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Gilbert Cell Mixer Design Tutorial
J P Silver
Email: [email protected]
1
ABSTRACT
Frequency translation in a system, is performed by a
nonlinear device known as a mixer. There are vari
ous topographies from simple single ended, single
balanced mixers to more complicated double & triple
balanced mixers that provide better isolation from
the Local Oscillator (LO) and spurious.
The most popular doublebalanced mixer used in
RFIC designs is the Gilbert Cell mixer.
The design of this mixer is the subject of this paper.
2
INTRODUCTION
Mixers are nonlinear devices used in systems to trans
late (multiply) one frequency to another. All mixer types
work on the principle that a large Local Oscillator (LO)
RF drive will cause switching/modulating the incoming
Radio Frequency (RF) to the Intermediate Frequency
(IF).
The multiplication process begins by inputting two sig
nals:
)
Bsin(
b
signal
and
)
Asin(
a
2
2
1
1
φ
ω
φ
ω
+
=
+
=
t
t
The resulting multiplied signal will be:
(
)
(
2
2
1
1
t
.
sin
.
t
.
ABsin
a.b
)
φ
ω
φ
ω
+
+
=
This can be multiplied out thus:
(
)
(
[
]
(
)
(
)
2
2
1
1
t
.
B
and
t
.
A
Where
B

A
cos
B
A
cos
2
1

sinAsinB
..
identity
trig
this
Using
φ
ω
φ
ω
+
=
+
=
−
+
=
)
(
)
(
)
(
)
(
)
(
(
)
[
]
)
(
)
(
)
(
)
(
)
(
(
)
[
]
2
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
t
cos
t
cos
2
AB

t
.
t
.
cos
t
.
t
.
cos
2
AB

φ
φ
φ
ω
φ
φ
ω
ω
φ
ω
φ
ω
φ
ω
φ
ω
−
−
−
−
+
+
+
=
+
−
+
−
+
+
+
=
)
3
MIXER DEFINITIONS
(1) Conversion Gain
: This is the ratio (in dB) between
the IF signal
(usually the difference frequency between
the RF and LO signals) and the RF signal.
(2) Noise Figure
: Noise figure is defined as the ratio of
SNR at the IF port to the SNR of the RF port.
(i) Single sideband (SSB)
: This assumes the only
noise from the signal
ω
1
and not the image frequency
ω
1
1
, this would be the case if a bandpass filter was
added in front of the mixer eg.
RF = 1694 MHz, LO = 1557MHz to give an IF of
137MHz.
Also an image IF will add to 137MHz from an RF of
1420MHz ie 1557MHz1420MHz = 137MHz
(ii) Double sideband (DSB)
:
In DSB both side
bands are available thus it has twice as much power
available at the IF port compared to the SSB signal. As a
result, it’s conversion loss is 3dB less than that of an
SSB signal, as shown:
(
)
(
)
(
)
(
)
2
LC
LC
ratios
loss
of
in terms
or
)
(
3
LC
LC
by
given
is
loss
conversion
and
P
2
P
SSB
(IF)
DSB
(IF)
SSB
DSB
SSB
DSB
dB
=
−
=
=
(iii) DSB to SSB Noise Figure conversion
Sum frequency (re
moved by filtering)
Difference frequency
ie
I.F
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