1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
462
APPLICATIONS OF IMPROVED GILBERT MULTIPLIER
Komal Mehna and Prof. B. P. Singh
FET, Mody Institute of Technology & Science Lakshmangarh,
Sikar (Rajsathan), India
ABSTRACT
With the advancement in the field of electronics at an incredible pace, the power
efficient and high-speed VLSI designs are gaining more popularity and are highly in demand.
The decrease in battery weight, size and increase in the lifetime are the key factors for
portable equipments. Most of the reported multipliers have very poor performance and/or
become non-functional in case of low-voltage, low-power environment. This paper describes
various applications of analog multiplier such as frequency doubler, modulator, demodulator
etc. All the simulation work has been done on Tanner EDA tool at 45nm technology.
Keywords : VLSI, Analog Multiplier, Gilbert Cell, CMOS Technology.
1. INTRODUCTION
The growing demand of data transfer via the wireless communication systems results
in the fast development of various portable products [1]. The analog multipliers are basic
building blocks, used in many applications like mixers and modulators in communication
systems, continuous time signal processing, automatic variable gain amplifiers, adaptive
filters, and neural networks [2]. The multiplier performs a linear product of continuous
signals x and y yielding an output z=kxy, where k is a constant of suitable dimension [3]. The
Gilbert Cell Mixer is very useful building blocks in transceiver design [4]. Gilbert-cell mixers
are among the popular classes of mixers which are used extensively in wireless transceivers.
Among the important features of Gilbert-cell mixers are their large bandwidth and high
conversion gain (CG) [5].
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ISSN 0976 – 6464(Print)
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
463
2. DESCRIPTION OF THE PROPOSED CIRCUIT
Gilbert cell has two important properties. The first property is that the small-signal
gain of the circuit is a function of its tail current. The second property tells that the two
transistors in a differential pair provide a simple means of streeing the tail current to one of
the two destinations [6], [7]. Existing 12T Gilbert cell multiplier [8] has been modified by
grounding the body terminal of all the nMOS transistors and connecting the body terminal of
transistor MP4 to DDV [9]. The positive and negative terminals of the output voltage ( OUTV ) are
indicating Outp and Outn respectively in the proposed multiplier circuit of Fig. 1. Here CV is
the control voltage.
For the conditions
tnGSDS VVV −≥ and tnGS VV ≥
Equation of the drain current in the saturation region for the nMOS is given by
( )2
2
tnGS
n
D VV
k
I −=
All the transistors in Fig. 1 operate in the saturation region. Input signals are applied in the
complementary form i.e.
2121 & CC VVVV −=−=
The input signal being varied and 4 2
1V is taken to approximately zero. So the output current
[9]
OUT
nCD
OUT
R
kVVR
I 122
=
OUTI ∝ CVV1 (1)
Where
OUT
nD
R
kR
k
22
1 =
Equation (1) indicates that the output current ( OUTI ) is proportional to the product of input
voltages which is the property of the voltage multiplier so it is a voltage multiplier.

3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
464
Fig. 1 Proposed multiplier
3. SIMULATION RESULTS
In order to verify the circuit operation and characteristics, several experimental
simulations have been carried out at the 45nm technology using Tanner EDA tool. The
transient response of the proposed multiplier is shown in Fig. 2. Here input signals are
sinusoidal with 10mv peak amplitude, frequency of V1 and VC are 500kHZ and 0.1GHZ
respectively and the supply voltage is ± 0.8v. The aspect ratio of all transistors is taken 1. The
proposed multiplier had power consumption and power-delay product less than the existing
12T Gilbert cell based multiplier almost 2 times and 4 times respectively [9].
Fig. 2 Transient response of proposed multiplier

4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
465
4. APPLICATIONS OF PROPOSED MULTIPLIER
4.1 Frequency Doubler
When a sinusoidal voltage ( tA ωsin ) is applied to the both inputs of the proposed
multiplier, output produced is double frequency of the input signal.
tAVo ω22
sin=
( )t
A
Vo ω2cos1
2
2
−=
Thus the output signal contains the DC component and cosine component of
frequency ω2 , which twice of the input frequency.
For example if the sinusoidal voltage of 50mv amplitude and frequency of 500kHz is given to
the inputs then the output voltage is proportional to ,as shown in Fig. 3. Thus proposed
multiplier can operate as frequency doubler.
Fig. 3 Frequency doubler using proposed multiplier
4.2 Modulator
The growing demand of data transfer via the wireless communication systems results
in the fast development of various portable products [10]. The purpose of a communication
system is to deliver a message signal from an information source in recognizable form to a
user destination, with the source and the user being physically separated from each other [11].
Modulation is the systematic alteration of one waveform, called the carrier, according to the
characteristics of another waveform, the modulating signal or message [12]. A circuit, stage
or piece of hardware that modulates is called a modulator.
When two sinusoidal voltages of different frequencies (500 kHz and 0.1GHz) are applied
to the inputs of proposed multiplier presented in Fig. 1, the output results in a modulated sine
wave as shown in Fig. 4 (a).

5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
466
Fig. 4 (b) represents the triangular modulation of sine wave when one input is a sinusoidal
voltage and the other is a triangular voltage of lower frequency, the output is triangular
modulation of sinusoidal voltage. Thus the proposed multiplier circuit can also behave as
modulator.
Fig. 4(a) Output waveform of modulator for sinusoidal input
Fig. 4(b) Output waveform of modulator for triangular input
4.3 Demodulator
To reconstruct the transmitted signal, modulated signal must pass through a reversal
process known as demodulation. A circuit, stage or piece of hardware that demodulates is
called a demodulator. Proposed multiplier presented in Fig.1 can also act as demodulator
after connecting capacitors at the output shown in Fig. 5.

6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
467
Fig. 5 Demodulator using proposed multiplier
Transient response of the proposed multiplier as demodulator is shown in Fig. 6. In
this circuit two capacitor c1 and c2, each of 0.1pf, have been used. Here input signals are
sinusoidal with 50mv peak amplitude, frequency of V1 and VC are 500kHZ and 0.1GHZ
respectively and the supply voltage is ± 0.8v. Where 2121 & CC VVVV −=−= .
Fig. 6 Output waveform of demodulator
5. CONCLUSION
Applications of the proposed multiplier have been simulated at the 45nm technology
using Tanner EDA tool. Simulation results demonstrate that the proposed multiplier can act
as frequency doublers when both inputs have the same frequency. It can also be used as
modulator when one input has a higher frequency than other and demodulator.

7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
468
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