Circuits and Systems, 2010, 1, 1-4
doi:10.4236/cs.2010.11001 Published Online July 2010 (http://www.SciRP.org/journal/cs)
Two Simple Analog Multiplier Based Linear VCOs
Using a Single Current Feedback Op-Amp
Data Ram Bhaskar1, Raj Senani2*, Abdhesh Kumar Singh3, Shanti Swarup Gupta4
1Department of Electronics and Communication Engineering, Faculty of Engineering a nd Techn ol o gy,
Jamia Millia Islamia, New Delhi, India
2Division of Electroni cs a nd C om muni cation Engineeri n g , Netaji Subhas Institute of Technology,
Azad Hind Fauj Marg, New Delhi, India
3Electronics and Communication Engineering Department, ITS Engineering College,
Greater Noida, India
4Ministry of Commerce and Industry, Government of India, New Delhi, India
Received February 27, 2010; revised March 29, 2010; accepted April 5, 2010
Abstract
Two simple voltage-controlled-oscillators (VCO) with linear tuning laws employing only a single current
feedback operational amplifier (CFOA) in conjunction with two analog multipliers (AM) have been
highlighted. The workability of the presented VCOs has been demonstrated by experimental results based
upon AD844 type CFOAs and AD534 type AMs.
Keywords: Voltage-Controlled Oscillators, Current Feedback Op-Amps, Current-Mode Circuits, Analog
Multipliers
1. Introduction
Although a number of new building blocks and circuit
concepts related to current-mode circuits have been inve-
stigated in recent literature [1-3], the use of current feed-
back operational amplifiers (CFOAs) as an alternative to
the traditional voltage-mode op-amps (VOA), has
attracted considerable attention (see [4-7] and the
references cited therein) in various instrumentation, sig-
nal processing and signal generation applications due to
their commercial availability as off-the-shelf ICs as well
as due to the well known advantages offered by CFOAs
over the VOAs. Because of these reasons, use of CFOAs
has been extensively investigated in realizing oscillators,
for instance, see [6,8-11] and the references cited therein.
Although, a variety of CFOAs are available from various
manufacturers, AD844 (from Analog Devices) which
contains a CCII+ followed by a voltage buffer is particu-
larly flexible and popular due to the availability of z-ter-
minal of the CCII+ therein as an externally accessible
lead which permits AD844 to be used as a CCII+ (one
AD844) or as CCII- (employing two AD844s) or as a
general 4-terminal building block [6].
Voltage-Controlled Oscillators (VCO) are important
building blocks in several instrumentation, electronic and
communication systems, such as in function generators,
in production of electronic music to generate variable
tones, in phase locked loops and in frequency synthesiz-
ers [12-17].
A known method of realizing VCOs is to devise an
RC-active oscillator configuration with two analog mul-
tipliers (AM) appropriately embedded to enable indep-
endent control of the oscillation frequency through an
external control voltage VC applied as a common multip-
licative input to both the multipliers. When two AMs are
appropriately embedded in such a configuration, this te-
chnique gives rise to a linear tuning law of the form
C
Vf 
0 (1)
Based upon this approach, a number of VCO configu-
rations have been proposed by various researchers in the
past [12,14-17] employing traditional VOAs and AMs.
A family of eight, CFOA-based linear VCOs of the
above kind has recently been presented in [18]; however,
all the circuits presented therein require two CFOAs al-
ong with two AMs. The main object of this communica-
tion is to highlight two simple linear VCOs of the above
kind, which are realizable with only a single CFOA
along with two AMs. Experimental results using AD844
CFOAs have been given and the advantages of the new

D. R. BHASKAR ET AL.
2
CFOA-based VCOs as compared to previously known
VOA-based VCOs of [12,14-17] have been highlighted.
2. VCO Configurations Based on CFOAs
A CFOA is characterized by the instantaneous terminal
equations Iy = 0, Vx = Vy , Iz = Ix and Vw = Vz. On the other
hand, the output of an AM with two inputs V1 and V2 is
of the form 








ref
oV
VV
KV 21 , where ref
V is the
reference voltage of the multiplier set internally (usually
at 10 volts in case of AD534) and K can be set up +1 or
–1 by grounding appropriate terminals of AD534. The
value of K used for the various multipliers is shown on
the symbolic notation itself.
The proposed circuits are shown in Figure 1 and are
derived from the op-amp-AM VCOs of Figure 2 of [14]
with the CFOA configured as a negative impedance
converter (NIC).
Choosing the same ref
V for both the multipliers, the
circuits of Figures 1(a), 1(b) have the condition of oscilla-
tion (CO) and frequency of oscillation (FO) given by
CO: 0)( 21  CC (2)
C
V
x
y
z
C1
C2
2
R
1
R
w
1
R
VCO-1
(a)
C
V
x
y
z
C1
C2
2
R
w
1
R
R1
VCO-2
(b)
Figure 1. CFOA-based VCOs.
FO:
ref
C
V
V
where
RRCC
f 


;
1
22121
0 (3)
Thus, it is seen that f0 is linearly controllable by the
external control voltage VC, as desired. However, as per
Equation (2), one needs a variable capacitor to adjust
CO.
3. Consideration of CFOA Parasitics
The prominent non-idealities of the CFOAs include―a
finite non-zero input resistance rx at port-x (typically around
50 ), y-port parasitics consisting of a parasitic
resistance Ry (typically 2 M) in parallel with a parasitic
capa- citance Cy (typically 2 pF) and z-port parasitic
impedance consisting of a parasitic resistance Rp (typically
3 M) in parallel with a parasitic capacitance Cp
(typically, between 4-5 pF). In case of an analog
multiplier, the finite non-zero output resistance rout, as per
datasheet of AD534, is merely 1  and hence, can be
ignored in all the cases. On the other hand, the input
impedance of the AM, being 10 M, is sufficiently high
and hence, its effect can be ignored since usually, R2 and
1/  C2 would be relatively much smaller over the
frequency range of interest. For a quantitative assessment of the effect of the vari-
ous CFOA non-idealities, we have carried out a re-ana-
lysis of both the VCOs and the nonideal expressions for
CO and FO are given in Tables 1 and 2 respectively. It
may be noted that since CFOA has y-w shorted, the
y-port parasitics do not affect the operation of the circuits
and hence, do not appear in the nonideal expressions of
CO and FO.
It is easy to infer from the expressions given in Tables
1 and 2 that the errors caused by the influence of CFOA
can be kept small by choosing all external resistors to be
much larger than rx but much smaller than Rp and choos-
ing both external capacitors to be much larger than Cp1
and Cp2.
Table 1. Ideal and non-ideal conditions of oscillation.
VCOIdeal CONonideal CO
1 21 CC 

p
x
p
x
pC
R
R
R
R
RR
R
R
R
CC 





























1
2
1
2
1
2
21 1
1
1
11
1

2 21 CC p
x
p
x
pC
R
R
R
R
RR
R
R
R
CC 




























1
1
2
1
2
21
1
1
11
1

D. R. BHASKAR ET AL.
3
Table 2. Ideal and non-ideal frequency of osc illation.
VCO Ideal FO Nonideal FO
1
2121
2
2
0RRCC

 





























21
2121
1
2
1
2
2
011
1
11
1
RR
RRRCCC
RR
R
R
R
xp
p
x
p


2
2121
2
2
0RRCC

 




























21
2121
1
1
2
2
011
1
11
RR
RRRCCC
RR
R
R
R
xp
p
x
p


An inspection of Tables 1 and 2 shows that including
the non-ideal parameters of the CFOA will result in a
condition of oscillation that can not be controlled without
disturbing the frequency of oscillation. Thus, it appears
that the advantage of the proposed circuits in providing
non-interacting controls of CO and FO is lost. However,
the same can be circumvented by proper selection of the
values of the resistors. This limits the ease of the design
process and affects the highest frequency realizable by
the proposed circuits.
A quantitative comparison of f0 calculated from non-
ideal formula and values obtained practically is given in
Section 5.
4. Frequency Stability Properties
Frequency stability is an important figure of merit for
oscillators. The frequency stability factor SF is defined as

du
ud
SF

 where
0


u is the normalized frequ-
ency and

u

is the phase of the open-loop transfer
function of the oscillator circuit. The expressions for the
frequency stability factors for both the VCOs for C1 = C2
= C, R1 = R and R2 = R/n have been derived and are
found to be 1
2

n
n.
It can be easily deduced that for n = 1, SF is exactly 1
for both the VCOs. This figure is better than several
classical oscillators such as Wein bridge oscillator and
thus, both the proposed VCOs can be regarded to be
quite satisfactory from this viewpoint.
5. Experimental Results
Both the VCOs have been experimentally studied using
AD844 type CFOAs and AD534 type AMs biased with
±15 volts DC power supplies and it has been possible to
generate oscillation frequencies from tens of kHz to sev-
eral hundreds of kHz with tolerable errors in the frequ-
ency.
Experimental results of the proposed VCOs are shown
in Figures 2 (a) and 2(b). The component values chosen
were as under: For the circuits of Figure 1, R1 = R2 = 1 k,
C1 = 1 nF and C2 was taken as a variable capacitor to
adjust the CO. Figure 2(a) shows the variation of
oscillation frequency with control voltage VC for the
VCO of Figure 1(a) whereas Figure 2(b) shows a
typical waveform (f0 = 68.7 kHz, V0p-p = 3 V) obtained
from the VCO of Figure 1(b).
The measured values of the THD for the two VCOs
are found to be 1.88% and 1.52% respectively. The
practical results show a reasonably good
correspondence between the theoretical and
experimental values and con- firm the workability of the
two VCOs.
23 4 5 67 8 910
10
20
30
40
50
60
70
80
V
c
in volts
Frequenc y i n kHz
Practical
Theoretical
Figure 2. Experimental results of the VCOs: (a) Variation
of frequency with VC for VCO-1; (b) A typical waveform
generated from VCO-2 ( f0 = 68.7 kHz, V0p-p = 3 V).

D. R. BHASKAR ET AL.
4
6. Concluding Remarks
In this communication, we highlighted two simple CFOA-
AM-based VCOs, providing linear tuning laws, which
are derivable from previously known op-amp-AM based
VCOs published in [14]. The workability of the new
VCOs has been confirmed by the experimental results,
based upon AD844 type CFOAs and AD534 type analog
multipliers.
A comparison with the previously known linear VCOs
of [12,14-17] is now in order. The VCOs presented here
have the advantage of requiring fewer AMs than those of
[15], fewer resistors than those of [14,16,17] and fewer
active elements than those of [15-17]. When the single-
CFOA-RC VCOs are compared with single-op-amp-RC
VCOs of [14] (Figure 2 therein), they have the
advantage of employing two less resistors. Furthermore,
when compared to op-amp-RC VCOs of [12,14-17], the
CFOA- RC VCOs presented here not only offer rela-
tively higher operational frequency range (several hun-
dred kHz as compared to only a few kHz available from
the op-amp- RC VCOs) they also exhibit lower distortion
level (THD being less than 2%). Lastly, when compared
with the CFOA-AM-RC circuits presented recently in
[18] all of which require two CFOAs, the circuits pre-
sented here have the advantage of employing only a sin-
gle CFOA.
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