Radio Frequency Integrated Circuit Design - Webs

High-Frequency Filter Circuits
LNA. Note that in the case of the bandpass filter, since the gain is very high,
this noise current could produce a large output voltage. This same noise current
in the case of the notch filters will create a large noise voltage on the notch
resonator due to its high Q. However, the output voltage will be much lower
due to the presence of a lower impedance.
Note once again that if a transformer were added to this circuit, then the
current could be stepped down to reduce the impact on the noise figure of the
circuit. The circuit that was considered in Figure 9.11 also uses a −Gm circuit,
but it is not differential, so with only minor modifications, (9.42) becomes
Nadded_filter
Nadded_LNA
≈
2qIsharp � (R L ) 2 + 2qI C
�
2qIC
�
339
2
Z eq �� R L
Z E� 2
+ 2qIC R 2
L + 4kTr b �� R L
Z E� 2
2
Z eq �� R L
Z E� 2
+ 2qIC R 2
L + 4kTr b �� R L
Z E� 2
(9.43)
It should be noted that the collector shot noise current from the −Gm
circuit also ends up developing a voltage at the collector in the same way as in
the previous circuit. The Colpitts circuit is harder to analyze analytically, so
rather than generating long and tedious equations, it is better simply to simulate
it. Essentially, an extra noise current will be added between the driver transistor
and the cascode, which will impact the noise figure of the circuit, just as in the
other two circuits.
9.8 Automatic Q Tuning
The notch filters discussed here cannot be considered much more than a curiosity
unless they can be tuned automatically on chip. To get a deep notch, the current
through the resonator must be set precisely so that the losses are perfectly
canceled. Too much or too little and the image rejection will suffer. Thus, some
form of feedback must be added to the circuit to make it practical.
As a starting point, consider an oscillator with no loading, as shown in
Figure 9.13. The oscillator will form the basis of the Q tuning circuit for the
filter. A simple current mirror sets the current through the oscillator with a
resistor as the reference. If the resonator current is set above that necessary for
perfect cancellation of the losses, the circuit will oscillate.
Now consider the circuit of Figure 9.13, modified to include two sensing
transistors Q 7 and Q 8, as shown in Figure 9.14. They are biased at a very low