Page 388 - Complete Wireless Design

Communications System Design

Communications System Design 387

Figure 9.2 Cascaded stages for
IP3 calculations.

1
IP
TOT 1 GAIN GAIN GAIN
1
1
2
IP3 IP3 IP3
1 2 3
where IP receiver’s total IP3 from its input to its output and IP3 and
TOT n
GAIN are linear terms, not decibels.
n
4. The importance of a low NF in a receiver is demonstrated by its linear rela-
tionship with SNR. For instance, if a receiver has an NF of 12 dB, and the
SNR at its output is 20 dB, we can improve the SNR to 30 dB (using the
same input signal power and receiver gain) by decreasing the receiver’s NF
to 2 dB. This is a 10-dB improvement in NF and in SNR. Thus, if a certain
signal power is placed at the input of a 5-dB NF receiver, and this creates
an output with an SNR of 20 dB, then the actual input SNR to the receiver
will have been 25 dB. In other words, the receiver added 5 dB to the noise
at its output: the receiver’s NF directly correlated into a decrease in the out-
put signal’s SNR. This also affects the power that the transmitter must
send to the receiver’s antenna to make up for the decreased SNR caused by
a receiver’s poor NF, with a relationship that is also dB for dB.
The NF for a receiver can be calculated by using Friis’s equation, with the
noise figure itself not needing to be referenced to any particular bandwidth,
since it is a ratio between the input and the output of a receiver (or amplifier)
over exactly the same bandwidth:

NF 2 /10
NF 3 /10
) 1
(10
(10
) 1
NF 10 log (10 NF 1 /10 )
TOTAL (10 G 1 /10 ) (10 G 1 /10 ) (10 G 2 /10 )
(10 NF n /10 ) 1

(10 G 1 /10 ) (10 G 2 /10 ) (10 G n /10 )
where NF total NF for the entire receiver, dB
TOTAL
NF noise figure for the first stage, dB
1
NF NF for the second stage, dB
2
NF NF for the nth stage, dB
n
G gain for the first stage, dB
1
G gain for the second stage, dB
2
G gain for the nth stage, dB.
n
Alternatively, we can calculate the required NF for a receiver if we wish a
desired receiver output SNR. These calculations need the receiver’s planned
bandwidth:
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