Second Generation Controlled Current Conveyors (CCCII) and Their Applications - Current Conveyors: Variants, Applications and Hardware Implementations - page 293

I in = I 0 I in > 0

i Z 1 ¼ ð 9 : 71 Þ

0 I in 0

and

I in = I 0 I in < 0

i Z 3 ¼ ð 9 : 72 Þ

0 I in 0

The CCCII-I and the CCCII-3 alternate for positive and negative input cycle. The
final output is then obtained as:

I in
I 0

I out ¼ ð 9 : 73 Þ

From the above it is clear that the circuit is a true four quadrant squaring circuit with
no constraint in the polarity of the input signal.
Square rooting circuits using op-amps and MOSFETs suffer from the drawbacks
of high frequency limitation finite gain bandwidth product of the op-amps and are
generally not suitable for IC implementation. A number of square rooting circuits
using CCs have also been advanced a discussion about which has been included in
Chap. 8 of this monograph. These circuits however use MOSFETs in non-saturation
regions.
In the following we show that using CCCIIs interesting square rooting circuits
can be evolved which do not require any MOSFETs and can perform the operation
of square rooting for a voltage input signal or current input signal.
A square rooting circuit capable of providing a voltage output proportional to
square root of input voltage using only two CCCIIs was proposed by Dejhan and
Netbut in [ 49 ] and Netbut et al. in [ 50 ] and is shown in Fig. 9.50 . In this circuit, the
variable resistor R eq is realized by the mixed translinear cell with terminal-Y
grounded and input impedance seen into terminal-X as shown in Fig. 9.51 .
The variable resistance R eq employed in the above circuit is realized by the
circuit shown in the Fig. 9.51 .
Using the usual characterizations of the CCCII and a straight forward analysis
taking I 01 ¼ I 02 ¼ I 0 and R x ¼ V T /2I 0 shows that the relation of V out is given by

(with Rc 1 ¼ R c2 ):

p

V T =

p

V in V out ¼ 2 ð 9 : 74 Þ

Therefore, from equation ( 9.74 ), it is clear that the circuit functions as a square
rooter.