SI9961A Datasheet, PDF (6/9 Pages) Vishay Siliconix – 12-V Voice Coil Motor Driver

Si9961A
Vishay Siliconix
Frequency Compensation:
The VCM transconductance (in siemens) of this simplified
case may be expressed in the s (Laplace) plane as:
1
g_v
+
s
Lv
)
Rv
Lv
Where R_v = VCM resistance in ohms
L_V = VCM inductance in henrys
s is the Laplace operator
In this case, the transconductance pole is at −Rv/Lv. It is
desirable to cancel this pole in the interest of stability. To do
this, a compensation amplifier is cascaded with the VCM and
its driver. The transfer function of this amplifier is:
H_c + A
ǒ Ǔ s ) _RL ¹ _CL
s
Where R_L =
C_L =
A=
Compensation amplifier feedback
resistor in ohms
Compensation amplifier feedback
capacitor in farads
Compensation amplifier and driver
voltage gain at high frequency
If R_L x C_L is set equal to L_v/R_v, then the combined open loop
transconductance in siemens becomes:
g_to
+_s
A
L_v
In this case, the transconductance has a single pole at the
origin. If this open loop transfer is closed with a
transimpedance amplifier having a gain of B ohms, the
resultant closed loop transconducatance stage has the
transfer function (in siemens) of:
A
g_tc
+
s
Lv
)
AB
Lv
Where B = Current feedback transimpedence amplifier gain in
ohms.
The entire transconductance now contains only a single pole
at −A*B/Lv. A and B are chosen to be considerably higher than
the servo bandwidth, to avoid undue phase margin reduction.
As a typical example, in the referenced schematic, assume
that Rsa and Rsb = 0.5 W, R₅= R₃ = 10 kW, VCM inductance
(Lv) = 1.5 mH, VCM resistance (Rv) = 15 W. Hence:
R_v = 15 W
L_v = 1.5 mH
B = 2W
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6
A = 16 x R_L/10000
C_L = L_v/(R_v x R_L) = 100 x 10^−6/R_L farads
Gain Optimization:
There are three things to consider when optimizing the gain (A)
above. The first is servo bandwidth. The main criterion here is
to avoid having the transconductance amplifier cause an
undue loss of phase margin in the overall servo (mechanical
+ electrical + firmware) loop. The second is to avoid confirguing
a bandwidth that is more than required in view of noise and
stability considerations. The third is to keep the voltage output
waveform overshoot to a level that will not cause
cross-conduction of the output FETs.
The first two problems can be considered together. Let us
assume a disk drive with a spindle RPM of 4400 and with
50 servo sectors per track. The sample rate is therefore:
f_s + 50
440
60
This is a sample frequency of 3667 Hz
As a rule of thumb, the open loop unity gain crossover
frequency of the entire servo (mechanical + electrical +
firmware) loop should be less than 1/10 of the sample
frequency. In this example, the servo open loop unity gain
crossover frequency would be less than 367 Hz. If we allow
only a 10_ degradation in phase margin due to the
transconductance amplifier, then a phase lag of 10_ at 367 Hz
is acceptable. This results in a 3-dB point in the
transconductance at :
f_3db
+
367
tan (10)
or a 3-dB point in the transconductance at 2081 Hz.
The pole in the closed loop transconductance (−A * B / Lv)
should then be 2081 * 2 * p = 13075. This means that A = 9.8.
From the above equation for A, R_L = 6.2 kW. This sets the
minimum gain limit governed by the servo bandwidth
requirements. The gain should not be much greater than this,
since increased noise will degrade the servo response.
The third problem, keeping the transconductance amplifier
voltage output wave form overshoot to a level that will not
cause the wrong output FETs to conduct, can be evaluated by
deriving the voltage transfer function of the closed loop
transconductance amplifier from input voltage to output
voltage (Vin to output A and B on the reference schematic).
This is :
H_to + A
s)p
s)x
Where
p = 1/R_L x C_L) or R_v/L_v Comp amplifier
zero/VCM pole
x = A x B/L_v closed loop pole
Document Number: 70014
S-40845—Rev. H, 03-May-04