Radio Frequency Integrated Circuit Design - Webs

338 Radio Frequency Integrated Circuit Design
vno,I C ≈ √ 2qIC R L
(9.38)
Base shot noise can be converted to input voltage by considering the
impedance Z eq it sees. If Z eq is the source impedance plus any matching circuitry
in parallel with the transistor input impedance, then
vno,I B ≈ √ 2qI C
� Z eq � R L
Z E
(9.39)
Note that if the circuit is differential, then each of the above three equations
must be multiplied by root 2.
These noise sources will be present in any tuned LNA, such as the ones
studied in Chapter 6, and now to these noise sources the noise due to resonators
must be added. This must be considered on a case-by-case basis. For example,
in the case of the circuit shown in Figure 9.7, if we assume that the noise
produced by the resonator is dominated by the collector shot noise, then the
output noise current is given by
Iout_-Gm ≈√�
2q √ Isharp
2 � 2 +� 2q √ Isharp
2 � 2
= √2qIsharp (9.40)
This noise current is then developed into a voltage across the load resistance;
thus,
vno,I sharp ≈ √ 2qI sharp � R L
(9.41)
Therefore, the noise present at the output produced by the circuit relative
to the noise that would have been present without the filter is
Nadded_filter
≈
Nadded_LNA 2qIsharp � (R L ) 2 + 4qIC
�
4qIC
�
2
Z eq �� R L
Z E� 2
+ 4qIC R 2
L + 8kTr b �� R L
Z E� 2
2
Z eq �� R L
Z E� 2
+ 4qIC R 2
L + 8kTr b �� R L
Z E� 2
(9.42)
This is the same as for an LNA except with an additional term due to
Isharp, and thus the LNA built with the filter can never be as quiet as a true