EECS 314 Fall 2007 HW 03 Problem 1
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Discussion section # __________
(Last name, first name, IN INK)
© 2007 Alexander Ganago
Page 1 of 2
The big picture
The circuit shown on this diagram
is known as an inverting summer, or
summing amplifier, a.k.a. adder.
This summer is inverting, because
the signals are fed into the inverting
() input terminal of the Op Amp.
Its output signal
V
OUT
is a sum of
the two input signals
V
OUT
= K
1
⋅
V
S1
+ K
2
V
S2
where the coefficients
K
1
and
K
2
can be individually – and independently! – changed
if the resistances
R
1
and
R
2
are varied. This is a great advantage of the inverting
summer: in its twin brother – the noninverting summer, where the signals are fed into the
noninverting (+) input terminal of the Op Amp – changing one of the resistors results in
a change of
both
gain values thus independent adjustment of gains is nearly impossible.
The inverting summer circuit has many applications; one of the most obvious is the mixer
at an audio recording studio, where the signals
V
S1
and
V
S2
come from two
microphones.
In control systems, a similar circuit with 3 inputs can play the
role of the adder (such as needed for P + I + D control, which
we will discuss later in the course).
For conditioning of sensor signals, one input
V
S1
might be
used for the sensor signal itself (to be amplified with the
desired gain) while the other input
V
S2
might be used for compensation of DC offset (see
Part 2 of this problem.
Problem
(Assume an ideal Op Amp and use the “Golden Rules” in all derivations;
show your work on additional pages)
Part 1 (10 points)
For the circuit shown on the diagram above, write a complete node voltage equation for
node A; then simplify the equation by applying the “Golden Rules” and derive the
coefficients
K
1
and
K
2
(since the circuit is based on an inverting amplifier, both are
negative).
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View Full DocumentEECS 314 Fall 2007 HW 03 Problem 1
Student's name ___________________________
Discussion section # __________
(Last name, first name, IN INK)
© 2007 Alexander Ganago
Page 2 of 2
Part 2 (15 points)
Assume that you measure temperature with a voltage divider based on a thermistor, as in
problem 3 of homework 02, and the voltage signals
V
S1
from your temperature sensor
linearly
depend on the temperature and equal
V
S1, 0˚F
= 4.0 V
at 0˚ F, and
V
S1, 100˚F
= 3.2 V
at 100˚ F
(these values are similar to what you obtain in the circuit of HW 02 problem 3).
For your application, you need to obtain the output voltage of the circuit equal to
V
OUT, 0˚F
= 0.0 V
at 0˚ F,
and
V
OUT, 100˚F
= 10.0 V
at 100˚ F
.
To achieve this goal, you have to design an inverting adder with
R
F
= 100 k
Ω
and
V
S2
=
–2 V,
a DC source, which remains the same at all temperatures.
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 Fall '07
 Ganago
 Amplifier, Operational Amplifier, Square wave, Electrical impedance, Sine wave, Alexander Ganago

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