
Figures of Merit
GAIN (G)
Many different types of gain are specified in RF engineering.
The type referred to here is called transducer gain and is
defined as the ratio of the power delivered to the load to the
available power from the source,
e
V
2
V
2
IN
/R
S
where V
OUT
is the voltage across the load R
L
and V
IN
is the
generator voltage with internal resistance R
S
. In terms of
scattering parameters, transducer gain is defined as
G
e
20 log (
l
S
21
l
)
where S
21
is the forward transmission parameter, which can
be measured using a network analyzer.
G
e
P
OUT
P
IN
OUT
/R
L
e
4R
S
V
2
OUT
R
L
V
2
IN
1 dB COMPRESSION POINT (P
1dB
)
A measure of amplitude Iinearity, 1 dB compression point is
the point at which the actual gain is 1dB below the ideal
linear gain. For a memoryless two-port with weak nonlineari-
ty, the output can be represented by a power series of the
input as
v
o
e
k
1
v
i
a
k
2
v
2
For a sinusoidal input,
v
i
e
Acos
0
1
t
the output is
i
a
k
3
v
3
i
a
. . .
v
o
e
1
2
A
2
a
#
k
1
A
a
k
1
A
D
1
a
3
3
A
3
J
3
3
/k
1
) A
2
(
cos
0
1
t
a
1
2
k
2
A
2
cos 2
0
1
t
a
1
3
A
3
cos 3
0
1
t
assuming that all of the fourth and higher order terms are
negligible. For an amplifier, the fundamental component is
the desired output, and it can be rewritten as
.
This fundamental component is larger than k
1
A (the ideally
linear gain) if k
3
l
0 and smaller if k
3
k
0. For most practi-
cal devices, k
3
k
0, and the gain compresses as the ampli-
tude A of the input signal gets larger. The 1 dB compression
point can be expressed in terms of either the input power or
the output power. Measurement of P
1dB
can be made by
increasing the input power while observing the output power
until the gain is compressed by 1 dB.
THIRD ORDER INTERCEPT (OIP
3
)
Third order intercept is another figure of merit used to char-
acterize the linearity of a two-port. It is defined as the point
at which the third order intermodulation product equals the
ideal linear, uncompressed, output. Unlike the P
1dB
, OIP
3
involves two input signals. However, it can be shown mathe-
matically (similar derivation as above) that the two are
closely related and OIP
3
&
P
1dB
a
10 dB. Theses two
figures of merit are illustrated in Figure 6.
TL/W/11814–16
FIGURE 6. Typical P
OUT
–P
IN
Characteristics
NOISE FIGURE (NF)
Noise figure is defined as the input signal to noise ratio di-
vided by the output signal to noise ratio. For an amplifier, it
can also be interpreted as the amount of noise introduced
by the amplifier itself seen at the output. Mathematically,
F
e
S
i
/N
i
S
o
/N
o
e
S
i
/N
i
G
a
S
i
/(N
a
a
G
a
N
i
)
NF
e
10 log (F)
e
N
a
a
G
a
N
i
G
a
N
i
where S
i
and N
i
represent the signal and noise power levels
available at the input to the amplifier, S
o
and N
o
the signal
and noise power levels available at the output, G
a
the avail-
able gain, and Na the noise added by the amplifier. Noise
figure is an important figure of merit used to characterize the
performance of not only a single component but also the
entire system. It is one of the factors which determine the
system sensitivity.
IMAGE FREQUENCY, DSB/SSB NF
Image frequency refers to that frequency which is also
down-converted by the mixer, along with the desired RF
component, to the intermediate frequency. This image fre-
quency is located at the same distance away from the LO,
but on the opposite side of the RF. For most mixers, it must
be filtered out before the signal is down-converted; other-
wise, an image-reject mixer must be used. Figure 7 illus-
trates the concept.
TL/W/11814–17
FIGURE 7. Input and Output Spectrum of Mixers
10