Page 272 - Mechatronics with Experiments

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i
R in i out
s
a c
+ K amp +
+
v in R R
v s in L v out
– – R
b out d –
(a)
R s i in R out i out

a c
+ +
+ R + R v
v in in L 0
– – K v
v s – –
b amp in d
(b)

FIGURE 5.8: Input and output loading effects as a result of the connection of an op-amp to an
input signal source and output load. (a) input and output connection of the op-amp device, (b)
model of the op-amp with input impedance, output impedance, and open circuit voltage gain.

The open circuit voltage gain, K amp , is assumed constant for low frequency signals
relative to the bandwidth of the amplifier,

V = K ⋅ V (5.75)
out,open amp in
where the V is the voltage across the input terminals of the amplifier, and V out,open is the
in
voltage across the output terminals of the amplifier when it is in open loop condition.
Let us recall the definition of the impedance and the fact that it is a generalization of
resistance. For the amplifier model shown in Figure 5.8, the input and output impedances
are defined as,

V (jw)
in
Z (jw) = (5.76)
in
i (jw)
in
V out (jw)
Z out (jw) = (5.77)
i out (jw)
The input impedance is the generalized resistance seen by the input signal source. The
output impedance is the generalized resistance of a voltage source which is the same
as the output resistance of its equivalent Thevenin’s circuit. The gain, input, and output
impendances are three parameters that effectively define the performance characteristics of
an amplifier.

5.4.3 Input and Output Loading Errors
Let us consider an amplifier connected between a voltage source and a load (Figure 5.8).
The input voltage is affected by the input impedance of the amplifier,
R in
V = v (5.78)
in s
R + R
in s