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Philips
Semiconductors
AN166
Basic feedback theory
1988 Dec
INTEGRATED CIRCUITS

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Application note
AN166
Basic feedback theory
2
1988 Dec
BASIC FEEDBACK THEORY
In AN165, the ideal op amp was defined. The ideal parameters are
never fully realized but they present a very convenient method for
the preliminary analysis of circuitry. So important are these ideal
definitions that they are repeated here. The ideal amplifier
possesses
1. Infinite gain
2. Infinite input impedance
3. Infinite bandwidth
4. Zero output impedance
From these definitions two important theorems are developed.
1. No current flows into or out of the input terminals.
2. When negative feedback is applied, the differential input voltage
is reduced to zero.
Keeping these rules in mind, the basic concept of feedback can be
explored.
VOLTAGE-FOLLOWER
Perhaps the most often used and simplest circuit is that of a
voltage-follower. The circuit of Figure 1 illustrates the simplicity.
–
+
E
S
E
OUT
E
OUT
= E
S
6
3
2
SL00931
Figure 1.
Voltage-Follower
Applying the zero differential input theorem, the voltages of Pins 2
and 3 are equal, and since Pins 2 and 6 are tied together, their
voltage is equal; hence, E
OUT
=E
IN
. Trivial to analyze, the circuit
nevertheless does illustrate the power of the zero differential voltage
theorem. Because the input impedance is multiplied and the output
impedance divided by the loop gain, the voltage-follower is
extremely useful for buffering voltage sources and for impedance
transformation.
The basic configuration in Figure 1 has a gain of 1 with extremely
high input impedance. Setting the feedback resistor equal to the
source impedance will cancel the effects of bias current if desired.
However, for most applications, a direct connection from output to
input will suffice. Errors arise from offset voltage, common-mode
rejection ratio, and gain. The circuit can be used with any op amp
with the required unity gain compensation, if it is required.
NON-INVERTING AMPLIFIER
Only slightly more complicated is the non-inverting amplifier of
Figure 2.
The voltage appearing at the inverting input is defined by
E
2
+
E
OUT
@
R
IN
R
F
)
R
IN
(1a)
Since the differential voltage is zero, E
2
=E
S
, and the output voltage
becomes
E
OUT
+
E
S
ǒ
1
)
R
F
R
IN
Ǔ
(1b)
–
+
E
S
E
OUT
6
3
2
R
F
R
IN
R
IN
|| R
F
E
2
SL00932
Figure 2.
Non-Inverting Amplifier
It should be noted that as long as the gain of the closed-loop is small
compared to open-loop gain, the output will be accurate, but as the
closed-loop gain approaches the open-loop value more error will be
introduced.
The signal source is shown in Figure 2 in series with a resistor equal
in size to the parallel combination of R
IN
and R
F
. This is desirable
because the voltage drops due to bias currents to the inputs are
equal and cancel out even over temperature. Thus overall
performance is much improved.
The amplifier does not phase-invert and possesses high input

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