
20
Appendix F
The IF stage, including the limiters, is of a differential design
to improve noise rejection and stability for these high gain
stages. The RF front end, on the other hand, is single ended
to reduce complexity. A receive chain block diagram is
shown in Figure 14.
Gain Distribution/IF Limiting Analysis
The minimum limiter 1 and 2 voltage gains are 39dB at 2.7V
and 400MHz. The radio design uses the part at a less extreme
operating point of 3.5V and 280MHz where the minimum
performance is 42dB. The limiter 1 and 2 output limiting voltage
is 200mV
P-P
into a differential 500
load. Using 3dB loss in the
limiter Bandpass Filter (BPF), the limiter chain (LIM1, BPF,
LIM2) cascaded voltage gain is 81dB, with typical performance
above 90dB. With a 200mV
P-P
output, the input limiting voltage
is 17.8
μ
V
P-P
or -98dBm at 250
source impedance.
This is calculated as follows: since the source and load
impedances are different (250
vs 500
) the input signal is
calculated in terms of voltage. Remember that the limiter is a
voltage gain device and so gain is independent of source
impedance. Substitute the result of Equation 1 into
Equation 2 and calculate V
IN(P-P)
.
Calculate the input power with a 250
impedance by using
Equation 3 to get V
RMS
and then substitute into Equation 4
with R = 250
to get power in Watts. Equation 3 assumes a
sinewave crest factor for the
√
2 term. Power in Watts is
converted to dBm with Equation 5 to get -98dBm input power
at 250
source impedance.
The limiters have a noise bandwidth of over 500MHz and so
the cascaded limiters will fully limit on their own noise, if no
BPF is used between the stages. The thermal noise voltage
delivered from the 250
source to the limiters in a 500MHz
band is -87dBm, as calculated from Equation 6. This thermal
noise adds to the limiter noise figure (NF) of 7dB resulting in
an equivalent input noise power of -80dBm, which is
significantly higher than the -98dBm required for limiting.
Where:
The RF front end 3dB bandwidth is 17MHz, with an
estimated noise bandwidth of 20MHz, as defined by the IF
SAW filter. This makes the available thermal noise at the
limiter input -101dBm and with the 7dB limiter noise figure, is
an equivalent -94dBm.
If the limiter BPF was also 20MHz, the front end would only
need to supply 7dB of noise floor gain to overcome the
limiter noise figure. This would result in a receiver that limits
in a 20MHz bandwidth from front end noise with no margin.
The 20MHz limiter BPF would require a second SAW filter
and therefore is not cost effective or practical.
The alternative chosen to be implemented is a simple one
pole LC BPF with a bandwidth wide enough so that the
variability of fixed components do not result in the filter being
off frequency. The filter selected has a 3dB bandwidth of
50MHz, and an estimated noise bandwidth of 100MHz.
Using this method, the front end gain must be increased to
compensate for excess limiter bandwidth.
gain
10
)
------------------------------
=
(EQ. 1)
V
OUT
gain
V
IN
=
(EQ. 2)
V
RMS
V
2
P
2
–
---------------
=
(EQ. 3)
Pwr Watts
)
V
2
----------------
=
(EQ. 4)
Pwr dBm
)
10
Pwr Watts
)
10
3
(
)
log
=
(EQ. 5)
(EQ. 6)
P Watts
)
A
kT f
=
P Watts
)
A
Available Noise Power
=
k
1.38042
Boltzmann
′
s Constant
300 Degree Kelvin
500MHz
10
23
–
×
=
T
=
=
f
LIMITER
BPF
LIM1
LIM2
500
DIFFERENTIAL
50
SINGLE-ENDED
FRONT
END
FIGURE 14. RECEIVE CHAIN GAIN DISTRIBUTION DIAGRAM
BW
N
= 20MHz
NF = 7.7dB
GAIN = 8.4dB
BW
N
= 500MHz
NF = 7dB
GAIN = 42dB
BW
N
= 100MHz
NF = 3dB
IL = 3dB
BW
N
= 500MHz
NF = 7dB
GAIN = 42dB
WHERE BW
N
= NOISE BANDWIDTH
250
SINGLE-ENDED
Application Note 9624