ME365
Homework Set 12
Out: December 1, 2011
Due: December 8, 2011
Problem No. 1
Given:
Consider the
linear variable
differential
transformer (LVDT)
circuit, (a) on the next page.
The iron core moves up and down between the primary and secondary coils. The
voltage induced in each of the secondary coils is given by
݁
௦,ଵ
ൌ ܯ
ଵ
݀݅
݀ݐ
݁
௦,ଶ
ൌ ܯ
ଶ
݀݅
݀ݐ
where M
1
and M
2
are the mutual inductances of the secondary coils. As the core moves up, M
1
increases and M
2
decreases. As the core moves down, M
1
decreases and M
2
increases.
Find:
(a)
Determine the net secondary voltage,
݁
௦
ൌ ݁
௦,ଵ
െ ݁
௦,ଶ
. Assuming that the voltage
measurement at
݁
has infinite impedance, determine the frequency response of
the system from input,
݁
௫
, to output,
݁
for a fixed core position.
(b)
Assume that the voltage measurement at
݁
has resistance,
ܴ
, determine the
frequency response of the system for a fixed core position.
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 Fall '07
 MERKLE
 Signal Processing, Electronic amplifier, Lowpass filter, Electronics terms

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