Root
Locus Problem
Problem
RLocus7
Dr. Abner Mallity has been working for a small electronics design company.
They need to produce a chip for a precise amplifier. Here the problems
they have.
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They have a design for
an amplifier stage with a gain of 100.
-
When they implement the
design the gain changes due to component variability, temperature (and
this is for a wide temperature range application).
-
They think that they can
use a feedback configuration to reduce the variability.
-
In the feedback configuration
they would use three stages. (Each stage is cheap, and there is plenty
of room on the chip.)
-
Each stage has a nominal
transfer function of 100/(10-5s + 1). (Check it
out. It has a DC gain of 100.)
Mallity has had a brain
wave. He figures that if they use three stages and put a voltage
divider on the output, the output of this configuration will be pretty
much the same as the input. That means that the input to the voltage
divider will be 100 times the output, so if they take the output at the
input to the voltage divider, they will have a gain of 100.
Mallity wants to be sure. He wants you to use root locus methods
to prove that the system will work. Determine if the system/circuit
is stable. We'll look at how accurate the gain is next period.
Using root locus analysis,
determine if they can use this configuration.