Basic Analog Circuit Building Blocks Using CCs and Application of CCs in Impedance Synthesis - Current Conveyors: Variants, Applications and Hardware Implementations - page 104

Fig. 5.24 Senani ' s lossy
floating inductance
simulator without any
component-matching [ 16 ]

R 1

CCII-

z

I 2

2

I 1

x

1 V 2

y

V 1 C

2

/

1 /

R 2

In [ 16 ], Senani demonstrated, for the first time ever , as to how a lossy FI (parallel
RL-type) can be realized by using only one CCII- along with only three passive
components (only two resistors and a capacitor) without requiring any component
matching condition . This circuit is shown in Fig. 5.24 .
By straight forward analysis, assuming to CCII

to be characterized by i y ¼ 0,

v x ¼ h 21 v y and i z ¼ h 32 i x where nominally h 21 ¼ 1 ¼ h 32, the non-ideal Y-matrix

of the circuit is found to be:

2
4

3
5

1
h 21

Y hi

1

1
R 1 þ

1
R 2

1
sCR 1 R 2

¼ þ ð : Þ

5 30

1
h 32

1
h 21 h 32

From the above, it can be seen that for h 21 ¼ h 32, the circuit simulates parallel

RL floating impedance with R eq and L eq given by:

1 ¼

R eq ¼ R 1 R 2 = ð R 1 þ R 2 Þ ,L eq ¼ CR 1 R 2 ð 5 : 31 Þ

From the above [Y] matrix, it is easy to deduce that the circuit enjoys very
low active and passive sensitivities all of which can be found to be belonging to
the range

S xj 0 1 ð 5 : 32 Þ

It is interesting to point out that from the above circuit, a grounded inductor circuit
can be obtained in two different ways.

If terminals 2-2 / are short-circuited a grounded inductor is realized between
1-1 / with equivalent inductance and resistance given by the same values as
shown above. However, since the non-ideal driving point admittance of the
circuit is given by:

(a)

1
R 1 þ

1
R 2

1
sCR 1 R 2 ¼

Y 11 ðÞ ¼ s þ Y 11 s ðÞ ideal ð 5 : 33 Þ

The above equation implies that

S L eq S L eq S R eq S R eq

h 21 ¼ h 32 ¼ h 21 ¼ h 32 ¼

0 ð 5 : 34 Þ