductance closed loop pole), then
Vo reduces to A. In other words, a step input results in a step
output without overshoot. If x < p then a step input results in an
increased rise time output and no overshoot. If x > p, a step
input results in a step output with an overshoot.
If this overshoot is large enough, there may be a
cross-conduction condition in the output FETs.
Let us look at the above equation at t = 0 and t >> 0, expressed
in terms of the open loop high frequency voltage gain, A.
V_O + A
V_O
+^p
L_v
B
At t = 0
At t uu 0
In the example shown above, p = 10,000 and A = 9.8. This
means that there is some overshoot. At t = 0, the output voltage
is 9.8 V per volt of input. At some later time, it has dropped to
7.5 V per volt of input. An overshoot of 31 % is thus produced.
The maximum overshoot voltage requires careful
consideration, since it constitutes a potentially catastrophic
problem area. If we had decided to optimize for no overshoot,
A would equal 7.5, and hence the closed loop pole (A * B / Lv)
would be 10,000, which is a frequency of 1.592 kHz. This
would have resulted in a phase margin degradation of 13_ at
the 367-Hz frequency desired. This may or may not be
acceptable. One must weigh the servo bandwidth, phase
margin degradation, and maximum voltage at the VCM for
each individual case.
Result:
In the example for the 2081-Hz roll-off case with 31%
overshoot and proper pole cancellation, the compensation
values are:
R_L = 6.2 kW
C_L = 0.016 mF
In the example for the 1592-Hz roll-off case with no overshoot
and proper pole cancellation, the compensation values are:
R_L = 4.7 kW
C_L = 0.022 mF
The linearity of the transconductance amplifier (around a
center value of 500 mA/volt) is shown in Figure 2. In this case,
the output current sense resistors (R_SA and R_SB) were "5%
tolerance, 0.5 W . Any mismatch between R_SA and R_SB
contribute directly to mismatch between the positive and
negative “full-scale”. Including the external resistor mismatch,
the overall loop nonlinearity is approximately 1% maximum
over a "250-mV input voltage range.
5
4
3
2
1
0
−1 V_DD = 12 V
R_SA = R_SB = 0.5 W ”5%
−2 R_m = 52 W
−3
G_m = 500 mA/V
−4
−5
−300 −200 −100 0 100 200 300
V_IN in mV
FIGURE 2. Si9961A Transconductance
End Point Non-Linearity
Document Number: 70014
S-40845—Rev. H, 03-May-04
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