0195136047.pdf

250 ANALOG BUILDING BLOCKS AND OPERATIONAL AMPLIFIERS

which is a negative resistance. The negative impedance converter is useful in transforming a

voltage source into a current source by means of a voltage-to-current converter (see Problem

5.4.9). It has also been used in a class of active filters.

Differential Amplifier

Figure 5.4.9 shows aweighted differencing amplifier,where “weighted” refers to the fact that

the output voltage has the formvo=wava+wbvb, in which the weighting coefficientswaand

wbare the voltage gains seen by the inputs. Since the network is linear, superposition can be

applied for analysis. First, by grounding the input terminal ofR 3 , let us makeva=0. Except

for the presence ofR 3 in parallel withR 4 , between terminal 2 and ground, the circuit is that of

an inverting amplifier of gain−R 2 /R 1 to the inputvb. Since no current flows at terminal 2, it

follows that

wb=−

R 2

R 1

(5.4.32)

Next, by grounding the left terminal ofR 1 , let us makevb=0. With respect to the voltage on

terminal 2, note that the circuit is that of a noninverting amplifier with gain 1+R 2 /R 1. The

voltage divider, consisting ofR 3 andR 4 , corresponds to a gain ofR 4 /(R 3 +R 4 )from the input to

terminal 2. Thus the overall gain becomes

wa=

(

1 +

R 2

R 1

)

R 4

R 3 +R 4

(5.4.33)

Finally, the overall response is obtained by superposition,

vo=wava+wbvb=

(

1 +

R 2

R 1

)

R 4

R 3 +R 4

va−

R 2

R 1

vb

or

vo=

R 2

R 1

[

1 +(R 1 /R 2 )

1 +(R 3 /R 4 )

va−vb

]

(5.4.34)

WhenR 1 /R 2 =R 3 /R 4 ,

vo=

R 2

R 1

(va−vb) (5.4.35)

−

+ vo

vb

b

3

2

1

R 1 R 2

R 3 R 4

va

a

Figure 5.4.9Weighted differencing amplifier.